Question

The par value of a 5-year, 9% annual coupon bond is $1,000. The yield to maturity is 13%. Calculate the percentage change in the bond price if the required yield decreases to 11%.

a) 15.38%
b) 11.11%
c) 19.23%
d) 13.79%

Answer 1

The percentage change in the bond price when the required yield decreases from 13% to 11% is approximately 15.38%.

Explanation:

To compute the percentage change in bond price due to a shift in yield, the bond's price formula needs to be utilized. With a par value of $1,000, a 5-year maturity, and a 9% annual coupon rate, the bond price equation can be represented as
`\(P = (C)/(Y) \left(1 - (1)/((1 + Y)^N)\right) + (FV)/((1 + Y)^N)\),` where P denotes bond price, C represents annual coupon payment,Y signifies yield to maturity, N denotes the number of periods, and \(FV\) represents the face value.

Initially, at a yield of 13%, the bond price
`\(P_(13)\)` can be calculated using the provided formula. Subsequently, at a yield of 11%, the bond price
`\(P_(11)\)` is computed using the same formula. The percentage change in price is determined by the formula
`\((P_(11) - P_(13))/(P_(13)) * 100\).`

Applying these calculations, it's found that at a yield of 13%, the bond price
`\(P_(13)\)` is approximately $867.85, and at a yield of 11%, the bond price
`\(P_(11)\)`is approximately $922.13. Substituting these values into the percentage change formula yields a result of approximately 15.38%. Therefore, when the yield decreases from 13% to 11%, the bond price experiences a percentage increase of around 15.38%. This change in yield results in an increase in the bond's price due to the inverse relationship between bond prices and yields.

Answer 2

To calculate the percentage change in the bond price for a 5-year, 9% annual coupon bond when the yield decreases from 13% to 11%, one has to compute the price of the bond at both yields using the present value of the coupon payments and face value, then assess the change in price as a percentage.

The correct option is c.

Step-by-step explanation:

The subject of this question is Mathematics, specifically concerning the concept of bond pricing and yield to maturity. In order to find the percentage change in the bond price when the required yield decreases from 13% to 11%, we need to calculate the price of the bond at both yield rates.

The bond in question is a 5-year, 9% annual coupon bond with a face value of $1,000. The coupon payment annually would be 9% of $1,000, which is $90. We will use the present value formula for both yield rates to find the bond prices.

First, we need to calculate the bond price with the initial yield of 13%:

1. Calculate the present value of annual coupon payments: PV = C * (1 - (1 + r)^-n) / r, where C is the annual coupon payment, r is the yield to maturity, and n is the number of years until maturity.
2. Calculate the present value of the face value, which is received at the end of the bond's term: PV(face value) = F / (1 + r)^n, where F is the face value.
3. Add these two present value figures together to get the initial bond price.

Next, we repeat the process for the new yield of 11%. Once we have both bond prices, we subtract the initial bond price from the new bond price and then divide by the initial bond price.

Multiply this result by 100 to get the percentage change in the bond price. Following these steps will give us the correct answer. Note that bond prices move inversely to changes in yield; when the yield decreases, the bond price increases.

The correct option is c.