Question

Factor Company is planning to add a new product to its line. To manufacture this product, the company needs to buy a new machine at a \(480,000 cost with an expected four-year life and a \)20,000 salvage value. All sales are for cash, and all costs are out-of-pocket, except for depreciation on the new machine. Additional information includes the following.

Expected annual sales of new product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $1,840,000 Expected annual costs of new product

Direct materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480,000

Direct labor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 672,000

Overhead (excluding straight-line depreciation on new machine) . . . . . . . . . . . . . . 336,000

Selling and administrative expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160,000

Income taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30%

Required

1. Compute straight-line depreciation for each year of this new machine’s life. (Round depreciation amounts to the nearest dollar.)

2. Determine expected net income and net cash flow for each year of this machine’s life. (Round answers to the nearest dollar.)

3. Compute this machine’s payback period, assuming that cash flows occur evenly throughout each year. (Round the payback period to two decimals.)

4. Compute this machine’s accounting rate of return, assuming that income is earned evenly throughout each year. (Round the percentage return to two decimals.)

5. Compute the net present value for this machine using a discount rate of 7% and assuming that cash flows occur at each year-end.

Short answer

Depreciation is $115,000, net income is $53,900 and the net cash flow is $168,900. The payback period is 2.84 years, the accounting rate of return is 21.56% and the net present value is $107,356.

Step-by-step solution

Step-by-Step Step 1: Computation of depreciation

$\begin{array}{c}\mathbf{Straight}\mathbf{}\mathbf{line}\mathbf{}\mathbf{depreciation}\mathbf{=}\frac{\mathrm{Cost}-\mathrm{SalvageValue}}{\mathrm{Estimatedlife}}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\$480,000-\$20,000}{4}\\ =\$115,000\end{array}$

Determining net income and net cash flow

EXPECTED NET INCOME
	Amount ($)	Amount ($)
Revenues:
Sales		$1,840,000
Expenses
Direct Materials	$480,000
Direct Labor	672,000
Overhead Excluding straight line Depreciation on a new machine	336,000
Selling and administration expenses	160,000
Straight-line depreciation on a new machine	115,000
Total Expenses		1,763,000
Income before taxes		77,000
Income tax expense		23,100
Net Income		$53,900
EXPECTED NET CASH FLOW
Net Income		$53,900
Straight-line depreciation on a new machine		115,000
Net cash flow		$168,900

Computation of payback period

$$\begin{gathered} \mathbf{Pay}\mathbf{}\mathbf{back}\mathbf{}\mathbf{Period}\mathbf{=}\frac{\mathrm{Cost}\mathrm{of}\mathrm{Investment}}{\mathrm{Annual}\mathrm{net}\mathrm{cash}\mathrm{flow}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\$480,000}{\$168,900} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{84}\mathbf{years} \end{gathered}$$

Computation of accounting rate of return

$$\begin{gathered} \mathbf{Accounting}\mathbf{}\mathbf{rate}\mathbf{}\mathbf{of}\mathbf{}\mathbf{return}\mathbf{=}\frac{\mathrm{Annual}\mathrm{after}-\mathrm{tax}\mathrm{net}\mathrm{income}}{\mathrm{Annual}\mathrm{average}\mathrm{investment}}\mathbf{\times }\mathbf{100} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\$53,900}{\$250,000}\mathbf{\times }\mathbf{100} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{21}\mathbf{.}\mathbf{56}\mathbf{\%} \end{gathered}$$

Computation of net present value

Cash flow	Select chart	Amount x	PV Factor =	Present Value
Annual Cash flow	Present Value of Annuity of 1	$168,900	3.3872	$572,098.08
Residual Value	Present Value of 1	$20,000	0.7629	15,258.00

	Present value of cash inflows	$587,356.08
	Present value of cash outflows	480,000.00
	Net present value	$107,356.00