Question

A(n) 8.0%, 20-year bond has a par value of $1,000 and a call price of $1,100. (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 $1,225. 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 $875. Now which yield is the highest? Which is the lowest? Which yield would you use to value this bond? Explain. a. If the bond is priced at $1,225, the current yield is %. (Round to two decimal places.) The annual yield-to-maturity with semiannual compounding is %. (Round to two decimal places.) The annual yield-to-call with semiannual compounding is %. (Round to two decimal places.) Which of these 3 yields is the highest? Which is the lowest? (Select from the drop-down menus.) V is the highest, while is the lowest Which yield would you use to value this bond? (Select the best answer below.) O A. It doesn't matter which yield you use. O B. The yield-to-call because convention is to use the lower more conservative measure of yield. O C. The yield-to-maturity because the bonds may not be called. OD. The yield-to-maturity is always used. b. If the bond is priced at $875, the current yield is %. (Round to two decimal places.) The annual yield-to-maturity with semiannual compounding is %. (Round to two decimal places.) The annual yield-to-call with semiannual compounding is %. (Round to two decimal places.) Which of these 3 yields is the highest? Which is the lowest? (Select from the drop-down menus.) V is the highest, while is the lowest Which yield would you use to value this bond? (Select the best answer below.) O A. It doesn't matter which yield you use. O B. The yield-to-maturity because convention is to use the lower of yield-to-maturity or yield-to-call for bonds selling at a discount. O C. The yield-to-maturity because the bonds may not be called. OD. The yield-to-maturity is always used.

Answer 1

a]

current yield = annual coupon payment / current bond price

annual coupon payment = face value * coupon rate = $1,000 * 8% = $80

current yield = $80 / $1,225 = 6.53%

YTM is calculated using RATE function in Excel with these inputs :

nper = 20*2 (20 years to maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 8% / 2 (semiannual coupon payment = face value * annual coupon rate / 2. This is a positive figure as it is an inflow to the bondholder)

pv = -1225 (current bond price. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 1000 (face value of the bond receivable on maturity. This is a positive figure as it is an inflow to the bondholder)

The RATE is calculated to be 3.02%. This is the semiannual YTM. To calculate the annual YTM, we multiply by 2. Annual YTM is 6.05%

A1 X fac =RATE(20*2,1000*8%/2,-1225,1000) *2 D E F G B C A 6.05%! 1

YTC is calculated using RATE function in Excel with these inputs :

nper = 5*2 (5 years to call date with 2 semiannual coupon payments each year)

pmt = 1000 * 8% / 2 (semiannual coupon payment = face value * annual coupon rate / 2. This is a positive figure as it is an inflow to the bondholder)

pv = -1225 (current bond price. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 1100 (call price of the bond receivable on call date. This is a positive figure as it is an inflow to the bondholder)

The RATE is calculated to be 2.35%. This is the semiannual YTC. To calculate the annual YTC, we multiply by 2. Annual YTC is 4.70%

A2 X fi =RATE(5*2, 1000*8%/2,-1225, 1100)*2 B C D F G A 4.70%! 2

The current yield is the highest, while the YTC is the lowest

B - The yield to call because the convention is to use the lower more conservative measure of yield

b]

current yield = annual coupon payment / current bond price

annual coupon payment = face value * coupon rate = $1,000 * 8% = $80

current yield = $80 / $875 = 9.14%

YTM is calculated using RATE function in Excel with these inputs :

nper = 20*2 (20 years to maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 8% / 2 (semiannual coupon payment = face value * annual coupon rate / 2. This is a positive figure as it is an inflow to the bondholder)

pv = -875 (current bond price. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 1000 (face value of the bond receivable on maturity. This is a positive figure as it is an inflow to the bondholder)

The RATE is calculated to be 4.70%. This is the semiannual YTM. To calculate the annual YTM, we multiply by 2. Annual YTM is 9.40%

X fac =RATE(20*2,1000*8%/2,-875, 1000)*2 D E F | B C A 9.40%!

YTC is calculated using RATE function in Excel with these inputs :

nper = 5*2 (5 years to call date with 2 semiannual coupon payments each year)

pmt = 1000 * 8% / 2 (semiannual coupon payment = face value * annual coupon rate / 2. This is a positive figure as it is an inflow to the bondholder)

pv = -875 (current bond price. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 1100 (call price of the bond receivable on call date. This is a positive figure as it is an inflow to the bondholder)

The RATE is calculated to be 6.48%. This is the semiannual YTC. To calculate the annual YTC, we multiply by 2. Annual YTC is 12.96%

A2 X fac =RATE(5*2,1000*8%/2,-875,1100)*2 D E F G B C A 12.96%! 2

The YTC is the highest, while the current yield is the lowest

B - The yield to maturity because the convention is to use the lower of YTM or YTC for discount bonds