Today you purchase a $1,000 par value convertible bond of Bunky’s Burgers. The b

Question

Today you purchase a $1,000 par value convertible bond of Bunky’s Burgers. The bond matures in 20 years and has an annal coupon of 10% payable semiannually. The yield to the maturity on the the bond is 12% a year, compounded semiannually. The bond is convertible into Bunky's common stock at a conversion price of $100 a share. You forecast that the earnings and dividends of Bunky's will grow at annual rates of 20% for the next 6 years and then 30% for another 6 years before settling at a 6% growth rate for the indefinite future. Yesterday the firm paid a dividend (D0) of $2.72. Stockholders require a return of 18% on stocks in Bunky's risk class.

A) You hold the bond for 8 years and then convert it. Assume that your forecasts hold. What IRR did you earn over the 7 year period?

B) If you hold the bond for 20 years and convert it the day it matures, what rate of return did you earn if all the forecasts come true? (Assume you do receive the final coupon payment)

Explanation / Answer

A) Par = $1000 , Convertible Price = $100 / share

n = 20 years = 40 half years , Is1 = 20% , n = 6 , Is2 = 30% , n = 6 years , In = 6% , n = infinity

c = 10% / yr , CSA = 100 / 2 = 50

YTM = 12% /yr, CSA = 6% per period

Do = $2.72 , k = 18%

P7 = D8 / (1+ ke)^1 + D9 / (1+ ke)^2 + D10 / (1+ ke)^3 + D11 / (1+ ke)^4 +  D12 / (1+ ke)^5 + P12 / (1+ ke)^5

= 2.72 (1.20)^6 (1.3)^2 / (1.18) + 2.72 (1.20)^6 (1.3)^3 / (1.18)^2 + 2.72 (1.20)^6 (1.3)^4 / (1.18)^3 +

2.72 (1.20)^6 (1.3)^5 / (1.18)^4 + 2.72 (1.20)^6 (1.3)^6 / (1.18)^5

+ 2.72 (1.20)^6 (1.3)^5 (1.06) / 0.18 - 0.06 x (1 / (1.18)^5)

= 11.63 + 12.82 + 14.12 + 15.55 + 17.14 + 177.56

= 248.82

1 bond = 1000 / 100 = 10 shares

So, the convertible value of the bond = 248.82 x 10 = $2488.20

P = 40 (PVIFc - 6% - 50 ) + 1000 / (1.06)^40

= 601.8519 + 97.222 = 699.07

699.07 = 40 (PVIFc - r - 14 ) + 2488.20 / (1+r)^14

r = 6.26% / period or = 12.52% per year CSA

B) P20 =  2.72 (1.20)^6 (1.3)^6 (1.06) / 0.18 - 0.06 = 367.897 x 10 = 3678.97

699.07 = 40 (PVIFc - r - 14 ) + 3678.97 / (1+r)^40

r = 5.59% per period or = 11.18% per year CSA

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