Question

starbucks has a 8.8% coupon 10 year bond (par value = 1,000). assume that coupon payments are semiannual and that the yield-to-maturity is 8.2%. what is the price of this bond?

Answer 1

Price of the bond = C×( 1-(1 + r)^-n)/r  + F/(1+r)ⁿ

where C = Periodic coupon payment,

F = Face / Par value of bond,

r = Yield to maturity (YTM) and

n = No. of periods till maturity

As the question is of semi annual payments , so

Coupon rate will be 8.8%/2 = 4.4% or 0.044

Coupon amount will be $1,000× 4.4%=$44

Yield to maturity will be 8.2%/2 =4.1% or 0.041

So the price of bond will be =

=44 × (1-(1+0.041)^-20)/0.041 +1,000/(1+0.041)²⁰

=44×(1-(1.041)^-20)/0.041 + 1,000/(1.041)²⁰

=44×(1-0.447)/0.041 + 1,000/(1.041)²⁰

=44×0.553/0.041 + 447.698

=$(593.463 + 447.698)

=$1041.161

PRICE OF THE BOND = $1041.161

Note ÷

As nothing is mentioned inthe question about rounding off , so the figures are rounded to 3 decimals.