Question

Answer the question. Calculate the rate of return of the 3-year project described below using the ERR method, assuming 8% reinvestment rate. Use the calculated rate of return of the project to determine whether the project should be accepted, assuming investors' opportunity cost of capital is 15%. The project requires $800,000 initial investment, and brings in net cash flows equal to $400,000 in year 1, 5500,000 in year 2, and $600,000 in year 3. In addition, there is a $100,000 salvage value at the end of year 3. X I B Ff

please solve in the word format

Answer 1

As a first step we need to find the future value of all the positive cash flows at the end of the terminal year i.e. at the end of year 3. Future value of a cash flow occurring at any time t, at the end of year n will be given by FV = C_t x (1 + r)^{n - t} where r is the reinvestment rate.

In our case, n = terminal year = 3

r = 8%

Hence, FV = C_t x (1 + 8%)^{3 - t} = C_t x 1.08^{3 - t}

Please see the table below:

Year, t	Cash flows	Reinvestment period	Future Value
		3 - t	FV = Ct x 1.083 - t
1	400,000	2	466,560
2	500,000	1	540,000
3	700,000	0	700,000
Total			1,706,560

Cash flows in year 3 = Project cash flows + salvage value = 600,000 + 100,000 = 700,000

Initial investment = 800,000

Hence, ERR will be given by the formula:

FV = Initial investment x (1 + ERR)ⁿ

Or, 1,706,560 = 800,000 x (1 + ERR)³

Hence, ERR = (1,706,560 / 800,000)^1/3 - 1 = 28.73%

Since ERR > opportunity cost of capital of 15%, hence the project should be accepted.