Question

On January 1, 2018, Tennessee Harvester Corporation issued debenture bonds that pay interest semiannually on June 30 and December 31. Portions of the bond amortization schedule appear below:

Payment		Cash Payment		Effective Interest		Increase in Balance		Outstanding Balance
								5,774,920
1		216,000		230,997		14,997		5,789,917
2		216,000		231,597		15,597		5,805,514
3		216,000		232,221		16,221		5,821,735
4		216,000		232,869		16,869		5,838,604
5		216,000		233,544		17,544		5,856,148
6		216,000		234,246		18,246		5,874,394
~		~		~		~		~
~		~		~		~		~
~		~		~		~		~
38		216,000		280,008		64,008		7,064,202
39		216,000		282,568		66,568		7,130,770
40		216,000		285,230		69,230		7,200,000

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

Answer 1.

Face Amount = $7,200,000

Answer 2.

Initial Selling Price = $5,774,920

Answer 3.

Number of semiannual coupons = 40

Term to Maturity = 20 years

Answer 4.

Effective interest is increasing by each payment, so interest is determined by effective interest method.

Answer 5.

Cash Payment = $216,000

Semiannual Coupon Rate = Cash Payment / Face Amount
Semiannual Coupon Rate = $216,000 / $7,200,000
Semiannual Coupon Rate = 3%

Annual Coupon Rate = 2 * 3%
Annual Coupon Rate = 6%

Answer 6.

Interest Expense on 1^st Payment = Semiannual Interest Rate * Carrying Value before 1^st Payment
$230,997 = Semiannual Interest Rate * $5,774,920
Semiannual Interest Rate = 4%

Annual Interest Rate = 2 * 4%
Annual Interest Rate = 8%

Answer 7.

Total Cash Interest Paid = Semiannual Cash Payment * Number of semiannual coupon payments
Total Cash Interest Paid = $216,000 * 40
Total Cash Interest Paid = $8,640,000

Answer 8.

Total Cash Paid = Total Cash Interest Paid + Maturity Value
Total Cash Paid = $8,640,000 + $7,200,000
Total Cash Paid = $15,840,000

Total Interest Expense = Total Cash Paid - Amount borrowed
Total Interest Expense = $15,840,000 - $5,774,920
Total Interest Expense = $10,065,080