Question

A bond has a face value of $1000 with a time to maturity ten years from now. The yield to maturity of the bond now is 10%.

a) What is the price of the bond today, if it pays no coupons?

b) What is the price of the bond if it pays annual coupons of 8%?

c) What is the price today if pays 8% coupon rate semi-annually?

Answer 1

Face(Par) Value = $ 1000

YTM = 10%

n = No of years to maturity = 10

a). Calculating the Price of the Bond with no coupons:-

Price = $ 385.54

b). Calculating the price of the bond if it pays annual coupons of 8%:-

Annual Coupon Payment = $1000*8% = $80

Price = $ 491.568 + $ 385.54

Price = $ 877.11

c). Calculating the price of the bond if it pays Semi-annual coupons of 8%:-

Sem-annual Coupon Payment = $1000*8%*1/2 = $40

Semi-annual YTM = 10%/2 =5%

n = 10yrs*2 = 20

Price = $ 498.488 + $ 376.89

Price = $ 875.38

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