Question

You are considering the following two mutually exclusive projects. Both projects will be depreciated using straight-line depreciation to a zero book value over the life of the project. Neither project has any salvage value.

Year	Project(A)	Project (B)
0	-$30,000	-$30,000
1	13,000	5,000
2	11,000	5,000
3	9,000	5,000
4	7,000	5,000
5	0	5,000
6 7 8 9 10	0 0 0 0 0	5,000 5,000 5,000 5,000 5,000

    The required rate of return is 10%

a. What is the NPV for each of the projects? Which project should be accepted if NPV method is applied? Explain why.

b. What is the IRR for each of the projects? Which project should be accepted if IRR method is applied? Explain why.

c. What is the payback period for each of the projects? Which project should be accepted if payback period method is applied? Assume that the target payback period is 4 years. Explain why.

d. What is the discounted payback period for each of the projects? Which project should be accepted if discounted payback period method is applied? Assume that the target discounted payback period is 4 years. Explain why.

e. What is the profitability index for each of the projects? Which project should be accepted if profitability index method is applied? Explain why.

f. What is the average accounting return (AAR) for each of the projects, assuming that cash flows occurring after year 0 are net income? Which project should be accepted if AAR method is applied? Also, assume that the target AAR is 20%.

g. Define and find the crossover rate.

h. Sketch the NPV profile. Plot all the relevant coordinates (i.e., the points on the x and y axis; and the cross-over rate) on the graph.

Answer 1

(A):

Year	A's CF	B's CF	1+r	PVIF = 1/(1+r)^n	PV of A	PV of B
0	-30000	-30000	1.1	1.0000	-            30,000	-            30,000
1	13000	5000		0.9091	11,818	4,545
2	11000	5000		0.8264	9,091	4,132
3	9000	5000		0.7513	6,762	3,757
4	7000	5000		0.6830	4,781	3,415
5	0	5000		0.6209	-	3,105
6	0	5000		0.5645	-	2,822
7	0	5000		0.5132	-	2,566
8	0	5000		0.4665	-	2,333
9	0	5000		0.4241	-	2,120
10	0	5000		0.3855	-	1,928
				NPV	2,452.02	722.84

Thus NPV of A is $2,452.02 and that of B is $722.84

As NPV of A is higher project A will be selected.

(b): IRR is the rate at which NPV becomes nil. I have computed the IRRs using trial and error method.

Year	A's CF	1+r	PV		B's CF	1+r	PV
0	-30000	1.141574	-30000		-30000	1.10558	-30000
1	13000		11388		5000		4523
2	11000		8441		5000		4091
3	9000		6050		5000		3700
4	7000		4122		5000		3347
5	0		0		5000		3027
6	0		0		5000		2738
7	0		0		5000		2477
8	0		0		5000		2240
9	0		0		5000		2026
10	0		0		5000		1833
		NPV	0				0

IRR of A is 14.16% and of B is 10.56%. On this basis A will be selected as its IRR is greater.

(c):  

Year	A's CF	B's CF	Cumulative cash flow of A	Cumulative cash flow of B
0	-30000	-30000	-30000	-30000
1	13000	5000	-17000	-25000
2	11000	5000	-6000	-20000
3	9000	5000	3000	-15000
4	7000	5000		-10000
5	0	5000		-5000
6	0	5000		0
7	0	5000
8	0	5000
9	0	5000
10	0	5000

Thus payback of A = 2 + (6000/9000) = 2.67 years. Payback of B is 6 years. A will be selected as its payback of 2.67 years is less than the target of 4 years.

(d): For discounted payback we use the PV of cash flows. Using the data from "a" we get discounted payback of A = 3+(2329.08/6761.83) = 3.34 years and B = 9+(1204.88/1927.72) = 9.63 years. Project A will be selected as its discounted payback is < target of 4 years.

(e): Profitability index = present value of future cash flows/Initial investment

From figures provided in "a" above we have: profitability index of A = 32452.02/30000 = 1.08 and of B = 30722.84/30000 = 1.02. A will be selected as its profitability index is higher.

(f): average accounting return = average net income/average book value

A: [(13000+11000+9000+7000)/4] / [30000/2] = 10,000/15,000 = 66.67%

B: 5000/[30000/2] = 33.33%

A will be selected as its ARR is double of that of B.

(g): Crossover rate is the cost of capital where two projects have the same net present values (NPV) or where their NPV profiles intersect. Using the data from "a" we can find the cross over rate as shown below:

Thus cross over rate is 7.76%

(h):

The highlighted numbers (in bold) are the crossover rates. Thus rate = 7.76% at which NPV of A and B = $3,922.94