In December 2010, Alpha Technologies Plc. issued coupon bonds with par value £100. The coupon rate...

In December 2010, Alpha Technologies Plc. issued coupon bonds with par value £100. The coupon rate is 8 percent annually and the bonds will be redeemed at par value in December 2015. What is the price of the bond if the competitive market interest rate is 10 percent? How would your answer change if the coupons were paid semi-annually?

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Expert Solution

Solution

First price of bond will be calculated for annual coupon payments

Current price of bond=Present value of coupon payments+Present value of face value

Current price of bond=Coupon payment*((1-(1/(1+r)^n))/r)+Face value/(1+r)^n

where

n=number of periods=5

r-discount rate per period=10%

Coupon payment=8% of par value=8%*100=8

Current price of bond=8*((1-(1/(1+.1)^5))/.1)+100/(1+.1)^5

=92.41843

Now price of bond will be calculated for Semi annual payments

Current price of bond=Present value of coupon payments+Present value of face value

Current price of bond=Semi annual Coupon payment*((1-(1/(1+r)^n))/r)+Face value/(1+r)^n

where

n=number of periods=5*2=10

r-discount rate per period=10/2=5%

Semi annual Coupon payment=(8% of par value)/2=8%*100/2=4

Current price of bond=4*((1-(1/(1+.05)^10))/.05)+100/(1+.05)^10

=92.27827

The Current price of the bond will be reduced on semi annual coupon payments as the effective discount rate increases on semiannual compounding

jeff jeffy answered 1 year ago

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