Chapter 24, Problem 2PSA

1.

To determine

To compute: Annual expected net cash flows.

Explanation of Solution

Given below is the table for the computation of annual expected net cash flows:

Annual cash flow
Particulars	Project Y ($)	Project Z ($)
Profit after tax	56,000	36,400
Depreciation	87,500	116,666.66
Cash flows after tax	143,500	153,066.66

Table(1)

Working notes:

Calculation of annual depreciation of Project Y,

$\begin{array}{c}\text{Annual depreciation}=\frac{\text{Investment in machinery}}{\text{Life of machinery}}\\ =\frac{\$350,000}{4\text{ years}}\\ =\$87,500\end{array}$

Calculation of annual depreciation of Project Z,

$\begin{array}{c}\text{Annual depreciation}=\frac{\text{Investment in machinery}}{\text{Life of machinery}}\\ =\frac{\$350,000}{\text{3 years}}\\ =\$116,666.66\end{array}$

Hence, cash flow after tax is from project Y is $143,500 and Project Z is $153,066.67

2.

To determine

To compute: Payback period.

Explanation of Solution

Computation of payback period for project Y:

Given,
Cost of investment of Project Y is $350,000.
Annual net cash flow from Project Y is $143,500.

Formula to calculate payback period,

$\text{Payback period}=\frac{\text{Initial investment}}{\text{Net annual cash inflow}}$

Substitute $350,000 for initial investment and $143,500 for net annual cash inflow.

$\begin{array}{c}\text{Payback period}=\frac{\text{\$350,000}}{\text{\$143,500}}\\ =\text{2}\text{.44 years}\end{array}$

Computation of payback period for project Z:

Given,
Cost of investment of Project Z is $280,000.
Annual net cash flow from Project Z is $153,066.66.

Formula to calculate payback period,

$\text{Payback period}=\frac{\text{Initial investment}}{\text{Net annual cash inflow}}$

Substitute $280,000 for initial investment and $153,066.66 for net annual cash inflow.

$\begin{array}{c}\text{Payback period}=\frac{\text{\$280,000}}{\$153,066.66}\\ =1.83\text{ years}\end{array}$

Hence, payback period of project Y is 2.44 years and Project Z is 1.83 years.

3.

To determine

To compute: Accounting rate of return (ARR).

Explanation of Solution

Computation of accounting rate of return (ARR) for Project Y:

Given,
Average annual profit of Project Y is $56,000.
Average investment in Project Y is $175,000.

Formula to calculate accounting rate of return,

$\text{Accounting rate of return}=\frac{\text{Average annual profit}}{\text{Average investment}}$

Substitute $56,000 for average annual profit and $175,000 for average investment.

$\begin{array}{c}\text{Accounting rate of return}=\frac{\text{\$56,000}}{\text{\$175,000}}\\ =\text{0}\text{.32 or 32\%}\end{array}$

Computation of accounting rate of return (ARR) for Project Z:

Given,
Average annual profit of Project Z is $36,400.
Average investment in Project Z is $140,000.

Formula to calculate of accounting rate of return,

$\text{Accounting rate of return}=\frac{\text{Average annual profit}}{\text{Average investment}}$

Substitute $56,000 for average annual profit and $175,000 for average investment.

$\begin{array}{c}\text{Accounting rate of return}=\frac{\text{\$36,400}}{\text{\$140,000}}\\ =\text{0}\text{.26 or 26\%}\end{array}$

Working notes:

Calculation of average investment of Project Y,

$\begin{array}{c}\text{Average investment}=\frac{\text{Opening investment}+\text{Closing investment}}{2}\\ =\frac{\$350,000+\$0}{2}\\ =\$175,000\end{array}$

Calculation of average investment of Project Z,

$\begin{array}{c}\text{Average investment}=\frac{\text{Opening investment}+\text{Closing investment}}{2}\\ =\frac{\$280,000+\$0}{2}\\ =\$140,000\end{array}$

Hence, ARR for Project Y is 32% and Project Z is 26%.

4.

To determine

To compute: Net present value.

Explanation of Solution

Computation of net present value (NPV) for Project Y:

Given,
Annual net cash flows from Project Y is $143,500
Cost of investment is $350,000.
Market interest rate is 8%.
Number of periods is 4 years.
Present value factor for cumulative 4 years is 3.31.

Formula to calculate NPV,

$\text{NPV}=\text{Present value of cash flows}-\text{Cost of investment}$

Substitute $457,290.20 for the present value of cash flows and $350,000 for the cost of investment.

$\begin{array}{c}\text{NPV}=\$457,290.20-\$350,000\\ =\$107,290.20\end{array}$

Computation of Net present value (NPV) for Project Z:

Given,
Annual net cash flow from Project Z is $153,066.66.
Cost of investment is $280,000.
Market interest rate is 8%.
Number of periods is 3 years.
Present value factor for cumulative 3 years is 2.58.

Formula to calculate NPV,

$\text{NPV}=\text{Present value of cash flows}-\text{Cost of investment}$

Substitute $394,467.63 for the present value of cash flows and $280,000 for the cost of investment.

$\begin{array}{c}\text{NPV}=\text{\$394,467}\text{.63}-\text{\$280,000}\\ =\$\text{114,467}\text{.63}\end{array}$

Working notes:

Calculation of present value of cash flows of Project Y,

$\begin{array}{c}\text{Present vale of cash flow}=\text{Annual net cash flow}\times \text{PVIFA}\\ =\text{\$143,500}\times 3.31\\ =\$457,290.20\end{array}$

Calculation of present value of cash flows of Project Z,

$\begin{array}{c}\text{Present vale of cash flow}=\text{Annual net cash flow}\times \text{PVIFA}\\ =\text{\$153,066}\text{.66}\times 2.58\\ =\$394,467.63\end{array}$

Hence, NPV for project Y is $125,290.20 and Project Z is $114,467.63.

5.

To determine

To identify: Recommendation to management to pursue Project Y.

Explanation of Solution

ul

It is recommended to management to pursue Project A since Project A has higher NPV, which is $125,290.20 as compared to Project Z, which is $114,467.63.

It is also to be noted that accounting rate of return of Project Y is higher, which is 32% as compared to Project Z, which is 26%.

Although Project Z has lower payback period, it is insufficient to make up for the extra year’s income from Project Y.

Hence, it is recommended to management to pursue Project Y.