Question

Coupon payments are fixed, but the percentage return that investors receive varies based on market conditions. This percentage returned is referred to as a yield.

A bond’s yield to maturity (YTM) is the percentage return that it is expected to generate if the bond is assumed to be held until it matures. Calculating a bond’s YTM requires you to make several assumptions. Which of the following is one of these assumptions?

The bond is callable.

The probability of default is zero.

Consider the following case of Purple Whale Foodstuffs Inc.:

Purple Whale Foodstuffs Inc. has 9% annual coupon bonds that are callable and have 18 years left until maturity. The bonds have a par value of $1,000, and their current market price is $1220.35. However, Purple Whale Foodstuffs Inc. may call the bonds in eight years at a call price of $1,060.

What are the YTM and yield to call (YTC) on bonds?

Purple Whale Foodstuffs Inc.’s bonds have a yield-to-maturity (YTM) of    and a yield-to-call (YTC) of   .

If interest rates are expected to remain constant, what is the best estimate of the remaining life left for Purple Whale Foodstuffs Inc.’s bonds?

18 years

8 years

5 years

13 years

If Purple Whale Foodstuffs Inc. issued new bonds today, what coupon rate must the bonds have to be issued at par?

Answer 1

A bond’s yield to maturity (YTM) is the percentage return that it is expected to generate if the bond is assumed to be held until it matures. Calculating a bond’s YTM requires us to make several assumptions --one of which is

The probability of default is zero.

that the bond will run through its full term , without any interest defaults.

Purple Whale Foodstuffs Inc.

We can find the YTM by using the formula to find the bond price

ie. Bond's current market price=PV of all its coupons+PV of Fv to be recd. At its maturity----Both discounted at the YTM

ie. Price= ($ Coupon Amt.*(1-(1+YTM)^-n)/YTM)+(FV/(1+YTM)^n

Substituting the given values,

ie.1220.35=((1000*9%)*(1-(1+YTM)^-18)/YTM)+(1000/(1+YTM)^18)

Solving the above, we get the Ytm as

6.84%

Given that

Purple Whale Foodstuffs Inc. may call the bonds in eight years at a call price of $1,060

Yield to Call (YTC) can be calculated in the same manner

substituting ,

FV, 1000 as $ 1060

& n, 18 as   8

ie.1220.35=((1000*9%)*(1-(1+YTC)^-8)/YTC)+(1060/(1+YTC)^8)

Solving the above, we get the YTC as

6.05%

Purple Whale Foodstuffs Inc.’s bonds have a yield-to-maturity (YTM) of 6.84%   and a yield-to-call (YTC) of 6.05%.

If interest rates are expected to remain constant, what is the best estimate of the remaining life left for Purple Whale Foodstuffs Inc.’s bonds?

ie. If market interest rates stay at 6.84%

the best estimate of the remaining life left for Purple Whale Foodstuffs Inc.’s bonds

is. 18 years

Answer: a---- 18 yrs.

(The same equation holds)----ie. Substituting in the same equation

ie.1220.35=((1000*9%)*(1-(1+6.84%)^-n)/6.84%)+(1000/(1+6.84%)^n)

solving for n, we get the remaining life as

18 years

If Purple Whale Foodstuffs Inc. issued new bonds today, what coupon rate must the bonds have to be issued at par?

as the market interest rates today is 6.84%

a par bond has the same interest rate as the market interest rate

Issue Price=((1000*6.84%)*(1-(1+6.84%)^-18)/6.84%)+(1000/(1+6.84%)^18)

1000

when coupon rate < YTM(Mkt. interest rate)---Price > Par

when coupon rate > YTM(Mkt. interest rate)---Price < Par

& when coupon rate = YTM(Mkt. interest rate)---Price = Par

and for all the above, the converse is also TRUE----ie. Price & interest rates.