A project that provides annual cash flows of $16,500 for nine years costs $71,00

Question

A project that provides annual cash flows of $16,500 for nine years costs $71,000 today. What is the NPV for the project if the required return is 8 percent? (Do not round intermediate calculations. Round your answer to 2 decimal places, e.g., 32.16.) NPV $ At a required return of 8 percent, should the firm accept this project? Accept Reject What is the NPV for the project if the required return is 20 percent? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) NPV $ At a required return of 20 percent, should the firm accept this project? Accept Reject At what discount rate would you be indifferent between accepting the project and rejecting it? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Discount rate %

Explanation / Answer

NPV is the net present value for evaluting the profitability of the project considering the time value of money. If the sum total of all the present value of all future inflows is greater than the present value of investments, then the project is viable

NPV = Present value of cash inflows - Initial investment =

NPV = {Net Period Cash Flow/(1+R)^T} - Initial Investment

a) considering the required rate of return at 8%

Since the cashflows are even throughout the 9 years, the formula for calculating the present value of inflows is

= 16,500x (1-(1.08)-9/0.08 = $103,073.65

NPV = 103,073.65 - 71,000 = $32,073.65

Since NPV is positive, the firm should accept this project at 8% required return

b) Considering the required rate of return at 20%

present value of inflows = = 16,500x (1-(1.2)-9/0.2 = $66,510.95

NPV = $66,510.95 - $71,000 = (4,489.05)

Since NPV is negative, the firm should reject the project at 20% required return

c) calculating the indifferent point - This is the rate at which both the present value of inflows and investments will match. This is called as Internal Rate of Return (IRR)

Here the present value of cash flows should be equal to $71,000

$71,000 = 16,500x (1-(1+r)-9/r

We can arrive at this rate by trial and error method since at 20%, we got the inflows at $66,510.95 hence it will be between 20% to 8%

at 19% = $68,694.99

at 18% = $70,999.86

Hence at 18%, the firm would be indifferent to accepting or rejecting the project

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