Suppose a ten-year, $ 1 comma 000 bond with an 8.7 % coupon rate and semiannual coupons is trading for $ 1 comma 035.37. a. What is the bond's yield to maturity (expressed as an APR with semiannual compounding)? b. If the bond's yield to maturity changes to 9.6 % APR, what will be the bond's price?

a. 8.37%

b. $942.96 or

Explanation:

If a bond is held until maturity, the total return expected from the bond until maturity is known as Yield to maturity. It is considered as long term and expressed in annual term.

a.

Yield to maturity = [ C + ( ( F - P ) / n ) ] / [ ( F + P ) / 2 ]

Where

C = Coupon payment = 1,000 x 8.7% = 87 annually = 43.5 semiannually

F = Face value = $1,000

P = Price of bond = $1,035.37

n = number of periods = 2 per year x 10 year = 20 periods

Yield to maturity = [ C + ( ( F - P ) / n ) ] / [ ( F + P ) / 2 ]

Yield to maturity = [ 43.5 + ( ( 1,000 - 1035.37 ) / 20 ) ] / [ ( 1,000 + 1035.37 ) / 2 ]

Yield to maturity = 41.73 / 1017.69

Yield to maturity = 0.041 = 4.10% = 4.1% semiannually ( rounded off to 1 decimal place)

Annual YTM compounding semiannually = [ ( 1 + 4.1% )^2 ] -1 = 0.0837 = 8.37%

b.

Price of Bond = C x [ ( ( 1 - ( 1 + r )^-n ) / r ] + [ F / ( 1 + r )^n ]

Price of Bond = 43.5 x [ ( ( 1 - ( 1 + 0.48 )^-20 ) / 0.048 ] + [ 1,000 / ( 1 + 0.048 )^20 ]

Price of Bond = 551.42 + 391.54 = $942.96

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