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A(n) 11.0​%, ​25-year bond has a par value of​ $1,000 and a call price of ​$1 comma 025. ​(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 comma 150. 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 ​$800. Now which yield is the​ highest? Which is the​ lowest? Which yield would you use to value this​ bond? Explain.

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jepessoa

Answer:

the formula to calculate yield to maturity (YTM) is:

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

  • F = face value
  • P = market price
  • n = number of years x 2 =
  • C = coupon      

the formula to calculate yield to call (YTC) is:

YTC = [C + (F - CP)/n] / [(F + CP)/2]      

  • F = face value
  • CP = call price
  • n = number of years x 2 =
  • C = coupon      

the formula to calculate current yield is:

Current yield = C / P

  • C = coupon
  • P = market price

A)

25 year bond, $1,000 face value, semiannual coupons, 11%, call price $1,025, market price $1,150:

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

  • F = 1,000
  • P = 1,150
  • n = number of years x 2 = 25 x 2 = 50
  • C = 55      

YTM = [55 + (1,000 - 1,150)/50] / [(1,000 + 1,150)/2] =  [55 - 3] / 1,075 = 0.04837 or 4.84%  

YTC = [C + (F - CP)/n] / [(F + CP)/2]      

  • F = 1,000
  • CP = 1,025
  • n = number of years x 2 = 5 x 2 = 10
  • C = 55      

YTC = [55 + (1,000 - 1,025)/10] / [(1,000 + 1,025)/2] = [55 -2.50] / [1,012.50] = 0.05185 or 5.19%

Current yield = C / P

  • C = 55
  • P = 1,150

Current yield = 55 / 1,150 = 0.0478 or 4.78%

The highest value is the Yield to Call (5.19%) while the lowest value is the current yield (4.78%). Since the bonds were sold at a premium, the coupon rate is higher than the market rate, therefore, it is likely that the company will actually call them. So we should use the yield to call value.

B)

25 year bond, $1,000 face value, semiannual coupons, 11%, call price $1,025, market price $800:

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

  • F = 1,000
  • P = 800
  • n = number of years x 2 = 25 x 2 = 50
  • C = 55      

YTM = [55 + (1,000 - 800)/50] / [(1,000 + 800)/2] =  [55 + 4] / 900 = 0.06555 or 6.56%  

YTC = [C + (F - CP)/n] / [(F + CP)/2]      

  • F = 1,000
  • CP = 1,025
  • n = number of years x 2 = 5 x 2 = 10
  • C = 55      

YTC = [55 + (1,000 - 1,025)/10] / [(1,000 + 1,025)/2] = [55 -2.50] / [1,012.50] = 0.05185 or 5.19%

Current yield = C / P

  • C = 55
  • P = 800

Current yield = 55 / 800 = 0.06875 or 6.88%

The highest value is the current yield (6.88%) while the lowest value is the Yield to Call (5.19%). Since the bonds were sold at a discount, the coupon rate is lower than the market rate, therefore, it is not likely that the company will actually call them. So we should use the yield to maturity value.