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?

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%

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

$$\begin{gathered} Costoffinancing=Borrowedfunds\times Interestrate\times Time \\ =\$150,000\times \$8\%p.a.\times 3 \\ =\$36,000 \end{gathered}$$

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

$$\begin{gathered} Costoffinancing=Borrowedfunds\times Interestrate\times Time \\ =\$150,000\times \$10\%p.a.\times 3 \\ =\$45,000 \end{gathered}$$

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

$$\begin{gathered} Interestsavings=Costofthreeyearloan-Costofshorttermfinancing \\ =\$45,000-\$36,000 \\ =\$9,000 \end{gathered}$$

The cost of borrowing is $58,500.

$$\begin{gathered} Costoffinancing=Borrowedfunds\times Interestrate\times Time \\ =\left(\$150,000\times \$8\%p.a.\times 1\right)+ \\ \left(\$150,000\times \$13\%p.a.\times 1\right)+ \\ \left(\$150,000\times \$18\%p.a.\times 1\right) \\ =\$12,000+\$19,500+\$27,000 \\ =\$58,500 \end{gathered}$$

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

$$\begin{gathered} ExtraCost=Costofshorttermloanwhenratesarechanging-Costofshorttermloanwhenratesarecons\tan t \\ =\$58,500-\$45,000 \\ =\$13,500 \end{gathered}$$