Question

King’s Department Store is contemplating the purchase of a new machine for \(22,802. The machine will provide \)3,500 per year in cash flow for nine years. King’s has a cost of capital of 10 percent. Using the internal rate of return method, evaluate this project and indicate whether it should be undertaken.

Short answer

Answer

The business should not undertake the project.

Step-by-step solution

Definition of Capital Budgeting

Capital budgeting is the technique used by the investors to determine the different available investment options. It includes methods such as the payback method, Net present value, and IRR.

Calculation of internal rate of return

Internal rate of return using the formula:

$$\begin{gathered} NPW=\sum _{t=0}^T\frac{C_t}{{\left(1+IRR\right)}^t} \\ 0=\left(\begin{array}{c}\frac{-22,802}{{\left(1+IRR\right)}^0}+\frac{\$3,500}{{\left(1+IRR\right)}^1}+\frac{\$3,500}{\left(1+IRR\right)}+\\ \frac{\$3,500}{{\left(1+IRR\right)}^3}+\frac{\$3,500}{{\left(1+IRR\right)}^4}+\frac{\$3,500}{{\left(1+IRR\right)}^5}+\\ \frac{\$3,500}{{\left(1+IRR\right)}^7}+\frac{\$3,500}{{\left(1+IRR\right)}^0}+\frac{\$3,500}{{\left(1+IRR\right)}^7}+\frac{\$3,500}{{\left(1+IRR\right)}^8}+\\ \frac{\$3,500}{{\left(1+IRR\right)}^9}\end{array}\right) \\ IRR=7\% \end{gathered}$$

Internal rate of return using Appendix D: Present value of an annuity

$$\begin{gathered} P{V}_{IFA}=\frac{Initialinvestment}{Cashfloweachyear} \\ =\frac{\$22,802}{\$3,500} \\ =6.515 \end{gathered}$$

For n=9, we will find 6.515 under the column of 7%. Therefore, the internal rate of return of the project is 7%.

Important Note: The internal rate of return is lower than the cost of capital. Therefore the project must not be accepted.