A 10% bond with semiannual coupons has a face amount of 100,000,000 and was issued on June 18, 2010. The first coupon was paid on Dec 18, 2010 and the bond has a maturity date of June 18, 2030.

Find the price of the bond on its issue date using 2) equal to (i) 5%, (ii) 10%, and (iii) 15%

(i) $121,880,160

(ii) $100,000,000

(iii) $82,839,798

Explanation:

Price of the bond is the present value of all cash flows of the bond. These cash flows include the coupon payment and the maturity payment of the bond.

According to given data

Face value of the bond is $100,000,000

Coupon payment = C = $100,000,000 x 10% = $10,000,000 annually = $5,000,000 semiannually

Number of periods = n = 20 years x 2 = 40 period

Price of the bond is calculated by following formula:

Price of the Bond = C x [ ( 1 - ( 1 + r )^-n ) / r ] + [ $1,000 / ( 1 + r )^n ]

(i)

Yield to Maturity = r = 5% / 2  = 2.5% semiannually

Price of the Bond = $5,000,000 x [ ( 1 - ( 1 + 2.5% )^-20 ) / 2.5% ] + [ $100,000,000 / ( 1 + 2.5% )^20 ]

Price of the Bond = 43,760,319.65 + 78,119,840.17  = $121,880,159.83 = $121,880,160

(ii)

Yield to Maturity = r = 10% / 2  = 5% semiannually

Price of the Bond = $5,000,000 x [ ( 1 - ( 1 + 5% )^-20 ) / 5% ] + [ $100,000,000 / ( 1 + 5% )^20 ]

Price of the Bond = $100,000,000

(i)

Yield to Maturity = r = 15% / 2  = 7.5% semiannually

Price of the Bond = $5,000,000 x [ ( 1 - ( 1 + 7.5% )^-20 ) / 7.5% ] + [ $100,000,000 / ( 1 + 7.5% )^20 ]

Price of the Bond = 34,320,404.78 + 48,519,392.83   = $82,839,797.61 = $82,839,798

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