Question

You buy a 7 percent coupon, 10-year maturity bond, which was issued in 2015. The yield to maturity is 6 percent. a) Is this a discount or a premium bond? Explain your answer! (4 points) b) What is the price of the bond today (in 2017)? (4 points) c) Tell (without any calculation) the price at which the bond would trade if today the yield to maturity would be exactly 7%. Support your answer. (7 points)

Answer 1

Given about a bond,

coupon rate = 7%

was issued in 2015 with 10-years to maturity

YTM = 6%

a). When YTM of a bond is less than coupon rate, bonds price is greater than its face value and it sells at premium.

Since for this bond, YTM is less than coupon rate, its is a premium bond.

b). today in 2017, years to maturity of bond = 8 years Face value = $1000

=> annual coupon payment = 7% of 1000 = $70

So, price of the bond can be calculated on financial calculator using following values:

FV = 1000

PMT = 70

N = 8

I/Y = 6

solve for PV, we get PV = -1062.10

So, price of the bond today = $1062.10 or 106.21%

c). It YTM of the bond = 7%, then its YTM equals to its coupon rate. For a bond if its YTM equals its coupon rate, they are priced at Par and their price equals to face value

So, price of the bond = $1000 or 100%