Westerlo needs to resurface a section of its roads this spring. The town council
ID: 2384117 • Letter: W
Question
Westerlo needs to resurface a section of its roads this spring. The town council is considering using one of two technologies. The first involves putting down stone and gravel and grading the road on an annual basis. The second involves the application of a road surface called sure-pack. Sure-Pack only requires maintenance every five years. Based on experience, the counselors know the gravel road will last ten years. The folks in Berne, the next town up route 1, Sure-Packed their roads and expect to get 15 years from them before they will need to be resurfaced again. The cash flows for each alternative are shown in the table below.
Period
Gravel
Sure-Pack
0
$200,000
$300,000
1
$15,000
2
$15,000
3
$15,000
4
$15,000
5
$15,000
$45,000
6
$15,000
7
$15,000
8
$15,000
9
$15,000
10
$15,000
$45,000
11
12
13
14
15
If Westerlo’s cost of capital is 9%, which alternative should they choose? Support your answer with the appropriate time-value-of-money calculations.
Period
Gravel
Sure-Pack
0
$200,000
$300,000
1
$15,000
2
$15,000
3
$15,000
4
$15,000
5
$15,000
$45,000
6
$15,000
7
$15,000
8
$15,000
9
$15,000
10
$15,000
$45,000
11
12
13
14
15
Explanation / Answer
First of All, these are all cash outflows, that is they should be negative.
Cost of Capital = 9%
We will use the Equivalent Annual Annuity Method to determine which alternative to choose. The steps of the method are as follows:
1. Net Present Value of both the alternatives is calculated.
2. For each project, EAA is calculated that is, the expected payment over the project's life, where the future value of the project would equal zero.
3. The alternative with a lower EAA is will be chosen as the present value will be negative (because there is no cash inflow)
Alternative 1 : Gravel
Cost of Capital = 9%
Therefore, present value = -$296264.87
No of periods =10
Cost of Capital = 9%
PV = -$296264.87
EAA (calculated as PMT ) = $46164.02
Alternative 2 : Sure Pack
Cost of Capital = 9%
Therefore, present value = -$348255.40
No of periods =15
Cost of Capital = 9%
PV = -$348255.40
EAA (calculated as PMT ) = $43204.18
Now, comparing EAA for both alternatives
Alternative 1 - Gravel - EAA = $46164.02
Alternative 2 - Sure Pack - EAA = $43204.18
Since EAA for Sure Pack is lower than that of Gravel, Alternative 2 (Sure Pack) should be chosen.
Period Gravel Present Value 0 -200000.00 -200000.00 1 -15000.00 -13761.47 2 -15000.00 -12625.20 3 -15000.00 -11582.75 4 -15000.00 -10626.38 5 -15000.00 -9748.97 6 -15000.00 -8944.01 7 -15000.00 -8205.51 8 -15000.00 -7527.99 9 -15000.00 -6906.42 10 -15000.00 -6336.16 NPV -296264.87Related Questions
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