Question

3. A 12-year, 12% semiannual coupon bond with a par value of $1,000 may be called in 6 years at a call price of $1,030. The bond sells for $1,150. (Assume that the bond has just been issued.)

a. What is the bond’s yield to maturity?

b. What is the bond’s current yield?

c. What is the bond’s capital gain or loss yield?

d. What is the bond’s yield to call?

Answer 1

Answer(a):YTM = [C + (F-P) /n ] / (F + P)/2

C: 1000*12% * 6 /12 = $60, F = $1000, P = $1150, n = 12 years

YTM = [60 + (1000-1150) / 12] / (1000 + 1150) / 2

YTM = 9.842% (Annual)

(b): Current Yield = Annual Coupons / Current bond price

(As it is the semiannual coupon bond so coupon will be divided by 2)

Coupon payment: 1000*12%*6/12 = $60

Current yield = 60 / 1150

Current Yield = 5.22%

(d): Yield to Call = [Annual Coupons + (Call price-Bond price) / Number of years to call] / (Call price + Bond price)/2

YTC = [60 + 1030-1150)/6] / (1030+1150)/2

Bond's Yield to call is 9.09% (annual)

Note: YTM and YTC are calculated by considering semiannual coupon but final answer will be in annual percentage so multiplied by 2)