Question

Suppose a​ seven-year, $1,000 bond with a 9.43%coupon rate and semiannual coupons is trading with a yield to maturity of 6.87%.

a. Is this bond currently trading at a​ discount, at​ par, or at a​ premuim? Explain. The bond is currently trading...  ​(Select the best choice​ below.)

A. ... at a premium because the yield to maturity is greater than the coupon rate.

B... at par because the coupon rate is equal to the yield to maturity

C... at a discount because the coupon rate is greater than the yield to maturity

D.... at a premium because the coupon rate is greater than the yield to maturity

b. If the yield to maturity of the bond rises to 7.13% (APR with semiannual​ compounding), at what price will the bond​ trade?

Answer 1

Solution :-

Semiannual Yield = 6.87% / 2 = 3.435%

Semiannual Coupon Rate = 9.43% * 6 / 12 = 4.715%

Semiannual Coupon = $1,000 * 9.43% * 6 / 12 = $47.15

Semiannual Period = 7 * 2 = 14

Price of Bond = $47.15 * PVAF ( 3.435% , 14 ) + $1,000 * PVF ( 3.435% , 14 )

= ( $47.15 * 10.968 ) + ( $1,000 * 0.623 )

= $1,140.39

Therefore Correct Answer is (D) that at a premium because the coupon rate is greater than the yield to maturity .

(b)

If Yield to Maturity = 7.13%

Now Semiannual Yield = 7.13% / 2= 3.565%

Price of Bond = $47.15 * PVAF ( 3.565% , 14 ) + $1,000 * PVF ( 3.565% , 14 )

= ( $47.15 * 10.873 ) + ( $1,000 * 0.6123 )

= $1,125.04

The Price at which the bond trade = $1,125.04

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