Question

Question: Sherwin Williams will receive \(18,500 a year for the next 25 years as a result of a picture he has painted. If a discount rate of 12 percent is applied, should he be willing to sell out his future rights now for \)165,000?

Short answer

Sherwin Williams should sell the future rights at $165,000.

Step-by-step solution

Identification of the required information

Payment (PMT) = $18,500

Period (n) = 25 year

Interest Rate (i) = 12%

Current value (PV)

$$\begin{gathered} \text{PV}\mathbf{=}\text{PMT}\times \left[\frac{1-{\left(1+i\right)}^{-n}}{i}\right] \\ \mathbf{=}\$18,500\times \left[\frac{1-{\left(1+12\%\right)}^{-25}}{12\%}\right] \\ \mathbf{=}\$145,098.07 \end{gathered}$$

Final Decision

Sherwin Williams should be willing to sell his future rights at $165,000 because the present value of the future rights, $145,098.07, is lower than $165,000.