Question

The Althenon Corporation issues bonds with a $1 million face value on January 1, Year One. The bonds pay a stated interest rate of 5 percent each year on December 31. They come due in eight years. The Zephyr Corporation also issues bonds with a $1 million face value on January 1, Year One. These bonds pay a stated interest rate of 8 percent each year on December 31. They come due in eight years. Both companies actually issue their bonds to yield an effective annual interest rate of 10 percent. Both companies use the effective rate method. The present value of $1 at a 10 percent interest rate in eight years is $0.46651. The present value of an ordinary annuity of $1 at a 10 percent interest rate over eight years is $5.33493.

a. What interest expense does Althenon report for Year One and also for Year Two?

b. What interest expense does Zephyr report for Year One and also for Year Two?

Answer 1

computation of issue price:

Issue price=Present value of interest payments+Present value of face vale on maturity

For althenon corporation,

Present value of interest payments=interest payment*present value at 10% for 8 years=(1000000*5%)*5.33493=266746.50

Present value of face vale on maturity=face value*present value at 10% for 8th year=1000000*0.46651=466510

Issue price=266746.50+466510=733256.5

For Zephyr corporation,

Present value of interest payments=interest payment*present value at 10% for 8 years=(1000000*8%)*5.33493=426794.40

Present value of face vale on maturity=face value*present value at 10% for 8th year=1000000*0.46651=466510

Issue price=426794.40+466510=893304.4

Hence we can understand that both the bonds are issued at discount

Interest expense=opening book value of the bonds*Effective annual interest rate

For althenon corporation,

Year 1

Interest expense=opening book value of the bonds*Effective annual interest rate=733256.50*10%=73325.65

Year 2

opening book value of the bonds=previous year book value+bond discount amortized

Bond discount amortized=Interest expense for year 1-interest paid in cash for year 1=73325.65-(1000000*5%)=23325.65

opening book value of the bonds=733256.50+23325.65=756582.20

Interest expense=opening book value of the bonds*Effective annual interest rate=756582.20*10%=75658.22

For Zephyr corporation,

Year 1

Interest expense=opening book value of the bonds*Effective annual interest rate=893304.40*10%=89330.44

Year 2

opening book value of the bonds=previous year book value+bond discount amortized

Bond discount amortized=Interest expense for year 1-interest paid in cash for year 1=89330.44-(1000000*8%)=9330.44

opening book value of the bonds=893304.40+9330.44=902634.8

Interest expense=opening book value of the bonds*Effective annual interest rate=902634.80*10%=90263.48

Summary:

a.

Interest expense

Year 1

73325.65

Year 2

75658.22

b.

Interest expense

Year 1

89330.44

Year 2

90263.48