A service bureau is considering renting a computer for $24$ months at $\$15,000$ per month. The first $11$ months will be required to test software for the particular application to be offered by the firm. During each of the remaining $13$ months, the service is expected to yield $\$32,000$ in revenue. On a present value basis, is the investment worthwhile if the interest rate is $1\%$ per month, compounded monthly? Is it worthwhile at an interest rate of $1.25\%$ per month? (Assume payments and income flow at the beginning of each month.)
(For just the 1% case)
Simple analysis shows:
24 months $\times$ \$15,000/month = \$ 360,000 cost
13 months of revenue $\times$ 32,000/month = \ 416,000 revenue
Net value = 416k - 360k = \ 56,000
So for present value of these payments we use the equation:
$ PVs(p,D,m) = p \cdot \frac{ 1-D^m } {1-D} $ where $D$ is discount rate (of interest rate) $= \dfrac{1}{1+r}$ , $m$ is series of payments $= 24$, $p$ is monthly cash flow $= \$15,000$.
So the present value of the 15k spent for 24 months is $ 15000 \cdot \frac{(1-.99^{24})}{(1-.99)} = \$ 321,482 ,$ (vs. the $\$ 360,000$).
The question is - do I need to get the present value of the 32k a month in revenue to compare?
PVs(32k,D,13) of revenue = \391,932 (vs. 416,000) .
-> Giving present net value 391,932 - 321,482 = \ 70,450 (vs. \$ 56,000)?