Question

What is the price of a bond with a 14% semi-annual coupon for 8 years to maturity at the end of which it repays a principal of 1000, with a YTM of 12%? Will the bond sell at a premium, at par, or at a discount? How can you tell?

Answer 1

Given Information:

Coupon rate (C) = 14% semi-annual coupon i.e. 7% per period

Coupon payment = 1000 * 7% = 70

Period (n) = 8 years i.e. 16 periods

Redemption value (R) = 1000

Yield to maturity (YTM) (i) = 12% i.e. 6% per period

a. Price of bond:

Price of a bond is the sum of present value of coupon payments & redemption value.

P₀ = C * PVIFA _(i%,n) + R * PVIF _(i%,n)

(Note: Present value interest factor of annuity (PVIFA) is used to calculate the present value of a series of annuity payments. It is the sum of present values @ i% for n periods.

Similarly, Present value interest factor (PVIF) is used to calculate the present value of a single payment @ i%, n periods from now).

P₀ = 70 * PVIFA _(6%,16) + 1000 * PVIF _(6%,16)

P₀ = 70 * 10.1059 + 1000 * 0.3936

P₀ = 707.4127 + 393.6463

P₀ = 1101.06 or 1101 (approx)

b. Will bond sell at par, premium or discount:

Par value of bond = 1000

Price of bond (as calculated above) = 1101

Hence, the bond will sell at a premium.

Note: Value of a bond can be ascertained by comparing the bonds's coupon rate with YTM.

If YTM < Coupon rate - The bond will sell at a premium. The investor's expectation is less than the coupon rate offered by the company, so the investors are willing to pay more than the par value,

If YTM > Coupon rate - The bond will sell at a discount. The investor's expectation is more than the coupon rate, so the investors will demand a discount from the company to compensate for the lower rate.

If YTM = Coupon rate - Bond will sell at par.

In the given situation, YTM (6%) < Coupon rate (7%), hence, the bond will sell at a premium.