Question

1. An investor must choose between two bonds: Bond A pays $102 annual interest and has a market value of $890. It has 10 years to maturity. I Bond B pays $88 annual interest and has a market value of $800. It has five years to maturity. Assume the par value of the bonds is $1,000. What is the approximate yield to maturity on Bond B? The exact yield to maturity? (Use the approximation formula to compute the approximate yield to maturity and use the calculator method to compute the exact yield to maturity. Do not round intermediate calculations. Input your answers as a percent rounded to 2 decimal places.) Approximate yield to maturity % Exact yield to maturity %

Answer 1

For Bond A

Approximate yield to maturity = [C + (F-P)/n] / [(F+P)/2]

Where,

C = Coupon rate or interest payment on Bond A = $102 per year

F = Face value on the Bond = $1,000

P = Market Price of Bond A = $890

n = Years to maturity of Bond A = 10 years

Therefore,

Approximate yield to maturity = [$102 + ($1,000 - $890)/10] / [($1,000+$890)/2]

= $113 /$945 = 0.1196 or 11.96%

We have following formula for calculation of bond’s exact yield to maturity (YTM) of bond A

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

Where,

P0 = the current market price of bond = $890

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

C = coupon payment = $102

n = number of payments (time remaining to maturity) = 10 years

YTM = interest rate, or yield to maturity =?

Now we have,

$890 = $102 * [1 – 1 / (1+YTM) ^10] /YTM+ 1000 / (1+YTM) ^10

By trial and error method we can calculate the value of YTM = 12.16% per year

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

“= Rate(N,PMT,PV,FV)”

“Rate(10,102,-890,1000)” = 12.16%]

Therefore exact YTM = 12.16% per year

For Bond B

Approximate yield to maturity = [C + (F-P)/n] / [(F+P)/2]

Where,

C = Coupon rate or interest payment on Bond B = $88 per year

F = Face value on the Bond = $1,000

P = Market Price of Bond B = $800

n = Years to maturity of Bond B = 5 years

Therefore,

Approximate yield to maturity = [$88 + ($1,000 - $800)/5] / [($1,000+$800)/2]

= $128 /$900 = 0.1422 or 14.22%

We have following formula for calculation of bond’s exact yield to maturity (YTM) of bond B

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

Where,

P0 = the current market price of bond = $800

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

C = coupon payment = $88

n = number of payments (time remaining to maturity) = 5 years

YTM = interest rate, or yield to maturity =?

Now we have,

$800 = $88 * [1 – 1 / (1+YTM) ^5] /YTM+ 1000 / (1+YTM) ^5

By trial and error method we can calculate the value of YTM = 14.73% per year

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

“= Rate(N,PMT,PV,FV)”

“Rate(5,88,-800,1000)” = 14.73%]

Therefore exact YTM = 14.73% per year

Therefore Investor must choose Bond B as it has higher approximate yield to maturity as well as higher exact yield to maturity.