Question

A firm is considering a group of 3 contingent projects. Each project is 5 years long and the firm has a cost of capital of 9%. The firm is certain of the cash flows for project A and project B. However, the firm is not sure of the annual cash flow for project C. Using the information, find the minimum annual cash flow for project C (year 1 to year 5) for the firm to accept all 3 projects?

	A	B	C
YEAR 0 CASH FLOW	-$100,000.00	-$150,000.00	-$275,000.00
YEAR 1 CASH FLOW	$25,000.00	$35,000.00	$???
YEAR 2 CASH FLOW	$25,000.00	$35,000.00	$???
YEAR 3 CASH FLOW	$25,000.00	$35,000.00	$???
YEAR 4 CASH FLOW	$25,000.00	$35,000.00	$???
YEAR5 5 CASH FLOW	$25,000.00	$35,000.00	$???

Answer 1

Sol. For calculating the annual cashflows for the Project C, we will use annuity formula:

Present value of annuity = C * [{1−(1+i)^-n } / i ] Where, C = Annual Cash flow

275,000 = C * [1 - {(1+0.09)^-5 } / 0.09 ] PV of annuity = Amount of outflow at year O

275,000 = C * [ {1 - 0.6499} / 0.09] i = cost of capital

275,000 = C * [0.3501/0.09] n = Period of incoming cashflow

C = 275000 / 3.89 = $70,694

Thus, the firms needs minimum $70,694 as inflows for all five years, in order to accept Project C