Chapter 25, Problem 2AP

1.

To determine

Ascertain the annual expected net cash flows for each project.

Explanation of Solution

Cash inflows: The amount of cash received by a company from the operating, investing, and financing activities of the business during a certain period is referred to as cash inflow.

Cash outflows: The amount of cash paid by a company for the operating, investing, and financing activities of the business during a certain period is referred to as cash outflow.

Ascertain the annual expected net cash flows for each project as follows:

Project Y:

$\begin{array}{c}\text{Net cash flow = Net income + Depreciation expense}\\ \text{=\$56,000 + }\$87,500(\text{W}\text{.N}\text{. 1)}\\ \text{=\$143,500}\end{array}$

Therefore, the net cash flow of project Y is $143,500.

Project Z:

$\begin{array}{c}\text{Net cash flow = Net income + Depreciation expense}\\ \text{=\$36,400 + }\$116,667(\text{W}\text{.N}\text{. 2)}\\ \text{=\$153,067}\end{array}$

Therefore, the net cash flow of project Z is $153,067.

Working note 1:

Calculate the depreciation expense for Project Y:

$\begin{array}{c}\text{Depreciation = }\frac{\left[\text{Purchase cost of investment– Salvage value}\right]}{\text{Useful life}}\\ \text{= }\frac{\text{\$350,000}-\text{\$0}}{\text{4 years}}\\ \text{= \$87,500}\end{array}$

Working note 2:

Calculate the depreciation expense for Project Z:

$\begin{array}{c}\text{Depreciation = }\frac{\left[\text{Purchase cost of investment– Salvage value}\right]}{\text{Useful life}}\\ \text{= }\frac{\text{\$350,000}-\text{\$0}}{\text{3 years}}\\ \text{= \$116,667}\end{array}$

2.

To determine

Ascertain the payback period for each project.

Explanation of Solution

Payback period: 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 proposal of long-term investment (fixed assets) of the business.

Ascertain the payback period for each project as follows:

Project Y:

$\begin{array}{c}\text{Payback}\text{Period}\text{=}\frac{\text{Amount to be invested}}{\text{Estimated annual net cash }}\\ \text{=}\frac{\text{\$350,000}}{\text{\$143,500}}\\ \text{=3}\text{.44}\text{years}\end{array}$

Therefore, the payback period of Project Y is 3.44 years.

Project Z:

$\begin{array}{c}\text{Payback}\text{Period}\text{=}\frac{\text{Amount to be invested}}{\text{Estimated annual net cash }}\\ \text{=}\frac{\text{\$350,000}}{\text{\$153,067}}\\ \text{=2}\text{.29}\text{years}\end{array}$

Therefore, the payback period of Project Z is 2.29 years.

3.

To determine

Ascertain the accounting rate of return for each project.

Explanation of Solution

Accounting rate of return method:

Accounting 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 average rate of return.

Ascertain the accounting rate of return for each project as follows:

Project Y:

$\begin{array}{c}\text{Accounting rate of return =}\frac{\text{Estimated annual income}}{\left[\frac{\text{Cost of investment}}{2}\right]}\\ =\frac{\$56,000}{\left[\frac{\$350,000}{2}\right]}\times 100\\ =\frac{\$56,000}{\$175,000}\times 100\\ =32\%\end{array}$

Therefore, the accounting rate of return of Project Y is 32%.

Project Z:

$\begin{array}{c}\text{Accounting rate of return =}\frac{\text{Estimated annual income}}{\left[\frac{\text{Cost of investment}}{2}\right]}\\ =\frac{\$36,400}{\left[\frac{\$350,000}{2}\right]}\times 100\\ =\frac{\$36,400}{\$175,000}\times 100\\ =20.8\%\end{array}$

Therefore, the accounting rate of return of Project Z is 20.8%.

4.

To determine

Ascertain the net present value for each project.

Explanation of Solution

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.

Ascertain the net present value for each project as follows:

Project Y:

Net present value of investment opportunity
Particulars	$
Present value of annual net cash flow (W.N. 3)	475,286
Less: Amount to be invested	350,000
Net present value	125,286

Table (1)

Therefore, the net present value of project Y is $125,286.

Working note 3:

Calculate the present value of annual net cash flow:

$\begin{array}{c}\begin{array}{l}\text{Present value of }\\ \text{annual net cash flow}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Annual cash flow}\times \\ \text{Present value of annuity at 8\% for 4 years}\end{array}\right)\\ \text{=}\$143,500\times 3.3121\\ =\$475,286\end{array}$

Note: The Present value of an ordinary annuity of $1 for 4 years at 8% is 3.3121 (refer table 3 in Appendix B).

Project Z:

Net present value of investment opportunity
Particulars	$
Present value of annual net cash flow (W.N. 4)	394,469
Less: Amount to be invested	350,000
Net present value	44,469

Table (2)

Therefore, the net present value of project Z is $44,469.

Working note 4:

Calculate the present value of annual net cash flow:

$\begin{array}{c}\begin{array}{l}\text{Present value of }\\ \text{annual net cash flow}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Annual cash flow}\times \\ \text{Present value of annuity at 8\% for 3 years}\end{array}\right)\\ \text{=}\$143,500\times 2.5771\\ =\$394,469\end{array}$

Note: The Present value of an ordinary annuity of $1 for 3 years at 8% is 2.5771 (refer table 3 in Appendix B).

5.

To determine

Identify the project which would be recommended to management and explain it.

Explanation of Solution

Identify the project which would be recommended to management and explain it as follows:

In this case, project Y is better for the investment, and it would be recommended to the management, because project Y ($125.286) has higher net present value than project Z ($44,469). At the same time, project Y (32%) has higher accounting rate of return than project Z (20.8%). Hence, project Y is betterfor the investment.