Chapter 12, Problem 6PB

1.

To determine

Compute the cash payback period for each of the 4 proposals.

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 cash flows	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:

  $\begin{array}{c}\text{No}\text{. of months = }\left(\frac{\text{Balance amount of intital investment}}{\text{Total cash flow for particular year}}\right)\times \text{No}\text{. of months in a year}\\ \text{=}\frac{\$20,000}{\$60,000}\times 12\text{ months}\\ \text{= 4 months}\end{array}$

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:

  $\begin{array}{c}\text{No}\text{. of months = }\left(\frac{\text{Balance amount of intital investment}}{\text{Total cash flow for particular year}}\right)\times \text{No}\text{. of months in a year}\\ \text{=}\frac{\$40,000}{\$80,000}\times 12\text{ months}\\ \text{= 6 months}\end{array}$

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.

To determine

Compute the average rate of return for the give proposals.

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:

$\text{Average}\text{Rate}\text{of}\text{Return}\text{=}\frac{\text{Estimated}\text{Average}\text{Annual}\text{Income}}{\text{Average}\text{Investment}}\times 100$

Calculate the cash payback period:

Proposal A:

$\begin{array}{c}\text{Average rate of investment = }\left(\frac{\frac{\text{Income from operations}}{\text{Useful life of years}}}{\left(\frac{\text{Cost of investment}}{2}\right)}\right)\times 100\\ =\frac{\left(\frac{\$60,000}{5\text{ years}}\right)}{\left(\frac{\$450,000}{2}\right)}\times 100\\ =\frac{\$12,000}{\$225,000}\times 100\\ \text{ = 5}\text{.3\% }\left(\text{rounded to one decimal place}\right)\end{array}$

Hence, the average rate of return for Proposal A is 5.3%.

Proposal B:

$\begin{array}{c}\text{Average rate of investment = }\left(\frac{\frac{\text{Income from operations}}{\text{Useful life of years}}}{\left(\frac{\text{Cost of investment}}{2}\right)}\right)\times 100\\ =\frac{\left(\frac{\$90,000}{5\text{ years}}\right)}{\left(\frac{\$200,000}{2}\right)}\times 100\\ =\frac{\$18,000}{\$100,000}\times 100\\ \text{ = 18}\text{.0\% }\left(\text{rounded to one decimal place}\right)\end{array}$

Hence, the average rate of return for Proposal B is 18.0%.

Proposal C:

$\begin{array}{c}\text{Average rate of investment =}\left(\frac{\frac{\text{Income from operations}}{\text{Useful life of years}}}{\left(\frac{\text{Cost of investment}}{2}\right)}\right)\times 100\\ =\frac{\left(\frac{\$120,000}{5\text{ years}}\right)}{\left(\frac{\$320,000}{2}\right)}\times 100\\ =\frac{\$24,000}{\$160,000}\times 100\\ \text{ = 15}\text{.0\% }\left(\text{rounded to one decimal place}\right)\end{array}$

Hence, the average rate of return for Proposal C is 15.0%.

Proposal D:

$\begin{array}{c}\text{Average rate of investment = }\left(\frac{\frac{\text{Income from operations}}{\text{Useful life of years}}}{\left(\frac{\text{Cost of investment}}{2}\right)}\right)\times 100\\ =\frac{\left(\frac{\$220,000}{5\text{ years}}\right)}{\left(\frac{\$540,000}{2}\right)}\times 100\\ =\frac{\$44,000}{\$270,000}\times 100\\ \text{ = 16}\text{.3\% }\left(\text{rounded to one decimal place}\right)\end{array}$

Hence, the average rate of return for Proposal D is 16.3%.

3.

To determine

Summarize the results of the computations in part 1 and 2 in the given table.

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.

To determine

Compute the net present value for the accepted proposals.

Explanation of Solution

Net present value method: Net present value method is used to compare the initial cash outflow of the investment with the present value of its cash inflows. In the net present value, the interest rate is determined by the business based on the net income received from the investment. This is also called as the discounted cash flow method.

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.

To determine

Compute the present value index for each of the proposals in part (4).

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:

$\text{Present value index =}\frac{\text{Total present value of net cash flow}}{\text{Amount to be invested}}$

Calculate the present value index:

Proposal B:

$\begin{array}{c}\text{Present value index for proposal B = }\frac{\text{Total presest value of cash flow}}{\text{Amount to be invested}}\\ \text{=}\frac{\text{\$226,200}}{\text{\$200,000}}\\ \text{=1}\text{.13}\end{array}$

Hence, the present value index for proposal B is 1.13.

Proposal D:

$\begin{array}{c}\text{Present value index for proposal D= }\frac{\text{Total presest value of cash flow}}{\text{Amount to be invested}}\\ \text{=}\frac{\text{\$569,000}}{\text{\$540,000}}\\ \text{=1}\text{.05}\end{array}$

Hence, the present value index for proposal Dis 1.05.

6.

To determine

Rank the proposals from most attractive to least attractive, based on present values of net cash flows computed in part (4).

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.

To determine

Rank the proposals from most attractive to least attractive, based on the present value indexes computed in part (5).

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.

To determine

Comment on the relative attractiveness of the proposals ranked on the basis of analysis in parts (6) and (7).

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