Fianancial Management & international finance
2.3. Capital Budgeting
This Section includes :
Capital Budgeting Process
Time Value of Money
—Future Value
—Present Value
Investment Appraisal Techniques
—Payback Period
—Accounting Rate of Return
—Earnings Per Share
—Net Present Value
—Internal Rate of Return
—Net Terminal Value
—Profitability Index
—Discounted Payback Period
Capital Rationing
INTRODUCTION :
Capital Budgeting is the art of finding assets that are worth more than they cost to achieve a
predetermind goal i.e., ‘optimising the wealth of a business enterprise’.
Capital investment involves a cash outflow in the immediate future in anticipation of
returns at a future date.
A capital investment decidion involves a largely irreversible commitment of resources that is
generally subject to significant degree of risk. Such decisions have for reading efforts on an
enterprise’s profitability and flexibility over the long-term. Acceptance of non-viable proposals
acts as a drag on the resources of an enterprise and may eventually lead to bankrupcy.
For making a rational decision regarding the capital investment proposals, the decision maker
needs some techniques to convert the cash outflows and cash inflows of a project into meaningful
yardsticks which can measure the economic worthiness of projects.
CAPITAL BUDGETING PROCESS :
A Capital Budgeting decision involves the following process :
(1) Investment screening and selection
(2) The Capital Budget proposal
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(3) Budgeting Approval and Authorization
(4) Project Tracking
(5) Post-completion Auditor
TIME VALUE OF MONEY :
Concept
We know that Rs. 100 in hand today is more valuable than Rs. 100 receivable after a year.
We will not part with Rs. 100 now if the same sum is repaid after a year. But we might part
with Rs. 100 now if we are assured that Rs. 110 will be paid at the end of the first year. This
“additional Compensation” required for parting Rs. 100 today, is called “interest” or “the
time value of money”. It is expressed in terms of percentage per annum.
Why should money have time value?
Money should have time value for the following reasons :
(a) Money can be employed productively to generate real returns;
(b) In an inflationary period, a rupee today has higher purchasing power than a rupee in
the future;
(c) Due to uncertainties in the future, current consumption is preferred to future
consumption.
(d) The three determinants combined together can be expressed to determine the rate of
interest as follows :
Nominal or market interest rate
= Real rate of interest or return (+) Expected rate of inflation (+) Risk premiums to
compensate for uncertainty.
Methods of Time Value of Money
(1) Compounding : We find the Future Values (FV) of all the cash flows at the end of the
time period at a given rate of interest.
(ii) Discounting : We determine the Time Value of Money at Time “O” y comparing the
initial outflow with the sum of the Present Values (PV) of the future inflows at a given rate of
interest.
Time Value of Money
Compounding Discounting
(Future Value) (Present Value)
(a) Single Flow (a) Single Flow
(b) Multiple Flows (b) Uneven Multiple Flows
(c) Annuity (c) Annuity
(d) Perpetuity
Fianancial Management & international finance 109
Future Value of a Single Flow
It is the process to determine the future value of a lump sum amount invested at one point of
time.
FVn = PV (1+i)n
Where,
FVn = Future value of initial cash outflow after n years
PV = Initial cash outflow
i = Rate of Interest p.a.
n = Life of the Investment
and (1+i)n = Future Value of Interest Factor (FVIF)
Illustration :
The fixed deposit scheme of Punjab National Bank offers the following interest rates :
Period of Deposit Rate Per Annum
46 days to 179 days 5.0
180 days <>
1 year and above 6.0
An amount of Rs. 15,000 invested today for 3 years will be compounded to :
FVn = PV (1+i)n
= PV × FVIF (6,3)
= PV × (1.06)3
= 15,000 (1.191)
= Rs. 17,865
Doubling Period “How long will it take for the amount invested to be doubled for a given
rate of interest”?
(i) By Applying “Rule of 72”
Rate of Interest
72
Doubling Period =
For instance, if the rate is 5%, then the doubling period is 14 4
5
72
= . years.
(ii) Rule of 69 : For a better and accurate way of calculating the doubling period :
= Interest Rate
.
69
0 35 +
0 35 13 8 14 15
5
69
= 0.35 + = . + . = . years.
If compounding it done for shorter periods (i.e. other than annual compounding)
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FV =
m n
n m
i
PV
×
⎟⎠
⎞ ⎜⎝
⎛1+
PV = Initial Cash Outflow
i = Rate of interest p.a.
m = no. of times compounding is done per year
n = no. of years for which compounding is done.
Illustration : Calculate the Future value of Rs. 1000 invested in State Bank Cash Certificate
Scheme for 2 years @ 5.5% p.a., compounded semi-annully.
FVn =
m n
m
i
PV
×
⎟⎠
⎞ ⎜⎝
⎛1+ ( )4 =1000 1.0275
=
2 2
2
0 055
1 000 1
×
⎟⎠
⎞ ⎜⎝
⎛ + .
, =1000 ×1.11462 = Rs.1,114.62
Future Value of Multiple Flows
Rate of Interest = 6% p.a. Total Accumulation after 3 years
Being of Year Investment (Rs.) EVIF Compounded Value (Rs.)
0 4,000 1.2625 5,050
1 6,000 1.191 7,146
2 5,000 1.1236 5,618
3 5,000 1.06 5,300
Total 20,000 23,114
The total compounded value is Rs. 23.114
Future Value of Annuity
Annuity is a term used to describe a series of periodic flows of equal amounts. These flows
can be inflows or outflows.
The future value of annuity is expressed as :
= n FVA ⎥⎦
⎤
⎢⎣
⎡ + −
i
( i)
A
1 n 1
where, A = Amount of Annuity
i = rate of interest
n = time period
FVAn = compounded at the end of n years.
and ⎥⎦
⎤
⎢⎣
⎡ + −
i
(1 i)n 1
is the Future Value of Interest Factor for Annuity (FVIFA)
Fianancial Management & international finance 111
Illustration :
Calculation the maturity value of a recurring deposit of Rs. 500 p.a. for 12 months @ 9% p.a.
compounded quarterly.
Effective rate of interest per annum 1
4
0 09
1
4
− ⎟⎠
⎞ ⎜⎝
= ⎛ + .
= 1.0931 – 1 = 0.0931
Rate of interest per month
= (1 ) 1 1 + i m −
= (1 0.0931 )12 1
1 + −
= 1.0074 – 1
= 0.0074
= 7.4%
Maturity Value can be calculated as follows :
FVAn =
⎭ ⎬ ⎫
⎩ ⎨ ⎧
+ −
i
( i)
A
1 n 1
=
⎭ ⎬ ⎫
⎩ ⎨ ⎧
+ −
0 0074
1 0 0074 1
500
12
.
( . )
= 500 ×12.50 = Rs. 6250/-
Present Value of a Single Flow :
n
n n
( i)
FV
FVIF(i, n)
FV
PV
+
= =
1
Where, PV = Present Value
FVn = Future Value receivable after n years
i = rate of interest
n = time period
and PVIF (i, n)
FVIF(i, n)
= 1
[ Present Value of Interest Factor ]
Illustration :
Calculate the Present Value of Rs. 1000 receivable after 3 years. Cost of Capital @ 10% p.a.
P.V. of Re. 1 @ 10% p.a. receivable after 3 years.
= 0.7513
∴ P.V. of Rs. 1000 = Rs. 1000 × 0.7513 = Rs. 751.30
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Present Value of Uneven Multiple Flows
Year Cash Inflows P.V. @ 10% Discounted Cash Flows
1 50,000 0.9091 45,455
2 90,000 0.8264 74,376
3 1,20,000 0.7513 90,156
2,60,000 2,09,087
∴ The present value of Rs. 2,60,000 discounted @ 10% will be Rs. 2,09,987.
Present Value of Even Cash Inflows
Calculate P.V. of Rs. 50,000 receivable for 3 years @ 10%
P.V. = Cash Flows × Annuity @ 10% for 3 years.
= 50,000 × 2.4868 = Rs. 1.24,340/-
Present Value of an Annuity :
The present value of an annuity ‘A’ receivable at the end of every year for a period of n years
at the rate of interest ‘i’ is equal to
PVAn = ( i)n
A
Where, i = normal rate of interest p.a.
r = effective rate of interest p.a.
m = no. of terms compounded in a year.
Fianancial Management & international finance 113
Step (2) Calculate effective rate of interest per month.
= (1 )12 1
1 + r −
= (1 0 1255)12 1
1 + . −
= 0.00990
Step (3) The present value of deposits :
PVAn = ⎥⎦
⎤
⎢⎣
⎡
+
+ −
n
n
i ( i)
( i)
A
1
1 1
= ⎥⎦
⎤
⎢⎣
⎡
+
+ −
12
12
0 00990 1 0 00990
1 0 00990 1
100
. ( . )
( . )
= 100 11 26 1126
0 01114
0 1255
100 . Rs.
.
. = × = ⎥⎦
⎤
⎢⎣
⎡
INVESTMENT APPRAISAL TECHNIQUES
↓ ↓ ↓
Pay back of Capital Employed Accounting Profit Time Value of Money
↓ for Project Evuluation ↓
↓
Pay back Period Method (a) Accounting Rate of (a) Net Present Value (NPV)
Return (ARR) (b) Internal Rate of Return
(b) Earnings per share (EPS) (IRR)
(c) Net Terminal Value
(d) Profitability Index
(e) Discounted payback
period
Payback Period Method
The basic element of this method is to calculate the recovery time, by yearwise accumulation
of cash inflows (inclusive of depreciation) until the cash inflows equal the amount of the
original investment. The time taken to recover such original investment is the “payback period”
for the project.
“The shorter the payback period, the more desirable a project”.
Illustration : Initial Investment = Rs. 1,00,000
Expected future cash inflows Rs. 20,000, Rs. 40,000, Rs. 60,000, Rs. 70,000
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Calculation of Pay Back period.
Year Cash Inflows (Rs.) Cumulatige Cash Inflows (Rs.)
1 20,000 20,000
2 40,000 60,000
3 60,000 1,20,000
4 70,000 1,90,000
The initial investment is recovered between the 2nd and the 3rd year.
∴ Pay back Preiod = ⎟
⎟⎠
⎞
⎜ ⎜
⎝
⎛
2 + ×12
Cash Inflows during the year
Balance of Unrecovered Initial Investment
years
=
⎟ ⎟ ⎟ ⎟ ⎟
⎠
⎞
⎜ ⎜ ⎜ ⎜ ⎜
⎝
⎛
×
−
+ 12
Inflows in the 3rd year
Cash Inflows at the end of 2 year
Initial Investment Cumulative
2
nd
Cash
years
= ⎟⎠
⎞ ⎜⎝
+ ⎛ − ×12
60 000
1 60 000
2
,
,00,000 ,
years
= ⎟⎠
⎞ ⎜⎝
+ ⎛ ×12
60 000
40 000
2
,
,
years
= 2 years 8 months.
Illustration : Victory Ltd. decided to purchase a machine to increase th installed capacity.
The company has four machines under consideration. The relevant details including estimated
yearly expenditure and sales are given below. All sales are for cash. Corporate Tax Rate
@ 33.99% (inclusive of Surcharge @ 10%, Deduction less @ 2% and Secondary & Higher
Education less @ 1%)
Particulars M1 M2 M3 M4
Initial Investment (Rs. lacs) 30.00 30.00 40.00 35.00
Estimated Annual Sales (Rs. lacs) 50.00 40.00 45.00 48.00
Cost of Production (Estd) (Rs. lacs) 18.00 14.00 16.70 21.00
Economic Life (yrs) 2 3 3 4
Scrap Values (Rs. lacs) 4.00 2.50 3.00 5.00
Calculate Payback Period
Statement Showing Payback for four machines
Particulars M1 M2 M3 M4
(1) Initial Investment (Rs. lacs) 30.00 30.00 40.00 35.00
(2) Estd. Annual Cost of Production (Rs. Lacs) 50.00 40.00 45.00 48.00
(3) Estd. Cost of Production (Rs. lacs) 18.00 14.00 16.70 21.00
(4) Depreciation (Rs. lacs) 13.00 9.17 12.33 7.50
Fianancial Management & international finance 115
(5) Profit Before Tax (PBT) [2–3–4] 19.00 16.83 15.97 19.50
(6) Tax @ 33.99% (Rs. lacs) 6.4581 5.721 5.428 6.628
(7) Profit After Tax (PAT) [5–6] (Rs. lacs) 12.5419 11.109 10.542 12.872
(8) Net Cash Flow [7+4] 25.5419 20.279 22.872 20.372
M1 M2 M3 M4
Pay back Period (Years) 25 5419
30 00
.
= .
20 279
30 00
.
= .
22 872
40 00
.
= .
20 372
35 00
.
= .
⎥⎦
⎤
⎢⎣
⎡
Net Annual Cash Flow
Initial Investment
= 1.17 = 1.48 = 1.74 = 1.72
Analysis : Machine 1 is more profitable, as it has the lowest payback period.
Bailout Factor
This deals with the posibility of scrapping the machine during its estimated life.
Illustration :
Project × costs Rs. 20 lacs and project y costs Rs. 30 lacs both having a life of 5 years. Expected
cash flows Rs. 8 lacs p.a. for project × and Rs. 123 lacs p.a. for project y. Estimated scrap
values are project × Rs. 5 lacs, declining at an annual rate of Rs. 1 lacs p.a. and project y Rs.
8 lacs declining at an annual rate of Rs. 1 lac p.a.
Under Traditional payback :
Project X . years
8,00,000
20,00,000
= = 2 5
Project Y years
15,00,000
30,00,000
= = 2
Under Bailout Payback :
The bailout payback time is reached if the accumulated cash inflows plus the expected salvage
value at the end of a particular year equals the original/initial investment.
Project X Cumulative Cash Receipts (Rs.) Salvage Value (Rs.)
End of year 1 : 8,00,000 5,00,000 = 13,00,000
End of year 2 : 16,00,000 4,00,000 = 20,00,000
∴ Bailout payback period for Project X = 2 years.
Project Y Cumulative Cash Receipts (Rs.) Salvage Value (Rs.)
End of year 1 : 12,00,000 8,00,000 = 20,00,000
End of year 2 : 24,00,000 7,00,000 = 31,00,000
∴ Bailout is between years 1 & years 2.
∴ Project Y is choosen having a lower bailout pay back period, assuming that the major
objective is to avoid loss.
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Merits :
(1) No assumptions about future interest rates.
(2) In case of uncertainty in future, this method is most appropriate.
(3) A company is compelled to invest in projects with shortest payback period, if capital
is a constraint.
(4) It is an indication for th prospective investors specifying the payback period of their
investments.
(5) Ranking projects as per their payback period may be useful to firms undergoing liquidity
constraints.
Demerits :
(1) Cash generation beyond payback period is ignored.
(2) The timing of returns and the cost of capital is not considered.
(3) The traditional payback method does not consider the salvage value of an investment.
(4) Percentage Return on the capital invested is not measured.
(5) Projects with long payback periods are characteristically those involved in long-term
planning, which are ignored in this approach.
Payback Period Reciprocal
Payback period may be expressed alternatively as the “payback reciprocal” :
Payback period reciprocal 100
1 = ×
Payback preiod
Illustration :
If the payback period for a project is 5 years, then the payback period reciprocal would be :
100 20%
5
1 = ⎥⎦
⎤
⎢⎣
⎡ ×
The projects having lower payback period shall yield higher payback reciprocal, which reflects
the worth of such project.
Accounting Rate of Return
This method measures the increase in profit expected to result from investment.
ARR = ×100
Average or Initial Investment
AverageAnnual Profit After Tax
100
1 ×
−
=
Average Investment
Average EBIT ( t)
Where, Average Investment
2
Initial Investment + Salvage Value
=
Fianancial Management & international finance 117
Illustration :
A project costing Rs. 10 lacs. EBITD (Earnings before Depreciation, Interest and Taxes) during
the first five years is expected to be Rs. 2,50,000; Rs. 3,00,000; Rs. 3,50,000; Rs. 4,00,000 and
Rs. 5,00,000. Assume 33.99% tax and 30% depreciation on WDV Method.
Computation of Project ARR :
Particulars Yr 1 Yr 2 Yr3 Yr 4 Yr 5 Average
Rs. Rs. Rs. Rs. Rs. Rs.
EBITD 2,50,000 3,00,000 3,50,000 4,00,000 5,00,000 3,60,000
Less : Depreciation 3,00,000 2,10,000 1,47,000 1,02,900 72,030 1,66,386
EBIT (50,000) 90,000 2,03,00 2,97,100 4,27,970 1,93,614
Less : Tax @ 33.99% — 13,596 69,000 1,00,984 1,45,467 65,809
(50,000) 76,404 1,34,000 1,96,116 2,82,503 1,27,805
Book Value of Investment :
Begining 10,00,000 7,00,000 4,90,000 3,43,000 2,40,100
End 7,00,000 4,90,000 3,43,000 2,40,100 1,68,070
Average 8,50,000 5,95,00 4,16,500 2,91,550 2,04,085 4,71,427
ARR = 100
4 71 427
1 27 805
100
1 × = ×
−
, ,
, ,
Average Investment
Average EBIT ( t)
= 27.11%
Note : Unabsorbed depreciation of Yr. 1 is carried forward and set-off against profits of
Yr. 2. Tax is calculated on the balance of profits
= 33.99% (90,000 – 50,000)
= 13,596/-
Merits
(1) This method considers all the years in the life of the project.
(2) It is based upon profits and not concerned with cash flows.
(3) Quick decision can be taken when a number of capital investment proposals are being
considered.
Demerits
(1) Time Value of Money is not considered.
(2) It is biased against short-term projects.
(3) The ARR is not an indicator of acceptance or rejection, unless the rates are compared
with the arbitrary management target.
(4) It fails to measure the rate of return on a project even if there are uniform cash flows.
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Earnings Per Share (EPS)
EPS is one of the major criterion for capital investment appraisal. The value of a firm is
maximised if the market price of equity shares are maximised.
⎥⎦
⎤
⎢⎣
⎡ − − −
=
n
(EBIT I) ( t) D
EPS
1
Where EBIT = Earnings before Interest and Tax
I = Interest
t = Corporate tax rate
D = Preference Dividend
n = no. of equity shares
Note : The major drawback of this method is that it ignores cash flows, timing and risk.
Net Present Value (NPV) Method
= Present Value of Cash Inflows – Present Value of Cash Outflows
The discounting is done by the entitiy’s weighted average cost of capital.
The dicounting factors is given by : (1+ i)n
1
Where i = rate of interest per annum
n = no. of years over which discounting is made.
Illustration :
Z Ltd. has two projects under considereation A & B, each costing Rs. 60 lacs.
The projects are mutually exclusive. Life for project A is 4 years & project B is 3 years. Salvage
value NIL for both the projects. Tax Rate 33.99%. Cost of Capital is 15%
Net Cash Inflow (Rs. Lakhs)
At the end of the year Project A Project B P.V. @ 15%
1 60 100 0.870
2 110 130 0.756
3 120 50 0.685
4 50 — 0.572
Computation of Net Present Value of the Projects.
Project A (Rs. lakhs)
Yr. 1 Yr. 2 Yr. 3 Yr. 4
1. Net Cash Inflow 60.00 110.00 120.00 50.00
Fianancial Management & international finance 119
2. Depreciation 15.00 15.00 15.00 15.00
3. PBT (1–2) 45.00 95.00 105.00 35.00
4. Tax @ 33.99% 15.30 32.29 35.70 11.90
5. PAT (3–4) 29.70 62.71 69.30 23.10
6. Net Cash Flow 44.70 77.71 84.30 38.10
(PAT+Depn)
7. Discounting Factor 0.870 0.756 0.685 0.572
8. P.V. of Net Cash Flows 38.89 58.75 57.75 21.79
9. Total P.V. of Net Cash Flow = 177.18
10. P.V. of Cash outflow (Initial Investment) = 60.00
Net Present Value = 117.18
Project B
Yr. 1 Yr. 2 Yr. 3
1. Net Cash Inflow 100.00 130.00 50.00
2. Depreciation 20.00 20.00 20.00
3. PBT (1–2) 80.0 110.00 30.00
4. Tax @ 33.99% 27.19 37.39 10.20
5. PAT (3–4) 52.81 72.61 19.80
6. Next Cash Flow 72.81 92.61 39.80
(PAT+Dep.)
7. Discounting Factor 0.870 0.756 0.685
8. P.V. of Next Cash Flows 63.345 70.013 27.263
9. Total P.V. of Cash Inflows = 160.621
10. P.V. of Cash Outflows = 60.00
(Initial Investment)
Net Present Value = 100.621
As Project “A” has a higher Net Present Value, it has to be taken up.
Merits
(1) It recognises the Time Value of Money.
(2) It considers total benifits during the entire life of the Project.
(3) This is applicable in case of mutually exclusive Projects.
(4) Since it is based on the assumptions of cash flows, it helps in determining Shareholders
Wealth.
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Demerits
(1) This is not an absolute measure.
(2) Desired rate of return may vary from time to time due to changes in cost of capital.
(3) This Method is not effective when there is disparity in economic life of the projects.
(4) More emphasis on net present values. Initial investment is not given due importance.
Internal Rate of Return (IRR)
Internal Rate of Return is a persentage discount rate applied in capital investment desions
which brings the cost of a project and its expected future cash flows into equality, i.e., NPV
is zero.
Illustration :
Project Cost Rs. 1,10,000
Cash Inflows :
Year 1 Rs. 60,000
“ 2 Rs. 20,000
“ 3 Rs. 10,000
“ 4 Rs. 50,000
Calculate the Internal Rate of Retun.
Internal Rate of Return will be calculated by the trial and error method. The cash flow is not
uniform. To have an approximate idea about such rate, we can calculate the “Factor”. It
represent the same relationship of investment and cash inflows in case of payback claculation :
F = I/C
Wehre F = Factor
I = Original investment
C = Average Cash inflow per annum
Factor for the project 3 14
35 000
110 000
.
,
= , =
The factor will be located from the table “P.V. of an Annuity of Rs. 1” representing number
of years coresponding to estimated useful life of the asset.
The approximate value of 3.14 is located against 10% in 4 years.
We will now apply 10% and 12% to get (+) NPV and (–) NPV [Which means IRR lies in
between]
Year Cash Inflows P.V. @ 10% DCFAT P.V. @ 12% DCFAT
(Rs.) (Rs.) (Rs.)
1 60,000 0.909 54,540 0.893 53,580
2 20,000 0.826 16,520 0.797 15,940
3 10,000 0.751 7,510 0.712 7,120
4 50,000 0.683 34,150 0.636 31,800
Fianancial Management & international finance 121
P.V. of Inflows 1,12,720 1,08,440
Less : Initial Investment 1,10,000 1,10,000
NPV 2,720 (1,560)
Graphically,
For 2%, Difference = 4,280
10% 12%
NPV 2,720 (1560)
IRR may be calculated in two ways :
Forward Method : Taking 10%, (+) NPV
IRR = 10% + Difference in Rate
Total Difference
NPV at % × 10
= 10% + 2%
4280
2720 ×
= 10% + 1.27% = 11.27%
Backward Method : Taking 12%, (–) NPV
IRR = 12% + %
( )
2
4280
1560 ×
= 12% – 0.73% = 11.27%
The decision rule for the internal rate of retern is to invest in a project if its rate of returning
greater than its cost of capital.
For independent projects and situations involving no capital rationing, then :
Situation Signifies Decision
IRR = Cost of Capital The investment is expected Indifferent between
not to change shareholder Accepting & Rejecting
wealth
IRR > Cost of Capital The investment is expected Accept
to increase shareholders
wealth
IRR <>
to decrease shareholders
wealth
Merits :
(i) The Time Value of Money is considered.
(ii) All cash flows in the project are considered.
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Demerits
(i) Possibility of multiple IRR, interpretation may be difficult.
(ii) If two projects with different inflow/outflow patterns are compared, IRR will lead to
peculiar situations.
(iii) If mutually exclusive projects with different investments, a project with higher
investment but lower IRR contributes more in terms of absolute NPV and increases
the shareholders’ wealth.
NPV-IRR Conflict
Let us consider two mutually exclusive projects A & B.
Project A Project B Decision
Cost of Capital 10% 10%
IRR 13% 11% Project A
NPV 1,00,000 1,10,000 Project B
When evaluating mutually exclusive projects, the one with the highest IRR may not be the
one with the best NPV.
The conflict between NPV & IRR for the evaluation of mutually exclusive projects in due to
the reinvestment assumption :
NPV assumes cash flows reinvested at the cost of capital.
IRR assumes cash flows reinvested at the internal rate of return.
The reinvestment assumption may cause different decisions due to :
Timing difference of cash flows.
Difference in scale of operations.
Project life disparity.
Terminal Value Method
Assumption :
(1) Each cash flow is reinvested in another project at a predetermined rate of interest.
(2) Each cash inflow is reinvested elsewhere immediately after the completion of the
project.
Decision-making
If the P.V. of Sum Total of the Compound reinvested cash flows is greater than the P.V. of
the outflows of the project under consideration, the project will be accepted otherwise not.
Illustration :
Original Investment Rs. 40,000
Life of the project 4 years
Cash Inflows Rs. 25,000 for 4 years
Cost of Capital 10% p.a.
Fianancial Management & international finance 123
Expected interest rates at which the cash inflows will be reinvested :
Year-end 1 2 3 4
% 8 8 8 8
First of all, it is necessary to find out the total compounded sum which will be discounted
back to the present value.
Year Cash Inflows Rate of Int. (%) Yrs. of Compounding Total
(Rs.) Investment Factor Compounding
(Rs.) Sum (Rs.)
1 25,000 8 3 1.260 31,500
2 25,000 8 2 1.166 29,150
3 25,000 8 1 1.080 27,000
4 25,000 8 0 1.100 25,000
1,12,650
Present Value of the sum of compounded values by applying the discount rate @ 10%
Present Value = n ( i)
Compounded Value of Cash Inflow
1+
= n ( . )
, ,
1 10
112 650
= 1,12,650 × 0.683 = 76,940/-
[ 0.683 being the P.V. of Re. 1 receivable after 4 years ]
Decision : The present value of reinvested cash flows, i.e., Rs. 76,940 is greater than the
original cash outlay of Rs. 40,000.
The project should be accepted as per the terminal value criterion.
Profitability Index :
Profitability Index =
P.V. of cash outflow
P.V. of cash inflow
If P.I > 1, project is accepted
P.I <>
The PI signifies present value of inflow per rupee of outflow. It helps to compare projects
involving different amounts of initial investments.
Illustration :
Initial investment Rs. 20 lacs. Expected annual cash flows Rs. 5 lacs for 10 years. Cost of
Capital @ 15%.
Calculate Profitability Index.
Solution :
Cumulative discounting factor @ 15% for 10 years = 5.019
∴ P.V. of outflows = 6.00 × 5.019 = Rs. 30.114 lacs.
∴ Profitability Index = 1 51
20
30 114
.
.
P.V. of Outflows
P.V. of Inflows = =
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Decision : The project should be accepted.
Discounted Payback Period
In Traditional Payback period, the time value of money is not considered. Under discounted
payback period, the expected future cash flows are discounted by applying the appropriate
rate, i.e., the cost of capital.
Illustration :
Initial Investment Rs. 1,00,000
Cost of Capital @ 12% p.a.
Expected Cash Inflows
Yr. 1 Rs. 25,000
Yr. 2 Rs. 50,000
Yr. 3 Rs. 75,000
Yr. 4 Rs. 1,00,000
Yr. 5 Rs. 1,50,000
Calculate Discounted Payback Period.
Solution :
Year Cash Inflows Discounting Factor Discounted Cumulative
(Rs.) @ 12% Cash Flows (Rs.) DCF (Rs.)
1 25,000 0.8929 22,323 22,323
2 50,000 0.7972 39,860 62,183
3 75,000 0.7117 53,378 1,15,561
4 1,00,000 0.6355 63,550 1,79,111
5 1,50,000 0.5674 85,110 2,64,221
The recovery was made between 2nd and 3rd year.
Discounted Payback Period = 12
115 561 62 183
1 00 000 62 183
2 ×
−
+ −
, , ,
, , ,
years
= 12
53378
37817
12 2
1,15,561 62,183
37817
2 × = + ×
−
years + years
=
2
1
2 years 8 months.
CAPITAL RATIONING:
Capital rationing is a situation where a constraint or budget ceiling is placed on the total size
of capital expenditures during a particular period. Often firms draw up their capital budget
under the assumption that the availability of financial resources is limited.
Under this situation, a decision maker is compelled to reject some of the viable projects having
positive net present value because of shortage of funds. It is known as a situation involving
capital rationing.
Fianancial Management & international finance 125
Factors Leading to Capital Rationing - Two different types of capital rationing situation can
be identified, distinguished by the source of the capital expenditure constraint.
I. External Factors - Capital rationing may arise due to external factors like imperfections
of capital market or deficiencies in market information which might have for the availability
of capital. Generally, either the capital market itself or the Government will not
supply unlimited amounts of investment capital to a company, even though the company
has identified investment opportunities which would be able to produce the required
return. Because of these imperfections the firm may not get necessary amount of
capital funds to carry out all the profitable projects.
II. Internal Factors - Capital rationing is also caused by internal factors which are as follows:
Reluctance to take resort to financing by external equities in order to avoid assumption
of further risk
Reluctance to broaden the equity share base for fear of losing control.
Reluctance to accept some viable projects because of its inability to manage the firm
in the scale of operation resulting from inclusion of all the viable projects.
Situations of Capital Rationing
Situation I - Projects are divisible and constraint is a single period one:
The following are the steps to be adopted for solving the problem under this situation:
a. Calculate the profitability index of each project
b. Rank the projects on the basis of the profitability index calculated in (a) above.
c. Choose the optimal combination of the projects.
Situation II - Projects are indivisible and constraint is a single period one
The following steps to be followed for solving the problem under this situation:
a. Construct a table showing the feasible combinations of the project (whose aggregate
of initial outlay does not exceed the fund available for investment.
b. Choose the combination whose aggregate NPV is maximum and consider it as the
optimal project mix.
PROBLEMS
Illustration 1 : Zenith Industrial Ltd. are thinking of investing in a project costing Rs. 20
lakhs. The life of the project is five years and the estimated salvage value of the project is
zero. Straight line method of charging depreciation is followed. The tax rate is 50%. The
expected cash flows before tax are as follows :
Year 1 2 3 4 5
Estimated Cash flow before depreciation
and tax (Rs. lakhs) 4 6 8 8 10
You are required to determine the : (i) Payback Period for the investment, (ii) Average Rate
of Return on the investment, (iii) Net Present Value at 10% Cost of capital, (iv) Benefit-Cost
Ratio.
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Calculation of Annual Cash Inflow After Tax (Rs. lakhs)
Particulars 1 year 2 year 3 year 4 year 5 year
Cash inflow before depreciation and tax 4 6 8 8 10
Less : Depreciation 4 4 4 4 4
EBT – 2 4 4 6
Less : Tax @ 50% – 1 2 2 3
EAT – 1 2 2 3
Add : Depreciation 4 4 4 4 4
Cash inflow after tax 4 5 6 6 7
(i) Pay Back Period :
Year Cash inflow after tax Cumulative cash inflow after tax
1 4 4
2 5 9
3 6 15
4 6 21
5 7 28
Pay Back Period = Months years months
Rs. lakhs
Rs. lacks
years 12 3 10
6
5
3 + × =
(ii) Average Rate of Return
Average return = Rs. 8 lakhs/5 years = Rs. 1.6 lakhs
Average investment = Rs. 20 lakhs/2 = Rs. 10 lakhs
Average rate of return = 100
10
1 6 . ×
= 16%
(iii) Net Present Value at 10% Cost of Capital (Rs. lakhs)
Year Cash inflow after tax Discount factor @ 20% Present Value
1 4 0.909 3.636
2 5 0.826 4.130
3 6 0.751 4.506
4 6 0.683 4.098
5 7 0.621 4.347
P.V. of cash inflows 20.717
Less : Initial investment 20.00
NPV 0.717
Fianancial Management & international finance 127
(iv) Benefit-Cost Ratio 1 036
20
20 717
.
.
P.V. of cash outflow
= P. V. of cash inflow = =
Illustration 2 : The relevant information for two alternative systems of internal transportation
are given below :
(Rs. Million)
ParticularsSysem 1 System 2
Initial investment 6 4
Annual operating costs 1 0.9
Life 6 years 4 years
Salvage value at the end 2 1.5
Which system would you prefer if the cost of capital is 6%? Justify your recommendation
with appropriate analysis.
[Present value of annuity at 6% for 6 years = 4.917 and for 4 years = 3.465. Present value of
Rs. 1.00 at 6% at the end of 6the year 0.705 and that at the end of 4th year 0.792].
P.V. of Costs of Internal Transportation - System 1 (Rs. Million)
Initial investment (6×1.000) 6.000
Add : Annual operating cost (1×4.917) 4.917
10.410
Less : Salvage value at the end of 6 years (2×0.705) 1,410
P.V. cash outflow 9.507
P.V. of Costs of Internal Transportation - System 2 (Rs. Million)
Initial investment (4×1.000) 4.000
Add : Annual operating cost (0.9×3.465) 3.1185
7.1185
Less : Salvage value at the end of 6 years (1.5×0.792) 1,185
P.V. cash outflow 5.9305
Equivalent Annual Cost
System 1 Rs. . Million
.
.
1 93
4 917
9 507 = = System 2 Rs. . Million
.
.
1 71
3 465
5 9305 = =
Analysis : The equivalent annual cost of System 2 is less than Sysem 1. Hence, System 2 is
suggested to takeup.
Illustration 3 : A company is considering which of two mutually exclusive projects is should
undertake. The Finance Director thinks that the project with the higher NPV should be chosen
whereas the managing Director think that the one with the higher IRR should be undertaken
especially as both projects have the same initial outlay and length of life. The company
anticipates a cost of capial of 10% and the net after-tax cash flows of the projects are as
follows :
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Year 0 1 2 3 4 5
Cash Flows :
Project X (200) 35 80 90 75 20
Project Y (200) 218 10 10 4 3
Required :
(a) Calculate the NPV and IRR of each project.
(b) Sate, with reasons, which project you would recommedn.
(c) Explain the inconsistency in the ranking of the two projects.
The discount factors are as follows :
Year 0 1 2 3 4 5
Discount Factors : (10%) 1 0.91 0.83 0.75 0.65 0.62
(20%) 1 0.83 0.69 0.58 0.48 0.41
(a) Calculation of the NPV and IRR of each Project
NPV of Project X
Year Cash Discount Discounted Discount Discounted
Flows Factors Values Factors Values
@ 10% @ 20%
0 (200) 1.00 (200) 1.00 (200)
1 35 0.91 31.85 0.83 29.05
2 80 0.83 66.40 0.69 55.20
3 90 0.75 67.50 0.58 52.20
4 75 0.68 51.00 0.48 36.00
5 20 0.62 12.40 0.41 8.20
NPV + 29.15 – 19.35
IRR of Project X
At 20% NPV is – 19.35
At 10% NPV is + 29.15
IRR 10
29 15 19 35
29 15
10 ×
+
= +
. .
.
. %
.
.
10 16 01
48 50
29 15
=10 + × =
Fianancial Management & international finance 129
NPV of Project Y
Year Cash Discount Discounted Discount Discounted
Flows Factors Values Factors Values
@ 10% @ 20%
0 (200) 1.00 (200) 1.00 (200)
1 218 0.91 198.38 0.83 180.94
2 10 0.83 8.30 0.69 6.90
3 10 0.75 7.50 0.58 5.80
4 4 0.68 2.72 0.48 1.92
5 3 0.62 1.86 0.41 1.23
NPV + 18.76 – 3.21
IRR of Project Y
At 20% NPV is – 3.21
At 10% NPV is + 18.76
IRR 10
18 76 3 21
18 76
10 ×
+
= +
. .
.
. %
.
.
10 18 54
21 97
18 76
=10 + × =
(b) Both the projects are acceptable because they generate the positive NPV at the company’s
cost of Capital at 10%. However, the Company will have to select Project X because it
has a higher NPV. If the company follows IRR method, then Project Y should be selected
because of higher internal rate of return (IRR). But when NPV and IRR give contradictory
results, a project with higher NPV is generally preferred because of higher return in
absolute terms. Hence, Project X should be selected.
(c) The inconsistency in the ranking of the projects arises because of the difference in the
pattern of cash flows. Project X’s major cash flows occur mainly in the middle three
years, whereas Y generates the major cash flows in the first itself.
Illustration 4 : Projects X and Y are analysed and you have determined the following
parameters. Advice the investor on the choice of a project :
Particulars Project X Project Y
Invest Rs. 7 cr. Rs. 5 cr.
Project life 8 years 10 years
Construction period 3 years 3 years
Cost of capital 15% 18%
N.P.V. @ 12% Rs. 3,700 Rs. 4,565
N.P.V. @ 18% Rs. 325 Rs. 325
I.R.R. 45% 32%
Rate of return 18% 25%
Payback 4 years 6 years
B.E.P. 45% 30%
Profitability index 1.76 1.35
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Relative Ranking of Project X and Project Y
Particulars Rank
Project X Project Y
IRR I II
Rate of return II I
Pay back I II
Profitability index I II
NPV @ 12% II I
NPV @ 18% Equal Equal
B.E.P. II I
Cost of Capital I II
Analysis : The major criterion i.e., IRR, Pay back and Profitability Index in which Project X
is ranking first and hence it could be selected.
Illustration 5 : A company is contemplating to purchase a machine. Two machine A and B
are available, each costing Rs. 5 lakhs. In comparing the profitability of the machines, a
discounting rate of 10% is to be used and machine is to be written off in five years by straight
line method of depreciation with nil residual value. Cash inflows after tax are expected as
follows :
(Rs. in lakhs)
Year Machine A Machine B
1 1.5 0.5
2 2.0 1.5
3 2.5 2.0
4 1.5 3.0
5 1.0 2.0
Indicate which machine would be profitable using the following methods of ranking
investment proposals :
(i) Pay back method : (ii) Net present value method; (iii) Profitability index method; and
(iv) Averge rate of return method.
The discounting factorfs at 10% are—
Year 1 2 3 4 5
Discount factors .909 .826 .751 .683 .621
(i) Payback Period (PB)
Annual cash inf lows
Initial Investment =
Fianancial Management & international finance 131
Calculation of Payback Period :
Machine A (Rs. lakhs)
Year Cash inflows Payback years required
Total Needed
1 1.50 1.50 1 year
2 2.00 2.00 1 year
3 2.50 1.50 . months
.
.
12 7 2
2 50
1 50 = ⎟⎠
⎞ ⎜⎝
⎛ ×
Machine B (Rs. lakhs)
Year Cash inflows Payback years required
Total Needed
1 0.50 0.50 1 year
2 1.50 1.50 1 year
3 2.00 2.00 1year
4 3.00 1.00 (1/3 × 12) = 4 months
5.00
Payback period for Machine b = 3 years 4 months.
Rank : Machine-A, Machine-B - II machine A is more profitable.
(ii) Calculate of Net Present Value of cash inflows for Machine A & Machine B.
Years Cash Inflows Discount P. V. of cash inflows
Machine A Machine B Factor @ 10% Machine A Machine B
1. 1.5 0.5 .909 1.36 0.45
2. 2.0 1.5 .826 1.65 1.24
3. 2.5 2.0 .751 1.88 1.50
4. 1.50 3.0 .683 1.02 2.05
5. 1.0 2.0 .621 0.62 1.24
6.53 6.48
Total P.V. 6.53 6.48
Initial Investment 5.00 5.00
Net Present Value (NPV) 1.53 1.48
Rank : Machine-A - I, Machine-B - II
Since Machine A has greater NPV compared to Machine B, Machine A is more profitable.
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(iii) Calculation of Profitability Index (Rs. lakhs)
Machine A Machine B
Profitability Index
Present value of Cash Inflows
= Present value of Cash Inflows 1 306
5 00
6 53
.
.
. = 296 1
5 00
6 48
.
.
. =
Rank I II
Machine A is more profitable.
(iv) Calculation of Average Rate of Return = ×100
Initial cost
Average annual earnings
(Rs. lakhs)
Machine A Machine B
Total Cash inflow 8.50 9.00
Less : Depreciation for 5 years 5.00 5.00
Net earning after tax and depreciation 3.50 4.00
Life of machine (yrs.) 5 5
Average earnings per year .70 0.80
Initial cost 5 5
ARR %
.
Rank II I
Machine B is more profitable.
Illustration 6 : Determine which of the following two mutually exclusive projects should be
selected it may are :
(i) One-off investments or (ii) It they can be repeated indefinitely :
(Rs.)
Particulars Project A Project B
Investment 40,000 60,000
Life 4 years 7 years
Annual net cash inflows 15,000 16,000
Scrap value 5,000 3,000
Cost of capital is 15%. Ignore taxation. The Present Value of annuity for 4 years and 7 years
at 15% are respectively 2.8550 and 4.1604 and the discounting factors at 4 years/7 years
respectively 0.5718 and 0.3759.
Fianancial Management & international finance 133
(i) Project A (Rs.)
Year Cash flow Discount factor Present value
0 (40,000) 1.0000 (40,000)
1-4 15,000 2.8550 42,825
4 5,000 0.5718 2,859
NPV = 5,684
(i) Project B (Rs.)
Year Cash flow Discount factor Present value
0 (60,000) 1.0000 (60,000)
1-7 16,000 4.1604 66,566
7 3,000 0.3759 1,128
NPV = 7,694
Suggestion : If Projects A and B are one-off investments, then Project B is preferable.
(ii) Uniform Annual Equivalent
1991
2 8550
5684 = =
.
A 1849
4 1604
7694 = =
.
B
Suggestion : Choose Project A for continual repeats.
Illustration 7 : Company x is forced to choose between two machines A and B. The two
machines are designed differently, but have identical capacity and do exactly the same job.
Machine A costs Rs. 1,50,000 and will last for 3 years. It costs Rs. 40,000 per year to run.
Machine B is an ‘economy’ model costing only Rs. 1,00,000, but will last only for 2 years, and
costs Rs 60,000 per year to run. These are real cash flows. The costs are forcasted in rupees of
constant purchasing power. Ignore tax. Opportunity cost of capital is 10 per cent. Which
machine company X should buy?
Working Notes :
Compound present value of 3 years @ 10% = 2.486
P.V. of Running cost of Machine A for 3 years = Rs. 40,000×2.486 = Rs. 99,440
Compound present value of 2 years @ 10% = 1.735
P.V. of Running cost of Machine B for 2 years = Rs. 60,000×1.735 = Rs. 1,04,100
Statement showing evaluation of Machine A and B (Rs.)
Particulars Machine A Machine B
Cost of purchase 1,50,000 1,00,000
Add : P.V. of running cost for 3 years 99,440 1,04,100
2,49,440 2,04,100
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P.V. of Cash outflow 2,49,440 2,04,100
2.486 1.753
Equivalent Present valu of annual Cash outflow = 1,00,338 = 1,17,637
Analysis : Since the annual Cash outflow of Machine is highest, Machine A can be purchased.
Illustration 8 : A particulars project has a four-year life with yearly projected net profit of
Rs. 10,000 after charging yearly Depreciation of Rs. 8,000 in order to write-off the capital
cost of Rs. 32,000. Out of the Capital cost Rs. 20,000 is payable immediately (Year 0) and
balance in the next year (which will be the Yea 1 for evaluation). Stock amounting to Rs.
6,000 (to be invested in Year 0) will be required throughout the project and for Debtors a
further sum of Rs. 8,000 will have to be invested in Year 1. The working capital will be
recouped in Year 5. It is expected that the machinery will fetch a redidual value of Rs. 2,000
a the end of 4th year. Income Tax is payable @ 40% and the Depreciation equals the taxation
writting down allowances of 25% pre annum. Income Tax is paid after 9 months after the
end of the year when profit is made. The residual value of Rs. 2,000 will also bear Tax @
40%. Although the project is for 4 years, for computation of Tax and realisation of working
capital, the computation will be required up to 5 years.
Taking Discount factor of 10%, calculate NPV of the project and give your comments regarding
its acceptability.
(NPV Factors @ 10% - Year 1-0.9091; Yr. 2-0.8264; Yr. 3-0.7513; Yr. 4-0.6830; Yr. 5-0.6209).
Calculation of NPV of Project (Rs.)
Year
Particularsr 0 1 2 3 4 5
Capital Expenditure (20,000) (12,000) — — — —
Working Capital (6,000) (8,000) — — — —
Net Profit — 10,000 10,000 10,000 10,000 10,000
Depreciation Add back — — 8,000 8,000 8,000 8,000
Tax — — (4,000) (4,000) (4,000) (4,800)
Salvage value — — — — 2,000 —
Recovery of working — — — — — 14,000
Capital
Net Cash inflow (26,000) (2,000) 14,000 14,000 16,000 9,200
Discount factor @ 10% 1.000 0.9091 0.8264 0.7513 0.6830 0.6209
Present Value (26,000) (1,819) 11,570 10,570 10,928 5,712
Suggestion : Since NPV is Rs. 10,910; it is suggested to accept the proposal.
Illustration 9 : Following are the data on a capital project being evaluated by the Management
of X Ltd. :
Fianancial Management & international finance 135
Project M
Annual cost saving Rs. 40,000
Useful life 4 years
I.R.R. 15%
Profitability Index (PI) 1.064
NPV ?
Cost of capital ?
Cost of project ?
Payback ?
Salvage value 0
Find the missing values considering the following table of discount factor only :
Discount 15% 14% 13% 12%
1 year 0.69 0.877 0.885 0.893
2 year 0.756 0.769 0.783 0.797
3 year 0.658 0.675 0.693 0.712
4 year 0.572 0.592 0.613 0.636
Calculation of Cost of Project i.e., Initial Cash Outlay of Project M
Annual cost saving = Rs. 40,000
Useful life = 4 years
I.R.R. = 15%
At 15% I.R.R., the total present value of cash inflows is equal to initial cash outlay.
Total present value of cash inflows @ 15% for 4 years is 2.855
= Rs. 40,000 × 2.885 = Rs. 1,14,200
∴ Project Cost is Rs. 1,14,200
Calculation of Payback Period of Project M
Payback Period 40 000
114 000
,
, ,
Annual cost saving
Cost of project = = = 2.855 or 2 years 11 months (approx.)
Calculation of Cos of Capital
Profitability Index = Cost of Project
Discounted cash inflows
Profitability Index = 1.064 given
Cost of Project = Rs. 1,14,200
1.064 = 1,14,200
Present value of cash inflows
Present value of cash inflows = 1.064 × 1,14,200 = Rs. 1,21,509
136 Fianancial Management & international finance
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Cumulative Discount Factor for 4 years
= 40 000
1 21 509
,
, ,
Annual cost saving
Present value of cash inflows = =3.038
Looking at present value table at discount compound discount factor for 4 years is 3.038
∴ Cos of capital = 12%
Calculation Net Present Value of Project
N.P.V = Present Value of Total Cash Inflows - Cost of Project
= 1,21,509 – 1,14,200 = Rs. 7,309
Illustration 10 : XYZ Ltd. is manufacturer of high quality running shoes. Devang. President,
is considering computerising the company’s ordering, inventory and billing procedures. He
estimates that the annual savings from computerisation include a reduction of 10 clerical
employees with annual salaries of Rs. 15,000 each, Rs. 8,000 from reduced production delays
caused by raw materials inventory problems, Rs. 12,000 from lost sales due to inventory
stockouts and Rs. 3,000 associated with timely billing procedures.
The purchase price of the system is Rs. 2,00,000 and installation costs are Rs. 50,000. These
outlays will be capitalised (depreciated) on a straight line basis to a zero book salvage value
which is also its market value at the end of five years. Operation of the new system requires
two computer specialists with annual salaries of Rs. 40,000 per person. Also is 40%***** rate
of return (cost of capital) for this projeft is 12%
You are required to :
(i) Find the project’s initial net cash outlay.
(ii) Find the project’s operating and terminal value cash flows over its 5 year life.
(iii) Evaluate the project using NPV method.
(iv) Evaluate the project using PI method.
(v) Calculate the project’s payback period.
(vi) Find the project’s cash flows and NPV [part (i) through (iii)] assuming that the system
can be sold for Rs. 25,000 at the end of five years even thogh the book salvage value will
be zero, and
(vii) Find the project’s cash flows and NPV [part (i) though (iii)] assuming that the book
salvage value for depreciation pourposes is Rs. 20,000 even though the machine is
worthless in terms of its resale value.
Note : (a) Present Value of annuity of Re. 1 at 12% rate of discount for 5 years is 3.605.
(b) Present Value of Re. 1 at 12% rate of discount, received at the end of 5 years is
0.567.
(i) Calculation of Project’s initial net cash outlay (Rs.)
Purchase price of system 2,00,000
Installation cost 50,000
Net cash outlay of project 2,50,000
Fianancial Management & international finance 137
(ii) Calculation of Project’s Operating and Terminal Value cash flows over its 5 year life
(Rs.)
Savings
Reduction in salaries (10 celrks×Rs. 15,000 p.a.) 1,50,000
Reduction in production delays 8,000
Reduction in cost sales 12,000
Savings from timely billing procedures 3,000
(a) 1,73,000
Expenses
Depreciation 50,000
Salaries of computer specialists 80,000
Maintenance & Operating expenses 12,000
(b) 1,42,000
Profit before tax (a) – (b) 31,000
Less : Tax @ 40% 12,400
Profit after tax 18,600
Add : Depreciation 50,000
Net cash inflows p.a. for 1 to 5 years 68,600
(iii) Evaluation of Project using NPV method (Rs.)
Year Cash inflow P.V. @ 12% Total P.V.
0 (2,50,000) 1.000 (2,50,000)
1 to 5 68,600 3.605 2,47,303
NPV –2,697
Analysis : Since NPV is negative, the project cannot be accepted under NPV method.
(iv) Evaluation of Project using PI method
Profitability Index (PI) = 0.99
2,50,000
2,47,303
Present value of outflows
Present value of cash inflows = =
Analysis : Since Profitability Index is less than 1, the Project cannot be accepted under this
method.
(v) Calculation of the Project’s Payback Period : (Rs.)
Year Net cash inflows Cumulative cash inflow
1 68,600 68,600
2 68,600 1,37,200
3 68,600 2,50,800
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4 68,600 2,74,400
5 68,600 3,43,000
The payback period is 3 years and fraction of the 4th year. The fraction year is calculated
as under :
0 64
68 600
44 200
12 .
,
= × , =
Hence, the payback period is 3.65 years.
(vi) Calculation of Project Cash flows and NPV assuming that the system can be sold
for Rs. 25,000 at the end of 5 years.
Year Cash flows P.V. @ 12% Total P.V.
0 (2,50,000) 1.000 (2,50,000)
1 to 5 68,500 3.605 2,47,303
5 15,000* 0.567 8,505
NPV 5,808
* Post tax salvage value = 25,000 (1-0.40) = Rs. 15,000
Analysis : Since NPV is positive, the project can be selected.
(vii) Calculation of project’s cash flows and NPV assuming that the boos salvage value
for depreciation purposes is Rs. 20,000 even though the machine is worthless in
terms of its resale value :
Depreciation p.a. = Rs. , p.a.
years
, , ,
46 000
5
2 50 000 20 000 − =
Cash Inflow p.a. (Rs.)
Savings 1,73,000
Less : Depreciation 46,000
Salaries of computer specialists 80,000
Maintenance cost 12,000 1,38,000
Profit before tax 35,000
Less : Tax @ 40% 14,000
Profit after tax 21,000
Add : Depreciation 46,000
Cash Inflow p.a. 67,000
Year Cash flows P.V. factor Total P.V.
Rs. @ 12% Rs.
0 (2,50,000) 1.000 (2,50,000)
1 to 5 67,000 3.605 2,41,535
5 (tax credit) 8,000 0.567 4,536
Analysis : Since NPV is negative, Project can be rejected.
Illustration 11 : Xpert Engineering Ltd. is considering buying one of the following two mutually
exclusive investment projects :
Project A : Buy a machine that requires an initial investment outlay of Rs. 1,00,000 and will
generate the cash flows after tax (CFAT) of Rs. 30,000 per year for 5 years.
Project B : Buy a machine that requires an initial investment outlay of Rs. 1,25,000 and will
generate ‘cash flows after tax’ (CFAT) of Rs. 27,000 per year for 8 years.
Which project should be undertaken? The company uses 10% cost of capital to evaluate the
projects.
Note : Present value of Re. 1 for eight years @10% - 0.9091, 0.8264, 0.7513, 0.6830, 0.6209,
0.5645, 0.5132, and 0.4665.
Calculation of Net Present Value
Project A (Rs.)
Initial Investment (1,00,000×1.000) (1,00,000)
Cash Inflow After Tax (30,000×3.791) 1,13,730
NPV
Project B (Rs.)
Initial Investment (1,25,000×1.000) (1,25,000)
Cash Inflow After Tax (27,000×5.335) 1,44,045
NPV 19,045
Equalavent Annual NPV
Project A = 13,730/3.791 = Rs. 3.622 Project B = 19,045/5.335 = Rs. 3.570
Analysis
If it is one time Project, Project B suggested, since its NPV is greater than Project A
If a Project is to be replaced every time after the end of economic life of earlier Project,
then Project A is preferable, since its equivalent annual NPV is higher than Project B.
Illustration 12 : XYZ Ltd., an infrastructure company is evaluating proposal to build, operate
and transfer a section of 35 kms. of road at a projcet cost of Rs. 200 crores to be financed as
follows :
Equity Share Capital Rs. 50 crores, loan at the rate of interst of 15% p.a. from financial
institutions Rs. 150 crores. The Project after completion will be opened to traffic and a toll
will be collected for a period of 15 years from the vehicles using the road. The company is
also required to maintain the road during the above 15 years and after the completeion of
that period, it will be handed over to the Highway Authorities at zero value. It is estimated
that the toll revenue will be Rs. 50 crores per annum and the annual toll collection expenses
including maintenance of the roads will amount to 5% of the project cost. The company
considers to write off the total cost of the project in 15 years on a straight line basis. For
Corporate Income-tax purposes the company is allowed to take depreciation @ 10% on WDV
basis. The financial institutions are agreeable for the repayment of the loan in 15 equal annual
instalments–consisting of principal and interest.
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Calculate Project IRR and Equity IRR. Ignore Corporate taxation. Explain the differences in
Project IRR and Equity IRR.
Road Project cost = Rs. 200 crores
Financed by :
Equity Share Capital = Rs. 50 crores
Term Loan from financial institutions @ 15% p.a. = Rs. 150 crores
Annual net cash inflows = Rs. 50 crores - 5% of Rs. 200 crores
= Rs. 40 crores
Maintenance of road = 15 years
Salvage value at the end of 15 years = NIL
Calculation of IRR
Factor to be located 5 000
40
200
.
Rs. crores
Rs. crores
Average annual cash inf low
Original investment = = =
The Present Value annuity factor appearing nearest to 5.092 for 15 years @ 18%
NPV at 18% (Rs. Crores)
P.V. of annual cash inflow (40×5.092) 203.68
Initial cash outlay 200.00
NPV 3.68
NPV at 19% (Rs. Crores)
P.V. of annual cash inflow (40×4.876) 195.04
Initial cash outlay 200.00
NPV (4.96)
Now, the IRR of the Project is acertained by method of interpolation as follows :
%
. ( . )
.
IRR % 1
3 68 4 96
3 68
18 ×
− −
= + % % . % . %
.
.
% 1 18 0 426 18 43
8 64
3 68
=18 + × = + =
Illustration 13 : An oil company proposes to install a pipeline for transport of crude from
wells to refinery. Investments and operating costs of the pipeline very for different sizes of
pipelines (diameter). The following details have been conducted :
(a) Pipeline diamter (in inches) 3 4 5 6 7
(b) Investment required (Rs. lakhs) 16 24 36 64 150
(c) Gross annual savings in operating
costs before depreciation (Rs. lakhs) 5 8 15 30 50
The estimated life of the installation is 10 years. The oil comapany’s tax rate is 50%. There is
no salvage value and straight line rate of depreciation is followed.
Calculate the net savings after tax and cash flow generation and recommend therefrom, the
largest pipeline to tbe insalled, if the company desires a 15% post-tax return. Also indicate
Fianancial Management & international finance 141
which pipeline will have the shortest payback. The annuity P.V. factor at 15% for 10 years is
5.019.
Determination of CFAT (Rs. Lakhs)
Pipeline Gross Savings Depreciation Tax adv. of Total cost
Diameter (inches) savings p.a. after tax depreciation savings/(CFAT)
(1) (2) (3) (4) (5) (6)
[(2)×50%] [(4)×50%] [(3)×5%]
3 5 2.5 1.6 0.8 3.3
4 8 4.0 2.4 1.2 5.2
5 15 7.5 3.6 1.8 9.3
6 30 15.0 6.4 3.2 18.2
7 50 25.0 15.0 7.5 32.5
Payback Period in Years
Inches Rs. lakhs Years
3 16/3.3 4.848
4 24/5.5 4.615
5 36/9.3 3.871
6 64/18.2 3.516
7 150/32.5 4.615
Therefore, Pipeline diameter of 6 inches has shortest payback period.
Determination of NPV (Rs. in lakhs)
Pipeline dia CFAT PV factor Total PV Cash NPV
(inches) for 10 years @ 15% 10 yrs. outflow
3 3.3 5.019 16.5627 16 0.5627
4 5.2 5.019 26.0988 24 2.0988
4 9.3 5.019 46.6767 36 10.6767
6 18.2 5.019 91.3458 64 27.3458
7 32.5 5.019 163.1175 150 13.1175
Suggestion : Pipeline of 6 inches diameter has highest NPV and it is recommended for
installation.
Illustration 14 : Indo Plastics Ltd. is a manufacturer of high quality plastic products. Rasik,
President, is considering computerising the company’s ordering, inventory and billing
procedures. He estimates that the annual savings from computerisation include a reduction
of 4 clerical employees with annual salarie sof Rs. 50,000 each, Rs. 30,000 from rudeuced
production delays caused by raw materials inventory problems, Rs. 25,000 from lost sales
due to inventory stock outs and Rs. 18,000 associated with timely billing procedures.
The purchase price of the system in Rs. 2,50,000 and installation costs are Rs. 50,000. These
outlays will be capitalised (depreciated) on a straight line basis to a zero books salvage value
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which is also its market value at the end of five years. Operation of the new system requires
two computer specialists with annual salaries of Rs. 80,000 per person. Also annual
maintenance and operating (cash) expenses of Rs. 22,000 are emstimated to be required. The
company’s tax rate is 40% and its required rate of return (cost of capital) for this project is
12%
Your are required to—
(i) evaluate the project using NPV method;
(ii) evaluate the project using PI method;
(iii) calculate the Project’s payback period.
Note :
(a) Present value of annuity of Re. 1 at 12% rate of discount for 5 years is 3.605.
(b) Present value of Re. 1 at 12% rate of discount, received at the end of 5 years is 0.567.
Determination of NPV (Rs.)
Cost 2,50,000
Installation expenses 50,000
Total net Cash Outlay 3,00,000
Project’s operating and terminal value cash flows over its 5-year life (Rs.)
Savings
Reduction in clerks salaries (4×50,000) 2,00,000
Reduction in projection delays 30,000
Reduction in lost sales 25,000
Gains due to timely production 18,000 2,73,000
Less : Expenses
Depreciation (3,00,000/5) 60,000
Add : People cost (80,000×2) 1,60,000
Maintenance cost 2,000 2,42,000
Profit before Tax 31,000
Less : Tax (40%) 12,400
Profit After Tax 18,600
Cash flow = Profit After Tax – Depreciation = 18,600 + 60,000 = Rs. 78,600
The cash flows is the same for the years 1 to 5.
Fianancial Management & international finance 143
(i) Evaluation of the Project by using Net Present Value (NPV) Method :
Years Cash flow PV of Annuity of Rs. 1 Total present value
After tax (Rs.) at 12% for five years (Rs.)
1 to 5 78,600 3.605 2,83,353
Less : Total Initial Cash Outlay 3,00,000
NPV (16,647)
Since NPV is negative, therefore, the project is unviable.
(ii) Evaluation fo the Project by using PI Method.
Profitability Index (PI) = PV of cash in flows/Initial outlay
= 2,83,353/3,00,000 = 0.945
Since PI is less than 1.0, the project is unviable.
(iii) Calculation of the Project’s Payback Period (Rs.)
Year Net cashflow Cumulative cashflow
1 78,600 78,600
2 78,600 1,57,200
3 78,600 2,35,800
4 78,600 3,14,400
5 78,600 3,93,00
Hence, the payback period is 3 years plusa fraction of the 4th year. The fraction of the year
can be calculated as under :
0 82
78 600
64 200
.
,
, =
Therefore, the payback period is 3.82 years.
CAPITAL RATIONING
Illustration 15 : In a capital rationing situation (investment limit Rs. 25 lakhs), suggest the
most desirable feasible combination on the basis of the following data (indicate justification) :
(Rs. lakhs)
Year Net cashflow Cumulative cashflow
A 15 6
B 10 4.5
C 7.5 3.6
D 6 3
Projects B and C are mutually exclusive.
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Determination of feasible combination in Capital Rotationing Situation (Investment Limit
Rs. 25 lakhs)
(Rs. lakhs)
Combination Total outlay NPV
A & B 25.00 10.50
A & C 25.50 9.60
A & D 21.00 9.00
B & D 16.00 7.50
C & D 13.50 6.60
Analysis : From the above analysis it is observed that projects A&B combination give highest
NPV of Rs. 10.50 lakhs. Therefore by undertaking projects A and D, the wealth maximation
is possible.
Illustration 16 : The total available budget for a company is Rs. 20 crores and the total cost of
the projects is Rs. 25 crores. The projefts listed below have been ranked in order of profitability.
There is possibility of submitting X project where cost is assumed to be Rs. 13 crores and it
has the Profitability Index of 140.
Project Cost Profitability index
(Rs. crores) (P.V. of cash inflow/PV of cash outflows) × 100
A 6 150
B 5 125
C 7 120
D 2 115
E 5 110
25
Which projects, including X, should be acquired by the company?
N.P.V. of Projects (Rs. Crores)
Project Cost PI P.V. of cash NPV
inflow
(1) (2) (3) (2)×(3) = (4) (4) – (2) = (5)
A 6 1.5 9.00 3.00
B 5 1.25 6.25 1.25
C 7 1.20 8.40 1.40
D 2 1.15 2.30 0.30
E 5 1.10 5.50 0.50
X 13 1.40 18.20 5.20
Fianancial Management & international finance 145
Selection of project based on NPV, should to the availability of total funds Rs. 20 crores.
(Rs. Crores)
Project NPV Project cost
X 5.20 13
A 3.00 6
8.20 19
The company will maximise its NPV by undertaking X and A, which require total funds of
Rs. 19 crores. This option is suggested even though there is no full utilisation of total funds.
The surplus funds of Rs. 1 crore can be deployed elsewhere profitably.
The following combination of projects will not maximise NPV : (Rs. crores)
Project NPV Project cost
(i) X 5.20 13
B 1.25 5
6.45 18
(ii) X 5.20 13
C 1.40 7
6.60 20
(iii) X 5.20 13
B 1.25 5
D 0.30 2
6.75 20
Illustration 17 : S. Ltd., has Rs. 10,00,000 allocated for capital budgeting purpose. The
following proposal and associated profitability indexes have been determined :
Project Amount (Rs.) Profitability Index
1 3,00,000 1.22
2 1,50,000 0.95
3 3,50,000 1.20
4 4,50,000 1.18
5 2,00,000 1.20
6 4,00,000 1.05
Which of the above investment should be undertaken? Assume that projects are indivisible
and there is not alternative use of the money allocated for capital budgeting.
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Statement Showing Ranking of Projects on the basis of Profitability Index (P.I.)
Project Amount (Rs.) P.I. Rank
1 3,00,000 1.22 1
2 1,50,000 0.95 5
3 3,50,000 1.20 2
4 4,50,000 1.18 3
5 2,00,000 1.20 2
6 40,00,000 1.05 4
Statement showing NPV of Projects (Rs.)
Project Amount P. I. Cash inflow NPV
(2) × (3) (2) – (3)
(1) (2) (3) (4) (5)
1 3,00,000 1.22 3,66,000 66,000
2 1,50,000 0.95 1,42,5000 (7,500)
3 3,50,000 1.20 4,20,000 70,000
4 4,50,000 1.18 5,31,000 81,000
5 2,00,000 1.20 2,40,000 40,000
6 4,00,000 1.05 4,20,000 20,000
Selection Projects
Profitability Index method : Assuming the projects are indivisible and there is no
alternative use of unutilised amount, S. Ltd. is advised to undertake investment in
projects 1, 3 and 5, which will give N.P.V. of Rs. 1,76,000 and unutilised amount will
be Rs. 1,50,000.
Net present value method : As per this method projects 3, 4 and 5 can be undertaken
which will be Rs. 1,91,000 and no money will remain unspent.
Suggestion : From the above analysis, we can observe that, selection of projects under NPV
method will maximise S Ltd.’s net cash inflow by Rs. 15,000 (i.e., 1,91,000 – 1,76,000). Hence,
it is suggested to undertake investments in protest 3, 4 and 5.
Illustration 18 : Alpha Limited is considering five capital projects for the years 2003 and
2004. The company is financed by equity entirely and its cost of capital is 12%. The experted
cash flows of the projects are as belows :
Fianancial Management & international finance 147
Year and Cash flows (Rs. ’000)
Project 2003 2004 2005 2006
A (70) 35 35 20
B (40) (30) 45 55
C (50) (60) 70 80
D (90) 55 65
E (60) (20) 40 50
Note : Figures in brackets represent cash outflows.
All projects are divisible i.e., size of investment can be reduced, if necessary in relation to
availability of funds. None of the projects can be delayed or undertaken more than once.
Calculate which project Alpha Limited should undertake if the capital available for investment
is limited to Rs. 1,10,000 in 2003 and with no limitation in subsequent years. For your analysis,
use the following present value factors :
Years 2003 2004 2005 2006
Factors 1.00 0.89 0.80 0.71
Calculation of NPV and Profitability Index (PI) (Rs. ’000)
Discounted cash flows
NPV PI
Year 2003 2004 2005 2006
Discount Factors @ 12% 1.00 0.89 0.80 0.71
Project
A (70) 31.15 28 14,20 3.35 1.048
B (40) (26.70) 36 39.05 8.35 1.125
C (50) (53.40) 56 56.80 9.40 1.091
D — (80.10) 44 46.15 10.05 1.251
E (60) 17.80 32 35.50 25.30 1.422
Ranking of Projects Based on Profitability Index
Rank I II III IV V
Project E D B C A
Anlysis and Selection
Conditions
1. Capital available for investment is limited to Rs. 1,10,000 in 2003, with no limitation in
subsequent years.
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2. All projects are divisible i.e., size of investment can be reduced if necessary in relation to
availability of funds.
3. None of the projects can be delayed or undertaken more than once.
Project D’s cash outflow will start in the year 2004, and hence this will not form a s constraint
in selection of projects. Since there is no scarcity of funds from the year 2004 onwards. This
can be taken up in 2004.
Project Rank Initial investment (Rs.)
E I 60,000
B II 40,000
C IV 10,000*
* Since the project C is divisible, the balance funds of Rs. 10,000 (i.e., 1,10,000–60,000–40,000)
can be allocated to project C. One of the condition in the problem is none of the projects can
be undertaken more than once. Hence project C will continue with initial investment of
Rs. 10,000. Project D can be undertaken in the year 2004 since there is no scarcity of funds
from the year 2004.
Ranking of Projects excluding ‘D’ which is to start in 2004 when no limitation on capital
availability :
Project E B C A
Rank I II III IV
Illustration 19 : Five Projects M, N, O, P and Q are available to a company for consideratio.
The investment required for each project and the cash flows it yields are tabulated below.
Projects N and Q are mutually exclusive. Taking the cost of capital @ 10%, which combination
of projects should be taken up for a total capital outlay not exceeding Rs. 3 lakhs on the basis
on NPV and Benefit-Cost Ratio (BCR)? (Rs.)
Project Investment Cash flow p.a. No of years P.V. @ 10%
M 50,000 18,000 10 6.145
N 1,00,000 50,000 4 3.170
O 1,20,000 30,000 8 5.335
P 1,50,000 40,000 16 7.824
Q 2,00,000 30,000 25 9.077
Total Capital outlay <>
Fianancial Management & international finance 149
Computation of Net Present Value and Benefit-Cost Ratio for 5 Projects (Rs.)
Project Investment Cash flow No. of years P.V. @ 10% P.V. NPV BCR (PV/
p.a. Investment)
M 50,000 18,000 10 6.145 1,10,610 60,160 2.212
N 1,00,000 50,000 4 3.170 1,58,500 58,500 1.585
O 1,20,000 30,000 8 5.335 1,60,050 40,050 1.334
P 1,50,000 40,000 16 7.824 3,12,960 1,62,960 2.086
Q 2,00,000 30,000 25 9.077 2,72,310 72,310 1.362
Statement showing Feasible Combination of Projects and their NPV, BCR
Feasible Combination Investment NPV Rank BCR Rank
of projects (Rs.) (Rs.)
(i) M, N and P 3,00,000 2,82,070 1 1.940 1
(ii) M, N and O 2,70,000 1,59,160 4 1.589 4
(iii) O & P 2,70,000 2,03,010 3 1.752 3
(iv) M & Q 2,50,000 1,32,920 5 1.532 5
(v) N & P 2,50,000 2,21,460 2 1.886 2
(vi) N & Q 3,00,000 1,30,810 6 1.436 6
Illustration 20 : C Ltd. is considering its capital investment programme for 19x0 and 19x1.
The company is financed entry by equity shares and has a cost of capital of 15% per annum.
The company have reduced their initial list of projects to five, the expected cash flows of
which are as follows : (Rs.)
Project Cash flows
19x0 19x1 19x2 19x3
A –60,000 +30,000 +25,000 +25,000
B –30,000 –20,000 +25,000 +45,000
C –40,000 –50,000 +60,000 +70,000
D 0 –80,000 +45,000 +55,000
E –50,000 +10,000 +30,000 +40,000
None of the above projects can be delayed. All the projects are divisible, outlays may be
reduced by any proportion and net inflows will then be reduced in the dame proportion. No
project can be undertaken more than once. C Ltd. is able to invest surplus funds in a bank
deposit account yielding an annual return of 10%. C Ltd. cost of capital is 15%.
Required :
(i) Prepare calculations showing which projects C. Ltd. should undertake, if capital is
expeected to be available a indefinitely large amounts at 15% per annum during all
future periods.
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(ii) Show how your answer to (i) would vary if capital available for investment was limited
to Rs. 1,00,000 in 19x1 but was not limited thereafter.
(iii) Provide a mathematical programming formulation which would assist C Ltd. in
choosing investment projects capital available in 19x0 is limited to Rs. 1,00,000, capital
is available in 19x1 is limited to Rs. 90,000, capitals available thereafter without limited
at 15% per annum, and the shareholders required return from the company was 15%
per annum at all relevant times.
Ignore taxation. Present value factors at 15% year 1-0.8696; 2-0.7561; 3-0.6575.
(i) Net Present Value Calculations (Rs.)
Project A = (60,000) + 30,000 × .8696 + 25,000 × .7561 + 25,000×.6575 = 1,428
Project B = (30,000) + (20,000) × .8696 + 25,000 × .7561 + 45,000×.6575 = 1,098
Project C = (40,000) + (50,000) × .8696 + 60,000 × .7561 + 70,000×.6575 = 7,911
Project D = + (80,000) × .8696 + 45,000 × .7561 + 55,000×.6575 = 619
Project E = (50,000) + 10,000 × .8696 + 30,000 × .7561 + 40,000×.6575 = 7,679
A projects should be accepted since each has a positive Net Present Value.
(ii) Preferred Investments.
Project Rs. Ranking
D 0 I
C 40,000 II
E 50,000 III
B 10,000 IV
1,00,000
Z (in maximise) 1428 a + 1098 B + 7911 C + 619 D + 7679 E – 0.44F
= 60,000 A + 30,000 B + 40,000 C + 50,000 E + F ≤ 1,00,000
= 20,000 B + 50,000 C + 80,000 D ≤ 1.1F+30,000 A+10,000 E + 90,000 D
A, B, C, D, E, F
Working : The NPV of F . . F
.
.
1 044
1 15
1 1 = ⎟⎠
⎞ ⎜⎝⎛
Illustration 21 : A company is considering a cost saving project. This involves purchaing a
machine costing Rs. 7,000 which result in annual savings on wage costs of Rs. 1,000 and on
material costs of Rs. 400.
The following forcasts are made of the rates of inflation each year for the next 5 years :
Wages costs 10%
Material costs 5%
General prices 6%
Fianancial Management & international finance 151
The cost of capital of the company, in monetary terms, is 15%.
Evaluate the project, assuming that the machine has a life of 5 years and no scrap value.
Calculation of Net Present Value (Rs.)
Year Labour Cost Saving Material Cost Total DCF Present
Saving Savings @ 15% Values
1 1000 × (1.1) = 1,100 400 × (1.05) = 420 1,520 0.870 1,322
2 1000 × (1.1)2 = 1,210 400 × (1.05)2 = 441 1,651 0.756 1,248
3 1000 × (1.1)3 = 1,331 400 × (1.05)3 = 463 1,794 0.658 1,180
4 1000 × (1.1)4 = 1,464 400 × (1.05)4 = 486 1,950 0.572 1,115
5 1000 × (1.1)5 = 1,610 400 × (1.05)5 = 510 2,120 0.497 1,054
Present value of Total Savings 5,919
Less : Initial Cash Outflow 7,000
Net Present Value (Negative) (1,081)
Analysis : Since the present value of cost of project exceeds the cost of savings form it is not
suggested to purchase the machine.
Illustration 22 : D Limited, has under reivew a project involing the outlay of Rs. 55,00 and
expected to yield the following net cash savings in current terms :
Year 1 2 3 4
Rs. 10,000 20,000 30,000 5,000
The company’s cost of capital, incorporating a requirement for growth in dividends to keep
pace with cost inflation is 20%, and this is used for the purpose of investment appraisal. On
the above basis the divisional manager involved has recommended rejection of the proposal.
Having regard to your on forecast that the rate of inflation is likely to be 15% in year 1 and
10%, in each of the following years, you are asked to comment fully on his recommendation.
(Disounting figures at 20% are 0.833, 0.694, 0.579 and 0.482 respectively for year 1 to year 4.)
Calculation of Net Present Value (Rs.)
Year Cash inflows Discount factor (20%) Present value
1 10,000 0,833 8,330
2 20,000 0.694 13,880
3 30,000 0.579 17,370
4 5,000 0.482 2,41
P.V. of Cash Inflows 41,990
Less : Initial Investment 55,000
Net Present Value (13,010)
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Analysis : Since NPV is negative it is suggested not to take up the project. Company’s cost of
capital is fixed at 20% keeping in vie the requirement for growth in dividend as well as cost
inflation.
Calculation Net : Present Value based on Inflation Adjusted Cash Flow (Rs.)
Year Cash Inflation Inflation DCF Present
flow adjustmwnt adjusted @ 20% value
of cash flow
1 10,000 1.15 11,500 0.833 9,580
2 20,000 1.15×1.10 25,300 0.694 17,558
3 30,000 1.15×1.102 41.745 0.579 24,170
4 5,000 1.15×1.103 7.653 0.482 3,689
Present Value of Inflation Adjusted Cash Inflows 54,997
Less : Initial Investment 55,000
Net Present Value (–) 3
Analysis : The negative NPV is due to rounding of, otherwise it would be zero. Hence, it is
indifferent to suggest or reject the proposal.
Illustration 23 : A company is considering a new project. The project would involve an
intitial investment of Rs. 1,20,000 in equipment which would have a life of 5 years and no
scrap value. The selling price now (year 0) would be Rs. 60 and is expected to increase in line
with the retail price index. Sales are expected to be constant at 2000 units each year. The
following estimates about unit costs are available :
Cost element Cost at year 0 prices Rate of increases
Rs.
Wages 20 2% per annum faster than retail prices
Other 25 In line with retail prices
Total 45
All transactions take place at yearly intervals on the last day of the year. No increase in
working capital will be required. The following estimates of the rate of increase in retail
prices and of interest rates are available :
Year Rates of increase in retail prices Interest rate
% %
1 15 16
2 20 20
3 25 22
4 40 20
5 30 18
Fianancial Management & international finance 153
Assuming Purchaseing Power Parity Theorem hold in the present case, changes in interest
rates will affect the money value. Hence Cost of Capital is taken in money terms.
Year 0 1 2 3 4 5
Inflation rate for contribution before wages
(interest over previous year) 1.15 1.20 1.25 1.40 1.30
Inflation rate for wages
(interest over previous year) 1.17 1.22 1.27 1.42 1.32
Contribuion before wates, per unit sold Rs. Rs. Rs. Rs. Rs. Rs.
35 40.25 *48.30 60.38 84.53 109.88
Wages per unit 20 23.40 28.55 **36.26 51.49 67.97
Contribution after wages, per unit sold 15 16.85 19.75 24.12 33.04 41.91
Total contribution from 2000 units sold 30,000 33,700 39,500 48,240 66,080 83,820
* 35×1.15×1.20; similarly other figures in this row.
** 20×1.17×1.22×1.27; similarly, other figures in this row.
Calculation of Net Present Value using Money Estimates (Rs.)
Year Money cash flow Money discount factor Present value
0 (1,20,000) 1.000 (1,20,000)
1 33,700 0.862 [1×1/1.16] 29,049
2 39,500 0.718 [0.862×1/12] 28,361
3 48,240 0.589 [0.718×1/1.22] 28,413
4 66,080 0.491 [0.589×1/12] 32,445
5 83,820 0.416 [0.491×1/1.18] 34,869
Analysis : Since the NPV is Positive, the project is worthwhile.
Illustration 24 : E. Ltd. is considering the replacement of a machine used exclusively for the
manufactuer of one of its Product Y. The existing machine have a book value of Rs. 65,000
after deducting straight line depreciation from historical costs, however, it could be sold only
for Rs. 45,000. The new machine would cost Rs. 1,00,000. E. Ltd. expects to sell Product Y for
four more years. The existing mahcine could be kept in operation for that period of time is it
were economically desirable to do so. After four years, the scrap value of both the existing
machine and the new machine would be zero.
The current costs per unit for manufacturing Y on the existing a new machine are as follows :
(Rs.)
Existing Machine New Machine
Materials 22.00 20.00
Labour (32 hours @ Rs. 1.25 40.00 (16 hours @ Rs. 1.25) 20.00
Overheads (32 hours @ Rs. 0.60) 19.20 (16 hours @ Rs. 1.80) 28.80
Total cost 81.20 68.80
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Overheads are allocated to products on the labour hour rate method. The hourly rates of
0.60 and 1.80 comprise 0.25 and 0.625 for variable overheads and 0.35 and Rs. 1.175 for
fixed overheads, including dereciation.
Current sales of Y are 1000 units per annum at Rs. 90 each, if the new machine were
purchased, output would be increased to 1200 units and selling price would be reduced to
Rs. 80.
E. Ltd. requires a minimum rate of return on investment of 20 per cent per annum in
money terms. Material cost, overheads and selling pices are expected to increase at the rate
of 15% per annum, in line with the index of retail prices. Labout costs are expected to increase
at the rate of 20% per annum.
You are required to :—
(i) Give calculatios to show whether purchase of the new machine would b worthwise.
(ii) Comment on th treatment of inflation and the estimation of 20% money cost of capital.
(i) Cost of replacement = 1,00,000 – 45,000 = Rs. 55,000
Manufacturing cost
Fixed items, including depreciation, should be disregarded on the assumption :
(a) Fixed costs do not change as a result of the new machine.
(b) Additional 200 units of extra production would be sold.
(c) All variable elements in the costs given represent cash flows (i.e., labour, material and
vaiable overhead).
Operating cash flow Comparision (Rs.)
Particulars New Machine (1200 units) Existing Machine (1000 units) Increamental
P.U. Total P.U. Total Cash flow
Sales 80 96,000 90 90,000 6,000
Materials 20 24,000 22 40,000 (2,000)
Labour 20 24,00 40 40,000 16,000
Overheads 10 12,000 8 8,000 (4,000)
Next cash 36,000 20,000 16,000
flows
Operating savings are Rs. 16,000 p.a. in fabour of new machine.
Notes :
a. Current prices are assumed in the above table i.e., prices at time 0.
b. Time increase in revenue from new machine Rs. 6,000 is exactly offset by the increases
in materials and variable overheads i.e. Rs. 6,000. Revenue, materials and variable
overheads are stated to be subject to the same rate of inflation i.e. 15% and therefore
will continue to increase at the same rate.
c. The net savings of Rs. 16,000 represent the saving on labour costs which is expected to
increase @ 20% p.a.
Fianancial Management & international finance 155
Operating cash flow Comparision (Rs.)
Year Cash Flows Discount factor @ 20% PV
0 (55,000) 1.000 (55,000)
1 *19,200 0.833 15,994
2 23,040 0.694 15,990
3 27,648 0.579 16,008
4 33,178 0.482 15,992
Next Present Value 8,984
* 1,600×12
Saving is compounded @ 20% p.a. inflation rate, discounted at 20% money cost of capital,
will be Rs. 16,000 p.a.
For 4 years Rs. 16,000×4 = Rs. 64,000.
NPV Rs. 64,000 – Rs. 55,000 = Rs. 9,000.
The above result is due to approximation.
(ii) The relationship between money cost of capial and real cost of capial is givne by—
(1+m) = (1–r) (1+i) Where, m = money cost of capital
r = real cost of capital
i = is the inflation rate
Hence, 1 + 0.20 = (1+r) (1+0.15)
Hence, r = 4.3%
Analysis : Real cost of capital consists of time value of money return required on a elatively
risk less security in a non-inflationary situation and the risk premium to compensae investors
for the uncertainity association with the investment in the said security 43% ia a very low
figure and therefore when inflation is @ 15% p.a., money cost of capital should much higher
than 20%. This project might have been rejected if money cost of capital is calculated correctly.
Illustration 25 : A Company is reviewing an investment proposal in a project involving a
capital outlay of Rs. 90,00,000 in plant and machinery. The project would have a life of 5
years at the end of which the plant and machinery could reach a resale value of Rs. 30,00,000.
Further the project would also need a working capital of Rs. 12,50,000 which would be built
during the year 1 and to be released from the project at the end of year 5. The project is
expected to yield the following cash profits :
Year Cash profit (Rs.)
1 35,00,000
2 30,00,000
3 25,00,000
4 20,00,000
5 20,00,000
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A 25% depreciation for plant and machinery is available on WDV basis as Income-tax
exemption. Assume that the Corporate Tax is paid on e year in arrear of the periods to wich
it relates and the fist year’s depreciation allowance would be claimed against the profits of
year 1.
The Assistant Management Accountant has calculated NPV of the project using the company’s
corporate target of 20% pre-tax rate of return and has ignored the taxation effect in the cash
flows.
As the newly recruited Management Accountant, you realise that the project’s cash flows
should incorporate the effects of tax. The Corporate Tax i sexpected to be 35% during the life
of the project and thus the company’s rate of return post-tax is 13% (65% of 20%).
Your Assistant is surprised to note the difference between discounting the pre-tax cash flows
at a pre-tax DCF rate and post-tax cash flows at a post-tax rate.
Required :
a. Calculate the NPV of the project as the Assistant Management Accountant would
have calculated it ;
b. Re-calculate the NPV of the project taking tax into consideration;
c. Comment on the desirability of the project vis-a-vis your findings in (b).
a. Assistant Management Accountant’s Calculation (i.e., Ignoring taxation)
Year Investment Cash Net Discount Present
Plant and Working Profit Cashflows factor at value
Machinery Capital 20%
0 (90.0) – – (90.0) 1.00 (90,000)
1 – (12.5) 35.0 22.5 0.83 18,675
2 – 30.0 30.0 0.69 20,700
3 – 25.0 25.0 0.58 14,500
4 – 20.0 20.0 0.48 9,600
5 30.0 12.5 20.0 62.5 0.40 25,000
NPV (1,525)
Itis assumed that working capital (debtors, stocks etc.) reduce cashflows inyear 1 and would
be recovered soon after the end of year 5. The working capital cashflows are therefore assigned
to years 1 an 5.
Here it is observed that NPV is negative and hence, the Assistant Management Accountant
would have concluded that the project should be rejected.
Fianancial Management & international finance 157
(b) Allowing for taxation :
(i) Tax on Cash Profit (Rs.)
Year Cash Profit Tax 35% Year of Tax
Profit Payment
1 35 12.25 2
2 30 10.50 3
3 25 8.75 4
4 20 7.00 5
5 20 7.00 6
Year Reducing Depreciation Tax Rebate Year of
Balance (Tax payable) cashflow
0 90,000 – – –
1 67,500 22,500 7,875 2
2 50,625 16,875 5,906 3
3 37,969 12,656 4,430 4
4 28,476 9,492 3,322 5
5 21,357 7,119 2,492 6
*Profit on sale of Palant & (8,643)* (3,025) 6
Machinery (30,000 – 21,357)
Calculation of NPV of the Project : (Rs.)
Year Investment Deprn. Cash Tax on Net Disc. Present
Plant Working Allow. Profits Profits Cash factor Value
& Capital Tax flow at 13%
Machinery saved
0 (90,000) – – – – (90,000) 1.00 (90,000)
1 – (12,500) – 35,000 – 22,500 0.88 19,800
2 – – 7,875 30,000 (12,250) 25,625 0.78 19,988
3 – – 5,906 25,00 (10,500) 20,406 0.69 14,080
4 – – 4,430 20,000 (8,750) 15,680 0.61 9,565
5 30,000 12,500 3,322 20,000 (7,000) 58,822 0.54 31,764
6 – – (0.533) – (7,000) (7,533) 0.48 (3,616)
NPV + 1,581
(c) The NPV is positive, although it is very samll in relation to the Capital outlay of rs. 90
lakhs. It is also apparent the positive NPV depends heavily on the assumption that the plant
and machinery would have a resale value of Rs. 30 lakhs at the end of year 5. Such projects
which rely on their residual values for their positive NPV should normally be regarded highrisk
venture. It can be further seen that a drop of around 10% i.e., Rs. 3 lakhs in resale value
would make the project negative.
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Illustration 26 : SCL Limited, a highly profitable company, is engaged in the manufacture of
power intensive products. As part of its diversification plans, the company proposes to put
up a Windmill to generate electicity. The details of the scheme are as follows :
(1) Cost of the Windmill — Rs. 300 lakhs
(2) Cost of Land — Rs. 15 lakhs
(3) Subsidy from State Govenment to be received at the end of — Rs. 15 lakhs
first year of installation
(4) Cost of electricity will be Rs. 2.25 per unit in year 1. This will incerease by Rs. 0.25 per
unit every year till year 7.
After that it wil increae by Rs. 0.50 per unit.
(5) Maintennce cos will be Rs. 4 lakhs in year 1 and the same will increase by Rs. 2 lakhs
every year.
(6) Estimated life 10 years.
(7) Cost of capital 15%.
(8) Residual value of Windmill will be nil. However land value will go up to Rs. 60 lakhs,
at the end of year 10.
(9) Depreciation will be 10% of the cost of the Windmill in year 1 and the same will be
allolwed for tax purposes.
(10) As Windmills are expected to work based on wind velocity, the efficiency is expected
to be an average 30%. Gross electricity generates at this level will be 25 lakh units per
annum. 4% of this electricity generated will be committed free to the State Electriciy
Board as per the agreement.
(11) Tax rate 50%.
From the above information you are required to :
(a) Calculate the net present value. [Ignor tax on capital profits.]
(b) List down two non-financial factors that should be considered before taking a decision.
For your exercise use the following discount factors.
Year 1 2 3 4 5 6 7 8 9 10
Discoun Factors 0.87 0.76 0.66 0.57 0.50 0.43 0.38 0.33 0.28 0.25
Working Notes :
1. Initial Investment (Rs. lakhs)
Cost of Land 15
Cost of Windmills 300
Total
2. Net units generated (No. of units)
Gross units genered 25 lakhs
Less : 4% Free Supply to SEB 1 lakh
Net Units sold 24 lakhs
Fianancial Management & international finance 159
3. Cost per unit Rs. 2.25 per unit in year 1. it will increase by Rs. 0.25 per unit every year till
year 7. After that it will increase by Rs. 0.50 per unit Maintenance Cost will be Rs. 4 lakhs
in year 1 and the same will increase by Rs. 2 lakhs every year.
Calculation of Net Present Value (Rs. lakhs)
Year 1 2 3 4 5 6 7 8 9 10
Unit Cost (Rs.) 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.25 4.75 5.25
Savings
(24 lakh unit×unit cost) 54 60 66 72 78 84 90 102 114 126
Maintenance Cost 4 6 8 10 12 14 16 18 20 22
Gross Savings 50 54 58 62 66 70 74 84 94 104
Less : Tax @ 50% 25 27 29 31 33 35 37 42 47 52
Savings after Tax 25 27 29 31 33 35 37 42 47 52
Add : Tax saving on
depreciation 150 – – – – – – – – –
Subsidy 15 – – – – – – – – –
Net savings 190 27 29 31 33 35 37 42 47 52
Discount Factor 15% 0.87 0.76 0.66 0.57 0.50 0.43 0.38 0.33 0.28 0.25
Present Value 165.30 20.52 19.14 17.67 16.50 15.05 14.06 13.86 13.16 13.00
(Rs. lakhs)
Total Present Value 308.26
Add : Present valu of Land (Rs. 60 lakhs ×0.25) 15.00
323.26
Less : Initial Cost 315.00
Net Present Value 8.26
(b) Non-financial Factor : The follwoing non-financial factors may be taken into consideration
while taking the investment decision.
- Cost of purchase of electricity from State Electricity Board.
- Machinery and skilled manpower availability.
- Wind velocity in the proposed project area.
- Risk coverage.
- Technology availability.
- Authorisation in the Memorandum of Association to take the business etc.
Illustration 27 : TSL Ltd., a highly profitable and tax paying company is planning to expand
its present capacity by 100%. The estimated cost of the project is Rs. 1,000 lakhs out of which
Rs. 500 lakhs is to be met out of loan funds. The company has received two offers from their
bankers :
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Option 1 Option 2
Value of loan Rs. 500 lakhs US $ 14 lakhs equal to Rs. 500 lakhs
Interest 15% payable yearly 6% payable (fixed) yearly in US $
Period of Repayment 5 years (In 5 instal- 5 years
ment is payable
after draw down)
Other expenses (to be treated 1% of the value of 1% at US $ = Rs. 36 (Average)
as revenue expenditure) the loan
Future exchange rate — End of 1 year 1US $ = Rs. 38 thereafter to
incease by Rs. 2 per annum
The company is liable to pay income-tax at 35% and eligible for 25% depreciation on W.D.
value. You may assume that at the end of 5th year the company will be able to claim balance
in WDV for tax purposes. The company follows Accounting Standard AS-11 for accounting
changes in Foreign Exchange Rate.
(1) Companre the total outflow of cash under the above options.
(2) Using discounted cash flow technique, evaluate the above offers.
(3) is there any risk, which the company should take care of?
(4) In case TSL has large volume of exports would your advice be different. The following
discounting table may be adopted :
Year 0 1 2 3 4 5
Discount Factor 1 0.921 0.848 0.781 0.720 0.663
Option I
Years Repayment Interest Other Tax saving Net Outflow
of Principal at 15% Expenses
0 100 – 5.00 1.75 3.25
1 100 75 – 26.25 148.75
2 100 60 – 21.00 139.00
3 100 45 – 15.75 129.25
4 100 30 – 10.50 119.50
5 100 15 – 5.25 109.75
Total Outflows 500 +225 +5.00 –80.50 649.50
Fianancial Management & international finance 161
Option II
Exch- Year Repay- Inter- Other Total Repay- Balance Interest Other Total Tax Net
ange ment of est charges Amt. ment of being charges payment savings Outrate
pricipal principal premium flow
US$ (Rs. in lakhs)
36 0 – – 0.140 0.140 – – – 5.04 5.04 1.764 3.276
38 1 2.8 0.840 – 3.640 100.00 6.4 31.920 138.32 11.732 126.588
40 2 2.8 0.672 – 3.472 100.00 12.0 26.880 138.88 10.878 128.002
42 3 2.8 0.504 – 3,304 100.00 17.6 21.168 138.768 10.048 128.720
44 4 2.8 0.336 – 3.136 100.00 23.2 14.784 137.984 9.184 128.800
46 5 2.8 0.168 – 2.968 100.00 28.8 7.728 136.528 24.814 ????
14.0 2.4520 0.140 16,660 500.00 88.0 102.48 504 695.520 68.420 627.100
As per AS-11, the premium paid on exchange rate difference, on loans acquired for the
purpose of capital expenditure should be capitalised. The same is applicable unde the Indian
Income-tax Act for tax calculatons also.
Tax Savings on Premium Capitalisation (Rs.)
Year Opening Premium Total Depreciation Tax Closing WDV
Value on premium Saving
at 25% at 35%
1 – 6.40 6.40 1.60 0.56 4.80
2 4.80 12.00 16.80 4.20 1.47 12.60
3 12.60 17.60 30.20 7.55 2.64 22.65
4 22.65 23.20 45.85 11.46 4.01 34.39
5 34.39 28.80 63.19* 63.19 22.11 Nil
*Assumed that full benefit will be claimed for tax purposes.
Tax Saving on Interest, Other Charges and Premium (Rs. lakhs)
Year Amount Tax savings Tax saving Total
ot Interest on premium Tax savings
& other charges
0 5.040 1.764 — 1.764
1 31.920 11.172 0.560 11.732
2 26.880 9.408 1.470 10.878
3 21.168 7.408 2.640 10.048
4 14.784 5.174 4.010 9.184
5 7.728 2.704 22.110 24.814
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(2) Discount Cash Flow : Option I
Year Net Out flow Discounting factor Discounted value
0 3.250 1.000 3.25
1 148.750 0.921 136.99
2 139.750 0.848 117.87
3 129.250 0.781 100.94
4 119.500 0.720 86.04
5 109.750 0.663 72.76
517.85
Discount Cash Flow : Option II (Rs. lakhs)
Year Gross Total Net Discounting Discounted
outflow tax saving outflow factor value
0 5.040 1.764 3.276 — 3.276
1 138.320 11.732 126.588 0.921 116.587
2 138.880 10.878 128.002 0.848 108.545
3 138.768 10.048 128.720 0.781 100.530
4 137.984 9.184 128.800 0.720 92.736
5 136.528 24.814 111.714 0.663 74.066
495.740
(3) The discounted value of Option II seems to be better than Option I. However the company
has to be careful about future exchange rae. The rate indicated is more by rule of thumb than
based on any scientific approach. The company should cover the foreign exchange rate and
then work out the value.
(4) In case the company has good volume of exports,then it may help the company to hedge
the future payments with outflow. In that case th company may take a leninent view of the
possible exchange risk.
Illustration 28 : A large profit making company is condidering the installation of amachine
to process the waste produced by one of its existing manufacturing process to be converted
into a marketable product. At present, the waste is removed by a contractor for disposal on
payment by the company of Rs. 50 lakhs per annum for the next four years. The contract can
be terminated upon installation of the aforesaid machine on payment of compensation of Rs.
30 lakhs before the processing operation starts. This pcmpensation is not allowed ad deduction
of tax pruposes.
The machine required for carrying out the processing will cost Rs. 200 lakhs to be financed
by a loan repayable in 4 equal instalments commencing from the end of year 1. The interest
rate is 16% per annum. At the end of the 4th year, the machine can be sold for Rs. 20 lakhs
and the cost of dimantling and removal will be Rs. 15 lakhs.
Fianancial Management & international finance 163
(Rs. lskhs)
Year 1 2 3 4
Sales 322 322 418 418
Material consumption 30 40 85 85
Wages 75 75 85 100
Other expenses 40 45 54 70
Factory overheads 55 60 110 145
Depreciation (as per income-tax rules) 50 38 28 21
Initial stock of materials required befor commencement of the processing operations is Rs. 20
lakhs at the start of year 1. The stock levels of materials to be maintained at the end of year 1,
2 and 3 will be Rs. 55 lakhs and the stocks at the end of year 4 will be nil. The storae of
materials will utilise space hich would otherwise have been rented out for Rs. 10 lakhs per
annum. Labour costs include wages of 40 workers, whose transfer to this process will reduce
idle time payments of Rs. 15 lakhs in year 1 and Rs. 10 lakhs in year 2. Factory overheads
include apportionment of general factory overheads except to the extent of insurance charges
of Rs. 30 lakhs per annum payable on this venture. The company’s tax rate is 50%.
Present value factors for four years are as under :
Year 1 2 3 4
Present value factors 0.870 0.756 0.658 0.572
Advice the management on the desirability of installing the machine for processing the waste.
All calculations should form part of the answer.
Statement of Incremental profit (Rs. lakhs)
Particulars Year
1 2 3 4
Sales (A) 322 322 418 418
Costs
Material 30 40 85 85
Wages 60 65 85 100
Other Expenses 40 45 54 70
Factory Overheads (Insurance) 30 30 30 30
Loss of Rent 10 10 10 10
Interest 32 24 16 8
Depreciation (as per IT Act) 50 38 28 21
(B) 252 252 308 324
Incremental profit (A) - (B) 70 70 110 94
Tax @ 50% 35 35 55 47
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Statement of Incremental profit (Rs. lakhs)
Particulars Year
0 1 2 3 4
Stocks of Materials Increae (20) (35) – – –
Compensation for Contract (30) – – – –
Saving of Contract Payment – 50 50 50 50
Tax on Contract Payment – (25) (25) (25) (25)
Incremental Profit – 70 70 110 94
Tax on Incremental Profit – (35) (35) (55) (47)
Depreciation added back – 50 38 28 21
Loan Repayment – (50) (50) (50) (50)
Profit on sale of Machinery – – – – –
Total Incremental Cash flows (50) 25 48 58 48
P.V. Factor @ 1.00 0.870 0.756 0.658 0.572
NPV of Cash flows (50) 21.75 36.288 38.164 27.456
Net Present Value = Rs. 73.66 lakhs.
Analysis : Since the NPV of Cash flows of proposal to install a machine to process the waste
into marketable product is positive, the proposal can be accepted.
Assumptions : The following assumptions were considered while computation of NPV of
the proposal :
– Material stock increase will lead of cash outflow
– Idle-time wages are also taken into consideration while calculation of wages.
– Insurance charges are only taken as relevant for Computation of cashflow.
– Interest is calculated at 16% p.a. base on diminishing balance. The repayment of loan is
in 4 equal instalments.
– Capital gains tax ignored on profit on sale of machinery.
– Saving in contract payment and income-tax thereon considered in computation of cash
flows.
Illustration 29 : A company produces main product ‘Super’ and a co-product ‘Mild’ . The
main product is sold entirely to its collaborator, but eh product ‘Mild’ is sold at the local
market. The company increased its capacity as a reslut of which the output of ‘Mild’ increased
to 15,000 m/t per annum at a price Rs. 1,000 pt.
However, in the face of increased competition to sell the entire output of 15,000 m/t of ‘Mild’
the company will have to reduce the sale price by Rs. 50 pt. every year for next 5 years and
hereafter the price will stabilise at Rs. 750 pt.
As an alternative, the company can convert ‘Mild’ into ‘Medium’ at a variable cost of Rs. 200
per (metric) tonne. However to enter the market the sale price will have to be Rs. 1.200 pt. in
the first year and Rs. 1.300 pt. in the second year.
Fianancial Management & international finance 165
The sale of Medium will be 1,000 m/t in the first year and there upon going up by 1,000 m/
t each year. The company will have to invest Rs. 30 lakhs in capital outlay to produce ‘Medium’.
You are required to present the projected sales volume (quantity and value) of products
‘Mild’ and ‘Medium’ and also appraise the investment of Rs. 30 lakhs at 12% per annum for
the period of next 5 years.
Present value of Rupee one at 12% p.a.
Year 1 2 3 4 5
Discount factor 0.89 0.79 0.71 0.64 0.57
Alternative I
Present Value of Sales of Mild Product
Year Quantity Price Sales DCF Present
M.T. Per M.T Rs. lakhs @ 12% value
Rs. lakhs
1 15,000 950 142.5 0.89 126.83
2 15,000 900 135.0 0.79 106.65
3 15,000 850 127.5 0.71 90.52
4 15,000 800 120.0 0.64 76.80
5 15,000 750 112.5 0.57 64.13
Alternative II (Rs. lakhs)
Year Quantity Contribution Net Sales DCF Present value
M.T. Per M.T. Rs. Rs. lakhs @ 12% Rs. lakhs
1 1,000 1,000 10.00 0.89 8.90
2 2,000 1,100 22.00 0.79 17.38
3 3,000 1,200 36.00 0.71 25.56
4 4,000 1,300 52.00 0.64 33.28
5 5,000 1,400 70.00 0.57 39.90
Total Present Value of Net Sales 125.02
Present Value of Sales of Mild
Year Quantity Price Sales DCF Present value
M.T. Per M.T. Rs. Rs. lakhs @ 12% Rs. lakhs
1 14,000 950 133.00 0.89 118.37
2 13,000 900 117.00 0.79 92.43
3 12,000 850 102.00 0.71 72.42
4 11,000 800 88.00 0.64 56.32
5 10,000 750 75.00 0.57 42.75
Total Present Value of Sales 382.29
166 Fianancial Management & international finance
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(Rs. lakhs)
P.V of Sales of medium 125.02
P.V. of sales of mild 382.29
Total present value 507.31
Less : Initial investment 30.00
Net Present Value of Alternative II 477.31
Analysis : Since NPV is higher for alternative II, it is suggested to select Alternative II.
Illustration 30 : B Ltd. is considering whether to set up a division in order to manufacture a
new Product A. The following statement has been prepared, showing the projected profitability
per unit of the new product : (Rs.)
Selling price 22.00
Less : Direct labout (2 hours @ Rs. 2.50 per hour) 5.00
Material (3 kg. @ Rs. 1.50 per kg.) 4.50
Overheads 11.50 21.00
Net profit per unit 1.00
A feasibility study, recently undertaken at a cost of Rs. 50,000, suggests that a selling price of
Rs. 22 per unit should be set. At this price, it is expected that 10,000 units of A would be sold
each year. Demand for A is expected to cease after 5 years. Direct Labour and Material Costs
would be incurred only for the duration of the product life.
Overhead per unit have been calculated as follows : (Rs.)
Variable overheads 2.50
Rent (Note 1 : Rs. 8,000/10,000 units) 0.80
Manager’s salary (Note 2 : Rs. 7,000/10,000 units) 0.70
Depreciation (Note 3 : Rs. 50,000/10,000 units) 5.00
Head office costs (Note 4 : Rs. 2 hours @ Rs. 1.25 per hour) 2.50
11.50
Notes :
1. Product A would be manufactured in a factory rented specially for the purpose. Annual
rental would be Rs. 8,000 payable only for as long as the factory was occupied.
2. A manager would be employed to supervise production of Product A, at a salary of Rs.
7,000 p.a. The Manager is at present employed by B Ltd. but is due to retire in the near
future on an annual pension of Rs. 2,000, payable by the company. If he continued to be
employed, his pension would not be paid during the period of his employement. His
subsequent pension rights would not be affected.
3. Manufacturing of the Product A would required a specialised machine costing
Rs. 2,50,000. The machine would be capable of producing Product A for an indefinite
period, although due to its specialised nature, it would not have any resale or scrap
Fianancial Management & international finance 167
value when the producion of Product A ceased. It is the policy of B Ltd. to provide
depreciation on all fixed asset using Straight Line Method. The annual charge of Rs.
50,000 for the new machine is based on a life of five years, equal to the period which
Product A to the company to be produced.
4. B Ltd. allocates its head office fixed costs to all products at the rate of Rs. 1.25 per direct
labour hour. Total head office fixed costs would not be affected by the introduction of
the Product A to the company’s range of products.
The Cost of capital of B Ltd. is estimated at 5% p.a. in real terms and you may assume that all
costs and prices given above will reamin constant in real terms. All cash flows would arise at
the end of each year, with the exception of the cost of the machine which would be payable
immediately.
The Management of B Ltd. is very confident about the accuracy of all the estimates given
above, with the exception of those relating to product life, the annual sales volume and
material cost per unit of Product A.
You are required to :
(i) Decide whether B Ltd. should proceed with manufacture of the Product A.
(ii) Prepare a statement showing how sensitive the NPV of manufacturing Product A is to
errors of estimation in each of the three factors : Product life. Annual sales volume and material
cost per unit of Product A.
Ignore taxation.
The Present Value of annuity for 3 years, 4 years and 5 years at 5% respectively are 2.72, 3.55
and 4.33.
Working Notes :
1. Cost of Machine at 0 years = Rs. 2,50,000
2. Variable Production Cost per annum (Rs.)
Material cost P.U. 4.50
Direct Labour cost P.U. 5.00
Variable overheads P.U. 2.50
12.00
Per annum (10,000 units×Rs. 12) 1,20,000
2. Variable Production Cost per annum (Rs.)
Salary payable p.a. 7,000
Less : Pension not payable 2,000
Net salary payable 5,000
4. Depreciation is a non-cash item, need not be considered in computation of cash flow.
5. Head office cost is committed cost and is irrelevant for decision making.
168 Fianancial Management & international finance
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Calculation of N.P.V. (Rs.)
Sales p.a. 2,20,000
Less : Variable production cost p.a. 1,20,000
Maager salary p.a. 5,000
Factory Rent p.a. 8,000 1,33,000
Cash inflow p.a. 87,000
Present calue of cash inflows for 1 to 5 years
Discount factor @ 5% (87,000×4.33) 3,76,710
Less : Cost of machine 2,50,000
Net present value 1,26,710
Since, Net Present Value is positive, it is suggested to manufacture Product A.
(ii) Sensitive of Forecast Errors :
a. Product 3.2 years 36% lower limit of error
b. Annual Sales Volume 7074 units 29% lower limit
c. Material Cost A Rs. 7,426 65% upper limit
Illustration 31 : ABC Company Ltd. has been producing a chemical product by using Machine
Z for the last two years. Now the management of the company is thinking to replace this
Machine either by X or by Y Machine. The following details are furnished to you :
(Rs.)
Z X Y
Book value 1,00,000 – –
Resale value now 1,10,000 – –
Purchase price – 1,80,000 2,00,000
Annual Fixed Cost (including depreciation) 92,000 1,08,000 1,32,000
Variable running costs (including labour) per unit 3 1.50 2.50
Production per hour (units) 8 8 12
You are also provided with the following details :
Selling price per unit Rs. 20
Cost of materials per unit Rs. 10
Annual operating hours 2,000
Working life of each of the three machines (as from now) 5 years
Salvage value of Machines Z - Rs. 10,000; X - Rs. 15,000; Y - Rs. 18,000.
The company charges depreciaion using straight line method. it is anticipated that an
additional cost of Rs. 8,000 per annum would be incurred on special advertising to sell the
extra output of Machine Y. Assume tax rate of 50% and cost of capital 10%. The present
value of Re. 1 to be received at the end of the year at 10% is as under.
Fianancial Management & international finance 169
Year 1 2 3 4 5
Present Value .909 .826 .751 .683 .621
Required Using NPV method, you are required to analysis the feasibility of the proposal and
make recommendations.
Statement Showing Computation of Annual Cash Inflow of Three Machines
Machines
Z X Y
Sales (Units) 16,000 16,000 24,000
Sales @ Rs. 20 P.V. (A) 3,20,000 3,20,000 4,80,000
Costs :
Variable Running Cost 48,000 24,000 60,000
Material Cost 1,60,000 1,60,000 2,40,000
Fixed Cost 92,000 1,08,000 1,32,000
Special Advertising – – 8,000
(B) 3,00,000 2,92,000 4,40,000
PBT (A) – (B) 20,000 28,000 40,000
Less : Tax @ 50% 10,000 14,000 20,000
PAT 10,000 14,000 20,000
Add : Depreciation 20,000 33,000 36,400
Annual Cash Inflow 30,000 47,000 56,400
Computation of Net Present Value
Year Discounting Machines
factors @10% Z X Y
Cash flow P.V. Cash flow P.V. Cash flow P.V.
0 1.000 (1,10,000) (1,10,000) (1,80,000) (1,80,000) (2,00,000) (2,00,000)
1 0.909 30,000 27,270 47,000 42,723 56,400 51,268
2 0.826 30,000 24,780 47,000 38,822 56,400 46,586
3 0.751 30,000 22,530 47,000 35,297 56,400 42,356
4 0.683 30,000 20,490 47,000 32,101 56,400 38,521
5 0.621 30,000 18,630 47,000 29,187 56,400 35,025
5* 0.621 10,000 6,210 15,000 9,315 18,000 11,178
Net present value 9,910 7,445 24,934
* Salvage value at the end of 5th year.
170 Fianancial Management & international finance
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Calculation of Profitability Index (PI)
P.V. Cash outflows
P.V. Cash inflows =
Machine Z 1 09
110 000
119 910
.
, ,
= , , = Machine X 041 1
1 80 000
1 87 445
.
, ,
= , , = Machine Y 1 12
2 00 000
2 24 934
.
, ,
= , , =
Analysis : Based on NPV method, Machine Y is to be selected, since its NPV is highest at Rs.
24,934. But the initial investmnt of three machines is different, NPV method is not appropriate.
Profitability Index Method is most suitable for evaluation. The Profitability Index of Machine
Y is highest and hence Machine Z is to be replaced with Machine Y.
Illustration 32 : The Super Specialists Ltd. constructs customized parts for satellites to be
launched by USA and China. The parts are constructed in eight locations (including the
central head uarters) around the world. The Finance Director, Mr. Kamni, chooses to
implement video conferencing to speed up the budget process and save travel costs. She
finds that, in earlier years, the company sent two officers from each location to the central
headquarters to discuss the budget twice a year. The average travel cost per perosn, including
air fare, hotels and meals, is Rs. 18,000 per trip. The cost of using video conferencing is Rs.
550,000 to set up a system at each location plus Rs. 300 per hour average cost of telephone
time to transmit signals. A total 32 hours of transmissiontime will be needed to complete the
budget each year. The company depreciates this type of equipment over five years by using
straight line method. An alternative approach is to travel to local rented video conferencing
facilities, which can be rented for Rs. 1,500 per hour plus Rs. 400 per hour averge cost for
telephone charges.
Your are Senior Officer Finance Department. You have been asked by Ms. Kamni to evaluate
the proposal and suggest if it would be worthwhile for th company to implement video
conferencing.
Option I : Cost of travel, in case Video Conferencing facility is not provided (Rs.)
Total Trip = No. of Locations × No. of Persons × No. of Trips per Person
7×2×2=28 Trips
Total Travel Cost (including air fare, hotel accommodation and meals)
(28 trips × Rs. 18,000 per trip) 5,04,000
Option II : Video Conferencing Facility is provided by Installation of
Own Equipment at Different Locations (Rs.)
Cost of Equipment at S location (Rs. 5,50,000×8 locations) 44,00,000
Economic life of Machines (5 years)
Annual depreciation (44,00,000/5) 8,80,000
Annual transmission cost (32 hrs. transmission×8 locations ×
Rs. 300 per hour) 76,800
Annual cost of operation (8,80,000+76,800) 9,56,800
Fianancial Management & international finance 171
Option III : Engaging Video Conferencing Facility on Rental Basis (Rs.)
Rental cost (32 hrs. ×8 location×Rs. 1,500 per hr.) 3,84,000
Telephone cost (32 hrs.×8 locations×Rs. 400 per hr.) 1,02,400
Total rental cost of equipment (3,84,000+1,02,400) 4,86,400
Analysis : The annual cash outflow is minimu, if video conferencing facility is engaged on
rental basis. Therefore, Option III is suggested.
Illustration 33 : X Ltd. an existing profit-making company, is planning to introduce a new
product with a projected life of 8 years. Initial equipment cost will be Rs. 120 lakhs and
additional equipoment costing Rs 10 lakhs will be needed at the beginning of third year. At
the end of the 8 years, the original equipment will have resale value equivalent to the cost of
removal, but the additional equipment would be sold for Rs. 1 lakh. Working Capital of rs.
15 lakhs will be needed. The 100% capacity of the plant is of 4,00,000 units per annum, but
the production and sales-volume expected are as under :
Year Capacity (%)
1 20
2 30
3-5 75
6-8 50
A sale price of Rs. 100 per unit with a Profit-Volume Ratio of 60% is likely to be obtained.
Fixed Operating Cash Cost are likely to be Rs. 16 lakhs per annum. In addition to this the
advertisement expenditure will have to be incurred as under.
Year 1 2 3-5 6-8
Expenditure 30 15 10 4
The company is subject to 50% tax, straight-line method of depreciation, (permisible for tax
purposes also) and taking 12% as appropriate after tax cost of capital, should the project be
accepted?
Present Value of Cash outflow (Rs.)
Year 0 Equipment cost (1,20,00,000×1,000) 1,20,00,000
Year 0 Working capital (15,00,000×1,000) 15,00,000
Year 2 Additional equipment (10,00,000×0.797 7,97,000
P.V. of Cash outflow 1,42,97,000
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Calculation of Cash inflows
Years 1 2 3-5 6-8
Capacity utilisation 20% 30% 75% 50%
Production & Sales (units) 80,000 1,20,000 3,00,000 20,000
Contribution @ Rs. 60 p.u. (i) 48,00,000 72,00,000 1,80,00,000 1,20,00,000
Fixed cost 16,00,000 16,00,000 16,00,000 16,00,000
Advertisement 30,00,000 15,00,000 10,00,000 4,00,000
Depreciation 15,00,000 15,00,000 16,50,000 16,50,000
(ii) 61,00,000 46,00,000 42,50,000 36,50,000
PBT (i) - (ii) (13,00,000) 26,00,000 1,37,50,000 83,50,000
Less : Tax @ 50% – 13,00,000 68,75,000 41,75,000
PAT (13,00,000) 13,00,000 68,75,000 41,75,000
Add : Depreciation 15,00,000 15,00,000 16,50,000 16,50,000
Cash inflow 2,00,000 28,00,000 85,25,000 58,25,000
Calculation of Present Value of Cash inflows (Rs.)
Years Cash inflow Discount factor Present Value
1 2,00,000 0.893 1,78,000
2 28,00,000 0.797 22,31,600
3 85,25,000 0.712 60,69,800
4 85,25,000 0.636 54,21,900
5 85,25,000 0.567 48,33,675
6 85,25,000 0.507 29,53,275
7 85,25,000 0.452 26,32,900
8 85,25,000 0.404 23,53,300
8 (Working Capital) 15,00,000 0.404 6,06,000
8 (Salvage value) 1,00,000 0.404 40,400
P.V. of cash inflow 2,73,21,450
NPV = 2,73,21,450 – 1,42,97,000 = Rs. 1,30,24,450
Analysis : Since NPV is positive, the Project can be accepted.
Illustration 34 : Playmates Ltd. manufactures toys and other short-lived fad items. The
Research and Development Department has come up with an item that would make a good
promotional gift for office equipment dealers. As a result of efforts by the Sales personnel, the
firm has commitments for this product. To produce the quantity demanded Playmates ltd.
will need to buy additional machinery and rent additional space. It appears that about 25,000
sq. ft. will be needed; 12,500 sq. ft. of presnetly unused space, but leased at the rate of Rs. 3
per sq. fit. per year is available. There is another 12,500 sq. ft. adjoining the facility available
at the annual rent of Rs. 4 per sq. ft.
Fianancial Management & international finance 173
The equipment will be pruchased for Rs. 9,00,000. It will require Rs. 30,000 in modification
and Rs. 1,50,000 for installation. The equipment will have a salvage value of about Rs. 2,80,000
at the end of the third year. It is subject to 25% depreciation on Reducing Balance Basis. The
firm has no other assets in this block. No additional general overhead costs are expected to
be incurred.
Estimates of revenue and costs for this product for three years have been developed asfollows :
(Rs.)
Particulars Year 1 Year 2 Year 3
Sales 10,00,000 20,00,000 8,00,000
Less : Costs :
Material, Labour and Overheads 4,00,000 7,50,000 3,50,000
Overheads allocated 40,000 75,000 35,000
Rent 50,000 50,000 50,000
Depreciation 2,70,000 2,02,500 Nil
Total Costs 7,60,000 10,77,000 4,35,000
Earnings befor taxes 2,40,000 9,22,500 3,65,000
Less : Taxes 84,000 3,22,875 1,27,750
Earnings after taxes 1,56,000 5,99,625 2,37,250
If the company sets a required rate of return of 20% after taxes, sould this project be accepted?
Note : P.V. factor @ 20% for Year 1 = 0.833; Year 2 = 0.694; and Year 3 = 0.579
Tax rate %
, ,
,
100 35
2 40 000
84 000 = × =
Calculation of Loss on Sale of Equipment (Rs.)
Cost of equipment 9,00,000
Modification cost (30,000+1,50,000) 1,80,000
Initial cash outlay 10,80,000
Less : 1st Year Depreciation (10,80,000×25/100) 2,70,000
8,10,000
Less : 2nd Year Depreciation (8,10,000×25/100) 2,02,500
Written down value at the beginning of 3rd year 6,07,500
Less : Salvage value 2,80,000
Loss on sale of equipment 3,27,500
Opportunity cost of lease rent lost = 12,500 sq. ft. × Rs. 3 = Rs. 37,500
174 Fianancial Management & international finance
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Calculation of Cash inflow (Rs.)
Particulars Year 1 Year 2 Year 3
Sales (i) 10,00,000 20,00,000 8,00,000
Incremental cost
Material, Labour and overhead 4,00,000 7,50,000 3,50,000
Oppotunity cost of lease rent lost 37,500 37,500 37,500
Rent payable 50,000 50,000 50,000
Depreciation 2,70,000 2,02,000
(ii) 7,57,500 10,40,000 4,37,500
EBT (i) - (ii) 2,42,000 9,60,000 3,62,500
Less : Tax @ 35% 84,875 3,36,000 1,26,875
EAT 1,57,625 6,24,000 2,35,625
Add : Depreciation 2,70,000 2,02,500
Cash inflow after tax 4,27,625 8,26,500 2,35,625
Calculation Present Value of Cash Inflow After Tax
Year Cash inflow Discount factor Present Value
after tax @ 20%
1 4,27,625 0.833 3,56,212
2 8,26,500 0.694 5,73,591
3 2,35,625 0.579 1,36,427
3 (Salvage value) 2,80,000 0.579 1,62,120
3 Tax advantage on short term loss 1,14,625 0.579 66,365
(3,27,500×0.35)
P.V. of Cash injflow 12.94.718
NPV = 12,94,715 – 10,80,000 = Rs. 2,14,718
Analysis : Since NPV of the Project is positive, it is suggested to accept the Project.
Illustration 35 : X Ltd. has for some years manufactured a product called C which is used as
a compnent in a variety of electrical items. Although the product C is in demand, the
technology of the design is becoming obsolete. The company has developed a new product D
which is based on new technology.
The management of X Ltd. is considering whether to continue production of C or discontinue
the C and start production of D. The company do not have the reasources to produce both
the products.
If C is produced, unit Sales in year 1 are forecast to be 24,000 but declining by 4,000 units in
each subsequent year. Additional equipment costing Rs. 70,000 must be purchased now if D
production is to continue.
Fianancial Management & international finance 175
If D produced, then unit sales in year 1 are forecast to be 6,000 but after that the sales will
increase rapidl. Additional equipment costing Rs. 6,20,000 should be purchased now if D
production is to start.
Relevant details of the two products are as follows : (Rs.)
C D
Variable cost per unit 25 50
Selling price per unit 55 105
The company appraises investments using 12% per annum compound cost of Money and
ignores cash flows beyond five year from the start of investment.
(a) Advise the company on the minimum annual growth in units sales of D needed to
justify sarting production of D now. Support your answerwith financial evaluation.
(b) Advise management of the number of years to which its investment appraisal time
horizon (Currently five years) would have to be extended in order to justify sarting
production D now if the forecast annual increase in D sales is 2,800 units.
P. V of Re. 1 at 12% discount are as follows :
Year 1 2 3 4 5 6 7 8
P.V. 0.8929 0.7972 0.7118 0.6355 0.5674 0.5067 0.4523 0.4039
(a) The minimum annual growth in unit sales of D needed to justify production of D now
is approximately 3400 units per annum. As existing fixed fosts are unaffected by the
decision and the alternatives are mutually excluisve, th erelevant cash flows are the
extra investment cost for and contributions from D.
Assume that the sales of D Increase by 6000 units per annum
Year Net Contribution Contribution Net cash Discount Present
investment foregone from from D flow factor value
C
0 *(5,50,000) — — (5,50,000) 1.000 (5,50,000)
1 — (7,20,000) 3,30,000 (3,90,000) 0.8929 (3,45,200)
2 — (6,00,000) 6,60,000 60,000 0.7972 47,800
3 — (4,80,000) 9,90,000 5,10,000 0.7118 3,63,000
4 — (3,60,000) 13,20,000 9,60,000 0.6355 6,10,100
5 — (2,40,000) 16,50,000 14,10,000 0.5674 8,00,000
NPV 9,22,800
* Additional cost of equipment for D less cost saved by not buying additional equipment
for C.
176 Fianancial Management & international finance
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Additional sales of D incease by 3,000 units p.a.
Year Net Contribution Contribution Net cash Discount Present
investment foregone from from D flow factor value
C
0 (5,50,000) — — (5,50,000) 1.000 (5,50,000)
1 — (7,20,000) 3,30,000 (3,90,000) 0.8929 (3,48,200)
2 — (6,00,000) 4,84,000 1,16,000 0.7972 (92,500)
3 — (4,80,000) 6,38,000 1,58,000 0.7118 1,12,500
4 — (3,60,000) 7,92,000 4,32,000 0.6355 2,74,500
5 — (2,40,000) 9,46,000 7,06,000 0.5674 4,00,600
NPV = (2,03,100)
6 (1,20,000) 11,00,000 9,80,000 0.5066 4,96,500
Therefore the time horizon is extended by approximately 0 41
4 96 500
2 03 100
.
, ,
, , = of a year (i.e., 5
months) to 5 years and 5 months.
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