Sunday, 3 August 2014

Problem 8-1 Calculating Payback [LO 1] Consider the following cash flows: Year Cash Flow 0 –$6,800 1 1,950 2 4,100 3 1,750 4 1,450

Problem 8-1 Calculating Payback [LO 1]
Consider the following cash flows:

Year Cash Flow
0 –$6,800        
1 1,950        
2 4,100        
3 1,750        
4 1,450        


Required:
What is the payback period for the above set of cash flows? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

  Payback period years  


Explanation:
To calculate the payback period, we need to find the time the project needs to recover its initial investment. After two years, the project has created:
 
$1,950 + 4,100 = $6,050
 
in cash flows. The project still needs to create another:
 
$6,800 – 6,050 = $750
 
in cash flows. During the third year, the cash flows from the project will be $1,750. So, the payback period will be 2 years, plus what we still need to make divided by what we will make during the third year. The payback period is:
 
Payback = 2 + ($750 / $1,750)
Payback = 2.43 years

Kaleb Konstruction, Inc., has the following mutually exclusive projects available. The company has historically used a three-year cutoff for projects. The required return is 11 percent.

Kaleb Konstruction, Inc., has the following mutually exclusive projects available. The company has historically used a three-year cutoff for projects. The required return is 11 percent.

Year   Project F   Project G
0 –$ 139,000      –$ 209,000     
1   58,000        38,000     
2   52,000        53,000     
3   62,000        92,000     
4   57,000        122,000     
5   52,000        137,000     


Required:
(a)
Calculate the payback period for both projects. (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).)

  Payback period
  Project F years  
  Project G years  


(b)
Calculate the NPV for both projects. (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).)

  Net present value
  Project F $    
  Project G $    


(c) Which project should the company accept?
   
  Project G


Explanation:

Kerron Company is presented with the following two mutually exclusive projects. The required return for both projects is 19 percent. Year Project M Project N 0 –$140,000 –$355,000 1 63,500 152,500 2 81,500 180,000 3 72,500 137,500 4 58,500 110,000

Kerron Company is presented with the following two mutually exclusive projects. The required return for both projects is 19 percent.

Year Project M Project N
0 –$140,000      –$355,000     
1 63,500      152,500     
2 81,500      180,000     
3 72,500      137,500     
4 58,500      110,000     


Required:
(a)
What is the IRR for each project? (Do not round intermediate calculations. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)

     IRR  
  Project M %  
  Project N %  


(b)
What is the NPV for each project? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).)

         NPV  
  Project M $  
  Project N $  


(c) Which, if either, of the projects should the company accept?
   
  Project M


Explanation: (a)
The IRR for each project is:

  M: $140,000 = $63,500 / (1 + IRR) + $81,500 / (1 + IRR)2 + $72,500 / (1 + IRR)3 + $58,500 / (1 + IRR)4

Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

IRR = 34.47%

  N: $355,000 = $152,500 / (1 + IRR) + $180,000 / (1 + IRR)2 + $137,500 / (1 + IRR)3 + 110,000 / (1 + IRR)4

Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

IRR = 24.61%

The IRR decision rule implies we accept project M because the IRR for M is greater than the IRR for N.

(b)
The NPV for each project is:


  M: NPV = – $140,000 + $63,500 / 1.19 + $81,500 / 1.192 + $72,500 / 1.193 + $58,500 / 1.194
  NPV = $43,108.55

  N: NPV = – $355,000 + $152,500 / 1.19 + $180,000 / 1.192 + $137,500 / 1.193 + $110,000 / 1.194
  NPV = $36,709.17

The NPV criterion implies we accept project M because project M has a higher NPV than project N.

(c)
Accept project M since the NPV is higher. IRR cannot be used to rank mutually exclusive projects.
   
Calculator Solution:
 
Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.
    
Project M      
CFo
 –$140,000
CFo
 –$140,000
C01
 $63,500
C01
 $63,500
F01
 1
F01
 1
C02
 $81,500
C02
 $81,500
F02
 1
F02
 1
C03
 $72,500
C03
 $72,500
F03
 1
F03
 1
C04  $58,500 C04  $58,500
F04  1 F04  1
  CPT IRR   I = 19
  34.47%   NPV CPT
    $43,108.55
   
Project N      
CFo
 –$355,000
CFo
 –$355,000
C01
 $152,500
C01
 $152,500
F01
 1
F01
 1
C02
 $180,000
C02
 $180,000
F02
 1
F02
 1
C03
 $137,500
C03
 $137,500
F03
 1
F03
 1
C04  $110,000 C04  $110,000
F04  1 F04  1
  CPT IRR   I = 19
  24.61%   NPV CPT
    $36,709.17

Problem 8-9 Calculating NPV [LO 4] Consider the following cash flows: Year Cash Flow 0 –$ 32,000 1 14,200 2 17,500 3 11,600

Problem 8-9 Calculating NPV [LO 4]
Consider the following cash flows:

Year Cash Flow
0   –$ 32,000
1     14,200  
2     17,500  
3     11,600  


Requirement 1:
What is the NPV at a discount rate of zero percent? (Do not round intermediate calculations.)
Net present value $  

Requirement 2:
What is the NPV at a discount rate of 10 percent? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

  Net present value $  

Requirement 3:
What is the NPV at a discount rate of 20 percent? (Do not round intermediate calculations. Negative amount should be indicated by a minus sign.Round your answer to 2 decimal places (e.g., 32.16).)

  Net present value $  

Requirement 4:
What is the NPV at a discount rate of 30 percent? (Do not round intermediate calculations. Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places (e.g., 32.16).)

  Net present value $  


Explanation:
1:
The NPV of a project is the PV of the outflows plus the PV of the inflows. At a zero discount rate (and only at a zero discount rate), the cash flows can be added together across time. So, the NPV of the project at a zero percent required return is:
 
NPV = – $32,000 + 14,200 + 17,500 + 11,600
NPV = $11,300
 
2:
The NPV at a 10 percent required return is:
 
NPV = – $32,000 + $14,200 / 1.10 + $17,500 / 1.102 + $11,600 / 1.103
NPV = $4,087.15
 
3:
The NPV at a 20 percent required return is:
 
NPV = – $32,000 + $14,200 / 1.20 + $17,500 / 1.202 + $11,600 / 1.203
NPV = –$1,300.93
 
4:
And the NPV at a 30 percent required return is:
 
NPV = – $32,000 + $14,200 / 1.30 + $17,500 / 1.302 + $11,600 / 1.303
NPV = – $5,441.97
 
Notice that as the required return increases, the NPV of the project decreases. This will always be true for projects with conventional cash flows. Conventional cash flows are negative at the beginning of the project and positive throughout the rest of the project.
   
Calculator solution:
 
Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.
  
CFo
 –$32,000
CFo
 –$32,000
C01
 $14,200
C01
 $14,200
F01
 1
F01
 1
C02
 $17,500
C02
 $17,500
F02
 1
F02
 1
C03
 $11,600
C03
 $11,600
F03
 1
F03
 1
  I = 0%   I = 10%
  NPV CPT   NPV CPT
  $11,300.00   $4,087.15
   
CFo
 –$32,000
CFo
 –$32,000
C01
 $14,200
C01
 $14,200
F01
 1
F01
 1
C02
 $17,500
C02
 $17,500
F02
 1
F02
 1
C03
 $11,600
C03
 $11,600
F03
 1
F03
 1
  I = 20%   I = 30%
  NPV CPT   NPV CPT
  –$1,300.93   –$5,441.97

Problem 8-8 Calculating IRR [LO 3] Consider the following cash flows: Year Cash Flow 0 –$ 32,000 1 14,200 2 17,500 3 11,600

Problem 8-8 Calculating IRR [LO 3]
Consider the following cash flows:

Year Cash Flow
0   –$ 32,000  
1     14,200  
2     17,500  
3     11,600  


Required:
What is the IRR of the above set of cash flows? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

  Internal rate of return %  


Explanation:
The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equation that defines the IRR for this project is:
 
0 = – $32,000 + $14,200 / (1 + IRR) + $17,500 / (1 + IRR)2 + $11,600 / (1 + IRR)3
 
Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:
 
IRR = 17.32%
   
Calculator solution:
 
Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.
  
CFo
 –$32,000
C01
 $14,200
F01
 1
C02
 $17,500
F02
 1
C03
 $11,600
F03
 1
  IRR CPT
  17.32%

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:

A firm evaluates all of its projects by applying the IRR rule. Year Cash Flow 0 –$ 158,000 1 58,000 2 81,000 3 65,000

A firm evaluates all of its projects by applying the IRR rule.

Year Cash Flow
0 –$ 158,000       
1 58,000       
2 81,000       
3 65,000       


Requirement 1:
What is the project's IRR? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

  Internal rate of return    %  

Requirement 2:
If the required return is 15 percent, should the firm accept the project?
No


Explanation: