Question

(a) Fill in the table and determine the price and duration of a bond with a maturity of 4 years, $100 face value, paying a 8% coupon annually, and trading at a yield to maturity of 9%? Fill in the cells of the table + (28 marks T Cashflow Discount factor PV Proportion of T x Proportion of total PV- (Year) total Pve - UM SUMA Price Duration (b) Use the duration of the bond that you have calculated in 4(a) to predict the change in the bond price if interest rates rise by 100 basis points. (6 marks)

Answer 1

1 Maturity 2 Face value 3 Present value 4 Coupon 5 Yield to maturity 6 7 8 10 8 Discount factor 1/(1+r) PV (CF*discount fact Prop of PV (PV/Sum T*Prop of PV 0.917431193 7.339449541 0.075851884 0.075851884 0.841679993 6.733439946 0.069588884 0.139177769 0.77218348 6.17746784 0.063843013 0.19152904 108 0.708425211 76.5099228 0.790716218 3.162864874 96.76028012 3.569423566 4

Cash flow = coupon rate*Face value for year 1,2 and 3. Cash flow at the end of 4th year = Face value*(1+coupon rate)

Discount factor = 1/(YTM+1)^T

PV of that cash flow = discount factor* cash flow

Price of bond = sum of PV of all cash flows = $96.76

Duration = sum of T*Proportion of PV = 3.569 years

This is Macauley duration. Modified duration = Macauley duration / (1+YTM/n ) = 3.569/(1+0.09)= 3.274

change in bond price/ current bond price = -Modified duration * change in YTM (in decimals)

100 basis points = 0.01 decimals

change in Bond price/current bond price = -3.274*0.01 = -0.0327

chang in bond price = -0.0327* = -$3.16

Hence, new bond price = $93.59