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%.

(4). 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.

Explain why.

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

(6). 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%.

(7). Define and find the crossover rate.

(8). 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

Solution:-

To Calculate Discounted Payback Period-

Discounted Payback Period formula =

Project A-

Discounted Payback Period of Project A
Year	Cash flow	Discounting Factor @10%	Discounted Cash flows	Cummulative Discounted Cash flows
0	-30000	1.00	-30000
1	13000	0.909	11818.18	11818.18
2	11000	0.826	9090.91	20909.09
3	9000	0.751	6761.83	27670.92
4	7000	0.683	4781.09	32452.02

Discounted Payback Period =

Discounted Payback Period = 3.487 years

Project B-

Discounted Payback Period of Project B
Year	Cash flow	Discounting Factor @10%	Discounted Cash flows	Cummulative Discounted Cash flows
0	-30000	1.00	-30000
1	5000	0.909	4545.45	4545.45
2	5000	0.826	4132.23	8677.69
3	5000	0.751	3756.57	12434.26
4	5000	0.683	3415.07	15849.33
5	5000	0.621	3104.61	18953.93
6	5000	0.564	2822.37	21776.30
7	5000	0.513	2565.79	24342.09
8	5000	0.467	2332.54	26674.63
9	5000	0.424	2120.49	28795.12
10	5000	0.386	1927.72	30722.84

Discounted Payback Period =

Discounted Payback Period = 9.63 years

Discounted payback period is lower the Better. Hence, Accept Project A.

To Calculate Profitability Index-

Profitability Index Formula =

Project A -

Present Value of Future Cash Flows for Project A
Year	Cash flow	Discounting Factor @10%	Discounted Cash flows
1	13000	0.909	11818.18
2	11000	0.826	9090.91
3	9000	0.751	6761.83
4	7000	0.683	4781.09
		Present Value	32452.02

Profitability Index =

Profitability Index = 1.08

Project B-

Present Value of Future Cash Flows for Project B
Year	Cash flow	Discounting Factor @10%	Discounted Cash flows
1	5000	0.909	4545.45
2	5000	0.826	4132.23
3	5000	0.751	3756.57
4	5000	0.683	3415.07
5	5000	0.621	3104.61
6	5000	0.564	2822.37
7	5000	0.513	2565.79
8	5000	0.467	2332.54
9	5000	0.424	2120.49
10	5000	0.386	1927.72
		Present Value	30722.84

Profitability Index =

Profitability Index = 1.024

Profitability Index is a measure of Projects attractiveness. An project whose PI is greater than 1 is good investment. In Mutually Exclusive Projects Choose Higher PI Project. Choose Project A.

To Calculate Average Accounting Return-

Average Accounting Return Formula =

Project A -

Average Accounting Return =

Average Accounting Return = 33.33%

Project B -

Average Accounting Return =

Average Accounting Return = 16.67%

Company Accounting Rate of Return is 20%. Best is higher the Better. So Choose Project AA.

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