Consider 3 Treasury bonds which pay semi-annual coupons. Bond A has 5 years rema

Question

Consider 3 Treasury bonds which pay semi-annual coupons. Bond A has 5 years remaining to maturity and a coupon rate of 10%. Bond B has 20 years remaining to maturity and a coupon rate of 10%, and Bond C has 20 years remaining to maturity and a coupon rate of 4%.

A. If all bonds provided a 10% return (APR, compounded semiannually) if they were purchased today and held to maturity, what is the price today of each of the bonds? Essentially, what is the price of each bond if the YTM is 10%?

B. What is the price of each bond if the YTM was 4%? What if it was 16%

Explanation / Answer

Ans

Details YTM is 10% YTM is 4% YTM is 16% Bond A Bond B Bond C Bond A Bond B Bond C Bond A Bond B Bond C Annual Coupon Rate 4% 10% 10% 4% 10% 10% 4% 10% 10% 4% Semi annual Coupon rate       4,000.00 5% 5% 2% 5% 5% 2% 5% 5% 2% YTM 2% 10% 10% 10% 4% 4% 4% 16% 16% 16% YTM Semi annual rate( Compounded semi annaually)              5.00 5% 5% 5% 2% 2% 2% 8% 8% 8% Face value 1,00,000.00 1000 1000 1000 1000 1000 1000 1000 1000 1000 Remaining Maturity in semi annual periods         10.00         40.00         40.00         10.00         40.00         40.00         10.00         40.00         40.00 Market value =Present value of remaiining payments on bond=C*((1-(1+r^-n))/r))+(FV*1+r^-n) 1,000.00 1,000.00      485.23 1,269.48 1,820.66 1,000.00      798.70      642.26      284.52 Where C= Coupon Amount=Face value * Semi annual coupon rate r=Semi annual YTM n-Maturity Period FV=Face value

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