Question

A business has two investment choices. Alternative 1 requires an immediate outlay of $1,100 and offers a return of
$5,000 in eight years. Alternative 2 requires an immediate outlay of $700 in return for which $200 will be received at the end of every six months for the next eight years. The required rate of return on investment is 11% semi-annually. Compute the net present value of each alternative and determine which investment should be accepted or rejected according to the net present value criterion.

Answer 1

Hello Sir/ Mam

As the rate is 11% semi-annually, lets' break 1 year into 2 periods of 6 months each.

Alternative 1

Time Period	Cashflow	PVF	PV
0	-$1,100.00	1.00	-$1,100.00
1	$0.00	0.95	$0.00
2	$0.00	0.90	$0.00
3	$0.00	0.85	$0.00
4	$0.00	0.81	$0.00
5	$0.00	0.77	$0.00
6	$0.00	0.73	$0.00
7	$0.00	0.69	$0.00
8	$0.00	0.65	$0.00
9	$0.00	0.62	$0.00
10	$0.00	0.59	$0.00
11	$0.00	0.55	$0.00
12	$0.00	0.53	$0.00
13	$0.00	0.50	$0.00
14	$0.00	0.47	$0.00
15	$0.00	0.45	$0.00
16	$5,000.00	0.42	$2,122.91
NPV			$1,022.91

Alternative 2

Time Period	Cashflow	PVF	PV
0	-$700.00	1.00	-$700.00
1	$200.00	0.95	$189.57
2	$200.00	0.90	$179.69
3	$200.00	0.85	$170.32
4	$200.00	0.81	$161.44
5	$200.00	0.77	$153.03
6	$200.00	0.73	$145.05
7	$200.00	0.69	$137.49
8	$200.00	0.65	$130.32
9	$200.00	0.62	$123.53
10	$200.00	0.59	$117.09
11	$200.00	0.55	$110.98
12	$200.00	0.53	$105.20
13	$200.00	0.50	$99.71
14	$200.00	0.47	$94.51
15	$200.00	0.45	$89.59
16	$200.00	0.42	$84.92
NPV			$1,392.43

As the NPV of both the projects are positive, hence, as nothing is mentioned about nature of projects, accept both the projects.

Case	Project 1	Project 2
Independent Projects	Accept	Accept
Mutually Exclusive Projects	Reject	Accept

Thanks!

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