Question

Project A requires a \(280,000 initial investment for new machinery with a five-year life and a salvage value of \)30,000. The company uses straight-line depreciation. Project A is expected to yield annual net income of $20,000 per year for the next five years. Compute Project A’s payback period.

Short answer

The payback period of the project is 4 years.

Step-by-step solution

Step-by-Step SolutionStep 1: Computation of annual cash flow

$$\begin{gathered} \mathbf{Depreciation}\mathbf{=}\frac{\mathrm{Cost}-\mathrm{Salvage}\mathrm{value}}{5} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{280,000-30,000}{5} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{50}\mathbf{,}\mathbf{000} \end{gathered}$$

$$\begin{gathered} \mathbf{Annual}\mathbf{}\mathbf{Cash}\mathbf{}\mathbf{flows}\mathbf{=}\mathbf{Annual}\mathbf{}\mathbf{net}\mathbf{}\mathbf{Income}\mathbf{+}\mathbf{Depreciation}\mathbf{}\mathbf{per}\mathbf{}\mathbf{annum} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{20}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{50}\mathbf{,}\mathbf{000} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{70}\mathbf{,}\mathbf{000} \end{gathered}$$

Computation of payback period

$$\begin{gathered} \mathbf{Pay}\mathbf{}\mathbf{back}\mathbf{}\mathbf{Period}\mathbf{=}\frac{\mathrm{Cost}\mathrm{of}\mathrm{investement}}{\mathrm{Annual}\mathrm{net}\mathrm{cashflow}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\$280,000}{\$70,000} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{4} \end{gathered}$$