1. Capital Investment Analysis

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Indian Institute of ManagementAhmedabad

Prepared by Professor Jahar Saha, Indian Institute of Management, Ahmedabad.

1976 by the Indian Institute of Management, Ahmedabad.

IIMA/QM0024TEC

Technical Note

Capital Investment Analysis

Any Capital budgeting decision consists of four stages:

1. Listing the projects for investment i.e., identifying the alternatives,

2. For each alternative, determining the cash flows,

3. Measuring the worth, (using a suitable indicator) of each alternative project,finally.

4. Allocating the budgeted amount and among the alternatives chosen in the lightof the (3) above.

Though extremely crucial the first and second stages requiring the technical know-how forthe estimate of present outlays, future costs and future benefits, will not be discussed in thisnote. Nor shall we deal with the mathematical complexities of optimal allocation of alimited, budget among competing projects. We will be concerned here primarily with themeasurement and comparison of the worth of investments.

InpracticeThere are several measures - the ones among these are:

(1) Payback period

(2) Average return on investment

(3) Net present value

(4) Yield

The last two measures are based on the concept of time valueof money.

Each of the measure listed above has its own advantages and disadvantages. These are bestexplained through the following illustrations of six investments:

Table 1Investment

Initialoutlay Rs.

Net Cash Proceeds per year (Rs.)

Year 1 Year 2 Year 3

A 10,000 10,000 500 500

B 10,000 5,000 5,000 5,000

C 10,000 2,000 4,000 12,000

D 10,000 10,000 3,000 3,000

E 10,000 6,000 4,000 5,000

F 10,000 8,000 8,000 2,000

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1Payback Period:

This is the simplest measure for evaluating the worth of investment proposals. Paybackperiod as the phrase indicates, is the period in which the initial outlay is recovered in theform of cash savings or benefits. If cash savings of benefits are the same each year, then the

payback period is obtained by dividing the initial investment by the annual savings

P = IC

where P = payback period

C = annual cash benefits (i.e. Income or savings) and

I = Initial investment

When cash flows are unequal each year as in Table 1 above, the definition is used directly toobtain P. Normally a maximum payback period is stipulated by the top management inscreening projects for investment. Investments with longer pay back periods than thestipulated ones are rejected. To determine the priorities, investments are ranked in theincreasing order of their pay back periods. The investment with the least payback periodtops the list. Table 2 below gives the payback periods for investment listed in Table 1.

* modified from an example given by Bierman & Smidt - "Capital Budgeting".

Table 2

Investment Pay BackPeriod Ranks

A 1 1

B 2 4

C 2 1/3 6

D 1 1

E 2 4

F 1 1/4 3

The advantage of using the payback period as a measure of the worth of aninvestment liesin its ease of calculation. But this case or simplicity of computation is achieved at the cost ofthe discriminating abilities of this measure. For instance: Consider investments A and D.Though they obtainidentical ranks, a glance at Table 1 demonstrates 'the clear superiority ofproject D over A, Similarly E is superior to B though the ranks in Table 2 fail to reveal thesedifferences.

This is because the payback period

(a) ignores the cash proceeds received after the payback period and

(b) ignores the time value of money.




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2 Average Return on Investment:

The average return on investment is defined as the ratio of average annual income after

depreciation from the project to theinitial investment.

In computing the average return on investment, from the total income over the life of theproject, the initial investment is deducted. This net incomeis then divided by the number ofyears of the life of the project, to obtain the average income per year. The average is thendivided by the initial investmentgives the return. The computations for the six investmentsof Table 1 are shownin Table 3,

Table 3

Investment InitialOutlay TotalIncome

Income

afterDepreciation

Average

incomeafterDepreciation

Average

return onInvestment

Bank

A 10,000 11,000 1,000 333 3.33 6

B 10,000 15,000 5,000 1,667 16.67 4

C 10,000 18,000 8,000 2,667 26.67 1

D 10,000 16,000 6,000 2,000 20.00 3

E 10,000 15,000 5,000 1,667 16.67 4

F 10,000 18,000 8,000 2,667 26.67 1

This measure, unlike the payback period takes into account all the benefits generated duringthe life of the investment. But it does not recognize the timings of savings i.e., it gives equalweigh-tage to money received at various points of time. For instance, in terms of averagereturn on investment, investments C and F are ranked equally. But F is obviously superior toE as it generates higher income in the initial periods. Same is the case of projects B and E. Eis superior to B.

3. Net Present Value:

Present value concept is based on the fact that Re. 1 received now is worth more than Re. 1received one year hence. This is so because Re. 1 received today can be invested to earnmore money. When management stipulates the minimum rate ('opportunity investment rate'or 'cost of capital') at which an investment must generate income, this rate is used to'discount' the cash flows of the future to bring them on a comparable basis to their "presentvalue". For example, if the rate is 10% per year, Rs. 100 obtained a yearhence is discountedto

100 _ 100 = Rs. 90.9.(1+.1) 1.1

We say that the present value of Rs. 100 received 1 year hence is Rs. 90.9 when thedisocuntrate is 10%. The present value of Re. 1 obtained 1year hence, 2 year hence, 50 yearhence is tabulated in the "Tables for Capital Investment Analysis for different discounting




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rates. Using these multipliers, present values of any sums of money received at differentpoints of time in the future can be computed.

Table 4

Investment

Present value factor (fromTables) for 6% end of year Sum of

P.V.(4)

InitialInvestment

(5)

N.P.V.(4) - (5)

Rank

1.9434

2.8900

3.8396

A 10,000 500 500 10,299 10,000 299 6

B 5,000 5,000 5,000 13,365 10,000 3,365 5

C 2,000 4,000 12,000 15,522 10,000 5,522 2

D 10,000 3,000 3,000 14,623 10,000 4,623 3

E 6,000 4,000 5,000 13,418 10,000 3,418 4

F 8,000 8,000 2,000 16,246 10,000 6, 346 1

Because the computations involve the discounting of future cash flows, this method is alsoknown as the Discounted Cash Flows (QCF) method.

Yield of an Investment

The yield of an investment also called the internal rate of return, bread even rate, etc., i.e.,

at which the NPV is zero. In other words yield is the rate which equals the present value ofthe future cash benefits to the initial outlay.

To judge whether an investment is worthwhile, the yield is compared with the minimumacceptable rate of return, determined as the cost of capital by top management. If yield ishigher than the minimum acceptable rate of return, the decision will be in favour of theinvestment.

It is to be emphasized that in some situations (when in some years, cash outflows exceedinflows) there could be more than one yield and this could lead to anamoly. Further, theNPV and the yield, in ranking the projects may not givethe same results.

Consider the following example:

Initial Investment = Rs. 100

Cash Inflow at the end of the first year = Rs. 220

Cash Outflow nt the end of the second year = Rs. 121




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The Internal rate r is determined by the equation

100 = 220 - 1211 + r (l*r)2

The solution is r =8 %

a nd 12%.

From (fosse considerations, NPV is preferred to yield in Judging the worth of severalinveStinsnts.



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1. Capital Investment Analysis