Question

15 6 A 10% coupon rate bond makes semi-annual Interest rate payments. Par value is $1,000. The bond matures in 12 years. The required rate of return is 9.57%. What is the current price If the current price is 1,030.29, calculate the bonds YTM. a 9.15% b 7.25% Be Careful - This is Semi-Annual 5.20% 4.20% с

Answer 1

Face Value = 1000

Semi -annual coupon amount = 0.05*1000 =50

Number of payments = 12*2 = 24

semi -annual ytm = 0.0957/2 = 0.04785

We know that,

Current Price of a bond = Present value of all the semi annual coupons and face value discounted at semi annual ytm

Price = 50/(1+0.04785)^1 + 50/(1+0.04785)^2 + 50/(1+0.04785)^3 + 50/(1+0.04785)^4 + 50/(1+0.04785)^5 + 50/(1+0.04785)^6 + ............. 50/(1+0.04785)^24 + 1000/(1+0.04785)^24

Price = 1030.30 Answer

YTM Calculation:

1030.29 = 50/(1+ytm/2)^1 + 50/(1+ytm/2)^2 + 50/(1+ytm/2)^3 + 50/(1+ytm/2)^4 + 50/(1+ytm/2)^5 + 50/(1+ytm/2)^6 + ............. 50/(1+ytm/2)^24 + 1000/(1+ytm/2)^24

We will use heat and trial method to get required value

ytm/2 = 4.785

ytm = 9.57% Answer

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