Sauer Food Company has decided to buy a new computer system with an expected lif

Question

Sauer Food Company has decided to buy a new computer system with an expected life of three years. The cost is $250,000. The company can borrow $250,000 for three years at 11 percent annual interest or for one year at 9 percent annual interest. Assume interest is paid in full at the end of each year.  

a. 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 9 percent rate? Compare this to the 11 percent three-year loan.
  

b. What if interest rates on the 9 percent loan go up to 14 percent in year 2 and 17 percent in year 3? What would be the total interest cost compared to the 11 percent, three-year loan?
  

Explanation / Answer

As mentioned in question, interest is paid in full at the end of the year. So no compounding would take place here. It would be a case of simple interest.

Simple Interest = Principle * Interest Rate * Time

Part a

Simple interest (11%) = 250,000 * 11% * 3 = $82,500

Simple interest (9%) = (250,000 * 9% * 1) + (250,000 * 9% * 1) + (250,000 * 9% * 1) = (250,000 * 9% * 3) = $67,500

So, saving here with rollover loan = $82,500 - $67,500 = $15,000

Part b

Simple interest (11%) = 250,000 * 11% * 3 = $82,500

Simple interest (9%, 14%, 17%) = (250,000 * 9% * 1) + (250,000 * 14% * 1) + (250,000 * 17% * 1) = $100,000

So, interest cost in rollover loan would be higher by = $100,000 - $82,500 = $17,500

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