Question

Suppose you are offered an investment that will pay you $2,975 a month for 15 years. If your required return is 9% per year, compounded monthly, what would you be willing to pay for this investment?

Answer 1

Here, the cash inflows will be same every month, so it is an annuity. We need to calculate the present value of annuity, by the following formula:

PVA = P * (1 - (1 + r)^-n / r)

where, PVA = Present value of annuity, P is the periodical amount = $2975, r is the rate of interest =9% compounded monthly, so monthly rate = 9% 12 = 0.75% and n is the time period = 15 * 12 = 180 months

Now, putting these values in the above formula, we get,

PVA = $2975 * (1 - (1 + 0.75%)^-180 / 0.75%)

PVA = $2975 * (1 - ( 1+ 0.0075)^-180 / 0.0075)

PVA = $2975 * (1 - ( 1.0075)^-180 / 0.0075)

PVA = $2975 * (1 - 0.26054943373) / 0.0075)

PVA = $2975 * (0.73945056626 / 0.0075)

PVA = $2975 * 98.5934088351

PVA = $293315.39

So, we would be willing to pay $293315.39 for this investment.