Concept explainers
LO1, LO3, LO4, LO6 15. Comparing Investment Criteria. Consider the following two mutually exclusive projects:
Year | Cash Flow (A) | Cash Flow (B) |
0 | –$235,000 | –$47,000 |
1 | 29,000 | 28,700 |
2 | 45,000 | 19,900 |
3 | 51,000 | 17,300 |
4 | 325,000 | 16,200 |
Whichever project you choose, if any, you require a return of 13 percent on your investment.
a. If you apply the payback criterion, which investment will you choose? Why?
b. If you apply the
c. If you apply the
d. If you apply the profitability index criterion, which investment will you choose? Why?
e. Based on your answers in parts (a) through (d), which project will you finally choose? Why?
a)
To compute: The payback period.
Introduction:
Capital budgeting is a process, where the business identifies and assesses potential investments or expenses that are larger (in general).
Answer to Problem 15QP
Explanation of Solution
Given information:
The cash flows for two mutually exclusive projects are $29,000, $45,000, $51,000, $325,000 for Project A for year 1, year 2, year 3, and year 4 respectively. Project A has an initial investment of $235,000. The cash flows of Project B are $28,700, $19,900, $17,300, and $16,200 for year 1, year 2, year 3, and year 4 respectively. The initial investment for Project B is $47,000. The rate of return is 13%.
Formula to compute the payback period of a project:
Compute the payback period of a project for Project A:
Hence, the payback period is 3.34 years for Project A.
Compute the payback period of a project for Project B:
Hence, the payback period is 1.92 years for Project B.
b)
To compute: The NPV (Net Present Value).
Introduction:
Capital budgeting is a process, where the business identifies and assesses potential investments or expenses that are larger (in general).
Answer to Problem 15QP
Explanation of Solution
Given information:
The cash flows for two mutually exclusive projects are $29,000, $45,000, $51,000, $325,000 for Project A for year 1, year 2, year 3, and year 4 respectively. Project A has an initial investment of $235,000. The cash flows of Project B are $28,700, $19,900, $17,300, and $16,200 for year 1, year 2, year 3, and year 4 respectively. The initial investment for Project B is $47,000. The rate of return is 13%.
Formula to calculate the NPV:
Calculate the NPV for Project A:
Hence, the NPV for Project A is $60,579.46.
Calculate the NPV for Project B:
Hence, the NPV for Project B is $15,908.38.
c)
To compute: The IRR for the project.
Introduction:
Capital budgeting is a process, where the business identifies and assesses potential investments or expenses that are larger (in general).
Answer to Problem 15QP
Explanation of Solution
Given information:
The cash flows for two mutually exclusive projects are $29,000, $45,000, $51,000, $325,000 for Project A for year 1, year 2, year 3, and year 4 respectively. Project A has an initial investment of $235,000. The cash flows of Project B are $28,700, $19,900, $17,300, and $16,200 for year 1, year 2, year 3, and year 4 respectively. The initial investment for Project B is $47,000. The rate of return is 13%.
Equation of IRR of Project A:
Compute IRR for Project A using a spreadsheet:
Step 1:
- Type the equation of NPV in H6 in the spreadsheet and consider the IRR value as H7.
Step 2:
- Assume the IRR value as 10%.
Step 3:
- In the spreadsheet, go to data and select the what-if analysis.
- In the what-if analysis, select goal seek.
- In set cell select H6 (the formula).
- The “To value” is considered as 0 (the assumption value for NPV).
- The H7 cell is selected for the by changing cell.
Step 4:
- Following the previous step click OK in the goal seek. The goal seek status appears with the IRR value.
Step 5:
- Thevalue appears to be 21.0164258735852%.
Hence, the IRR value is 21.02%.
Equation of IRR of Project B:
Compute IRR for Project B using a spreadsheet:
Step 1:
- Type the equation of NPV in H6 in the spreadsheet and consider the IRR value as H7.
Step 2:
- Assume the IRR value as 10%.
Step 3:
- In the spreadsheet, go to data and select the what-if analysis.
- In the what-if analysis, select goal seek.
- In set cell, select H6 (the formula).
- The “To value” is considered as 0 (the assumption value for NPV).
- The H7 cell is selected for the by changing cell.
Step 4:
- Following the previous step, click OK in the goal seek. The goal seek status appears with the IRR value.
Step 5:
- Thevalue appears to be 30.5678172386103%.
Hence, the IRR value is 30.57%.
d)
To compute: The profitability index.
Introduction:
Capital budgeting is a process, where the business identifies and assesses potential investments or expenses that are larger (in general).
Answer to Problem 15QP
Explanation of Solution
Given information:
The cash flows for two mutually exclusive projects are $29,000, $45,000, $51,000, $325,000 for Project A for year 1, year 2, year 3, and year 4 respectively. Project A has an initial investment of $235,000. The cash flows of Project B are $28,700, $19,900, $17,300, and $16,200 for year 1, year 2, year 3, and year 4 respectively. The initial investment for Project B is $47,000. The rate of return is 13%.
Formula to compute the profitability index:
Compute the profitability index for Project A:
Hence, the profitability index for Project A is $1.258.
Compute the profitability index for Project B:
Hence, the profitability index for Project B is $1.338.
e)
To discuss: The project that Person X will select with a reason.
Introduction:
Capital budgeting is a process, where the business identifies and assesses potential investments or expenses that are larger (in general).
Explanation of Solution
In this case, the criteria of NPV denote that Project A must be accepted, while payback period, profitability index, and IRR denote that Project B must be accepted. The overall decision must be based on the NPV as it does not have the ranking problem when compared with the other techniques of capital budgeting. Hence, Project A must be accepted.
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