Chapter 12, Problem 40E

To determine

Provide appropriate answer for (a) to (e).

Explanation of Solution

Provide appropriate answer for (a) to (e) as follows:

(a) Calculate the payback period for project A.

$\begin{array}{c}\text{Payback period = }\frac{\text{Initial investment}}{\text{Cash inflow}}\\ =\frac{\$5,000}{\$1,800}\\ =2.78\text{ years}\end{array}$

(b) Calculate the payback period for project B.

Year	After tax cash inflows	Cumulative after tax cash inflows
1	$ 500	$ 500
2	$ 1,200	$ 1,700
3	$ 2,000	$ 3,700
4	$ 2,500

Table(1)

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

(c) Calculate the payback period for project C.

$\begin{array}{c}\text{Payback period = }\frac{\text{Initial investment}}{\text{Annual after-tax net cash inflow (3)}}\\ =\frac{\$5,000}{\$2,125}\\ =2.35\text{ years}\end{array}$

Working note (1):

Calculate the depreciation expense per year.

$\begin{array}{c}\begin{array}{l}\text{Depreciation }\\ \text{expense per year}\end{array}\}\text{=}\frac{\left(\begin{array}{l}\text{Cost of investment}-\\ \text{Salvage value}\end{array}\right)}{\text{Useful life}}\\ =\frac{\$5,000}{5\text{ years}}\\ =\$1,000\end{array}$

Working note (2):

Calculate the taxable income each year.

$\begin{array}{c}\begin{array}{l}\text{Taxable income }\\ \text{each year}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Net cash inflow}-\\ \text{Depreciation expense (1)}\end{array}\right)\\ =\$2,500-\$1,000\\ =\$1,500\end{array}$

Working note (3):

Calculate the annual after-tax net cash inflow.

$\begin{array}{c}\begin{array}{l}\text{Annual after-tax }\\ \text{net cash inflow}\end{array}\}=\left(\begin{array}{l}\text{Net cash inflow}-\\ \left(\text{Taxable income}\times \text{Tax rate}\right)\end{array}\right)\\ =\$2,500-\left(\$1,500\times 25\%\right)\\ =\$2,500-\$375\\ =\$2,125\end{array}$

(d) (1) Calculate the accounting rate of return based on the original investment of project D.

$\begin{array}{c}\text{Accounting rate of return = }\frac{\text{Operating income after tax (5)}}{\text{Initial investment}}\times 100\\ =\frac{\$1,200}{\$5,000}\times 100\\ =24\%\end{array}$

Working note (4):

Calculate the depreciation expense for project D.

$\begin{array}{c}\text{Depreciation expense =}\frac{\left(\begin{array}{l}\text{Cost of investment}-\\ \text{Estimated salvage value}\end{array}\right)}{\text{Estimated years}}\\ \text{= }\frac{\left(\$5,000-\$500\right)}{5\text{ years}}\\ =\$900\end{array}$

Working note (5):

Calculate the operating income after tax for project D.

Particulars	Amount ($)	Amount ($)
Sales		$ 4,000
Less: Expenses
Cash expenditures	$ 1,500
Depreciation (4)	$ 900	$ 2,400
Operating income before tax		$ 1,600
Less: Income tax @25%		$ 400
Operating income after tax		$ 1,200

Table (2)

(d) (2) Calculate the accounting rate of return based on the average investment of project D.

$\begin{array}{c}\text{Accounting rate of return = }\frac{\text{Operating income after tax (5)}}{\text{Average investment (6)}}\times 100\\ =\frac{\$1,200}{\$2,750}\times 100\\ =43.64\%\end{array}$

Working note (6):

Calculate the average book value.

$\begin{array}{c}\text{Average book value = }\frac{\text{Original investment + Salvage value}}{2}\\ =\frac{\$5,000+\$500}{2}\\ =\$2,750\end{array}$

e. Calculate the net present value for project A, project B, project C and project D.

Table (3)

Workings:

Table (4)