Question

Last year Charlie Investments issued a 10 year, 12% semiannual coupon bond at it's par value of $1000. Currently the bond can be paid in 4 years at a price of $1060 and it sells for $1100. Calculate the bond's nominal yield to maturity and it's nominal yield to call. Would an investor be more likely to earn the YTM or the YTC? Briefly explain your answer.

Answer 1

Solution

Coupon Bond's Par/ Face Value $=\$1,000$

Annual Rate $=12\%$

Semiannual rate $=\frac{12\%}{2}=6\%$

Maturity Period $=10$ years

Years to call $= 4$ yrears

Call-able Price $=\$1060$

Call-able Sale Price $=\$1100$

We know the formula,

Annual Coupon Payment $=$ Par value $\times$ Annual coupon rate

Replacing vales, we get

Annual Coupon Payment $=\$1000\times 12\%$

$=\$120$

Now, the current yield is $=\frac{annual\ coupon\ payment}{current\ price}$

$=\frac{\$120}{\$1100}\\=0.1090909....\\ =10.91\%$

Bond's nominal yield to maturity is calculated by taking promised interest rate and multiplying by the number of years until maturity

Therefore,

Bond's nominal yield to maturity $=12\%\times 10 = \$ 120$

Yield to Call is calculated as

$= \frac{{Annual\,Coupon\,Yield + \frac{{\left( {Call\,price - Bond\,face\,value} \right)}}{{Number\,of\,years\,to\,call}}}}{{\frac{{\left( {Call\,price + Bond\,Bond\,face\,value} \right)}}{2}}}$

$= \frac{{120 + \frac{{\left( {1060 - 1100} \right)}}{4}}}{{\frac{{\left( {1060 + 1100} \right)}}{2}}} = \frac{{120 - 10}}{{1080}} = 0.10185185185...\\ = 10.85\%$