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Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 12 percent, has a YTM of 10 percent, and has 16 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 10 percent, has a YTM of 12 percent, and also has 16 years to maturity. The bonds have a $1,000 par value. What is the price of each bond today?

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Respuesta :

Answer:

Price of x bond = $1158.02  

Price of y bond  = $1000

Explanation:

given data

bonds value = $1,000 par value

x bond

coupon rate = 12 percent = 0.12

YTM = 10 percent = 0.10 = 0.05 semi annual

maturity = 16 years = 32 semi annual

y bond

coupon rate = 10 percent = 0.10

YTM = 12 percent = 0.12 = 0.06 semi annual

maturity = 16 years  = 32 semi annual

solution

For x bond

first we get here semi annual coupon payment that is express as

semi annual payment = bonds value × coupon rate × time period   .........1

semi annual payment = $1000 × 0.12 × 0.5

semi annual payment = $60

and

Price of bond will be

Price of bond = semi annual payment × [tex]\frac{1-(1+r)^{-time} }{rate} + \frac{maturity}{(1+rate)^{time}}[/tex]       ..........................2

put here value and we get

Price of bond = 60 × [tex]\frac{1-(1+0.05)^{-32} }{0.05} + \frac{1000}{(1+0.05)^{32}}[/tex]  

Price of bond = $1158.02  

and

For y  bond

semi annual payment = bonds value × coupon rate × time period   .........3

semi annual payment = $1000 × 0.10 × 0.5

semi annual payment = $50

and

Price of bond will be

Price of bond = semi annual payment × [tex]\frac{1-(1+r)^{-time} }{rate} + \frac{maturity}{(1+rate)^{time}}[/tex]       ..........................4

put here value and we get

Price of bond = 50 × [tex]\frac{1-(1+0.06)^{-32} }{0.06} + \frac{1000}{(1+0.06)^{32}}[/tex]  

Price of bond  = $1000

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