Question

Problem 6-9 Short-term versus longer-term borrowing [LO3] 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. 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 8 percent rate? Compare this to the 10 percent three-year loan. b.  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?
Input variables:
Number of years	3	years
Cost	$150,000
3-year Interest rate	0.10
1-year interest rate	0.08
a. Years 2-3 interest rate	0.08
b.  Year 2 interest rate	0.13
b. Year 3 interest rate	0.18
Solution and Explanation:
a.
Interest for 3 years @	1-yr rate
Interest for 3 years @	3-yr rate
Interest savings
b.
Interest for 3 years @	3-yr rate
Variable rate:
Interest - Year 1
Interest - Year 2
Interest - Year 3
Total variable-rate  interest
Extra interest

Answer 1

Answer:

a.

Interest for 3 years @1-yr rate	36,000
Interest for 3 years @3-yr rate	45,000
Interest savings	9,000

b.

Interest for 3 years @ 3-yr rate	45,000
Variable rate:
Interest - Year 1	12,000
Interest - Year 2	19,500
Interest - Year 3	27,000
Total variable-rate  interest	58,500
Extra interest	13,500

Calculation:

a.

Here we need to  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.

Then we need to compare this to the 10 percent three-year loan.

So, here the rates are constant.

The 3 year rate = 8%

The 1 year rate = 10%

$150,000 borrowed × 8% per annum × 3 years = $36,000

$150,000 borrowed × 10% per annum × 3 years =$45,000

Then,interest savings = 45,000 - 36,000 = $9,000

b.

Here the interest rates on the 8 percent loan go up to 13 percent in year 2 and 18 percent in year 3.

We need to calculate the total interest cost compared to the 10 percent, three-year loan.

So first step is to find the total interest cost:

1st year = $150,000 borrowed × 8% = 12,000

2nd year = $150,000 borrowed × 13% = 19,500

3rd year = $150,000 borrowed × 18% = 27,000

Then the Total variable-rate interest = 12,000 + 19,500 + 27,000 = 58,500

After that We need to calculate the total interest cost compared to the 10 percent, three-year loan.

The 10 percent, three-year loan is calculated in (a) is below:

$150,000 borrowed × 10% per annum × 3 years =$45,000

So, Extra interest = 58,500 - 45,000 = 13,500