Question

B2B Co. is considering the purchase of equipment that would allow the company to add a new product to its line. The equipment is expected to cost \(360,000 with a 12-year life and no salvage value. It will be depreciated on a straight-line basis. The company expects to sell 144,000 units of the equipment’s product each year. The expected annual income related to this equipment follows.

Compute the (1) payback period and (2) accounting rate of return for this equipment.

Sales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \)225,000

Costs

Materials, labor, and overhead (except depreciation on new equipment) . . . . . . . . . . . . . . . 120,000

Depreciation on new equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30,000

Selling and administrative expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22,500

Total costs and expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172,500

Pretax income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52,500

Income taxes (30%) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15,750

Net income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $ 36,750

Short answer

The payback period is 5.39 years and the accounting rate of return is 20.42%.

Step-by-step solution

Step-by-Step SolutionStep 1: Computation of payback period

$$\begin{gathered} \mathbf{Pay}\mathbf{}\mathbf{back}\mathbf{}\mathbf{period}\mathbf{=}\frac{\mathrm{Cost}\mathrm{of}\mathrm{investment}}{\mathrm{Annual}\mathrm{netcash}\mathrm{flow}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\$360,000}{\$66,750} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{5}\mathbf{.}\mathbf{39}\mathbf{\text{}}\mathbf{years} \end{gathered}$$

Computation of accounting rate of return

$$\begin{gathered} \mathbf{Accounting}\mathbf{}\mathbf{rate}\mathbf{}\mathbf{of}\mathbf{}\mathbf{return}\mathbf{=}\frac{\mathrm{Annual}\mathrm{after}\mathrm{tax}\mathrm{net}\mathrm{income}}{\mathrm{Annual}\mathrm{average}\mathrm{investment}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\$36,750}{\$180,000} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{20}\mathbf{.}\mathbf{42}\mathbf{\%} \end{gathered}$$