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. PRIMARY POST: Question 1 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. Since Bonds are issued on market rate of interest, they would have been issued at par. It can be proved by bond price equation.

P₀ = C(PVIFA_R%,t) + $1000(PVIF_R%,t)

Semi annual interest = ($1000*10%)/2 = 50

Term = 15 years * 2 = 30

Market rate = 10% p.a. i.e. 5% for half year

P₀ = $50(PVIFA_5%,30) + $1000(PVIF_5%,30) = $1000

So, these are neither a premium bond nor discount bond.

2. Selling price of bond

1) at the time of issue

  P₀ = $50(PVIFA_5%,30) + $1000(PVIF_5%,30) = $1000

2) Two years after issue

Market rate = 13% per annum i.e. 6.5% for half year

P₂ = $50(PVIFA_6.5%,26) + $1000(PVIF_6.5%,26) = $814.11

3) Five years after issue

P₅ = $50(PVIFA_6.5%,20) + $1000(PVIF_6.5%,20) = $834.72

3. Selling price for the bonds assuming annual interest payment

Coupon amount = 1000*10% = 100, Market rate= 10% at the time of issue, 13% two years after issue

1) Two years after issue

   P₂ = $100(PVIFA_13%,13) + $1000(PVIF_13%,13) = $816.35

2) Five years after issue

  P₅ = $100(PVIFA_13%,10) + $1000(PVIF_13%,10) = $837.21

4. Required return(K_e) = 7%, Dividend = $3.45 per share, Growth = 0%

Value of common stock by gordon's growth model = D₁/(K_e-g)

= $3.45/(0.07-0)

= $49.29