Capital budgeting decisions are much vital than the decisions on management of working capital as these decisions requires careful analysis of the expected costs and benefits to be derived from each capital expenditure on acquisition of land, building, equipments and for permanent additions to working capital associated with the plant expansion. The level of investments that maximizes the present value of the firm is simultaneously determined by the interaction of supply and demand forces under conditions of uncertainty

1. 1
UNIT # 5
INVESTMENT APPRAISAL DECISIONS UNDER CERTAINTY
OR
CAPITAL BUDGETING DECISIONS
Introduction:
Capital budgeting decisions are much vital than the decisions on management of working
capital as these decisions requires careful analysis of the expected costs and benefits to be
derived from each capital expenditure on acquisition of land, building, equipments and for
permanent additions to working capital associated with the plant expansion.
The level of investments that maximizes the present value of the firm is simultaneously
determined by the interaction of supply and demand forces under conditions of uncertainty.
Supply forces refer to the supply of capital to the firm or its cost of capital schedule. Demand
forces relate to the investment opportunities open to the firm as measured by the stream of
revenues that will result from an investment decision.
Uncertainty enters the decisions as it is impossible to know exactly either the cost of capital or
the stream of revenues.
Types of Capital Expenditure
1. Capital Expenditure on Giant Plant
Such expenditures are incurred on the new plants or buildings either for
introduction ‘a’ new product or increase the market potentialities of the existing
product
2. Ordinary Capital Expenditure:
Such expenditure is incurred on replacing old machines by new ones, establishing
new office.

2. 2
3. Capital Expenditure on Development Work
Is expenditure on publicity, advertisement, on exploration of new market e.t.c.
4. Capital Expenditure on Research:
Researches are conducted within the business to modify the product or on
improvement of the model or innovation of the new product.
5. Capital Expenditure on Housekeeping Projects
In Health & Safety Projects, Welfare Projects, Training & Education Projects, etc.
Capital Budgeting Process
A Capital Budgeting process involves a number of steps depending upon the size of the
concern, nature of projects, their numbers, complexities and diversities. However the Capital
budgeting process involves the following steps:-
1. Project Generation or Origination: It could be related to increasing the revenue by
adding new products and expanding the existing capacity or it could be related to reducing the
costs by replacement of the fixed assets. Such proposals may originate from top management level
to operatives’ level.
2. Project Evaluation: It involves estimating the costs and benefits in terms of cash flows
and selecting the appropriate criterion for judging the desirability and suitability of the
projects.
3. Project Selection: This step is related to the screening and selecting the projects. The
projects may be screened at various levels of management, though final approval may come from
top management. This also facilitates the accountability to be placed on lower levels of
management for the results to be achieved on such projects.
4. Project Execution: When capital expenditure proposals are finally selected, funds are
allocated to them. Such formal plan for the allocation of funds, is called Capital Budget Funds
should be spent in accordance with the allocation made in the capital budgets. A periodic report on
the amount spent, amount approved but not spent is sent to the Finance Controller.
5. Follow – up: A system to make a follow–up on the results on the completed projects
should be established. Comparison of Actual performance with the budgeted data would ensure
on the corrective measures to be taken.
Decision on Capital Expenditure
A most decisive factor in taking decision on capital expenditures is its profitability. The
accuracy of such type of decision depends upon the information which the management has and their

3. 3
experiences. The decision is taken on the basis of comparative study of ‘investment and savings’
which are termed as Net Cash Outflow and “Net Cash Inflow” respectively.
Net Cash Inflow: - Estimated future benefits accruing from the investment proposal is the
starting point of capital expenditure decisions. Net Cash flows after tax is calculated as under:-
1. Accounting Profit should be ascertained i.e. total revenue – total expenses including
depreciation.
2. The amount of tax applicable is deducted.
3. The amount of depreciation is added back.
Cash inflows may also emanate from salvage value and working capital released at the
end of economic life of the investment (asset). Cash salvage value is adjusted for any capital gain
tax. Working capital released would be such which was tied at the time of start of the project &
stayed throughout the period of the economic life of the asset.
If the investment proposal is such which makes free some part of the working capital,
such working capital is treated as inflow in the initial year & should be adjusted to the initial
investment (cash outflow). But in the terminating year of the project such freed capital should be
treated as such as cash outflow & must be adjusted to the cash inflow of that year.
Cash outflows:
To determine the initial investment requirement of the proposed capital expenditure, one should
take into account cash cost of new project including installation charges from the start of the
project until its completion i.e. before it puts into use, all the cash costs involved in the zero time
period are known as cash outflows.
Proceeds from Sale of old assets:
If the investment proposal involves the replacement of old asset by the new asset & if the
old asset is disposed off the net proceeds after tax of the old asset is deducted from the cost of
new project.
Cash outflow at zero time periods is calculated as under:-
Cost of New project XXX
Add: Installation Charges XXX
Add: Increased Working Capital required if any XXX
Less: Working Capital freed (if any) XX
Less :Net Sale proceeds of the old assets XX
Net Cash outflow XXX
---------
Example
A toy manufacturing co. is thinking of acquiring a new machine to replace the old one
which would cost Shs. 240,000,000 & would last for 4 years. Its expected salvage value
is zero. Installation charges are Shs. 10,000,000. The old machine can be sold for Shs.
40,000,000 net. The company expects to sell 10,000 toys @ Shs. 10, 000 each every year

4. 4
and the cash expenses will be Shs.2, 000 per toy. An increase in Shs. 40,000,000 working
capital at the beginning of the project will be required. Determine the cash inflow after
tax (CFAT) assuming the company pays 30% income tax on its income & use straight
line depreciation method.
Also calculate outflow at the beginning of the project.
In (000)
Cost of new project Shs. 240,000
Add: Installation Charges Shs. 10,000
Add: Additional working capital Shs. 40,000
290,000
Less: Net sale proceeds of the old machine 40,000
Net Cash Outflow 250,000
Computation of after – tax Cash Inflow
In (000)
Year Gross proceeds Cash exp Depreciation Accounting Tax Accounting Profit Cash Inflow
Profit After – Tax
1 100,000 20,000 60,000 20,000 6,000 14,000 74,000
2 100,000 20,000 60,000 20,000 6,000 14,000 74,000
3 100,000 20,000 60,000 20,000 6,000 14,000 74,000
4 100,000 20,000 60,000 20,000 6,000 14,000 74,000
A Simplified view of Capital Budgeting
Capital Budgeting is, in essence, an application of a classic proposition from the
economic theory of the firm that a firm should operate at a point where its marginal revenue is
just equal to its marginal cost. Marginal revenue is taken to be the percentage rate of return on
investment while the marginal cost is the marginal cost of capital
Rate of Return /
cost of Capital
0
12
16
20
24
%
B
C
Project
A
Marginal Cost
of Capital

5. 5
In the above figure Project A requires an investment of Shs. 3 million. The percentage rate of
return on investment is 20% while the marginal cost is 10%. In the project C the investment
required is Shs. 4 million while the % of rate of return on investment is 12% at a marginal cost of
10%. The firm can consider project A through C keeping in view the merits & demerits but must
reject the project D which is not viable.
Method of appraising capital Expenditure Proposal
The capital expenditures represent long–term commitment; as such the decisions in
respect of such expenditures have far reaching effect upon firm’s earning and growth.
Thus a sound appraisal method should be used to measure and evaluate the economic worth of a
capital expenditure project. Any appraisal method should satisfy at least the following
conditions:
1. It should serve as a basis for distinguishing between acceptable and reject able
proposals.
2. It should provide a basis for ranking the various proposals in order of their
desirability.
3. It should also help in choosing among alternative proposals.
4. It should equally be applicable to any conceivable proposal.
5. It should recognize the motto that “larger benefits are preferable to smaller ones and
early benefits are preferable to latter benefits”
6. It should relate the stream of future savings to the cost of obtaining these benefits.
In view of the above points, the number of appraisal methods have been developed which are as
follows:-
1. Accounting Rate of Return
4
1 10987652 4
3
X
8
Investment in Millions of Shillings
D

6. 6
2. Pay–back Period Method
3. Internal Rate of Return Method
4. Net Present Value Method
5. Profitability Index Method
Except the methods 1 & 2 the rest are based on the Time–Value of Money & have following
assumptions:-
(a) (Cost of Capital) Minimum rate of return is given.
(b) Risk & uncertainties are common to all proposals.
(c) The financing & dividend decisions are constant.
1. Accounting Rate of Return: - It is also know as average rate of return on
investment. It is a measure of profitability which relates income to investment, both
measured in accounting terms.
ARR = Average Income After tax X 100
Average investment
or
Initial Investment
Average Investment = ½ (initial cost – salvage vale) + salvage value + Net Working capital
Annual Average Income after tax = Total expected profits after tax
No. of years of economic life
2. Pay–back Period Method: - The most commonly used and simple technique for
taking decisions on capital expenditure is pay–back period method. This method
represents the period which is required to get back the original cost of investments by
annual savings. This period may be calculated by the following formula:-
Pay–back Period = NI
OS
Hence, NI = Net Investment
OS = Operating Saving or Cash inflow
It is worthwhile to remember that operating savings are before interest and depreciation but after
tax.The above formula assumes that the savings are even during the period. In case savings are
not even over the period, the formula would be:-
Pay – back Period = E + B

7. 7
C
E = No. of years immediately preceding the year of recovery
B = Balance of amount of investments to be recovered
C = Savings (cash inflow) during the year of final recovery.
All alternatives are ranked according to the lesser pay–back period.
Example: 1.
MOPROCO is considering acquiring a new machine which would carry out some
operations at present being performed by hands. The two alternative models are under
consideration namely CAMELEX & SHRILEX.
The following information is available in respect of both models.
Cost of Machines 600,000,000 1,000,000,000
Estimated life in year 10 20
Estimated savings in wastage p.a 40,000,000 60,000,000
Additional Cost of supervision p.a 48,000,000 64,000,000
Additional Cost of maintenance p.a 28,000,000 84,000,000
Additional Cost of indirect expenses p.a 24,000,000 52,000,000
Estimated savings in wages: - Wages p.a 360,000,000 540,000,000
Using the method of Pay – back period, suggest as which model be purchased. Ignore tax.
Statementof Annual Operating Savings
Model Model
CAMELEX SHRILEX
Estimated saving p.a
(i) Wastage 40,000,000 60,000,000
(ii) Wages 360,000,000 540,000,000
400,000,000 600,000,000
Estimated Additional Cost:
Cost of Supervision 48,000,000 64,000,000
Cost of Maintenance 28,000,000 84,000,000

8. 8
Indirect Exp 24,000,000 52,000,000
100,000,000 200,000,000
O.S. p.a 300,000,000 400,000,000
Pay – back Period = NI = 600,000,000 1,000,000,000
OS 300,000,000 400,000,000
= 2 Years 2.5 Years
Example: 2.
The following are the details relating to two projects:
Project X Project Y
Cost of the Project 160,000,000 200,000,000
Estimated scrap Value 16,000,000 25,000,000
Estimated savings Yr. 1 20,000,000 40,000,000
Yr. 2 30,000,000 60,000,000
Yr. 3 50,000,000 60,000,000
Yr. 4 50,000,000 60,000,000
Yr. 5 40,000,000 30,000,000
Yr. 6 30,000,000 20,000,000
Yr. 7 10,000,000 ---------
Calculate Pay – back Period and consider which project is better.
Note:
Cumulative totals of estimated savings are to be done up to the point where such total equals or
just exceeds the total cost.
Year Project X Project Y
Saving Cum.Saving Savings Cum. Savings
1 20,000,000 20,000,000 40,000,000 40,000,000
2 30,000,000 50,000,000 60,000,000 100,000,000
3 50,000,000 100,000,000 60,000,000 160,000,000
4 50,000,000 150,000,000 60,000,000 220,000,000

9. 9
5 40,000,000 190,000,000 -------- --------
Pay – back Period = E + B
C
= 4 + (160,000,000 – 150,000,000) 3 + (200,000,000 – 160,000,000)
40,000,000 60,000,000
= 4 + 10,000,000 3 + 40,000,000
40,000,000 60,000,000
= 4 years & 3 months 3 years & 8 months
Project Y is better
Advantages of Pay–back Period
1. It is very easy to calculate & easy to understand.
2. It states how rapidly the capital expenditure can be recovered
3. Where rapid technological changes are taken place, the shorter the pay – period,
the better it is.
4. The savings beyond pay–back period are not taken into account.
3. It is certainly an improvement over urgency method.
Disadvantages of Pay–back Period
It suffers from the following weaknesses:-
1. This method does not attempt to measure the return on investment. It emphasizes
only fast recovery of investment
2. This method ignores the savings after the recovery period
3. This method also ignores the time value of money, i.e. future cash flows are not
discounted in this method.
4. This method does not consider the cost of capital which is a base for sound
investment decision.
Because of the above limitations many firms use pay–back period method in conjunction with
one of the discounted cash flow method described below.

10. 10
3.0 Net Present Value Method: This method is based on the fact that a shilling received today
is preferable to a shilling received at some further date. This led to the development of
discounted cash flow (DCE) techniques to take account of the time value of money. In this
method the following steps are taken:
1. Minimum rate of return on investment is determined
2. Expected net cash flow during the life of the investment is ascertained.
3. The present value of expected net cash ascertained by using the
P.V.F (Present Value Factor) figure obtained from Annuity Table.
4. Initial cost outlay of the project is subtracted from the total of discounted value of
all net cash flows.
5. If the balancing figure (NPV) is positive the project is worth undertaking.
In case the projects are mutually exclusive, the project which has more balancing figure (NPV)
should be considered.
Example: 1.
Assume two projects are being considered by a firm. Each requires an investment of Shs.
100,000,000 which is mutually exclusive. The cost of capital/ marginal rate of return are 10%.
The net cash flow from project A and B are shown below:-
Project A Project B
Year Net cash flow Net Cash flow
1 50,000,000 10,000,000
2 40,000,000 20,000,000
3 30,000,000 30,000,000
4 10,000,000 40,000,000
5 ----------- 50,000,000
6 ----------- 60,000,000
The Annuity Table is given below at 10% discounting rate
Year PVF @ 10%
1 .909

11. 11
2 .826
3 .751
4 .683
5 .620
6 .560
Calculating the NPV of Project with a cost of Shs 100,000,000 each
ProjectA ProjectB
Year Net Cash PVF PV of Net Cash PVF PV of
flow at 10% cash flow flow @ 10% cash flow
1 50,000,000.909 45,450,000 10,000,000 .909 9,090,000
2 40,000,000.826 33,040,000 20,000,000 .826 16,520,000
3 30,000,000.751 22,530,000 30,000,000 .751 22,530,000
4 10,000,000.683 6,830,000 40,000,000 .683 27,320,000
5 50,000,000 .620 31,000,000
6 60,000,000 .560 33,600,000
---------- ---------
--
107,850,000 140,060,000
Less: Initial cost outlay 100,000,000 100,000,000
7,850,000 40,060,000
Project “B” is better.

12. 12
Example: 2.
A choice is to be made between two competing projects which require an equal
investment of Shs. 500,000,000 and are expected to generate net cash flows as follows:-
End of the Year Project A Project B
1 250,000,000 100,000,000
2 150,000,000 120,000,000
3 100,000,000 180,000,000
4 NIL 250,000,000
5 120,000,000 80,000,000
6 60,000,000 40,000,000
The cost of capital of company is 10%.
Using N.P.V. method recommend which proposal is to be preferred.
Calculation of N.P.V
Project A Project B
Year P.V.F at 10% Cash inflows P.V Cash flows P.V
1 .909 250,000,000 227,250,000 100,000,000 90,900,000
2 .826 150,000,000 123,900,000 120,000,000 99,120,000
3 .751 100,000,000 75,100,000 180,000,000 135,180,000
4 .683 NIL NIL 250,000,000 170,750,000
5 .621 120,000,000 74,520,000 80,000,000 49,680,000
6 .564 60,000,000 33,840,000 40,000,000 22,560,000
534,610,000 568,190,000

13. 13
Less: Initial Investment 500,000,000 500,000,000
34,610,000 68,190,000
Project “B” is to be preferred because it provides higher N.P.V as compares to Project A
Advantages
1. The desired rate of return fixed by the management represents the rate at which
other investment opportunities may be available.
2. It is consistent with the objective maximizing shareholders wealth.
3. It is also simple to calculate & understand.
Disadvantages or Limitations of N.P.V Method
1. The determination of desired rate of return proves to be difficult.
2. The method may fail to give satisfactory answer when projects under
consideration are involving different amounts of investments and with different economic
life periods.
4.0 Internal Rate of Return Method (I.R.R)
This method is also called Time adjusted Return on Investment or Discounted Rate of
return.This method measures the rate of return at which earnings are expected yield on
investments. This rate o return will be a rate discount at which the net present value of the
project exactly equals to zero.
In order to calculate the IRR, first of all Present Value Factor is find out by using the following
formula:-
A. When Savings are evenfor all the years
Present Value Factor= NI
OS
The closest Value to the PVF will be find out in the Present Value Factor for an Annuity
Table (PVFA) by reference to the Economic life of the Project.
The closest Present values above and lower the PVF along with the percentage will be
noted down and then the following formula will be used
I.R.R =LR + H.P.V – P.V.F x Diff. in rate
Diff. in calculated present values
Here I.R.R = Internal Rate of Return
L.R = Lower rate of return so found by ref. to the
Cumulative Present Value Table by seeing the no. of years

14. 14
of economic life of the Investment & which is closest to the
Present value factor.
H.P.V = Higher present value factor as compared to the
present value factor.
P.V.F = Actual present value factor
Example
The following particulars relate to two projects:-
Project A Project B
Cost in Shillings 90,000,000 100,000,000
Estimated Savings p.a 15,000,000 20,000,000
Economic life 10 years 8 years
Compute the Internal Rate of Return & state which of the two projects is better.
Solution for Project A
Present value factor = NI or 90,000,000 or 6.0
OS 15,000,000
Closest present value to 6.0 from the Cumulative Present value Table for 10 years (PVFA)
Years
5% 6% 8% 10% 12%
10 7.722 7.360 6.710 6.145 5.650
Closest present value Rate in %
6.145 10%
5.650 12%
Thus Internal Rate of Return would be between 10% and 12%
IRR = 10% + 6.145 – 6.0 x 12% - 10%
– 5.650
= 10% + .145 x 2%
.495

15. 15
= 10% + 0.6%
= 10.6%
Solution for Project B
Present Value Factor = NI or 100,000,000 or 5.0
OS 20,000,000
Closest Present value to 5.0 from the cumulative Present Value Table for 8 years
Years
5% 6% 8% 10% 12%
8 6.463 6.210 5.747 5.335 4.968
Closest Present Value Rate in %
5.335 10%
4.968 12%
Thus the Internal Rate of Return would be between 10% and 12%
IRR = 10% + 5.335 – 5.0 x 2%
– 4.968
= 10% + .335 x 2%
.367
= 10% + 1.8%
= 11.8%
On the basis of Time Adjusted Internal Rate of Return, Project B is Ranked No. 1 & it is better.
B. In case of Uneven Savings
Time Adjusted Rate of Return or D.R.R or I.R.R may also be found out when savings or
cash flows are uneven. But this can be done only though Trial & Error. The main problem is to
find out a rate on which the present values of uneven savings are just equal to the cost of
Investment. Thus IRR is a rate where cash outflows minus cash inflows is equal to zero. For this
purpose, the present values of cash inflows are calculated at varying rates. In that process the
rates on which present value of cost inflows are closest to the cost of investment is taken to be
IRR.
Steps to be taken

16. 16
Present Value Factor is Computed
NI
AS (Average Saving)
The rate is ascertained from the Cumulative Present Value Table by seeing the PVF, in which
percentage it falls.
Taking into account the percentage found in the Cumulative present Value Table, the Present
values for the no. of years are taken from Present Value Table of Sh. 1. These are multiplied by
the amount of cash inflows for the respective years. The values so found are added to know the
Total Present Value of expected future cash flows. The total is compared with the Actual amount
of investment.
If the totals of Present Value are more than the total investment, we go to calculate the P.V.F at a
higher percentage rate.
Example
A Project “AXE” involves an initial outlay of Shs.32, 400,000. Its economic life is
expected to be 3 years. The cash inflows are expected to be as under:
Year Inflows
2007 Shs. 16,000,000
2008 Shs. 14,000,000
2009 Shs. 12,000,000
Shs. 42,000,000
Calculate Internal Rate of Return:
PVF= NI
AS
NI = shs. 32,400,000
AS = shs. 42,000,000/3 = shs. 14,000,000
P.V.F = 32,400,000 = 2.314
14,000,000
This P.V.F of 2.314 in Cumulative P.V Table on the line of 3rd year we find 14% rate closest to
the above P.V.F we shall try first at 14%
The present vale factors at 14% rate of return for the 1, 2 &3 years are 0.877, 0.769. & 0.675
respectively.
Thus
Year Cash inflows P.V.F @ 14% Present Values
Shs. Shs.

17. 17
2007 16,000,000 .877 14,032,000
2008 14,000,000 .769 10,766,000
2009 12,000,000 .675 8,100,000
NPV= 32,898,000
If NPV is higher we go for higher percentage.
The present value of cash inflows is more that the initial cost outlay. Hence we are computing at
15% rate of return.
Year Cash inflows P.V.F @ 15% Present Values
2007 16,000,000 .870 13,920,000
2008 14,000,000 .756 10,584,000
2009 12,000,000 .658 7,896,000
32,400,000
The present values at 15% are just equal to the initial outlay. Thus IRR is 15%
In case the total of Net Present value of cash flows is not coming equal to the initial outlay, the
following formula is used:-
IRR = LR + Calculated P.V – Initial outlay at lower % x Diff. in rate
Diff. in calculated Present Value
LR = Lower rate of Percentage
Example
A company is considering the following Project:
Cost Shs. 11,000,000
Cash inflows Yr. 1 6,000,000
Yr. 2 2,000,000
Yr. 3 1,000,000
Yr.4 5,000,000
14,000,000
Average Saving = 14,000,000
4

18. 18
= 3,500,000
P.V.F 11,000,000 = NI
3,500,000 AS
= 3.14
In the Cumulative Present Value Table, this lies in the rate of return of 10%.
The present values are for:
P.V
Yr. 1 .909 multiplied by inflows 6,000,000 5,454,000
Yr. 2 826 2,000,000 1,652,000
Yr. 3 .751 1,000,000 751,000
Yr. 4 .683 5,000,000 3,415,000
11,272,000
This is higher than cash outlay of Shs.11, 000,000. Now we are trying the higher percentage at
12%. The present values are:-
P.V
Yr. 1 .893 multiplied by inflows Shs. 6,000,000 5,358,000
Yr. 2 .797 2,000,000 1,594,000
Yr. 3 .712 1,000,000 712,000
Yr. 4 .636 5,000,000 3,180,000
10,844,000
Which is short of Shs. 156,000
i.e. (11,000,000 – 10,844,000)
by applying the formula
IRR = LR + Calculated PV at less % - Initial outlay x Diff. in rate
Diff. in calculated Present values
= 10% + 11,272,000 – 11,000,000 x 2%
11,272,000 – 10,844,000
= 10% + 272,000 x 2%
428,000

19. 19
= 10% + 1.27%
IRR = 11.27%
Conclusion
Any criteria or combination of criteria can be used for taking decision on investment.
CAPITAL INVESTMENT DECISION
Question #1
The directors of Steel Ltd are considering closing on the business factories.
There has been reduction in demand for the products made at the factory in
recent years, and the directors are not optimistic about the long-term
prospects for these products. The factory is situated in the north of England,
in an area where unemployment is high.
The factory is leased, and there are still four years of the lease remaining.
The directors are uncertain whether the factory should be closed
immediately or at the end of the lease. Another business has offered to
sublease the premises from Steel Ltd at a rental of £40,000 a year for the
remainder of the lease period.
The machinery and equipment at the factory cost £ 1,500,000, and have a
balance sheet value of £400,000. In the event of immediate closure, the
machinery and equipment could be sold for £220,000. The working capital at
the factory is £420,000, and could be liquidated for that amount immediately, if
required. Alternatively, the working capital can be liquidated in full at the end of
the lease period. Immediate closure would result in redundancy payments to
employees £180,000.
If the factory continues in operation until the end of the lease period, the
following operating profits/(losses) are expected:
Year 1 Year 2 Year 3 Year 4
£000 £000 £000 £000
Operating Profit/(Loss) 160 (40) 30 20
The above figures include a charge of £90,000 a year for depreciation of
machinery and equipment. The residual value of the machinery and equipment
at the end of the lease period is estimated at £40,000.

20. 20
Redundancy payments are expected to be £150,000 at the end of the lease
period if the factory continues in operation. The business has an annual cost of
capital of 12%. Ignore taxation.
Required:
(a) Determine the relevant cash flows arising from a decision to
continue operations until the end of the lease period rather than to
close immediately.
(b) Calculate the net present value of continuing operations until the
end of the lease period, rather than closing immediately.
(c) What other factors might the directors take into account before
making the final decision on the timing of the factory closure?
(d) State, with reasons, whether or not the business should continue to
operate the factory until the end of the lease period.
SOLUTION
Relevant Cash flows
Year 0 Year 1 Year 2 Year 3 Year 4
£000 £000 £000 £000 £000
Operating Profit 160 (40) 30 20
Add back Depreciation - 90 90 90 90
Cash flows 250 50 120 110
Sale of Machinery (220) 40
Redundancy cost 180 (150)
Sublease rentals (40) (40) (40) (40)
Wording capital invested (420) 420
RELEVANT CASH FLOWS (460) 210 10 80 380
PVF @ 12 per cent 1.000 0.893 0.797 0.712 0.636
PV of Cash flows (460) 187.5 8.0 57.0 241.7
NPV in £000 34.2

21. 21
(C) Other factors that may influence the decision include:
1.0 The overall strategy of the business- already it is high unemployment
area.
2.0 Flexibility: NPV is still positive if the business continues.
3.0 Credit worthiness of the sub-lessee- Failure to receive expected sub-
lease payments make the closure option less attractive.
4.0 Accuracy of the forests should be examined carefully.
5.0 The shareholders will be better off if the business continues.
(d)The decision to continue operation rather than close immediately is
positive. Hence, shareholders would be better off if the directors took this
option in view of the NPV.
QUESTION # 2
Twiga Chemicals plc is considering buying some equipment to produce a
chemical named X02. The new equipment’s capital cost is estimated at
£100,000. If its purchase is approved now, the equipment can be bought and
production can commence by the end of this year. £50,000 has already spent
on research and development work. Estimates of revenues and costs arising
from the operation of the new equipment appear below:
Year 1 Year 2 Year 3 Year 4 Year 5
Sales price (£/liter) 100 120 120 100 80
Sales Volume (liters) 800 1,000 1,200 1,000 800
Variable costs (£/liter) 50 50 40 30 40
Fixed costs (£000) 30 30 30 30 30
If the equipment is bought, sales of some existing products will be lost, and
this will result in a loss of contribution of £15,000 a year over its life.
The accountant has informed you that the fixed costs include depreciation of
£20,000 a year on the new equipment. They also include an allocation of
£10,000 for fixed overheads. A separate study has indicated that if the new
equipment were bought, additional overheads, excluding depreciation, arising
from producing the chemical would be £8,000 a year. Production would require
additional working capital of £30,000. Ignore Taxation.
Required:
(a) Deduce the relevant annual cash flows associated with buying the
equipment.

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(b) Deduce the payback period.
(c) Calculate the net present value using a discount rate of 8 per cent.
SOLUTION
Relevant cash flows are as follows:
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
£000 £000 £000 £000 £000 £000
Sales Revenue 80 120 144 100 64
Loss of contribution (15) (15) (15) (15) (15)
Variable Costs (40) (50) (48) (30) (32)
Fixed Costs (8) (8) (8) (8) (8)
Operating Cash flows 17 47 73 47 9
Working capital (30) 30
Capital cost (100)
Net relevant cash
flows (130) 17 47 73 47 39
(b) The payback period is as follows:
Year Cash flows Cumulative cash flows
£000 £000
Year 1 17 17
Year 2 47 64
Year 3 73 137
Payback period = E + B/C
= 2+ 66/73 2.9 years
( c ) Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
£000 £000 £000 £000 £000 £000
Cash flows (130) 17 47 73 47 39
PVF @ 8% 1.000 0.926 0.857 0.794 0.735 0.681
PV of Cash flows (130) 15.74 40.3 57.96 34.55 26.56
NPV 45.11
The project can be undertaken.
QUESTION # 3
Chesterfield Wanderers is a professional football club that has enjoyed
considerable success in both national and European competitions in recent

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years. As a result, the club has accumulated £ 10m to spend on its further
development. The board of directors is currently considering two mutually
exclusive options for spending the funds available.
The first option is to acquire another player. The team manager has
expressed a keen interest in acquiring BASIL, a central defender, who
currently plays for a rival club. The rival club has agreed to release the
player immediately for £10m if required. A decision to acquired Basil would
mean that the existing central defender, Smith, could be sold to another
club. Chesterfield Wanderers has recently received an offer of £2.2m for this
player. This offer is still open but will only be accepted if Basil joins
Chesterfield Wanderers. If this does not happen, Smith will be expected to
stay on with the club until the end of his playing career in five years’ time.
During this period, Smith will receive an annual salary of £400,000 and a
loyalty bonus of £200,000 at the end of his five-year period with the club.
Assuming Basil is acquired, the team manager estimates that gate
receipts will increase by £2.5m in the first year and £1.3m in each of the
four following years. There will also be an increase in advertising and
sponsorship revenues of £1.2m for each of the next years if the player is
acquired. At the end of five years the player can be sold to a club in a lower
division and Chesterfield Wanderers will expect to receive £1m as a
transfer fee. During his period at the club, Basil will receive an annual salary
of £800,000 and a loyalty bonus of £400,000 after 5 years.
The second option is for the club to improve its ground facilities. The west
stand could be extended and executive boxes could be built for businesses
wishing to offer corporate hospitality to clients. These improvements would
also cost £10m and would take one year to complete. During this period, the
west stand would be closed, resulting In a reduction of gate receipts of
£1.8m. However the gate receipts for each of the following four years would
be £4.4m higher than current receipts. In five years’ time, the club has plans
to sell the existing grounds and to move to a new stadium nearby.
Improving the ground facilities is not expected to affect the ground’s value
when it comes to be sold. Payments for improvement will be made when the
work has been completed at the end of the first year. Whichever option is
chosen, the board of directors has decided to take on additional ground staff.
The additional wages bill is expected to be £350,000 a year over the next
five years.
The club has a cost of capital of 10%. Ignore taxation.
REQUIRED:
(a) Calculate the incremental cash flows arising from each of the options
available to the club.
(b) Calculate the net present value of each of the options.
(c) On the basis of the calculations made in (b) above, which of the two
options would you choose and why?

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(d) Discuss the validity of using the net present value method in making
investment decisions for a professional football club.
SOLUTION
Chesterfield Wanderers
(a) Or (b) option
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
£000 £000 £000 £000 £000 £000
Sale of player 2,200 1,000
Purchase of Basil (10,000)
Sponsorship etc. 1,200 1,200 1,200 1,200 1,200
Increased gate receipts 2,500 1,300 1,300 1,300 1,300
Salaries paid (800) (800) (800) (800) (1,200)
Salaries saved 400 400 400 400 600
Net Cash flows (7,800) 3,300 2,100 2,100 2,100 2,900
PVF @ 10% 1.000 0.909 0.826 0.751 0.683 0.621
PV of cash flows (7,800) 3,000 1,735 1,577 1,434 1,801
NPV 1,747
(b)Ground Improvements options
Year 1 Year 2 Year 3 Year 4 Year 5
Ground Improvements (10,000)
Increased gate receipts (1,800) 4,400 4,400 4,400 4,400
Cash flows (11,800) 4,400 4,400 4,400 4,400
Discount factor 10% 0.909 0.826 0.751 0.683 0.621
PV of cash flows (10,726) 3,634 3,304 3,005 2,732
NPV 1,949
(C)The ground improvement option provides the higher NPV, is therefore
preferable.
(d) The club may not wish to pursue an objective of shareholders wealth
maximization in comparison to future sporting success spirit, so it may go for
option 1.
PROFITABILITY INDEX

25. 25
• It is another time-adjusted method of evaluating the investment proposals. It is the ratio of
the present value of cash inflows, computed at the required rate of return divided by the
initial cash outflow of the investment.
• The formula to calculate the profitability index or benefit cost ratio is as follows:-
• PI= _PV of Cash Inflows
• Initial cash outlay
• The Acceptance rule
• Accept if PI is more than 1
• Reject if PI is less than 1
• May accept is PI = 1
• When PI is greater than 1, the project will have positive net value
Evaluation of PI Method
• Like the NPV and the IRR, PI is conceptually sound method of appraising investment
projects. It recognizes the time value of money. Since the present value of cash flows is
divided by the initial cash outflows, it is relative measure of project profitability.
• Example
• The initial cash outlay of the project is Shs. 10,000,000 and it can generate cash inflow of
Shs. 4,000,000, Shs. 3,000,000, Shs. 5,000,000 and Shs. 2,000,000 in the years 1 through 4.
Assume 10% rate of discount. The PV of cash inflow for 10% discount rate is:- yr. 1 0.909;
yr 2 0.826; yr 3 0.751 and yr 4 0.683.
Solution
• Year Cash Inflows Discount Rate PV of Cash Inflows
• 1 4,000,000 0.909 3,636,000
• 2 3,000,000 0.826 2,478,000
• 3 5,000,000 0.751 3,755,000
• 4 2,000,000 0.683 1,366,000
• 11,235,000
• Less Initial Cash Outlay 10,000,000
• NPV 1,235,000
• PI = PV of cash flows
• Initial Cash Outlay
• = 11,235,000 or 1.1235
• 10,000,000
• Accept the Project.
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