Question

Your division is considering two investment projects, each of which requires an up-front expenditure of $25 million. You estimate of capital is 10% and that the investments will produce the following after-tax cash flows (in millions of dollars): Year Project A Project B 10 15 (0) 29 20 What are the payback periods for the two projects? What are the BBs of the two projects? If the two projects are mutually exclusive and the cost of capital is 5%, which project should the firm undertake? that nanlants are mutually exclusive and the cost of capital is 15%, which project should the firm undertake?

Answer 1

Answer-

The upfront expenditure ( Immediately incurred ) = $ 25 million / year
Cost of capital = 10 %

Project A

Payback period

	Year	0	1	2	3	4
Project A	Net Cash Flow (NCF)	- $ 25	$ 5	$ 10	$ 15	$ 20
	Cumulative NCF	- $ 25	- $ 20	- $ 10	$ 5	$ 25

Payback period = full years until recovery + (unreovered cost at the beginning of last year / cash flow during the last year)

Payback period = 2 + ( $ 10 / $ 15 ) = 2 + 0.66 = 2.66 years

Project B

Payback period

	Year	0	1	2	3	4
Project B	Net Cash Flow (NCF)	- $ 25	$ 20	$ 10	$ 8	$ 6
	Cumulative NCF	- $ 25	- $ 5	$ 5	$ 13	$ 19

Payback period = 1 + ( $ 5 / $ 10 ) = 1 + 0.5 = 1.5 years

2)

IRR Project A

IRR will be calculated by setting NPV =0

0 = - $ 25 + $ 5 / ( 1 +IRR) + $ 10 / ( 1+IRR)2 + $ 15 / ( 1+ IRR)3 + $ 20 / ( 1+ IRR)4

IRR = 27.27 %

IRR Project B

0 = - $ 25 + $ 20 / ( 1 +IRR) + $ 10 / ( 1+IRR)2 + $ 8 / ( 1+ IRR)3 + $ 6 / ( 1+ IRR)4

IRR = 36.15 %

3)

If the cost of capital = 5 %

Project A

NPV = - $ 25 + $ 5 / (1 + 0.05) + $ 10 / (1 +0.05)2 + $ 15 / (1+0.05)3 + $ 20 / (1+0.05)4

NPV = - $ 25 + $ 5 / 1.05 + $ 10 / 1.052 + $ 15 / 1.053 + $ 20 / 1.054

NPV = - $ 25 + $ 5 / 1.05 + $ 10 / 1.1025 + $ 15 / 1.158 + $ 20 / 1.2155

NPV = - $ 25 + $ 4.76 + $ 9.07 + $ 12.95 + $ 16.45

NPV = - $ 25 + $ 43.23

NPV = $ 18.23

Project B

NPV = - $ 25 + $ 20 / (1 + 0.05) + $ 10 / (1 +0.05)2 + $ 8 / (1+0.05)3 + $ 6 / (1+0.05)4

NPV = - $ 25 + $ 20 / 1.05 + $ 10 / 1.052 + $ 8 / 1.053 + $ 6 / 1.054

NPV = - $ 25 + $ 20 / 1.05 + $ 10 / 1.1025 + $ 8 / 1.158 + $ 6 / 1.2155

NPV = - $ 25 + $ 19.05 + $ 9.07 + $ 6.91 + $ 4.94

NPV = - $ 25 + $ 39.97

NPV = $ 14.97

Since the projects are mutually exclusive only the project with higher NPV should be selected, therefore Project A ( $ 18.23 ) should be selected over Project B ( $ 14.97).

4)

If the cost of capital = 10 %

Project A

NPV = - $ 25 + $ 5 / (1 + 0.15) + $ 10 / (1 +0.15)2 + $ 15 / (1+0.15)3 + $ 20 / (1+0.15)4

NPV = - $ 25 + $ 5 / 1.15 + $ 10 / 1.152 + $ 15 / 1.153 + $ 20 / 1.154

NPV = - $ 25 + $ 5 / 1.15 + $ 10 / 1.3225 + $ 15 / 1.52 + $ 20 / 1.75

NPV = - $ 25 + $ 4.35 + $ 7.56 + $ 9.87 + $ 11.43

NPV = - $ 25 + $ 33.21

NPV = $ 8.21

Project B

NPV = - $ 25 + $ 20 / (1 + 0.15) + $ 10 / (1 +0.15)2 + $ 8 / (1+0.15)3 + $ 6 / (1+0.15)4

NPV = - $ 25 + $ 20 / 1.15 + $ 10 / 1.152 + $ 8 / 1.153 + $ 6 / 1.154

NPV = - $ 25 + $ 20 / 1.15 + $ 10 / 1.3225 + $ 8 / 1.52 + $ 6 / 1.75

NPV = - $ 25 + $ 17.39 + $ 7.56 + $ 5.26 + $ 3.43

NPV = - $ 25 + $ 33.64

NPV = $ 8.64

Since the projects are mutually exclusive only the project with higher NPV should be selected, therefore Project B ( $ 8.64 ) should be selected over Project A ( $ 8.21).