Question

An investment offers $5,000 per year for 10 years, with the first payment occurring 1 year from now. If the required return is 8 percent quarterly compounding, what is the value of the investment?

Answer 1

Here, the cash inflows will be same every year, so it is an annuity. We need to calculate present value of annuity. For calculating the present value of annuity, we will use the following formula:

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

where, PVA = Present value of annuity, P is the periodical amount = $5000, r is the rate of interest = 8% and n is the time period = 10

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

PVA = $5000 * (1 - (1 + 8%)^-10 / 8%)

PVA = $5000 * (1 - ( 1+ 0.08)^-10 / 0.08)

PVA = $5000 * (1 - ( 1.08)^-10 / 0.08)

PVA = $5000 * (1 - 0.46319348808) / 0.08)

PVA = $5000 * (0.536806651192 / 0.08)

PVA = $5000 * 6.710081399

PVA = $33550.41

So, value of investment today is $33550.41