Question

A(n)10.0?%,?25-yearbond has a par value of? $1,000and a call price of ?$1,125. ?(Thebond's first call date is in 5? years.)Coupon payments are made semiannually? (souse 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 $1,250. 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 ?$900. 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 $1250? the current yield is -----------?%.?(Roundto two decimal? places.)

The annual? yield-to-maturitywith semiannual compounding is -------?%.?(Roundto two decimal? places.)

The annual? yield-to-callwith semiannual compounding is ----------?%. (Roundto two decimal? places.)

Which of these 3 yields is the? highest?------------Which is the? lowest? ---------

Which yield would you use to value this? bond? ?(Selectthe best answer? below.)

A. The? yield-to-maturityis always used.

B. The? yield-to-maturitybecause convention is to use the lower of? yield-to-maturityor? yield-to-callfor bonds selling at a discount.

C. The? yield-to-maturitybecause the bonds may not be called.

D. It? doesn'tmatter which yield you use.

B. If the bond is priced at $900?,the current yield is---------------?%.?(Roundto two decimal? places.)

The annual? yield-to-maturitywith semiannual compounding is --------------?%.?(Roundto two decimal? places.)

The annual? yield-to-callwith semiannual compounding is ------------?%.?(Roundto two decimal? places.)

Which of these 3 yields is the? highest?Which is the? lowest????(Selectfrom the? drop-downmenus.)

Current yield

Yield-to-maturity

Yield-to-call

Which yield would you use to value this? bond??

?A. It? doesn'tmatter which yield you use.

B. The? yield-to-maturitybecause the bonds may not be called.

C. The? yield-to-maturitybecause convention is to use the lower of? yield-to-maturityor? yield-to-callfor bonds selling at a discount.

D.The? yield-to-maturityis always used.

Answer 1

a.

Current Yield=

Coupon interest/Current market price

(10%*1000)/1250=

8%

Yield to maturity

Equating the current market market price of the bond to thesum of PVs of future coupon payments till maturity +PV of face value to be received at maturity (both discounted at The YTM,

1250=((10%/2*1000)*(1-(1+YTM)^-50)/YTM)+(1250/(1+YTM)^50

Solving for YTM, we get,the semi-annual YTM as

4%

So,annual YTM=(1+0.04)^2-1=

8.16%

Yield to Call

Equating the current market market price of the bond to thesum of PVs of future coupon payments till call date +PV of call price to be received (both discounted at The YTC,

1250=((10%/2*1000)*(1-(1+YTC)^-10)/YTC)+(1125/(1+YTC)^10

Solving for YTC, we get,the semi-annual YTC as,

3.13%

So,annual YTC=(1+0.0313)^2-1=

6.36%

YTM is the highest (8.16%)

It is better to use YTM to value the bond, as it covers the entire duration of the bond.

ANSWER: A. The? yield-to-maturity is always used.

b.

Current Yield=

Coupon interest/Current market price

(10%*1000)/900=

11.11%

Yield to maturity

Equating the current market market price of the bond to thesum of PVs of future coupon payments till maturity +PV of face value to be received at maturity (both discounted at The YTM,

900=((10%/2*1000)*(1-(1+YTM)^-50)/YTM)+(1250/(1+YTM)^50

Solving for YTM, we get,the semi-annual YTM as

6%

So,annual YTM=(1+0.0556)^2-1=

11.43%

Yield to Call

Equating the current market market price of the bond to thesum of PVs of future coupon payments till call date +PV of call price to be received (both discounted at The YTC,

900=((10%/2*1000)*(1-(1+YTC)^-10)/YTC)+(1125/(1+YTC)^10

Solving for YTC, we get,the semi-annual YTC as,

7.34%

So,annual YTC=(1+0.0734)^2-1=

15.22%

YTC is the highest (15.22%)

It is better to use YTM to value the bond, as it covers the entire duration of the bond.

ANSWER: D.The? yield-to-maturity is always used.