Chapter 25, Problem 25.6APR

1.

To determine

Cash payback method:

Cash payback period is the expected time period which is required to recover the cost of investment. It is one of the capital investment method used by the management to evaluate the long-term investment (fixed assets) of the business.

Average rate of return method:

Average rate of return is the amount of income which is earned over the life of the investment. It is used to measure the average income as a percent of the average investment of the business, and it is also known as the accounting rate of return.

The average rate of return is computed as follows:

$\text{Average rate of return =}\frac{\text{Estimated average annual income}}{\text{Average investment}}$

Net present value method:

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

Present value index:

Present value index is a technique, 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 computed as follows:

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

The cash payback period for the given proposals.

Explanation of Solution

The cash payback period for the given proposals is as follows:

Proposal A:

Initial investment=$680,000

Cash payback period of Proposal A
Year		Net cash flows		Cumulative net cash flows
1		200,000		200,000
2		200,000		400,000
3		200,000		600,000
6 months (1)		80,000		680,000

Table (1)

Hence, the cash payback period of proposal A is 3 years and 6 months.

Working note:

1. Calculate the no. of months in the cash payback period:

$\begin{array}{c}\text{No}\text{. of months = }\left(\frac{\text{Balance amount of intital investment}}{\text{Total cash flow for particular year}}\right)\times \text{No}\text{. of months in a year}\\ \text{=}\frac{\$80,000}{\$160,000}\times 12\text{ months}\\ \text{= 6 months}\end{array}$ (1)

Proposal B:

Initial investment=$320,000

Cash payback period of Proposal B
Year		Net cash flows		Cumulative net cash flows
1		90,000		90,000
2		90,000		180,000
3		70,000		250,000
4		70,000		320,000

Table (2)

Hence, the cash payback period of proposal B is 4 years.

Proposal C:

Initial investment=$108,000

Cash payback period of Proposal C
Year		Net cash flows		Cumulative net cash flows
1		55,000		55,000
2		53,000		108,000

Table (3)

Hence, the cash payback period of proposal C is 2 years.

Proposal D:

Initial investment=$400,000

Cash payback period of Proposal D
Year		Net cash flows		Cumulative net cash flows
1		180,000		180,000
2		180,000		360,000
3 months (2)		40,000		400,000

Table (4)

Hence, the cash payback period of proposal D is 2 years and 3 months.

Working note:

2. Calculate the no. of months in the cash payback period:

$\begin{array}{c}\text{No}\text{. of months = }\left(\frac{\text{Balance amount of intital investment}}{\text{Total cash flow for particular year}}\right)\times \text{No}\text{. of months in a year}\\ \text{=}\frac{\$40,000}{\$160,000}\times 12\text{ months}\\ \text{= 3 months}\end{array}$ (2)

2.

To determine

The average rate of return for the give proposals.

Explanation of Solution

The average rate of return for the given proposals is as follows:

Proposal A:

$\begin{array}{c}\text{Average rate of investment = }\frac{\left(\frac{\text{Income from operations}}{\text{Useful life of years}}\right)}{\left(\frac{\text{Cost of investment}}{2}\right)}\\ =\frac{\left(\frac{\$240,000}{5\text{ years}}\right)}{\left(\frac{\$680,000}{2}\right)}\\ =\frac{\$48,000}{\$340,000}\\ =0.141\\ \text{In percentage 0}\text{.141}\times \text{100 = 14}\text{.1\%}\end{array}$

Hence, the average rate of return for Proposal A is 14.1%.

Proposal B:

$\begin{array}{c}\text{Average rate of investment = }\frac{\left(\frac{\text{Income from operations}}{\text{Useful life of years}}\right)}{\left(\frac{\text{Cost of investment}}{2}\right)}\\ =\frac{\left(\frac{\$20,000}{5\text{ years}}\right)}{\left(\frac{\$320,000}{2}\right)}\\ =\frac{\$4,000}{\$160,000}\\ =0.025\\ \text{In percentage 0}\text{.025}\times \text{100 = 2}\text{.5\%}\end{array}$

Hence, the average rate of return for Proposal B is 2.5%.

Proposal C:

$\begin{array}{c}\text{Average rate of investment = }\frac{\left(\frac{\text{Income from operations}}{\text{Useful life of years}}\right)}{\left(\frac{\text{Cost of investment}}{2}\right)}\\ =\frac{\left(\frac{\$142,000}{5\text{ years}}\right)}{\left(\frac{\$108,000}{2}\right)}\\ =\frac{\$28,400}{\$54,000}\\ =0.526\\ \text{In percentage 0}\text{.526}\times \text{100 = 52}\text{.6\%}\end{array}$

Hence, the average rate of return for Proposal C is 52.6%.

Proposal D:

$\begin{array}{c}\text{Average rate of investment = }\frac{\left(\frac{\text{Income from operations}}{\text{Useful life of years}}\right)}{\left(\frac{\text{Cost of investment}}{2}\right)}\\ =\frac{\left(\frac{\$300,000}{5\text{ years}}\right)}{\left(\frac{\$400,000}{2}\right)}\\ =\frac{\$60,000}{\$200,000}\\ =0.300\\ \text{In percentage 0}\text{.300}\times \text{100 = 30}\text{.0\%}\end{array}$

Hence, the average rate of return for Proposal D is 30.0%.

3.

To determine

To indicate: The proposals which should be accepted for further analysis, and which should be rejected.

Explanation of Solution

The proposals which should be accepted for further analysis, and which should be rejected is as follows:

Figure (1)

Proposals A and B are rejected, because proposal A and B 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 C and D are preferable.

4.

To determine

The net present value of preferred proposals.

Explanation of Solution

Calculate the net present value of the proposals which has 12% rate of return as follows:

Proposal C:

Figure (2)

Hence, the net present value of proposal C is $62,067.

Proposal D:

Figure (3)

Hence, the net present value of proposal D is $94,920.

5.

To determine

To determine:  The present value index for each proposal.

Explanation of Solution

The present value index for each proposal is as follows:

Proposal C:

Calculate the present value index for proposal C:

$\begin{array}{c}\text{Present value index for proposal C = }\frac{\text{Total presest value of cash flow}}{\text{Amount to be invested}}\\ \text{=}\frac{\$170,067}{\text{\$108,000}}\\ \text{=1}\text{.575}\end{array}$

Hence, the present value index for proposal C is 1.575.

Proposal D:

Calculate the present value index for proposal D:

$\begin{array}{c}\text{Present value index for proposal D= }\frac{\text{Total presest value of cash flow}}{\text{Amount to be invested}}\\ \text{=}\frac{\text{\$494,920}}{\text{\$400,000}}\\ \text{=1}\text{.237}\end{array}$

Hence, the present value index for proposal D is 1.237.

6.

To determine

To rank: The proposal from most attractive to least attractive, based on the present value of net cash flows.

Explanation of Solution

Proposals are arranged by rank is as follows:

Proposals	Net present value	Rank
Proposal D	$      94,920	1
Proposal C	$      62,067	2

Table (5)

7.

To determine

To rank: The proposal from most attractive to least attractive, based on the present value of index.

Explanation of Solution

Proposals are arranged by rank is as follows:

Proposals	Present value index	Rank
Proposal C	1.57	1
Proposal D	1.24	2

Table (6)

8.

To determine

To analysis: The proposal which is favor to investment, and comment on the relative attractiveness of the proposals based on the rank.

Explanation of Solution

On the basis of net present value:

The net present value of Proposal C is $62,067, and Proposal D is $94,920. In this case, the net present value of proposal D is more than the net present value of proposal C. Hence, investment in Proposal D is preferable.

On the basis of present value index:

The present value index of Proposal C is 1.57, and the present value index of Proposal D is 1.24. In this case, Proposal C has the favorable present value index, because the present value index of Proposal C (1.57) is more than Proposal D (1.24).  Thus, the investment in Proposal C is preferable (favorable).

Every business tries to get maximum profit with minimum investment. Hence, the cost of investment in Proposal C is less than the proposal D. Thus, investment in Proposal C is preferable.