Question

Olympic Corp sold an issue of bonds with a 15-year maturity, a $1,000 face value, and a 10% coupon rate with interest being paid semiannually. The market rate of interest when the bonds were issued was 10%. Two years after the bonds were issued, the market rate rose to 13%. The most recent common-stock dividend for Olympic Corp was $3.45 per share. Due to its stable sales and earnings, the firm’s management predicts dividends will remain at the current level for the foreseeable future.

1) Are these bonds a premium or a discount bond?

2) Calculate the selling price for the bonds at the following time periods:

1) Time of issue

2) Two years after issue

3) Five years after issue

3) Calculate the selling price for the bonds at the following time periods assuming annual interest payments:

1) Two years after issue

2) Five years after issue

4) If the required return is 7%, what is the value of the common stock for Olympic Corp?

Answer 1

1) At time of issue the coupon rate is equal to the market rate of interest. Therefore, the bonds must have been issued at Par/ face value. So, these are neither premium nor discount bonds.

2) Bond price is the present value of future cash inflows of the bond computed @market rate of interest or YTM.

i) Time of issue

Since, YTM = Coupon rate = 10%, Bond price = Par value = $1000

ii) Two years after issue

Since bonds pay semi annual interest, we need semi-annual rates and time periods.

Semi - annual YTM = 13% / 2 = 6.5%, No. of semi - annual periods remaining = (15 - 2) x 2 = 26, Semi-annual interest = $1000 x 10% x 6/12 = $50

Bond price = $50 x PVIFA (6.5%, 26) + $1000 x PVIF (6.5%, 26) = $50 x 12.3923725101 + $1000 x 0.19449578667 = $814.11

iii) Five years after issue

Assuming market rate of interest is the same, i.e., 13%.

Semi - annual YTM = 13% / 2 = 6.5%, No. of semi - annual periods remaining = (15 - 5) x 2 = 20, Semi-annual interest = $1000 x 10% x 6/12 = $50

Bond price = $50 x PVIFA (6.5%, 20) + $1000 x PVIF (6.5%, 20) = $50 x 11.0185072463 + $1000 x 0.28379702886 = $834.72

3) i) Two years after issue

YTM = 13%, No. of years = 15 - 2 = 13 years, Annual interest = $1000 x 10% = $100

Bond price = $100 x PVIFA (13%, 13) + $1000 x PVIF (13%, 13) = $100 x 6.1218115192 + $1000 x 0.20416450244 = $816.35

ii) Five years after issue

No. of years = 15 - 5 = 10

Bond price = $100 x PVIFA (13%, 10) + $1000 x PVIF (13%, 10) = $100 x 5.42624347582 + $1000 x 0.2945883481 = $837.21

4) Stock pice = Dividend / required return = $3.45 / 7% = $49.29