Both bond A and bond B have 7.6 percent coupons and are priced at par value. Bon
ID: 2777471 • Letter: B
Question
Both bond A and bond B have 7.6 percent coupons and are priced at par value. Bond A has 8 years to maturity, while bond B has 16 years to maturity.
If interest rates suddenly rise by 2 percent, what is the percentage change in price of bond A and bond B? (Negative answers should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)
If interest rates suddenly fall by 2 percent instead, what would be the percentage change in price of bond A and bond B? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)
a.
If interest rates suddenly rise by 2 percent, what is the percentage change in price of bond A and bond B? (Negative answers should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)
Explanation / Answer
Let the face value and price of bond A and B be $100. Duration to maturity of A = 8 years. coupon = 7.6%. annual coupon payments = $7.6 for 8 years. let the yield be "r"
Price ($100) = 7.6/(1+r)^1+7.6/(1+r)^2+7.6/(1+r)^3...7.6(1+r)^8+100/(1+r)^8
Solving using the "solver" function in excel,
100
Thus, yield = 1.076 - 1 = 7.6%. Now if rates rise by 2% to become 7.6%+2% = 9.6%, price of bond A will be sum of all present values.
% change in price of bond A = (89.17 - 100)/100 = -10.83% (decrease)
Bond B: Calculating yield by using solver in excel: This also gives a yield of 7.6%. If it becomes 9.6% (2% increase), the PV values will be:
% change = (83.97-100)/100 = -16.03% (decrease)
b. if rates fall by 2% to become (7.6% - 2%) = 5.6%, then Bond A's price will be:
% increase = (112.6186-100)/100 = 12.62% (increase)
if rates fall by 2% to become (7.6% - 2%) = 5.6%, then Bond B's price will be:
% Change = (120.78 - 100)/100 = 20.78% (increase)
Year Coupon 1+yield PV 1 7.6 1.076 7.063197 2 7.6 6.564309 3 7.6 6.100659 4 7.6 5.669758 5 7.6 5.269292 6 7.6 4.897111 7 7.6 4.551219 8 7.6 4.229757 8 100 55.6547 Total100
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