Question

10. Consider an investment costing $20,000. This investment will generate leveled cash flows for 8 years. If the interest rate is 8 percent, what is the amount of each cash flow? Make sure to show your work.

Answer 1

Here, the cash inflows will be same every year, so it is an annuity. For calculating the cash flows, we will use the present value of annuity formula as per below:

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

where, PVA = Present value of annuity = $20000, P is the periodical amount, r is the rate of interest =8%, and n is the time period = 8

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

$20000 = P * (1 - (1 + 8%)^-8 / 8%)

$20000 = P * (1 - ( 1+ 0.08)^-8 / 0.08)

$20000 = P * (1 - ( 1.08)^-8 / 0.08)

$20000 = P * (1 - 0.5402688845) / 0.08)

$20000 = P * (0.45973111549 / 0.08)

$20000 = P * 5.74663894373

P = $20000 / 5.74663894373

P = $3480.29

So. amount of each cash flow is $3480.29.