Question

www U ULJ DOU BOND VALUATION An investor has two bonds in his portfolio that have a face value of $1,000 and pay a 10% annual coupon. Bond L matures in 15 years, while Bond S matures in 1 year. a. What will the value of each bond be if the going interest rate is 5%, 8%, and 12%? Assume that only one more interest payment is to be made on Bond S at its maturity and that 15 more payments are to be made on Bond L. b. Why does the longer-term bond's price vary more than the price of the shorter-term bond when interest rates change?

need the answer please

Answer 1

Given,

Face value (FV) = $ 1000

Annual coupon rate = 10%

Coupon payment = $ 1000 x 10% = $ 100

Maturity of Bond L = 15 years

Maturity of Bond S = 1 year

Solution :-

When rate is 5%, going interest r = 5% g 0.05 Now, Value of Bond L where (= de n= Coupon Interest maturity payment rate of bond. Now, value of b Bond L 1ooo t 0.05 (1+0.05)' s Bool) +005) on - (1100375) + 0,7005 - 2000[1- osis) + 4.0093's

= 2000 - 201892818) + 2.09.20 2.07892818T looo 2.07892818 x 1.0789 28 18 2.078928187 looo 2.07892818 481.011098 = - 1037.9658 $ 1518.98 Value of bonds 11ton) T FV toon = (2.0004 o + lo = 95.238 + 952.38 = $ 1047.62

when is 8% going 8= of Bond interest 8% of L rate 0.08 Value - 100 0.08 (1+0.08) is T1+008)'s - 125 3.17216911 t T 1000 3.17216911 o 2.17216911 3.17216911 1000 T 3.17216911 + 315.2417 855.94 78 68 $1171.19 = Value of Bonds 0.08 [ +0.08 t 1000 (1+0.08) = 1250 [ 1 - 1 08] + 100 1.08

= [1250 + 0.08 0.08 + 1000 looo 1.08 2.08 + 925.9259 92.59259 $ 1018.52 When 12% going interest rate is &= 12 % f 0.12 of Bord L Value hot (2- TR + do 0.0 - 5.41356576) + 5.49356576 o 1000 5.47356576 S. 47356576 T [100 T0.12 & 4.47356576 5.47356576 5,47356576 + 18. 69 6261 681.086449 $863.78

value of Bonds - olete - 04.6230) + Contact loo 0.12 1000 2). 1.12 MO 1000 1.12 6.12 1.12 100 1.12 T looo 7.12 N 89.2857 + 892.857 $982.14 = The Change in the required rate of return increases when the maturity of bond decreases. Therefore, long- -term bonds vary more than the Short term bonds.