Let’s calculate the initial bond price
Bond price P0 = C* [1- 1/ (1+i) ^n] /i + M / (1+i) ^n
Where
M = value at maturity, or par value = $ 1000 (assumed)
C = coupon payment = 15.3% of $1000 = $153
n = number of payments = 30
i = interest rate, or required yield = 9% or 0.09
Bond Price = $153 * [1 – 1 / (1+0.09) ^30] /0.09 + $1000 / (1+0.09) ^30
= $1,571.87 + $75.37
= $1,647.24
e-1. Let’s calculate the exact bond price if it's yield to maturity rises to 10%.
Bond price P0 = C* [1- 1/ (1+i) ^n] /i + M / (1+i) ^n
Where
M = value at maturity, or par value = $ 1000 (assumed)
C = coupon payment = 15.3% of $1000 = $153
n = number of payments = 30
i = interest rate, or required yield = 10% or 0.10
Bond Price = $153 * [1 – 1 / (1+0.1) ^30] /0.1 + $1000 / (1+0.1) ^30
= $1,442.32 + $57.31
=$1,499.63
The price of the bond if its yield to maturity rises to 10% is $1,499.63
e-2. The price predicted by the duration rule
We have duration = 10.59 years and y is yield to maturity = 9%
Predicted price change = – Duration * (change in y)/ (1+y)* P0
= - 10.59 *(0.01)/ (1.09) * $1,647.24
= - $160.04
Therefore, predicted new price =- $160.04 +$1,647.24 = $1,490.06
e-3. Using Duration-with-Convexity Rule, assuming yield to maturity rises to 10%
Predicted price change
= [(– Duration * change in y/ (1+y)) + (0.5 * convexity *(change in y) ^2)] * P0
= [(- 10.59 * (0.01) / (1 +0.09)) + (0.5 * 163.0 * (0.01) ^2)] * $1,647.24
= -$146.87
Therefore, predicted price = -$146.87 +$1,647.24 = $1,503.23
e-4.
Percent Error |
||
YTM |
Duration Rule |
Duration-with- |
10% |
[($1,490.06– $1,499.63)/ $1,499.63] * 100 = -0.64% |
[($1,503.23 – $1,499.63)/ $1,499.63] * 100 = 0.240% |
Can you please show your work and/or calculator steps? Problem 11-26 A 30-year maturity bond making...
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