Concept explainers
1.
Compute the cash payback period for each of the 4 proposals.
1.

Explanation of Solution
Cash payback period: Cash payback period is the time period which the cost of investment is expected to be recovered. It is one of the capital investment methods used by the management to evaluate the long-term investment (fixed assets) of the business.
Calculate the cash payback period:
Proposal A:
Initial investment=$450,000
Cash payback period of Proposal A | ||
Year | Net | Cumulative net cash flows |
1 | $120,000 | $120,000 |
2 | $120,000 | $240,000 |
3 | $110,000 | $350,000 |
4 | $100,000 | $450,000 |
Table (1)
Hence, the cash payback period of proposal A is 4 years.
Proposal B:
Initial investment=$200,000
Cash payback period of Proposal B | ||
Year | Net cash flows | Cumulative net cash flows |
1 | $100,000 | $100,000 |
2 | $80,000 | $180,000 |
4 months (1) | $20,000 | $200,000 |
Table (2)
Hence, the cash payback period of proposal B is 2 years and 4 months.
Working note 1:
Calculate the no. of months in the cash payback period:
Proposal C:
Initial investment=$320,000
Cash payback period of Proposal C | ||
Year | Net cash flows | Cumulative net cash flows |
1 | $100,000 | $100,000 |
2 | $90,000 | $190,000 |
3 | $90,000 | $280,000 |
6 months (2) | $40,000 | $320,000 |
Table (3)
Hence, the cash payback period of proposal C is 3 years and 6 months.
Working note 2:
Calculate the no. of months in the cash payback period:
Proposal D:
Initial investment=$540,000
Cash payback period of Proposal D | ||
Year | Net cash flows | Cumulative net cash flows |
1 | $200,000 | $200,000 |
2 | $180,000 | $380,000 |
3 | $180,000 | $560,000 |
Table (4)
Hence, the cash payback period of proposal D is 3 years.
2.
Compute the average
2.

Explanation of Solution
Average Rate of Return: Average rate of return measures the average earnings of any particular business, as the percentage of the average investment. It is also commonly known as accounting rate of return. The following formula can be used to determine the average rate of return:
Calculate the cash payback period:
Proposal A:
Hence, the average rate of return for Proposal A is 5.3%.
Proposal B:
Hence, the average rate of return for Proposal B is 18.0%.
Proposal C:
Hence, the average rate of return for Proposal C is 15.0%.
Proposal D:
Hence, the average rate of return for Proposal D is 16.3%.
3.
Summarize the results of the computations in part 1 and 2 in the given table.
3.

Explanation of Solution
The proposals which should be accepted for further analysis, and which should be rejected is as follows:
Proposal | Cash Payback Period | Average Rate of Return | Accept for Further Analysis | Reject |
A | 4 years | 5.3% | ✓ | |
B | 2 years and 4 months | 18.0% | ✓ | |
C | 3 years and 6 months | 15.0% | ✓ | |
D | 3 years | 16.3% | ✓ |
Table (5)
Proposals A and C are rejected, because proposal A and C fails to meet the required maximum cash back period of 3 years, and they has less rate of return than the other proposals. Hence, Proposals B and D are preferable.
4.
Compute the
4.

Explanation of Solution
Net present value method: Net present value method is used to compare the initial
Calculate the net present value:
Proposal B:
Proposal B | |||
Year | Present Value of $1 at 12% | Net Cash Flow | Present Value of Net Cash Flow |
1 | 0.893 | $100,000 | $89,300 |
2 | 0.797 | $80,000 | $63,760 |
3 | 0.712 | $60,000 | $42,720 |
4 | 0.636 | $30,000 | $19,080 |
5 | 0.567 | $20,000 | $11,340 |
Total | $290,000 | $226,200 | |
Amount to be invested | ($200,000) | ||
Net present value | $26,200 |
Table (6)
Hence, the net present value of proposal B is $26,200.
Proposal D:
Proposal D | |||
Year | Present Value of $1 at 12% | Net Cash Flow | Present Value of Net Cash Flow |
1 | 0.893 | $200,000 | $178,600 |
2 | 0.797 | $180,000 | $143,460 |
3 | 0.712 | $160,000 | $113,920 |
4 | 0.636 | $120,000 | $76,320 |
5 | 0.567 | $100,000 | $56,700 |
Total | $760,000 | $569,000 | |
Amount to be invested | ($540,000) | ||
Net present value | $29,000 |
Table (7)
Hence, the net present value of proposal D is $29,000.
5.
Compute the present value index for each of the proposals in part (4).
5.

Explanation of Solution
Present value index: Present value index is a method, which is used to rank the proposals of the business. It is used by the management when the business has more investment proposals, and limited fund. The present value index is calculated as follows:
Calculate the present value index:
Proposal B:
Hence, the present value index for proposal B is 1.13.
Proposal D:
Hence, the present value index for proposal Dis 1.05.
6.
Rank the proposals from most attractive to least attractive, based on present values of net cash flows computed in part (4).
6.

Explanation of Solution
Proposals arranged by rank from most attractive to least attractive are as follows:
Proposals | Net present value | Rank |
Proposal D | $29,000 | 1 |
Proposal B | $26,200 | 2 |
Table (8)
7.
Rank the proposals from most attractive to least attractive, based on the present value indexes computed in part (5).
7.

Explanation of Solution
Proposals arranged by rank from most attractive to least attractive are as follows:
Proposals | Present value index | Rank |
Proposal B | 1.13 | 1 |
Proposal D | 1.05 | 2 |
Table (9)
8.
Comment on the relative attractiveness of the proposals ranked on the basis of analysis in parts (6) and (7).
8.

Explanation of Solution
On the basis of net present value:
The net present value of Proposal B is $26,200, and of Proposal D is $29,000. In this case, the net present value of proposal D is greater than the net present value of proposal B. Hence, investment in Proposal D is recommended.
On the basis of present value index:
The present value index of Proposal B is 1.13, and of Proposal D is 1.05. In this case, Proposal B has a more favorable present value index, because the present value index of Proposal B (1.13) is greater than Proposal D (1.05). Thus, the investment in Proposal B is recommended.
Every business desires to get maximum profit with minimum investment. Thus, the cost of investment in Proposal B is lesser than the proposal D. Hence, investment in Proposal B is most preferable
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