Question

Sauer Food Company has decided to buy a new computer system with an expected life of three years. The cost is \(150,000. The company can borrow \)150,000 for three years at 10 percent annual interest or for one year at 8 percent annual interest.

How much would Sauer Food Company save in interest over the three-year life of the computer system if the one-year loan is utilized and the loan is rolled over (reborrowed) each year at the same 8 percent rate? Compare this to the 10 percent three-year loan. What if interest rates on the 8 percent loan go up to 13 percent in year 2 and 18 percent in year 3? What would be the total interest cost compared to the 10 percent, three-year loan?

Short answer

The interest saving when a one-year loan is reborrowed in place of the three-year loan is $9,000. The extra cost of financing will be $13,500 when the organization reborrows the one-year loan instead of using the three-year loan.

Step-by-step solution

Information given in the question

The following information is provided:

Cost of computer system = $150,000

Expected life = 3 years

Interest for three years = 10%

Interest forthefirst year = 8%

Interest forthesecond year = 13%

Interest for the third year = 18%

Cost of renewing one-year loan for three years when rates are constant

The expected sales for next year are $36,000.

$$\begin{gathered} \mathbf{Cost}\mathbf{}\mathbf{of}\mathbf{}\mathbf{financing}\mathbf{=}\mathbf{Borrowed}\mathbf{funds}\mathbf{\times }\mathbf{Interest}\mathbf{rate}\mathbf{\times }\mathbf{Time} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{(}\mathbf{\$}\mathbf{150}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{8}\mathbf{\%}\mathbf{p}\mathbf{.}\mathbf{a}\mathbf{.}\mathbf{\times }\mathbf{3}\mathbf{)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{36}\mathbf{,}\mathbf{000} \end{gathered}$$

Cost of utilizing a three-year loan

The expected sales for next year are $45,000.

$$\begin{gathered} \mathbf{Cost}\mathbf{}\mathbf{of}\mathbf{}\mathbf{financing}\mathbf{=}\mathbf{Borrowed}\mathbf{funds}\mathbf{\times }\mathbf{Interest}\mathbf{rate}\mathbf{\times }\mathbf{Time} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{(}\mathbf{\$}\mathbf{150}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{10}\mathbf{\%}\mathbf{p}\mathbf{.}\mathbf{a}\mathbf{.}\mathbf{\times }\mathbf{3}\mathbf{)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{45}\mathbf{,}\mathbf{000} \end{gathered}$$

Interest savings when using a short-term loan

The interest savings when short-term financing is utilized is $9,000.

$$\begin{gathered} \mathbf{Interest}\mathbf{}\mathbf{savings}\mathbf{=}\mathbf{Cost}\mathbf{of}\mathbf{three}\mathbf{-}\mathbf{year}\mathbf{}\mathbf{Ioan}\mathbf{-}\mathbf{Cost}\mathbf{}\mathbf{of}\mathbf{}\mathbf{short}\mathbf{-}\mathbf{term}\mathbf{financing} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{(}\mathbf{\$}\mathbf{45}\mathbf{,}\mathbf{000}\mathbf{}\mathbf{-}\mathbf{\$}\mathbf{36}\mathbf{,}\mathbf{000}\mathbf{)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{9}\mathbf{,}\mathbf{000} \end{gathered}$$

Cost of short-term loans when rates are changing

The cost of borrowing is $58,500.

$$\begin{gathered} \mathbf{Cost}\mathbf{of}\mathbf{financing}\mathbf{=}\mathbf{Borrowed}\mathbf{funds}\mathbf{\times }\mathbf{Interest}\mathbf{rate}\mathbf{\times }\mathbf{Time} \\ \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{150}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{8}\mathbf{\%}\mathbf{p}\mathbf{.}\mathbf{a}\mathbf{.}\mathbf{\times }\mathbf{1}\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{150}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{13}\mathbf{\%}\mathbf{p}\mathbf{.}\mathbf{a}\mathbf{.}\mathbf{\times }\mathbf{1}\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{150}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{18}\mathbf{\%}\mathbf{p}\mathbf{.}\mathbf{a}\mathbf{.}\mathbf{\times }\mathbf{1}\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{12}\mathbf{,}\mathbf{000}\mathbf{}\mathbf{+}\mathbf{}\mathbf{\$}\mathbf{19}\mathbf{,}\mathbf{500}\mathbf{}\mathbf{+}\mathbf{}\mathbf{\$}\mathbf{27}\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{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{58}\mathbf{,}\mathbf{500} \end{gathered}$$

Extra cost of borrowing when short-term rates are changing

The extra cost of a short-term loan when the rates are changing is $13,500.

$$\begin{gathered} \mathbf{\text{Extra cost}}\mathbf{=}\mathbf{\text{Cost of short-term Ioan when rates are changing}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{-}\mathbf{\text{Cost of short-term loan when rates are constant}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{58}\mathbf{,}\mathbf{000}\mathbf{}\mathbf{-}\mathbf{}\mathbf{\$}\mathbf{45}\mathbf{,}\mathbf{000} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{13}\mathbf{,}\mathbf{500} \end{gathered}$$