Respuesta :
Answer:
Bond Sam = -8.11%
Bond Dave = -18.9%
Step-by-step explanation:
Let the face value of bonds be $1,000.
Bond Sam :
Coupon rate = 6%
yield = 6%
The number of years to maturity = 5 years
market interest rate suddenly rise by 2% = 8%
To calculate the present value of the bond, find the semiannual coupon payment.
Semi-annual coupon payment = Face value × Annual coupon rate × [tex][\frac{6}{12}][/tex]
= 1,000 × 6% × [tex][\frac{6}{12}][/tex]
= $30
Now convert the annual market interest rate to semi-annual interest rate.
Semi-annual interest rate = [tex][\frac{\text{annual market rate of interest}}{2}][/tex]
= [tex][\frac{0.08}{2}][/tex]
= 4%
Number of years converted in semi-annual periods
5 years = 5 × 2 = 10 semiannual periods
Now use excel and select "fx" and choose "PV" and enter the values into the formula :
PV = (rate,nperiod,pmt,fv)
= (4%,10,-30,-1000)
= $918.89
Change in price of bond Sam = [tex]\frac{918.89-1000}{1000}[/tex]
= -0.08111 or -8.11%
Bond Dave :
Coupon rate = 6%
yield = 6%
The number of years to maturity = 18 years
market interest rate suddenly rise by 2% = 8%
To calculate the present value of the bond, find the semiannual coupon payment.
Semi-annual coupon payment = Face value × Annual coupon rate × [tex][\frac{6}{12}][/tex]
= 1,000 × 6% × [tex][\frac{6}{12}][/tex]
= $30
Now convert the annual market interest rate to semi-annual interest rate.
Semi-annual interest rate = [tex][\frac{\text{annual market rate of interest}}{2}][/tex]
= [tex][\frac{0.08}{2}][/tex]
= 4%
Number of years converted in semi-annual periods
18 years = 18 × 2 = 36 semiannual periods
Now use excel and select "fx" and choose "PV" and enter the values into the formula :
PV = (rate,nperiod,pmt,fv)
= (4%,36,-30,-1000)
= $810.92
Change in price of bond Sam = [tex]\frac{810.92-1000}{1000}[/tex]
= -0.18908 or -18.9%
Percentage change in the price of Bond Sam -8.11% and Bond Dave -18.9%.
