Question

Your client, Keith Moreland Leasing Company, is preparing a contract to lease a machine to Souvenirs Corporation for a period of 25 years. Moreland has an investment cost of $365,755 in the machine, which has a useful life of 25 years and no salvage value at the end of that time. Your client is interested in earning an 11% return on its investment and has agreed to accept 25 equal rental payments at the end of each of the next 25 years.

Instructions You are requested to provide Moreland with the amount of each of the 25 rental payments that will yield an 11% return on investment.

Short answer

The amount of each payment will be $43,430.

Step-by-step solution

Given Information

$$\begin{gathered} \mathbf{Investment}\mathbf{}\mathbf{cost}\mathbf{=}\mathbf{\$}\mathbf{365755} \\ \mathbf{Interest}\mathbf{}\mathbf{Rate}\mathbf{=}\mathbf{11}\mathbf{\%} \\ \mathbf{Number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{payments}\mathbf{=}\mathbf{25}\mathbf{}\mathbf{periods} \end{gathered}$$

Computation of each annual payment

$$\begin{gathered} \mathbf{Amount}\mathbf{}\mathbf{of}\mathbf{}\mathbf{each}\mathbf{}\mathbf{annual}\mathbf{}\mathbf{payment}\mathbf{=}\frac{\mathbf{Investment}\mathbf{}\mathbf{Cost}}{\mathbf{Present}\mathbf{}\mathbf{Value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{annuity}} \\ \mathbf{=}\frac{\mathbf{365}\mathbf{,}\mathbf{755}}{\mathbf{8}\mathbf{.}\mathbf{42174}} \\ \mathbf{=}\mathbf{\$}\mathbf{43}\mathbf{,}\mathbf{430} \end{gathered}$$