A project that provides annual cash flows of $16,600 for eight years costs $72,0

Question

A project that provides annual cash flows of $16,600 for eight years costs $72,000 today.

  

What is the NPV for the project if the required return is 7 percent? (Do not round intermediate calculations. Round your answer to 2 decimal places, e.g., 32.16.)

  

  

At a required return of 7 percent, should the firm accept this project?

  

What is the NPV for the project if the required return is 19 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.)

  

At a required return of 19 percent, should the firm accept this project?

  

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.)

A project that provides annual cash flows of $16,600 for eight years costs $72,000 today.

Explanation / Answer

Net Present Value = Present value of cash outflow - Present value of cash inflows

If NPV is positive, the project can be accepted.

Formula for calculating the PV = FV / (1+r)n

Since NPV is positve, the project can be accepted

Considering the required return at 19%, here is the calculation of NPV

At 19%, the firm should not accept the project as the NPV is negative.

Lastly, the ask is the rate at which the project is indifferent to accepting or rejecting it. This is called as internal rate of return. This can be done by trial and error method.

Now we know that the project is negative at 19% and positive at 7% hence the indifferent rate will be inbetween these two.

At 15%, NPV = $2,489

At 16%, NPV = $103

Since at 16%, the NPV is zero hence the indifferent rate is 16%

Years cash flows PV value at 7% Present value Cumulative cash flow 1 16600                  1.0700                    15,514.02                          15,514.02 2 16600                  1.1449                    14,499.08                          30,013.10 3 16600                  1.2250                    13,550.54                          43,563.65 4 16600                  1.3108                    12,664.06                          56,227.71 5 16600                  1.4026                    11,835.57                          68,063.28 6 16600                  1.5007                    11,061.28                          79,124.56 7 16600                  1.6058                    10,337.65                          89,462.20 8 16600                  1.7182                       9,661.35                          99,123.56                    99,123.56 Less Cash outflow                    72,000.00 NPV $                    27,123.56

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