Question

A bond has a 10 year maturity, a $1000 face value, and a 7% coupon rate. If the market requires a yield of 8% on similar bonds, it will mostly trade at a:

A. discount

B. premium

C. discount or premium, depending on its duration

Please give example, such as calculation and so on...

Answer 1

The correct answer is Discount

The Bond price is based on the present value of all the cash flows that a bond is going to generate till the maturity period. The rate of discount used is the yield to maturity. So, When the yield is higher than the coupon rate it will lead to higher discounting resulting in present value less than the face value.

Bond Price = P * [ 1 - (1+r)^-n]/ r + Fv/(1+r)^n

Where, P is coupon payment

r = Yield per period

n = number of periods

Fv = Face value

In this case, Bond Price

= 70 [ 1 - (1+8%)^-10]/ 8%+ 1000 /(1+8%)^10

= 70 [ 1 - 0.46319] / 0.08 + 1000 / 2.158924

= 70 * 6.710081 + 463.1937020

= 469.7056 + 463.1937020

= 932.899

Thus, We have proved that the Bond price will be lower than the face value when the yield id higher than the coupon rate thus leading to trade at discount.