Luxury Properties offers bonds with a coupon rate of 8.8 percent paid semiannually. The yield to maturity is 11.2 percent and the maturity date is 11 years from today. What is the market price of this bond if the face value is $1,000?
A. $850.34B. $896.67C. $841.20D. $846.18E. $863.30

A) $850.33

Explanation:

The value of the bond is the present value(PV) of the future cash receipts expected from the bond. The value is equal to present values of interest payment plus the redemption value (RV).

Value of Bond = PV of interest + PV of RV

The value of bond for Luxury Properties can be worked out as follows:

Step 1

PV of interest payments

Semi annul interest payment

= 8.8% × 1000 × 1/2

= 44

Semi-annual yield = 11.2/2 = 5.6% per six months

Total period to maturity

= (2 × 11) = 22 periods

PV of interest =

44 × (1- (1+0.056^(-22)/0.056)

= 12.47189406

= $548.76

Step 2

PV of Redemption Value

= 1,000 × (1.056)^(-22)

= 301.57

Price of bond

=  $548.76 + 301.57

=   $850.34

A. $850.34

Explanation:

Cr 8.8%, n 11, ytm 11.2% FV %1000

Bond coupon payments are made semi annually

Coupon payments

= 1000*8.8%/2 = $44

n = 11*2 = 22

YTM = 11.2/2 =5.6%

Bond value equals the sum of present value of coupon payments plus the present value of par value maturity

BV = C * [1-(1+r)^-n/r] + FV/(1+r)^n

      =44 *[1-(1+0.056)^-22/0.056] +1000/(1+0.056)^22

       =548.76+ 301.57

        =$850.34

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