Question

Sauer Food Company has decided to buy a new computer system with an expected life of three years. The cost is $300,000. The company can borrow $300,000 for three years at 12 percent annual interest or for one year at 10 percent annual interest. Assume interest is paid in full at the end of each year.

Required:
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 8 percent rate?
b. 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?
c. What would the total interest cost compared to the 10 percent, three-year loan?

Answer 1

Step-by-step explanation:

From the given information;

Suppose the interest rate is constant. then at 10% three-year loan;

The total interest at 10% will be:

= $300000 × 10% × 3years

= $90000

Aso, 8% one year loan with rollover will be total interest at 8%:

= $300000 × 8% × 3 years

= $72000

Savings in interest of Sauer Food Company = $(90000 - 72000)

= $18000

Suppose short-term rates change, then for the first year, we will have:

= 300000 × 0.1

= $30000

second year will be = 300000 × 0.13

=$39000

third year will be= 300000 × 0.18

=$54000

As such, the total rate of the variable loan = $30000 + $39000 + $54000

= $123000

However, the fixed rate at 10% three year loan is equal to = $90000

As such, the additional total interest cost = $(123000 - 90000)

= $33000