Question

On January 1, 2021, Tennessee Harvester Corporation issued debenture bonds that pay interest semiannually on June 30 and ber 31. Portions of the bond amortization schedule appear below: Cash Payment Effective Interest Increase in Balance Payment ܢܬ ܚ 308,000 308,000 308,000 308,000 308,000 308,000 318,938 319,484 320,059 320,662 321,295 321,959 10,938 11,484 12,059 12,662 13, 295 13,959 Outstanding Balance 6,378,750 6,389,688 6,401,172 6,413,231 6,425,893 6,439,188 6,453,147 ܠ ܗ ܐ All ܐ ܐ ܐ ܣ ܐ 308,000 308,000 308,000 374,516 377,841 381,330 66,516 69,841 73,330 7,556,829 7,626,670 7,700,000 Required: 1. What is the face amount of the bonds? 2. What is the initial selling price of the bonds? 3. What is the term to maturity in years? 4. Interest is determined by what approach? 5. What is the stated annual interest rate? 6. What is the effective annual interest rate? 7. What is the total cash interest paid over the term to maturity? 8. What is the total effective interest expense recorded over the term to maturity?

Answer 1

1. Face Amount    = $7,700,000

Face amount is the value that is paid at the end of maturity period of a bond.

2. Initial selling price = $6,378,750

Bonds may be issued at discount or premium based on the market. The current bond is issued at a discount , therefore it is trading at a price less than face value of the bond.

Initial selling price is nothing but cumulative of present value of bond price paid at the end of maturity period and present value of interest paid on bond over the life of bond.

3.Term to maturity = 20 years

It is mentioned that the interest is paid semi annually. Therefore we should divide the given 40 periods by 2 i.e., 40/2 = 20 years..

4. Interest is determined by = effective interest method

5. Annual interest rate = 8%

   cash payment / Face value of bond = 308,000/7,700,000 x 100 = 4% semi annually

   Therefore, Annual interest rate = 4 x 2 = 8%

6. Effective annual interest rate = 10% per annum

Effective interest / outstanding balance = $318,938 / 6,378,750 = 5% semi annually which is 5x 2 = 10% per annum

7. Total cash interest paid = cash interest per period x no of periods (20 years semi annually )

= $ 308,000 x 40

   = $12,320,000

8. Effective interest expense = Total cash interest paid + difference between ( face value of bond - initial selling price )

= $12,320,000 + [ 7,700,000 - 6,378,750]

   = 12,320,000 + 1,321,250

= $ 13,641,250