A project that provides annual cash flows of $16,300 for eight years costs $69,000 today.

Problem 9-9 Calculating NPV and IRR [LO1, 5]

A project that provides annual cash flows of $16,300 for eight years costs $69,000 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.) Explanation Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. The NPV of a project is the PV of the inflows minus the PV of the outflows. Since the cash inflows are an annuity, the equation for the NPV of this project at required return of 7 percent is:   NPV = –$69,000 + $16,300(PVIFA7%, 8) = $28,332.17   At a required return of 7 percent, the NPV is positive, so we would accept the project.   The equation for the NPV of the project at a required return of 19 percent is:   NPV = –$69,000 + $16,300(PVIFA19%, 8) = –$4,543.84   At a required return of 19 percent, the NPV is negative, so we would reject the project.   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 = –$69,000 + $16,300(PVIFAIRR, 8)   IRR = 16.81%    Calculator Solution:   Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.                CFo  –$69,000 CFo  –$69,000 CFo  –$69,000 C01  $16,300 C01  $16,300 C01  $16,300 F01  8 F01  8 F01  8   I = 7%   I = 19%   IRR CPT   NPV CPT   NPV CPT   16.81%   $28,332.17   –$4,543.84

A firm evaluates all of its projects by applying the NPV decision rule. A project under consideration has the following cash flows:

Problem 9-8 Calculating NPV [LO1]

A firm evaluates all of its projects by applying the NPV decision rule. A project under consideration has the following cash flows:

  

Year	Cash Flow
0	–$	28,600
1		12,600
2		15,600
3		11,600

  

What is the NPV for the project if the required return is 11 percent?

Explanation

The NPV of a project is the PV of the inflows minus the PV of the outflows. The equation for the NPV of this project at an 11 percent required return is:

NPV = –$28,600 + $12,600/1.11 + $15,600/1.112 + $11,600/1.113 = $3,894.48

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

The equation for the NPV of the project at a required return of 25 percent is:

NPV = –$28,600 + $12,600/1.25 + $15,600/1.252 + $11,600/1.253 = –$2,596.80

At a required return of 25 percent, the NPV is negative, so we would reject the project.

  

Calculator Solution:

    

CFo	–$28,600	CFo	–$28,600
C01	$12,600	C01	$12,600
F01	1	F01	1
C02	$15,600	C02	$15,600
F02	1	F02	1
C03	$11,600	C03	$11,600
F03	1	F03	1
I = 11%		I = 25%
NPV CPT		NPV CPT
$3,894.48		–$2,596.80