Case Narrative: A firm’s capital structure includes the following securities. It
ID: 2779863 • Letter: C
Question
Case Narrative: A firm’s capital structure includes the following securities. It has 500,000 shares of common stock (equity) outstanding, selling for $20 per share. The preferred stock share price is $50 and which a $4 dividend with no growth expected. Each share of common stock sells for $20 and pays a $1.00 dividend, which is expected to grow by 2% per year. The current price of the bonds is $818, and the coupon rate is 5%. The bonds will mature in 10 years.
What is the cost (yield to maturity %) of the bonds?
Explanation / Answer
Assuming annual coupons
C1=C2=C3=C4=C5=C6=C7=C8=C9=C10=Coupon=1000*5%=50
FV=1000
Price of b+onds=C1/(1+r)+C2/(1+r)^2...........+C9/(1+r)^9+(C10+FV)/(1+r)^10
=50/(1+r)+50/(1+r)^2.....50/(1+r)^9+1050/(1+r)^10
This should equal 818
Hence, r=7.67%
Assuming semi-annual coupons
C1=C2=C3=C4=C5=C6=C7=C8=C9=C10=C11=C12=C13=C14=C15=C16=C17=C18=C19=C20=Coupon=1000*5%/2=25
FV=1000
Price of b+onds=C1/(1+r/2)+C2/(1+r/2)^2...........+C19/(1+r/2)^19+(C20+FV)/(1+r/2)^20
=25/(1+r)+25/(1+r)^2.....25/(1+r)^19+1025/(1+r/2)^20
This should equal 818
Hence, r=7.63%