Question

P 8-30 (similar to) Question Help You are considering the following two projects and can take only one. Your cost of capital is 11.3%. The cash flows for the two projects are as follows (S milion) Project Year 0 Year 1 $22 Year 2 Year 3 Year 4 $99 $99 $52 $30 $41 $41 $30 B $52 S21 a. What is the IRR of each project? b. What is the NPV of each project at your cost of capital? c. At what cost of capital are you indifferent between the two projects? d. What should you do? a. What is the IRR of each project?

Answer 1

Part-a:

Project-A:

At IRR,

Present Value of Cash Outflows = Present value of Cash Inflows

Let IRR of Project –A be “x%”

At IRR,

99 = 22/(1+x)^1 + 30/(1+x)^2 + 41/(1+x)^3 + 52/(1+x)^4

Computing for x , we get x = 14.785%

Therefore, IRR of Project A is 14.79%

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Project-B:

At IRR,

Present Value of Cash Outflows = Present value of Cash Inflows

Let IRR of Project –B be “y%”

At IRR,

99 = 52/(1+y)^1 + 41/(1+y)^2 + 30/(1+y)^3 + 21/(1+y)^4

Computing for y , we get y = 20.183%

Therefore, IRR of Project B is 20.18%

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Part-b:

NPV of Project-A:

Year	CashFlows	DF Working	Discounting Factor @ 11.3%	Present Value
0	-99	1	1	(99.00)
1	22	1/1.113^1	0.898472597	19.77
2	30	1/1.113^2	0.807253007	24.22
3	41	1/1.113^3	0.725294705	29.74
4	52	1/1.113^4	0.651657417	33.89
			NPV of Project-A:	8.61

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NPV of Project-B:

Year	CashFlows	DF Working	Discounting Factor @ 11.3%	Present Value
0	-99	1	1	(99.00)
1	52	1/1.113^1	0.898472597	46.72
2	41	1/1.113^2	0.807253007	33.10
3	30	1/1.113^3	0.725294705	21.76
4	21	1/1.113^4	0.651657417	13.68
			NPV of Project-B:	16.26

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Part-C:

Let the cost of capital at which both the two projects are indifferent be "z%

NPV of Project – A = NPB of Project – B

22/(1+z)^1 + 30/(1+z)^2 + 41/(1+z)^3 + 52/(1+z)^4 - 99 = 52/(1+z)^1 + 41/(1+z)^2 + 30/(1+z)^3 + 21/(1+z)^4 - 99

30/(1+z)^1 + 11(1+z)^2 -11/(1+z)^3 – 31/(1+z)^4 = 0

Computing for z , we get z = 0.98%

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Therefore , at cost of capital = 0.98% , we will be indifferent between the two projects.

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Part-D:

We should invest in Project-B , since it has higher NPV and higher IRR as compared to that of Project-B.