Question

One maintenance contract is free for two years and is followed by three years of $5,000 payments, while the other is $2,300 per year for five years the contract are equivalent if the interest rate is ?

Answer 1

We need to calculate the NPV at a rate where the following equation is satisfied:

$\frac{5000}{(1+r)^3}+\frac{5000}{(1+r)^4}+\frac{5000}{(1+r)^5} =\frac{2300}{(1+r)^1}+\frac{2300}{(1+r)^2}+\frac{2300}{(1+r)^3}+\frac{2300}{(1+r)^4}+\frac{2300}{(1+r)^5}$

Here the assumption that we have made is that all payments are done at the end of the year. Above equation can only be solved through hit and trial method or using financial calculator or excel.

Solving the LHS using a rate of 25.91% we get the PV of 6074.36 and using the same rate for the RHS we get a PV of 6071.71 as the difference between these two PVs is almost negligible, we can consider this rate to be the rate we are seeking or else we can also increase the decimal digits to further hit an try.