Consider three bonds with 5.2% coupon rates, all making annual coupon payments a
ID: 2760453 • Letter: C
Question
Consider three bonds with 5.2% coupon rates, all making annual coupon payments and all selling at a face value of $1,000. The short-term bond has a maturity of 4 years, the intermediate-term bond has maturity 8 years, and the long-term bond has maturity 30 years.
a. What will be the price of each bond if their yields increase to 6.2%? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
4 Years = $
8 Years = $
30 Years Bond price = $
b. What will be the price of each bond if their yields decrease to 4.2%? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
4 Years = $
8 Years = $
30 Years Bond price = $
c. Are long-term bonds more or less affected than short-term bonds by a rise in interest rates?
More affected
Less affected
d. Would you expect long-term bonds to be more or less affected by a fall in interest rates?
More affected
Less affected
Explanation / Answer
(a) Calculation of the price of bond.We have,
Price of bond = C[1 - 1/(1+r)n ] /r + FV / (1+r)n
Where,
C = Coupon payment
r = YTM
n = Number of years
FV = Face Value
(i) For 4 Years bond.
Price of bond = (1,000 x5.2%) [ 1 - 1/(1.062)4 ] /0.062+ 1,000/(1.062)4
Price of bond = 52 [ 1 - 0.7861]/0.062 + 1,000 x 0.7861
Price of bond = 179.40 + 786.10 = $ 965.50
(ii) For 8 years bond.
Price of bond = (1,000 x5.2%) [ 1 - 1/(1.062)8] + 1,000/(1.062)8
Price of bond = 52 [ 1 - 0.61802]/0.062 + 1,000 x 0.61802
Price of bond = 320.37 + 618.02 = $ 938.39
(iii) For 30 years bond.
Price of bond = (1,000 x5.2%) [ 1 - 1/(1.062)30] + 1,000/(1.062)30
Price of bond = 52 [ 1 - 0.16454]/0.062 + 1,000 x 0.16454
Price of bond = 700.71 + 164.54 = $ 865.25
(b) Computation of the price of bond if price of each bond if their yields decrease to 4.2%.We have,
(i) For 4 Years bond.
Price of bond = (1,000 x5.2%) [ 1 - 1/(1.042)4 ] /0.042+ 1,000/(1.042)4
Price of bond = 52 [ 1 - 0.84826]/0.042 + 1,000 x 0.84826
Price of bond = 187.87 + 848.26 = $ 1,036.13
(ii) For 8 years bond.
Price of bond = (1,000 x5.2%) [ 1 - 1/(1.042)8]/0.042 + 1,000/(1.042)8
Price of bond = 52 [ 1 - 0.71954]/0.042 + 1,000 x 0.71954
Price of bond = 347.23 + 719.54 = $ 1,066.77
(iii) For 30 years bond.
Price of bond = (1,000 x5.2%) [ 1 - 1/(1.042)30]/0.042 + 1,000/(1.042)30
Price of bond = 52 [ 1 - 0.29105]/0.042 + 1,000 x 0.29105
Price of bond = 877.75 + 291.05 = $ 1,168.80
(c) The long-term bonds are more affected than short-term bonds by a rise in interest rates. We see in above, when interest rate rise by 6.2%, the price of 30 years bond is $ 865.25, the price of 8 years bond is $ 938.39 and the price of 4 years bond is $ 965.50.Price of bond is decreases when years of maturity of bond is increases.
(d) The long-term bonds are more affected than short-term bonds by a rise in interest rates. We see in above, when interest rate fall by 4.2%, the price of 30 years bond is $ 1,168.80, the price of 8 years bond is $ 1,066.77 and the price of 4 years bond is $ 1,036.13.Price of bond is increases when years of maturity bond is increases.