67.5k views
2 votes
A five-year bond with a yield of 11% pays an 8% coupon at the

end of each year. a) What is the bond’s price? b) What is the
bond’s duration? c) Use the duration to calculate the effect on the
bond

1 Answer

5 votes

Final answer:

The bond's price is $1124.84. The bond's duration is 4.46 years. The effect on the bond is -12.55.

Step-by-step explanation:

a) To calculate the bond's price, we need to find the present value of its future cash flows. The bond pays an 8% coupon at the end of each year for five years, and has a yield of 11%. Using the formula for the present value of an annuity, the bond's price can be calculated as follows:

Price = (Coupon Payment / Yield) * (1 - 1 / (1 + Yield)^n) + Face Value / (1 + Yield)^n

Substituting the given values into the formula, we get:

Price = (0.08 * 5000 / 0.11) * (1 - 1 / (1 + 0.11)^5) + 5000 / (1 + 0.11)^5 = $1124.84

Therefore, the bond's price is $1124.84.

b) The bond's duration measures its sensitivity to changes in interest rates. It can be calculated using the formula:

Duration = [(1 * Coupon Payment) / Price] + [(2 * Coupon Payment) / Price] + ... + [(n * Coupon Payment + Face Value) / Price]

Substituting the given values into the formula, we get:

Duration = [(1 * 0.08 * 5000) / 1124.84] + [(2 * 0.08 * 5000) / 1124.84] + [(3 * 0.08 * 5000) / 1124.84] + [(4 * 0.08 * 5000) / 1124.84] + [(5 * (0.08 * 5000 + 5000)) / 1124.84] = 4.46

Therefore, the bond's duration is 4.46 years.

c) To calculate the effect on the bond, we can use the following formula:

Effect = - Duration * (Change in Yield) * (Price / (1 + Yield))

Substituting the given values into the formula, we get:

Effect = - 4.46 * (0.11 - 0.08) * (1124.84 / (1 + 0.11)) = - 12.55

Therefore, the effect on the bond is -12.55.

User Rohitax Rajguru
by
8.3k points

No related questions found