Question

​A(n)11.0​%,​25-year bond has a par value of​ $1,000 and a call price of​$1,050.​(The bond's first call date is in 5​ years.) Coupon payments are made semiannually​ (so use semiannual compounding where​ appropriate).

a. Find the current​ yield, YTM, and YTC on this​ issue, given that it is currently being priced in the market at$1,175.  Which of these 3 yields is the​ highest? Which is the​ lowest? Which yield would you use to value this​ bond? Explain.

b. Repeat the 3 calculations​ above, given that the bond is being priced at​$825.Now which yield is the​ highest? Which is the​ lowest? Which yield would you use to value this​ bond? Explain

Answer 1

a) Annual Coupon = $1000*11% = $110

Current Yield = Annual Coupon payments/ Current price = 110/1175 = 0.093617 or 9.36%

Semiannual Coupons = $55

No of coupons till maturity = 25*2 =50

Semiannual YTM(y) is given by

55/y*(1-1/(1+y)^50) + 1000/(1+y)^50 = 1175

Solving y = 0.046000

So, YTM = 0.046*2 = 0.092 or 9.20%

Semiannual Coupons = $55

No of coupons till Call = 5*2 =10

Semiannual YTC(r) is given by

55/r*(1-1/(1+r)^10) + 1050/(1+r)^10 = 1175

Solving r = 0.03786

So, YTC = 0.03786*2 = 0.07572 or 7.57%

The Current yield is the highest and the YTC is the lowest. We should use YTC to value the bonds as the call option will be exercised after 5 years and the investors will get YTC as the yield (as it is lower than the YTM). Hence, the bond should be valued keeping YTC as the yield and 5 years as the bond maturity with $1050 as redemption price.

b)

Annual Coupon = $1000*11% = $110

Current Yield = Annual Coupon payments/ Current price = 110/825 = 0.13333 or 13.33%

Semiannual Coupons = $55

No of coupons till maturity = 25*2 =50

Semiannual YTM(y) is given by

55/y*(1-1/(1+y)^50) + 1000/(1+y)^50 = 825

Solving y = 0.06724

So, YTM = 0.06724*2 = 0.134479 or 13.45%

Semiannual Coupons = $55

No of coupons till Call = 5*2 =10

Semiannual YTC(r) is given by

55/r*(1-1/(1+r)^10) + 1050/(1+r)^10 = 825

Solving r = 0.073097

So, YTC = 0.073097*2 = 0.1462 or 14.62%

The Current yield is the highest and the YTC is the lowest. We should use YTM to value the bonds as the call option will not be exercised after 5 years and the investors will get YTM as the yield (as it is lower than the YTC). Hence, the bond should be valued keeping YTM as the yield and 25 years as the bond maturity with $1000 as redemption price.