Answer:
3 years
Explanation:
<u>First method</u>
The PV of the investment can be written as:
PV1 = $15,000 + $32,500/(1+0.06)^n
<u>Second method</u>
The PV of the investment can be written as:
PV2 = $23,000 + $23,000/(1+0.06)^n
After n years both projects will be economically equal. Hence their present value must be equal PV1 = PV2
$15,000 + $32,500/(1.06)^n = $23,000 + $23,000/(1.06)^n
$23,000 - $15,000 = $32,500/(1.06)^n - $23,000/(1.06)^n
$8,000 = $9,500/(1.06)^n
(1.06)^n = $9,500/$8,000
(1.06)^n = 1.1875
Taking log on both sides we get:
nlog1.06 = log 1.1875
n = log 1.1875/log 1.06
n = 0.07463361829/0.02530586526
n = 2.94926166417121
n = 3
So, the answer is 3 years
