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You are looking at a 20-year, 5 percent annual coupon bond. The bond has a face value of $1,000. What is the percentage change in the price of this bond if the market yield to maturity decreases to 6 percent from the current rate of 6.5 percent?

User Chowwy
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1 Answer

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The first step is to calculate the current price of the bond using the current market yield to maturity of 6.5 percent.

To do this, we can use the bond pricing formula:

Bond price = (C / Y) x [1 - 1 / (1 + Y)^n] + (F / (1 + Y)^n)

where:

C = annual coupon payment

Y = yield to maturity (in decimal form)

n = number of years to maturity

F = face value

In this case, C = $50 ($1,000 x 5%), Y = 0.065, n = 20, and F = $1,000. Plugging these values into the formula, we get:

Bond price = ($50 / 0.065) x [1 - 1 / (1 + 0.065)^20] + ($1,000 / (1 + 0.065)^20) = $896.03

Next, we need to calculate the new price of the bond if the yield to maturity decreases to 6 percent. Using the same formula, but with Y = 0.06, we get:

Bond price = ($50 / 0.06) x [1 - 1 / (1 + 0.06)^20] + ($1,000 / (1 + 0.06)^20) = $943.27

The percentage change in the price of the bond can be calculated using the following formula:

Percentage change = (new price - old price) / old price x 100%

Plugging in the values, we get:

Percentage change = ($943.27 - $896.03) / $896.03 x 100% = 5.27%

Therefore, the percentage change in the price of the bond if the market yield to maturity decreases to 6 percent is 5.27%.

User Himerzi
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