Question

On January 1, 2016, Learned, Inc., issued $70 million face amount of 20-year, 14% stated rate bonds when market interest rates were 16%. The bonds pay interest semi-annually each June 30 and December 31 and mature on December 31, 2035.
REQUIRED:
A) Using the present value tables, calculate the proceeds (issue price) of Learned, Inc.’s bonds on January 1, 2016, assuming that the bonds were sold to provide a market rate of return to the investor.
B) Assume instead that the proceeds were $72,400,000. Use the horizontal model (or write the journal entry) to record the payment of semi-annual interest and the related premium amortization on June 30, 2016, assuming that the premium of $2,400,000 is amortized on a straight-line basis.
C) If the premium in PART B were amortized using the compound interest method, would interests expense for the year ended December 31, 2016 be more than, less than, or equal to the interest expense reported using the straightline method of premium amortization? Explain.
D) In reality, the difference between the stated interest rate and the market rate would be substantially less than 2% . The dramatic difference in the problem was designed so that you could use present value tables to answer PART A. What causes the stated rate to be different from the market rate, and why is the difference likely to be much less than depicted in the problem?

Answer 1

Answer:

A) $61,654,600

B) June 30, 2016, first coupon payment

Dr Interest expense 4,840,000

Dr Premium on bonds payable 60,000

    Cr Cash 4,900,000

C) If you use the effective interest rate, the bond premium is higher, so the actual interest expense would be lower:

June 30, 2016, first coupon payment

Dr Interest expense 4,756,406

Dr Premium on bonds payable 143,594

    Cr Cash 4,900,000

D) The actual difference between the coupon rate and the effective interest rate (with a $72,400,000 issue price) = 14% (coupon rate) - 13.93% = 0.07%.

The bond's issue price is generally determined by the market rate, but sometimes a company might believe that the interest rate applicable to them is actually different. A company might under estimate the riskiness of their operations, but the market doesn't. Generally the market rate is correct. So any variation in the coupon rate is due to a mistake by the firm. Usually companies do not make huge mistakes, if they miss on the coupon rate it generally is not significant.

Explanation:

issued $70 million face amount of 20-year, 14% stated rate bonds when market interest rates were 16%. The bonds pay interest semi-annually each June 30 and December 31, each coupon = $4,900,000

bonds market price = PV of maturity value + PV of coupons

• PV of maturity value = $70,000,000 x 0.04603 = $3,222,100
• PV of coupons = $4,900,000 x (8% annuity, 40 periods) = $4,900,000 x 11.925 = $58,432,500
• total issue price = $61,654,600

if instead the issue price was $72,400,000 (resulting in a $2,400,000 premium), then the premium would be amortized by $2,400,000 / 40 = $60,000 during each coupon payment

if the effective interest method, (not the compound interest method), was used to amortize bond premium, then we first need to calculate the effective interest rate:

$72,400,000 - $70,000,000 = $2,400,000 / 40 = $60,000

$4,900,000 + $60,000 = $4,960,000 / {($72,400,000 + $70,000,000) / 2} = 0.0696629

bond premium discount using effective interest rate = ($72,400,000 x 0.0696629) - $4,900,000 = $5,043,594 - $4,900,000 = $143,594