Question

You are working on a bid for a contract. Thus far, you have determined that you will need $156,000 for fixed assets and another $32,000 for net working capital at Time 0. You have also determined that you can recover $68,400 after-tax for the combined fixed assets and net working capital at the end of the 4-year project. What must be the annual operating cash flow each year, if the IRR of the project is 16 percent ?

Select one:

a. $50,725.50

b. $55,200.16

c. $48,929.74

d. $46,666.67

e. $53,686.06

Answer 1

Option (e) is the answer.

IRR is the rate at which present value of cash inflows is equal to the present value o cash outflows or initial investment.

Here,Initial investment = $156000 + $132000 (as investment in fixed assets and net working capital)

Initial investment = $188000

Now, present value of cash inflows = Present value of annual operating cash flows + Present value of cash flow after year 4

Present value of cash inflows = Annual operating cash flow * PVIFA (16%, 4 years) + $68400 * PVIF (16%, 4 years)

where, PVIFA (16%, 4 years) is the present value of annuity at 16% for 4 years and PVIF (16%,4 years) is the present value at 16% after 4 years. The value of PVIFA(16%, 4 years) will be found out from present value annuity table at the value of PVIF (16%, 4 years) will be found out from present value table.

Let A be the annual operating cash flows.

Now, at IRR = 16% , Present value of cash inflows = Initial investment

Putting the values in the statement, we get,

$188000 = A * PVIFA (16%, 4 years) + $68400 * PVIF (16%,4 years)

$188000 = A*$2.8 + $68400 * 0.55

$188000 = A*$2.801 + $37620

$188000 - $37756.8 = A *$2.801

$150380 = A*$2.801

A = $150380 / $2.801

A = $53687, which is the required annual cash flows.