A 6-year 5.9% annual coupon bond is selling to yield 7%. The bond pays interest
ID: 2773605 • Letter: A
Question
A 6-year 5.9% annual coupon bond is selling to yield 7%. The bond pays interest annually. The par value of the bond is $100. What is the price of the 4-year 5.9% coupon bond selling la yield 7%? What is the price of this bond one year later assuming the yield is unchanged at 7%? Suppose that one year later the yield of the bond decreases to 6.1%. What is the price change attributable to moving to maturity assuming no change in the discount rate? What is the price change attributable to a decrease in the discount rate from 7% to 6.1%? What is the total price change?Explanation / Answer
Price of the 6 year 5.9% annual coupon bond selling to yield 7% = 5.9/(1+7%)1+ 5.9/(1+7%)2+ 5.9/(1+7%)3 + 5.9/(1+7%)4+ 105.9/(1+7%)5 + 105.9/(1+7%)6 = $94.76
a. Time to Maturity = 4 years
Coupon Rate = 5.9%
Yield to Maturity = 7%
Par Value = $100
The bond pays interest annually.
Annual Coupon = 5.9% * 100 = $5.9
Price of the bond = 5.9/(1+7%)1+ 5.9/(1+7%)2+ 5.9/(1+7%)3+ 105.9/(1+7%)4 = $96.27
b) One year later, if yield remains 7%
Price of the initially 6-year bond mentioned at the top = 5.9/(1+7%)1+ 5.9/(1+7%)2+ 5.9/(1+7%)3 + 5.9/(1+7%)4+ 105.9/(1+7%)5 = $95.49
Price of the 4-year bond in part a)= 5.9/(1+7%)1+ 5.9/(1+7%)2+ 105.9/(1+7%)3 = $97.11
c) One year later, the yield of the bond decreases to 6.1%
Considering the 6 year bond mentioned at the top
New Price of the bond = 5.9/(1+6.1%)1+ 5.9/(1+6.1%)2+ 5.9/(1+6.1%)3 + 5.9/(1+6.1%)4+ 105.9/(1+6.1%)5
= $99.16
Total Price Change = 99.16 - 94.76 = $4.40
Assuming no change in the discount rate, price change in one year = 95.49 - 94.76 = $0.73
Price Change Due to a Decrease in Discount Rate from 7 to 6.1% = 4.4 -0.73 = $3.67
Price Change Attributable to Moving to Maturity assuming no change in the discount rate = (0.73 / 4.4) * 100
= 16.59%
Price Change Attributable to a decrease in the discount rate from 7% to 6.1% = (3.67 / 4.4) * 100 = 83.41%
Total Price Change = 99.16 - 94.76 = $4.40
Price Change in Percentage Terms = 4.4 / 94.76 = 4.64%
Considering the 4 year bond mentioned in part a)
New Price of the bond = 5.9/(1+6.1%)1+ 5.9/(1+6.1%)2+ 105.9/(1+6.1%)3
= $99.47
Total Price Change = 99.47 - 96.27 = $3.2
Assuming no change in the discount rate, price change in one year = 97.11 - 96.27 = $0.84
Price Change Due to a Decrease in Discount Rate from 7 to 6.1% = 3.2 -0.84 = $2.36
Price Change Attributable to Moving to Maturity assuming no change in the discount rate = (0.84 / 3.2) * 100
= 26.25%
Price Change Attributable to a decrease in the discount rate from 7% to 6.1% = (2.36 / 3.2) * 100 = 73.75%
Total Price Change = 99.47 - 96.27 = $3.2
Price Change in Percentage Terms = 3.2 / 96.27 = 3.32%
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