Chapter 12, Problem 40E

a.

To determine

Calculate the payback period of project A for the investment of $5,000 for five years.

Explanation of Solution

Payback Period Method:

Payback period method is a method of capital investment analysis. This method is used to evaluate the investment opportunity on the basis of the time taken to recover the initial cost of investment in cash.

Calculate the payback period of project A for the investment of $5,000 for five years:

$\begin{array}{c}\text{Payback period = }\left(\frac{\text{Original investment}}{\text{Average annual cash flow}}\right)\\ =\left(\frac{\text{\$5,000}}{\text{\$1,800}}\right)\\ =2.78\text{ years}\end{array}$

Conclusion

Therefore, the payback period of project A is 2.78 years.

b.

To determine

Calculate the payback period of project B for the investment of $5,000 for five years (assume that the cash inflows occur evenly throughout the year.

Explanation of Solution

Calculate the payback period of project B for the investment of $5,000 for five years (assume that the cash inflows occur evenly throughout the year:

	After-tax	Cumulative
Year	Cash Inflows	After-tax Inflows
1	$500	$500
2	$1,200	$1,700
3	$2,000	$3,700
4	$2,500	$6,200

Table (1)

$\begin{array}{c}\text{Payback period = }\left(3+\frac{\text{\$5,000}-\$3,700}{\$2,500}\right)\\ =\left(3+\frac{\text{\$}1,300}{\$2,500}\right)\\ =3+0.52\\ =3.52\text{ years}\end{array}$

Conclusion

Therefore, the payback period of project B for the investment of $5,000 for five years is 3.52 years.

c.

To determine

Calculate the payback period of project C for the investment of $5,000 for five years.

Explanation of Solution

Calculate the payback period of project C for the investment of $5,000 for five years:

$\begin{array}{c}\text{Payback period = }\left(\frac{\text{Original investment}}{\text{Average annual cash flow}}\right)\\ =\left(\frac{\text{\$5,000}}{\text{\$2,125}}\right)\\ =2.35\text{ years}\end{array}$

Working notes:

Calculate the annual after-tax net cash inflow:

Step 1: Calculate the depreciation expense per year:

$\begin{array}{c}\text{Depreciation expense per year =}\left(\frac{\text{ \$5,000}}{5}\right)\\ =\$1,000\end{array}$

Step 2: Calculate the taxable income for each year:

$\begin{array}{c}\text{Taxable income for each year =}\$2,500-\$1,000\\ =\$1,500\end{array}$

Step 3: Calculate the income tax for each year:

$\begin{array}{c}\text{Income tax for each year =}\$1,500\times 25\%\\ =\$375\end{array}$

Step 4: Calculate the annual after-tax net cash inflow:

$\begin{array}{c}\text{Annual after-tax net cash inflow = }\left(\text{\$2,500}-\$375\right)\\ =\$2,125\end{array}$

Conclusion

Therefore, the payback period of project C for the investment of $5,000 for five years is 2.35 years

d.(1)

To determine

Calculate the book rate of return based on the original investment.

Explanation of Solution

Calculate the book rate of return based on the original investment.

$\begin{array}{c}\begin{array}{l}\text{Book rate of return based }\\ \text{on the original investment}\end{array}\}\text{ =}\left(\frac{\$1,200}{\$5,000}\right)\\ =24\%\end{array}$

Working notes:

Calculate the depreciation expense per year:

$\begin{array}{c}\text{Depreciation expense per year =}\left[\frac{\left(\text{ \$5,000}-\$500\right)}{5}\right]\\ \text{=}\left[\frac{\left(\text{ \$}4,500\right)}{5}\right]\\ =\$900\end{array}$

Calculate the operating income:

Particulars	Amount ($)
Taxable Income:
Sales	$4,000
Expenses:
Cash	$1,500
Depreciation	$900
Pre-tax Operating Income	$1,600
Less: Income Taxes	$400
Operating Income	$1,200

Table (2)

Conclusion

Therefore, the book rate of return based on the original investment is 24%.

d.(2)

To determine

Calculate the book rate of return based on the average book value.

Explanation of Solution

Calculate the book rate of return based on the average book value:

$\begin{array}{c}\begin{array}{l}\text{Book rate of return based }\\ \text{on the average book value}\end{array}\}\text{ =}\left(\frac{\$1,200}{\$2,750}\right)\\ =43.64\%\end{array}$

Working note:

Calculate the average book value:

$\begin{array}{c}\text{Average book valu}e\text{=}\left[\frac{\left(\text{ \$5,000+}\$500\right)}{2}\right]\\ \text{=}\left[\frac{\left(\text{ \$}5,500\right)}{2}\right]\\ =\$2,750\end{array}$

Conclusion

Therefore, the book rate of return based on the average book value is 43.64%.

e.

To determine

Calculate the NPV of each project from A to D.

Explanation of Solution

Calculate the NPV of each project from A to D:

Project A:

$\begin{array}{c}\text{NPV = }\left[\begin{array}{l}\left(\text{\$1,800}\times \text{3}\text{.993}\right)\\ -\$5,000\end{array}\right]\\ =\left[\$7,187.4-\$5,000\right]\\ =\$2,187.4\end{array}$

Therefore, the NPV of project A is $2,187.4.

Project B:

Table (3)

Therefore, the NPV of project B is $1,279.

Project C:

$\begin{array}{c}\text{NPV = }\left[\begin{array}{l}\left(\text{\$2,125}\times \text{3}\text{.993}\right)\\ -\$5,000\end{array}\right]\\ =\left[\$8,485.13-\$5,000\right]\\ =\$3,485\end{array}$

Therefore, the NPV of project A is $3,485.

Project D:

Table (4)

Therefore, the NPV of project D is $3,726.