Question

A 6 percent coupon bond that has a $1,000 par value, semiannual coupon payments and a yield to maturity of 5.25 percent. The bond matures in 9 years.
What is the price of the bond, What will happen to the price if market interest rates rise to 6.45 percent, what can you say about the relationship between the price of a bond and the market interest rate?

Answer 1

Price of a bond is present value of all cashflows associated with the bond - namely coupons and maturity value.

It is mathematically represented as:

where P is price of a bond with periodic Coupon C, M Maturity Value, n periods to maturity and i as periodic market interest rates (or YTM)

For our bond in question, M = $1000, n = 9*2 = 18 semi-annual periods, C = $1000 * 6%/2 = $30

when i = 5.25% (annually) --> 2.625% (quarterly)

P = $1,053.25

when i = 6.45% (annually) --> 3.225% (quarterly)

P = $969.64

As the interest rate rises, price of bond declines.

When market interest rates (or YTM) > Coupon rates - bond price < par value

When market interest rates (or YTM) = Coupon rates - bond price = par value

When market interest rates (or YTM) < Coupon rates - bond price > par value

Increase in market interest rates, specifically means, that the bonds that are newly issued in market would offer higher coupon rates and hence, the demand for the existing bonds (with lower coupons) would decline. Similarly, when market interest rates decrease, specifically means, that the bonds that are newly issued in market would offer lower coupon rates and hence, the demand for the existing bonds (with higher coupons) would increase.