Question

Last year Carson Industries issued a 10-year, 13% semiannual coupon bond at its par value of $1,000. Currently, the bond can be called in 6 years at a price of $1,065 and it sells for $1,200.

a. What is the bond's nominal yield to maturity? Do not round intermediate calculations. Round your answer to two decimal places.

b. What is the bond's nominal yield to call? Do not round intermediate calculations. Round your answer to two decimal places.

c. What is the current yield? (Hint: Refer to Footnote 7 for the definition of the current yield and to Table 7.1.) Round your answer to two decimal places.

d. What is the expected capital gains (or loss) yield for the coming year? Use amounts calculated in above requirements for calcuation, if reqired. Round your answer to two decimal places. Enter a loss percentage, if any, with a minus sign.

Answer 1

a. What is the bond's nominal yield to maturity? Do not round intermediate calculations.

We have following formula for calculation of bond’s nominal yield to maturity (YTM) for the case when it is not called

Bond price P0 = C* [1- 1/ (1+YTM) ^n] /i + M / (1+YTM) ^n

Where,

P0 = the current market price of bond = $1,200

C = coupon payment = 13% of $1000 = $130 but semiannual coupon, therefore C = $130/2 = $65

n = number of payments = 10 *2 = 20

YTM = interest rate, or yield to maturity =?

M = value at maturity, or par value = $ 1000

Now we have,

$ 1,200 = $65 * [1 – 1 / (1+YTM) ^20] /i + 1000 / (1+YTM) ^20

By trial and error method we can calculate the value of YTM, which is 4.91% semiannual

Therefore yield to maturity of bond, YTM = 2 *4.91% = 9.82% per year

[Or you can use excel function for YTM calculation in following manner

“= Rate(N,PMT,PV,FV)”

“Rate(20,-65,1200,-1000)” = 4.91%]

b. What is the bond's nominal yield to call? Do not round intermediate calculations.

The formula to calculate the bond's nominal yield-to-call is as follows

P = the current market price of bond = $1,200

C = coupon payment = 13% of $1000 = $130 but semiannual coupon, therefore C = $130/2 = $65

CP = the call price = $1,065 (assumed it as the maturity value if the bond is callable)

t = the number of years remaining until the call date = 6 years, therefore payments = 6*2 =12

YTC = the yield to call =?

The complete formula to calculate yield to call is:

P = C * {(1 – 1/ (1 + YTC) ^ t) / (YTC)} + (CP / (1 + YTC) ^t)

$1,200 = $65 *{(1- 1/ (1+ YTC) ^12)/ (YTC)} + ($1,065/ (1+YTC) ^12)

With the help of above equation and by trial and error method we can calculate the value of YTC, which is 4.70% semiannual

The yield to call, YTC= 2 *4.70% = 9.39% per year

[Or you can use excel function for YTC calculation in following manner

“= Rate(N,PMT,PV,FV)”

“Rate(12,-65,1200,-1065)” = 4.70%]

c. What is the current yield?

Current yield = Annual coupon / current bond price

= $130 / $1,200

=10.83% per annum

d. What is the expected capital gains (or loss) yield for the coming year? Use amounts calculated in above requirements for calculation, if required.

Expected capital gains (or loss) yield = YTM - Current yield

= 9.82% -10.83% = -1.01%