Question

4. Calculate the present value for the following five year bond, which has a par value of $1000, a coupon payment of 3.5% and the following discount rates: r1 =1%, r2 = 1.5%, r3 = 1.6%, r4 = 1.85% r5 = 2.2% Show your work, step by step for partial credit. If your answer is wrong and you don’t show your work, you’ll receive no partial credit. (10 pts.)

Answer 1

Given about a 5 year bond,

Face value = $1000

coupon rate = 3.5%

So, annual coupon payment = 3.5% of 1000 = $35

discount rates: r1 =1%, r2 = 1.5%, r3 = 1.6%, r4 = 1.85% r5 = 2.2%

So, price of the bond is sum of PV of all future coupons and Face value discounted at its discount rate

=> Price = C/(1+r1) + C/(1+r2)^2 + C/(1+r3)^3 + C/(1+r4)^4 + (C+FV)/(1+r5)^5

=> Price = 35/1.01 + 35/1.015^2 + 35/1.016^3 + 35/1.0185^4 + 1035/1.022^5 = $1062.82

So, Present value of the bond = $1062.82