Chapter 24, Problem 2PSB

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:

Particulars	Project A ($)	Project B ($)
Net income $\left(\text{A}\right)$	39,900	25,900
Depreciation $\left(\text{B}\right)$	60,000	80,000
Net cash flows $\left(\text{C}\right)=\left(\text{A}\right)+\left(\text{B}\right)$	99,900	105,900

table(1)

Working note:

Calculation of annual depreciation of Project A,

$\begin{array}{c}\text{Annual depreciation}=\frac{\text{Investment in machinery}}{\text{Life of machinery}}\\ =\frac{\$240,000}{4\text{ years}}\\ =\$60,000\end{array}$

Calculation of annual depreciation of Project B,

$\begin{array}{c}\text{Annual depreciation}=\frac{\text{Investment in machinery}}{\text{Life of machinery}}\\ =\frac{\$240,000}{\text{3 years}}\\ =\$120,000\end{array}$

Hence, cash flow after tax is from project A is $99,900 and Project B is $105,900.

2.

To determine

To compute: Payback period.

Explanation of Solution

Computation of payback period for project A:

Given,
Cost of investment of Project A is $240,000.
Annual net cash flow from Project A is $99,900.

Formula to calculate payback period,

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

Substitute $240,000 for initial investment and $99,900 for net annual cash inflow.

$\begin{array}{c}\text{Payback period}=\frac{\text{\$240,000}}{\text{\$99,900}}\\ =\text{2}\text{.40 years}\end{array}$

Computation of payback period for project B:

Given,
Cost of investment of Project B is $240,000.
Annual net cash flow from Project B is $105,900.

Formula to calculate payback period,

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

Substitute $240,000 for initial investment and $105,900 for net annual cash inflow.

$\begin{array}{c}\text{Payback period}=\frac{\text{\$240,000}}{\$105,900}\\ =2.27\text{ years}\end{array}$

Hence, payback period of project A is 2.40 years and Project B is 2.27 years.

3.

To determine

To compute: Accounting rate of return.

Explanation of Solution

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

Given,
Average annual profit of Project A is $39,900.
Average investment in Project A is $120,000.

Formula to calculate of accounting rate of return,

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

Substitute $39,900 for average annual profit and $120,000 for average investment.

$\begin{array}{c}\text{Accounting rate of return}=\frac{\text{\$39,900}}{\text{\$120,000}}\\ =\text{0}\text{.3325 or 33}\text{.25\%}\end{array}$

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

Given,
Average annual profit of Project B is $25,900.
Average investment in Project B is $120,000.

Formula to calculate of accounting rate of return,

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

Substitute $25,900 for average annual profit and $120,000 for average investment.

$\begin{array}{c}\text{Accounting rate of return}=\frac{\text{\$25,900}}{\text{\$120,000}}\\ =\text{0}\text{.2158 or 21}\text{.58\%}\end{array}$

Working note:

Calculation of average investment of Project A,

$\begin{array}{c}\text{Average investment}=\frac{\text{Opening investment}+\text{Closing investment}}{2}\\ =\frac{\$240,000+\$0}{2}\\ =\$120,000\end{array}$

Calculation of average investment of Project B,

$\begin{array}{c}\text{Average investment}=\frac{\text{Opening investment}+\text{Closing investment}}{2}\\ =\frac{\$240,000+\$0}{2}\\ =\$120,000\end{array}$

Hence, ARR for project A is 33.25% and Project B is 21.58%.

4.

To determine

To compute: Net present value.

Explanation of Solution

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

Given,
Annual net cash flows from Project A is $199,900.
Cost of investment is $240,000.
Market interest rate is 8%.
Number of periods is 4 years.
Present value factor for cumulative 4 years is 3.3121.

Formula to calculate NPV,

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

Substitute $330,879 for the present value of cash flows and $240,000 for the cost of investment.

$\begin{array}{c}\text{NPV}=\$330,879-\$240,000\\ =\$90,879\end{array}$

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

Given,
Annual net cash flow from Project B is $105,900.
Cost of investment is $240,000.
Market interest rate is 8%.
Number of periods is 3 years.
Present value factor for cumulative 3 years is 2.5771.

Formula to calculate NPV,

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

Substitute $272,915 for the present value of cash flows and $240,000 for the cost of investment.

$\begin{array}{c}\text{NPV}=\$272,915-\$240,000\\ =\$32,915\end{array}$

Working notes:

Formula to calculate present value of cash flows of Project A,

$\begin{array}{c}\text{Present vale of cash flow}=\text{Annual net cash flow}\times \text{PVIFA}\\ =\text{\$99,900}\times 3.3121\\ =\$330,879\end{array}$

Formula to calculate present value of cash flows of Project B,

$\begin{array}{c}\text{Present vale of cash flow}=\text{Annual net cash flow}\times \text{PVIFA}\\ =\text{\$105,900}\times 2.5771\\ =\$272,915\end{array}$

Hence, NPV for project A is $90,879 and Project B is $32,915.

5.

To determine

To identify: Recommendation to management to pursue Project A.

Explanation of Solution

It is recommended to management to pursue Project A since Project A has higher NPV, which is $90,879 as compared to Project B, which is $32,915.

It is also to be noted that accounting rate of return of Project A is higher, which is 33.25% as compared to Project B, which is 21.58%.

Although Project B has lower Payback period, it is insufficient to make up for the extra year’s income from Project A.

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