Problem 8-7 Calculating NPV and IRR [LO 3, 4] A project that provides annual cash flows of $2,800 for nine years costs $9,200 today. Requirement 1: At a required return of 11 percent, what is the NPV of the project? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Problem 8-7 Calculating NPV and IRR [LO 3, 4]

A project that provides annual cash flows of $2,800 for nine years costs $9,200 today.

Requirement 1:

At a required return of 11 percent, what is the NPV of the project? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

NPV

$

Requirement 2:

At a required return of 27 percent, what is the NPV of the project? (Do not round intermediate calculations. A negative amount should be indicated by a minus sign. Round your answer to 2 decimal places (e.g., 32.16).)

NPV

$

Requirement 3:

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 percentage rounded to 2 decimal places (e.g., 32.16).)

Discount rate

%

Explanation:

1:

The NPV of a project is the PV of the outflows plus the PV of the inflows. Since the cash inflows are an annuity, the equation for the NPV of this project at an 11 percent required return is:

NPV = – $9,200 + $2,800(PVIFA11%, 9)

NPV = $6,303.73

At an 11 percent required return, the NPV is positive, so we would accept the project.

2:

The equation for the NPV of the project at a 27 percent required return is:

NPV = – $9,200 + $2,800(PVIFA27%, 9)

NPV = –$36.22

At a 27 percent required return, the NPV is negative, so we would reject the project.

3:

We would be indifferent to the project if the required return was equal to the IRR of the project, since at that required return the NPV is zero. The IRR of the project is:

0 = – $9,200 + $2,800(PVIFAIRR, 9)

IRR = .2686, or 26.86%

   

Calculator Solution:

 

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

  

CFo	–$9,200	CFo	–$9,200	CFo	–$9,200
C01	$2,800	C01	$2,800	C01	$2,800
F01	9	F01	9	F01	9
I = 11%		I = 27%		IRR CPT
NPV CPT		NPV CPT		26.86%
$6,303.73		–$36.22