Suppose you are offered an investment that will pay you $2,975 a month for 15 years....

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?

Solutions

Expert Solution

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.

jeff jeffy answered 2 years ago

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