PowerTap Utilities is planning to issue bonds with a face value of $1,300,000 an

Question

PowerTap Utilities is planning to issue bonds with a face value of $1,300,000 and a coupon rate of 7 percent. The bonds mature in 10 years and pay interest semiannually every June 30 and December 31. All of the bonds were sold on January 1 of this year. PowerTap uses the effective-interest amortization method. Assume an annual market rate of interest of 8 percent.

1. What was the issue price on January 1 of this year

2. What amount of interest expense should be recorded on June 30 and December 31 of this year?

3. What amount of cash should be paid to investors June 30 and December 31 of this year?

4. What is the book value of the bonds on June 30 and December 31 of this year?

Explanation / Answer

Solution:

1) Issue Price of the bonds on Jan 1

Coupon Rate = 7%

Semi Annual Interest Payment = Face Value 1,300,000 x 7%*1/2 = $45,500

Semi Annual maturity period (n) = 10*2 = 20

Current Market Interest Rate (R) = 8% annually or 4% semi annual market interest rate

Issue (Current) Price of Bond = Semi Annual Coupon Interest x PVIFA (R, n) + Par Value x PVIF (R, n)

Here,

R = Semi Annual Market Interest Rate = 4%

N = periods to maturity = 20

Par Value = Face Value = $1,300,000

Issue Price of the bonds = (45,500*13.59033) + (1,300,000*0.45639)

= 618,360 + 593,307

= $1,211,667

Note -- Calculation of Present Value Factor

PVIFA (R, n) = Present Value interest factory for ordinary annuity at R% for n periods = (1 – 1/(1+R)n) / R

PVIFA (4%,20) = (1 – 1/(1+0.04)20) / 0.04 = 13.59033

PVIF (R, n) = Present Value interest factor for ‘n’ period 10 at ‘R’% = 1/(1+R)n

PVIF (4%, 20) = 1/(1+0.04)20 = 0.45639

Present Value factor is taken for 5 decimal places.. Answer may be different due to decimal places..

2, 3 & 4) to solve these parts we need to prepare amortization table for the same.

Schedule of Amortization of Bond Discount (Effective Rate Method)

Payment intervals

Period End

Cash Interest (Par Value of the bonds 1,300,000 x Coupon Rate 7%*1/2 semi annual)

Interest Expenses (Book Value of Bonds x Market Rate 8%*1/2)

Amortization of Bond Discount (Interest Expenses - Cash Interest)

Balance of Unamortized Discount on Bonds Payable

Par Value of Bonds Payable

Book Value (Par Value - Balance of Unamortized Bond Discount)

0

Jan.1,

$88,333

$1,300,000

$1,211,667

1

June.30

$45,500

$48,467

$2,967

$85,366

$1,300,000

$1,214,634

2

Dec.31

$45,500

$48,585

$3,085

$82,281

$1,300,000

$1,217,719

Part - 2)

Amount of interest expense should be recorded on June 30 = $48,467

Amount of interest expense should be recorded on December 31 = $48,585

Part 3 –

Amount of cash should be paid to investors June 30 = $45,500

Amount of cash should be paid to investors December 31 of this year = $45,500

Part 4 -- -

Book Value on June 30 = 1,214,634

Book Value on Dec 31 = 1,217,719

Hope the above calculations, working and explanations are clear to you and help you in understanding the concept of question.... please rate my answer...in case any doubt, post a comment and I will try to resolve the doubt ASAP…thank you

Schedule of Amortization of Bond Discount (Effective Rate Method)

Payment intervals

Period End

Cash Interest (Par Value of the bonds 1,300,000 x Coupon Rate 7%*1/2 semi annual)

Interest Expenses (Book Value of Bonds x Market Rate 8%*1/2)

Amortization of Bond Discount (Interest Expenses - Cash Interest)

Balance of Unamortized Discount on Bonds Payable

Par Value of Bonds Payable

Book Value (Par Value - Balance of Unamortized Bond Discount)

0

Jan.1,

$88,333

$1,300,000

$1,211,667

1

June.30

$45,500

$48,467

$2,967

$85,366

$1,300,000

$1,214,634

2

Dec.31

$45,500

$48,585

$3,085

$82,281

$1,300,000

$1,217,719

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