A project that provides annual cash flows of $17,200 for eight years costs $78,0

Question

A project that provides annual cash flows of $17,200 for eight years costs $78,000 today. What is the NPV for the project if the required returm is 7 percent? (Do not round intermediate calculations. Round your answer to 2 decimal places, e.g., 32.16.) NPV $ 24705.33 At a required return of 7 percent, should the firm accept this project? Accept Reject 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.) NPV $ -9984.91 At a required return of 19 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 14.68 %

Explanation / Answer

NPV of Project = Present Value of Cash Inflow - Present Value of cash Outflow

= $ 17,200 * 1/( 1.07) ^ 1 +$ 17,200 * 1/( 1.07) ^ 2 + $ 17,200 * 1/( 1.07) ^ 3 +... + $ 17,200 * 1/( 1.07) ^ 8 - $ 78,000

= $ 24,706.33

Since the NPV is positive, the project should be accepted.

NPV of Project = Present Value of Cash Inflow - Present Value of cash Outflow

= $ 17,200 * 1/( 1.19) ^ 1 +$ 17,200 * 1/( 1.19) ^ 2 + $ 17,200 * 1/( 1.19) ^ 3 +... + $ 17,200 * 1/( 1.19) ^ 8 - $ 78,000

= - $ 9,984.91

Since the NPV is positive, the project should be Reject.

Let the IRR be x.

Now , Present Value of Cash Outflows=Present Value of Cash Inflows

78,000= 17,200/(1.0x) + 17,200/ (1.0x)^2 + 17,200/ (1.0x)^3+ 17,200/ (1.0x)^4+ 17,200/ (1.0x)^5+ 17,200/ (1.0x)^6+ 17,200/ (1.0x)^7+ 17,200/ (1.0x)^8

Or x= 14.68%

Hence the IRR is 14.68%

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