1 Question 1 . You do NOT need to submit programming code for this question. * T

Question

1 Question 1 . You do NOT need to submit programming code for this question. * The time today is to = 0. You are given a newly issued bond with a maturity of T-4 years. The face value of the bond is F 100. * The bond pays 8 coupons, at semi-annual intervals at times t·= 0.5, 1.0.1.5, 40, where . The amounts of the coupons are as follows: 1. The (annualized) coupons are the 8 digits of your student id. 2. For example if your student id is 23054617, the coupons are (2,3,0,5,4,6,1,7) 3. Hence in this case the bond fair value B is, for a yield y (note the factors of 2) 2/2 3/2 0/2 4/2 6/2 F+7/2 4. Therefore it is possible for some coupon amounts to be zero. . Calculate the theoretical fair value of the bond, if the yield of the bond is 5%. State your answer to 2 decimal places. .Calculate the yield of the bond, if the market price of the bond is 100. 1. Use a tolerance of 10. i.e. 0.0001 2. Denote the value of the yield by 3. Express your answer as a percentage, to 2 decimal places. The value of yi will be used in Question 6. (Optional) Prove that 0 y1S 9.0% for every student, without knowing their id numbers.

Explanation / Answer

Part - A

Value of the Bond

Value of bond = 96.04

Part - 2

YTM When Market Price of bond is 100

Total Interest = 14

Interest % = Interest /Number of Years

=14/4

=3.50%

YTM = 3.50/100

=3.50%

Particulars Year Cashflow PVF @ 2.50% DCF Interest 0.50 100*2%*0.50=1 0.9756 0.98 Interest 1 100*3%*0.50=1.50 0.9518 1.43 Interest 1.50 100*0% 0.9286 0 Interest 2 100*5%*0.50=2.50 0.9060 2.27 Interest 2.50 100*4%*0.50=2.00 0.8839 1.77 Interest 3 100*6%*0.50=3.00 0.8623 2.59 Interest 3.50 100*1%*0.50=0.50 0.8413 0.42 Interest 4 100*7%*0.50=3.50 0.8207 2.87 Maturity 4 100 0.8207 82.07 Value of Bond 96.04

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