The Corner Grocer has a 7-year, 6 percent annual coupon bond outstanding with a $1,000 par value. The bond has a yield to maturity of 5.5 percent.
Which one of the following statements is correct if the market yield suddenly increases to 6.5 percent?
The bond price will increase by $57.14.
The bond price will increase by 5.29 percent.
The bond price will decrease by $53.62.
The bond price will decrease by 5.43 percent.
The bond price will decrease by 5.06 percent.
Ravi Industries bond has a 12 percent coupon rate and Rs.1,000 face value.
Interest is paid on annual basis, and the bond has 10 years to maturity. If
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investors require a 14 percent yield, what is the bond’s value? What is the
effective annual yield on the bond? (
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To determine the impact of a change in market yield on the bond price, we can use the bond price formula:
Bond Price = Coupon Payment x (1 - (1 / (1 + Yield) ^ Number of Periods)) / Yield + (Par Value / (1 + Yield) ^ Number of Periods)
Given that the bond has a 7-year term, a 6 percent coupon rate, a $1,000 par value, and a yield to maturity of 5.5 percent, let's calculate the current bond price:
Bond Price = 60 x (1 - (1 / (1 + 0.055) ^ 7)) / 0.055 + (1000 / (1 + 0.055) ^ 7)
= $1054.86
Now, let's calculate the new bond price when the market yield increases to 6.5 percent:
Bond Price = 60 x (1 - (1 / (1 + 0.065) ^ 7)) / 0.065 + (1000 / (1 + 0.065) ^ 7)
= $1042.24
The difference in bond price is: $1054.86 - $1042.24 = $12.62
Therefore, the correct statement is: "The bond price will decrease by $12.62."
To determine the change in bond price when the market yield changes, we need to compare the current yield to maturity (YTM) with the new yield to maturity.
In this case, the bond's current YTM is 5.5 percent, and the new YTM is 6.5 percent. Since the new YTM is higher than the current YTM, the bond price will decrease.
To calculate the change in bond price, we can use the concept of bond price sensitivity to yield changes. This sensitivity is measured by a metric called duration. Duration measures the weighted average time it takes to receive the bond's cash flows.
The formula to calculate the approximate percentage change in bond price is:
Percentage change in bond price ≈ (-duration) * (change in YTM)
In this case, we don't have the duration explicitly provided, so we'll assume it's 7 years, matching the bond's maturity.
Using the given formula:
Percentage change in bond price ≈ (-7) * (0.065 - 0.055) = -0.7 or -70 basis points
Therefore, the bond price will decrease by 0.7 percent. None of the given options exactly matches this result. However, the closest option is "The bond price will decrease by 5.43 percent," which approximates the correct percentage change.