A project that provides annual cash flows of $16,700 for ten years costs $73,000

Question

A project that provides annual cash flows of $16,700 for ten years costs $73,000 today.

What is the NPV for the project if the required return is 9 percent? (Do not round intermediate calculations. Round your answer to 2 decimal places, e.g., 32.16.)

At a required return of 9 percent, should the firm accept this project?

What is the NPV for the project if the required return is 21 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 21 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 $16,700 for ten years costs $73,000 today.

Explanation / Answer

Answer:

1) Calculation of Net Present Value (if required rate of return is 9 percent)

Present Value of Cash Flow = Annual Cash Flow x PVIFA (9%, 10 years)

Present Value of Cash Flow = $16,700 x 6.418 = $107,180.60

Net Present Value = Present Value of Cash Flow – Present Value of Cash Outflow = $107,180.60 - $73,000 = $34,180.60

NPV = $34,180.60

The firm should accept this project since the NPV is positive at 9 percent required return.

2) Calculation of Net Present Value (if required rate of return is 21 percent)

Present Value of Cash Flow = Annual Cash Flow x PVIFA (21%, 10 years)

Present Value of Cash Flow = $16,700 x 4.054 = $67,701.80

Net Present Value = Present Value of Cash Flow – Present Value of Cash Outflow = $67,701.80 - $73,000 = -$5,298.20

NPV = -$5,298.20

The firm should reject this project since the NPV is negative at 21 percent required return.

3) At Internal Rate of Return (discount rate) the decision regarding accepting and rejecting the project would be indifferent. IRR is calculated on the basis of trial & error method.

Internal Rate of Return is a discounting rate at which Net Present Value of project equals to ZERO. In other word, Present Value of Cash flow is equals to Present Value of Outflow.

Internal Rate of Return (IRR) = Lower Rate + (NPV at Lower Rate / NPV at lower – NPV at higher rate) x Difference in Rate

Let Assume Lower Rate is 18.75%

NPV at lower rate = ($16,700*4.3769) - $73,000 = $94.23

Since, NPV calculate above is positive. Increase the discounting rate.

Let high rate = 18.80%

NPV at Higher Rate = (16,700*4.3692) - $73,000 = -$34.36

IRR = 18.75% + [94.23 / (94.23 -(-34.36)] x (18.8%-18.75%)

IRR = 18.75% + (94.23 / 128.59) x 0.5%

IRR = 18.75% + 0.7328 x 0.05%

IRR = 18.75% + 0.0366% = 18.786%

At discount rate 18.786%, the decision regarding accepting and rejecting the project would be indifferent. At 18.786% discount rate NPV become ZERO..

***********************

Verification---

NPV at 18.786% = (16,700*4.3712) - 73,000

= $72,999 or $73,000 - $73,000

= 0 or ZERO

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