Question

A town’s recreation department is trying to decide how to use a piece of land. One option is to put up basketball courts with an expected life of eight years. Another is to install a swimming pool with an expected life of 24 years. The basketball courts would cost $180,000 to construct and yield net benefits of $40,000 at the end of each of the eight years. The swimming pool would cost $2.25 million to construct and yield net benefits of $170,000 at the end of each of the 24 years. Each project is assumed to have zero salvage value at the end of its life.

Required:

Using a real discount rate of 4 percent, which project offers larger net benefits?

Pls be detailed.

 

Answer 1

As these are two are different projects with different timelines and different investment amounts we can conclude which one of them is better by calculating the Net Present Value of the two projects and comparing them. Which ever project has higher NPV we'll select that particular project.

Basketball Court

Year	Cash flow	Discount	Discounted cashflows
0	$ (1,80,000.00)	1	$           (1,80,000.00)
1	$     40,000.00	0.962	$                38,461.54
2	$     40,000.00	0.925	$                36,982.25
3	$     40,000.00	0.889	$                35,559.85
4	$     40,000.00	0.855	$                34,192.17
5	$     40,000.00	0.822	$                32,877.08
6	$     40,000.00	0.790	$                31,612.58
7	$     40,000.00	0.760	$                30,396.71
8	$     40,000.00	0.731	$                29,227.61
NPV	$                89,309.79

In above table assume investment is in year 0. As in question it is mentioned that cashflows of $40,000 are for 8 years. Year 0 cashflow is negative as it is an expense (or investment) all others are cashflows from the investment.

Discount for Year 1 is

Discount for Year 2 is

Similary discount is calculated for all other years. Using excel would make task easier.

By doing so we get a profit of $89,309.8 by making $180,000 investment on Basketball court.

Swimming Pool

Year	Cash flow	Discount	Discounted cashflows
0	$ (22,50,000.00)	1	$          (22,50,000.00)
1	$    1,70,000.00	0.9615	$             1,63,461.54
2	$    1,70,000.00	0.9246	$             1,57,174.56
3	$    1,70,000.00	0.8890	$             1,51,129.38
4	$    1,70,000.00	0.8548	$             1,45,316.71
5	$    1,70,000.00	0.8219	$             1,39,727.61
6	$    1,70,000.00	0.7903	$             1,34,353.47
7	$    1,70,000.00	0.7599	$             1,29,186.03
8	$    1,70,000.00	0.7307	$             1,24,217.33
9	$    1,70,000.00	0.7026	$             1,19,439.75
10	$    1,70,000.00	0.6756	$             1,14,845.91
11	$    1,70,000.00	0.6496	$             1,10,428.76
12	$    1,70,000.00	0.6246	$             1,06,181.50
13	$    1,70,000.00	0.6006	$             1,02,097.59
14	$    1,70,000.00	0.5775	$                98,170.76
15	$    1,70,000.00	0.5553	$                94,394.97
16	$    1,70,000.00	0.5339	$                90,764.39
17	$    1,70,000.00	0.5134	$                87,273.45
18	$    1,70,000.00	0.4936	$                83,916.78
19	$    1,70,000.00	0.4746	$                80,689.21
20	$    1,70,000.00	0.4564	$                77,585.78
21	$    1,70,000.00	0.4388	$                74,601.71
22	$    1,70,000.00	0.4220	$                71,732.42
23	$    1,70,000.00	0.4057	$                68,973.48
24	$    1,70,000.00	0.3901	$                66,320.65
NPV	$             3,41,983.73

By following same procedure as above we get net profit of $341,983.7 by making a $2.25 million investment on swimming pool.

As NPV of Swimming Pool is greater than that of Basket ball court, it is better to construct a swimming pool.