Answer to Question #112054 in Finance for Arminas Lensbergas

Question

Consider a two year coupon bond, with an annual coupon of £500 and a
balloon payment of £2400. Suppose at t=0 the yield on a riskless bond that mature in
one year is 5% and the annualized yield on a two-year bond is also 5%.

Compute the present value, at t=0 of the bond.
What is the duration of the bond?
What is the meaning of duration and why this is an important feature to assess a bond?

Answer 1

Present value of the bond is equial to discounted cash flow:

$$PV = C/(1+r1) + C/(1+r2)^2+N/(1+r2)^2$$

• , where PV - present value of the bond, C - annual coupon, r1 - yield of one-year bond, r2 - yield of two-year bond, N - baloon payment.

$PV = 500/1.05+500/1.05^2+2400/1.05^2= 3106.576$

• Duration measures how sensitive price of the bond is to changes in the interest rates. Duration is important because if we anticipate increase in the interest rates we are interested in bonds with low duration as price decrease of such bonds will be minimal and vice versa - if we anticipate decrease in intereste rates we will be interested in bonds with high duration as their price increase will be maximal.
• Duration can be calculated as :

$D = - (dPV/PV)/ (dr/(1+r))$ ,

where D - duration of the bond, r - yield to maturity of the bond (5% in our example)

$D =( C/(1+r) + 2C/(1+r)^2+2N/(1+r)^2)/PV$

$D = (500/1.05+2*500/1.05^2+2*2400/1.05^2)/3106.576 = 1.8467$ years