Example
A company has to select one of the following two projects:
A company has to select one of the following two projects:
Project A
Using the internal rate of return method suggest which project is preferable.
Solution
The cash inflow is not uniform and hence the internal rate of return will have to be calculated by the trial and error method. In order to have an approximate idea about such a rate, it will be better to find out the Factor. The factor reflects the same relationship of investment and cash inflows in case of payback calculation:
The factor thus calculated will be located in the table given at the end of the unit on the line representing number of years corresponding to estimated useful life of the asset.This would give the expected rate of return to be applied for discounting the cash inflows, the internal rate of return.
In case of Project A, the rate comes to 10% while in case of Project B it comes to 15%.
Solution
The cash inflow is not uniform and hence the internal rate of return will have to be calculated by the trial and error method. In order to have an approximate idea about such a rate, it will be better to find out the Factor. The factor reflects the same relationship of investment and cash inflows in case of payback calculation:
The factor thus calculated will be located in the table given at the end of the unit on the line representing number of years corresponding to estimated useful life of the asset.This would give the expected rate of return to be applied for discounting the cash inflows, the internal rate of return.
In case of Project A, the rate comes to 10% while in case of Project B it comes to 15%.
Project A
The present value at 10% comes to Rs. 11,272. The initial investment is Rs. 11,000. Internal rate of return may be taken approximately at 10%.In case more exactness is required another trial rate which is slightly higher than 10% (since at this rate the present value is more than initial investment may be taken) Taking a rate of 12%, the following results would emerge:
The internal rate of return is thus more than 10% but less than 12%. The exact rate may be calculated as follows. Difference calculated in present:
Actual IPR = (10 + (272/272) + 156 )× 2 = 11.27 %
Project B
Since present value at 15% adds up to Rs. 8,662, a lower rate of discount should be taken. Taking a rate of 10%, the following will be the result.
The present value at 10% cumulates Rs. 10067 which is more or less equal to the initial investment. Hence the internal rate of return may be taken as 10%. In order to have more exactness to internal rate of return can be interpolated as done in case of Project A.
Thus, internal rate of return in case of Project A is higher as compared to
Project B. Hence, Project A is preferable.
Example
A Company is considering a capital investment proposal where two alternatives involving differing degrees of mechanisation are being considered. Both investments would have a five-year life.
In Option 1, new machinery would cost Rs. 2,78,000 and in Option 2
Rs. 8,05,000. Anticipated scrap values after 5 years are Rs. 28,000 and 1,50,000 respectively. Depreciation is provided on a straight-line basis.
Option I would generate annual cash inflows of Rs. 1,00,000 and Option 2, Rs. 2,50,000. The cost of capital is 15%.
Required:
(a) Calculate for each option:
(i) the payback period
(ii) the accounting rate of return, based on average book value
(iii) the net present value
(iv) the internal rate of return
(b) Identify the preferred option, giving reasons for your choice.
Solution
(a) (i) Payback period:
Option 1 = 2,78,000/1,00,000
= 2.78 years
Option 2 = 8,05,000/2,50,000
= 3.32 years
(ii) Accounting rate of return:
Option 1
Option 2
(iii) Net present value (at 15% cost of capital):
Option 1
Option 2
Approx cumulative discount factor (5 year) = 7,40,000/2,50,000
= 2.96 =20%
Project B. Hence, Project A is preferable.
Example
A Company is considering a capital investment proposal where two alternatives involving differing degrees of mechanisation are being considered. Both investments would have a five-year life.
In Option 1, new machinery would cost Rs. 2,78,000 and in Option 2
Rs. 8,05,000. Anticipated scrap values after 5 years are Rs. 28,000 and 1,50,000 respectively. Depreciation is provided on a straight-line basis.
Option I would generate annual cash inflows of Rs. 1,00,000 and Option 2, Rs. 2,50,000. The cost of capital is 15%.
Required:
(a) Calculate for each option:
(i) the payback period
(ii) the accounting rate of return, based on average book value
(iii) the net present value
(iv) the internal rate of return
(b) Identify the preferred option, giving reasons for your choice.
Solution
(a) (i) Payback period:
Option 1 = 2,78,000/1,00,000
= 2.78 years
Option 2 = 8,05,000/2,50,000
= 3.32 years
(ii) Accounting rate of return:
Option 1
Option 2
(iii) Net present value (at 15% cost of capital):
Option 1
Option 2
Approx cumulative discount factor (5 year) = 7,40,000/2,50,000
= 2.96 =20%
(iv) Internal rate of return:
Option 2
Both projects are indicated as being worthwhile when the discounted cash flow returns are compared with the cost of capital. The payback period, accounting rate of return, and internal rate of return calculations all points to option 1 being preferred. The net present value calculation,on the other hand, favours option 2.
The basic reason for the different ranking provided by the NPV method is an absolute money measure that takes into account the scale of the investment as well as the quality. The other three appraisal methods provide measure, which express returns relative to the investment.
Investments of comparable relative quality will have the same returns regardless of scale. For example, an annual profit of Rs. 20 on an investment of Rs. 100 will have the same relative return as an annual profit of Rs. 2,00,000 on an investment of Rs. 10,00,000. If one were concerned especially with quality then the relative measures would provide the required ranking. However, if the objective is to maximise wealth, investment worth should be measured by the surplus net present value generated, over and above the cost of the capital.In the situation in the question, the differential between Option 1 and Option 2 provides an internal rate of return of 18% as follows:
The basic reason for the different ranking provided by the NPV method is an absolute money measure that takes into account the scale of the investment as well as the quality. The other three appraisal methods provide measure, which express returns relative to the investment.
Investments of comparable relative quality will have the same returns regardless of scale. For example, an annual profit of Rs. 20 on an investment of Rs. 100 will have the same relative return as an annual profit of Rs. 2,00,000 on an investment of Rs. 10,00,000. If one were concerned especially with quality then the relative measures would provide the required ranking. However, if the objective is to maximise wealth, investment worth should be measured by the surplus net present value generated, over and above the cost of the capital.In the situation in the question, the differential between Option 1 and Option 2 provides an internal rate of return of 18% as follows:
The additional investment of Rs. 5,27,000 in Option 2 is worthwhile as the IRR of 18 % exceeds the cost of capital.
Finally, it should be recognised that both the payback method and the accounting rate of return method have deficiencies. They do not provide an adequate measure of investment worth. The percentage return including the accounting rate of return calculations is not comparable with the cost of the capital.
The PI method is a conceptually sound method. It takes into consideration the time value of money. It is also consistent with the value maximisation principle. Like NPV and IRR methods, the PI method also requires estimations of cash flows and discount rate. In practice, the estimation of discount rates and cash flows is difficult.
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