Question

(1) A bond will mature in 30 years. It has a 7% coupon rate and will pay annual coupons. If the bond has a face value of $1,000 and a 6% yield to maturity, what should be the price of the bond today? What if YTM goes up to 7%? What if YTM goes up to 8%? Given: Term = 30 years; Coupon = 7% Bond Price at YTM=6%: Price = 70/(1+6%) +70/(1+6%)2 + ..... + (1000 + 70)/(1+6%)30 = $1137.65 Bond Price at YTM = 7%: When the YTM is same as coupon, the bond price will be same as face value (maturity value). Bond Price at YTM -8%: Price = 70/ (1+8%) +70/(1+8%)2 + ... + (1000 + 70)/(1+8%)30 = $887.42 (2) What would be the price of the bond above in (1) if the coupons were paid semiannually? N= 30 x 2 = 60 PMT = 70/2 = 35 FV = 1000 I/Y = 6%/2 = 3% => $1,138.38 (3) What is the relationship between the coupon rate of a bond and the yield to maturity in terms of the bond's price. In particular, when do we have a discount bond, a par bond, and a premium bond? Please explain the rational behind the relationship as if you are explaining this relationship to a novice of Finance. (4) Both Bond A and Bond B have 6% coupons, make semiannual payments, and are priced at par value. Bond A has three years to maturity, whereas Bond B has 20 years to maturity. If the interest rates suddenly rise by 2 percent point to 8%, what is the percentage change in the price of Bond A and Bond B? If rates were to suddenly fall by 2 percent points to 4% instead, what would be the percentage change in the price of Bond A and Bond B then?

4. Both Bond A and Bond B have 6% coupons, make semiannual payments, and are priced at par value. Bond A has three years to maturity, whereas Bond B has 20 years to maturity. If the interest rates suddenly rise by 2 percent point to 8%, what is the percentage change in the price of Bond A and Bond B? If rates were to suddenly fall by 2 percent points to 4% instead, what would be the percentage change in the price of Bond A and Bond B then?

QUESTION #4

Answer 1

Let say the bond A and B par value is 100 and they are also priced at par Bond A Bond B 100 3 Face value Coupon payment Number of periods Price 100 3 3*2 = 100 Face value Coupon Payment Number of periods price 40 20*2 = 100 Annual yield 6% annual yield 6% If the interest rate rises by 2% to 8%, then 100 Face value Coupon payment Number of periods Yield = 100 3 3*2 = 8%/2 Face value Coupon Payment Number of periods Yield = 20*2 = 8%/2 Use the financial calculator to calculate the price of bond Price 94.7579 price = 80.2072 percentage change in price percentage change in price (94.7579-100)/100 *100 (80.2072-100)/100 *100 -5.24 % -19.79 % if the yield were to fall by2% to 4%, then Similary change the yield in the calculator to 2% ( 4%/2 = periodic yield, since coupon payment is semiannual) use the financial calculator, keep the other variables same change the yield to (4%/2) So the periodic yield would be = 2% price 105.6014 price = 127.3554 percentage change in price percentage change in price (105.6014-100)/100 *100 27.3554 5.60 % 27.36 %