Answer:
(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
