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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)?

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@srivatsan: thank you for the edit, i am new here. how did you convert the image to text, did you type it all out?? – Greg McNulty Oct 23 '11 at 1:22
Yes, I typed it out. – Srivatsan Oct 23 '11 at 2:24
up vote 2 down vote accepted

Almost, but no cigar: yes, you have to get the NPV of the revenues, but you calculation takes it back to the start of the revenues when you need to bring it back to the start of the whole exercise so you can compare it with the NPV of the rental costs.

So using you method, you should multiply $391,932$ by $0.99^{11}$. Personally, if the interest rate is 1% then I would be dividing by $\frac{101}{100}$ throughout this exercise, rather your multiplying by $\frac{99}{100}$, though the difference is small.

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Thank you very much! – Greg McNulty Oct 23 '11 at 1:33

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