Crane, Inc., has a bond issue maturing in seven years that is paying a coupon rate of 9.5 percent (semiannual payments). Management wants to retire a portion of the issue by buying the securities in the open market. If it can refinance at 8.0 percent, how much will Crane pay to buy back its current outstanding bonds? (Round answer to 2 decimal places, e. g. 15.25.) Crane will pa

$1,079.22

Explanation:

The price of a bond is the present value (PV) of the future cash inflows expected from the bond discounted using the yield to maturity.

These cash flows include interest payment and redemption value

The price of the bond can be calculated as follows:

Step 1

PV of interest payment

Semi-annual coupon rate = 9.5%/2 = 4.75%

Semi-annual Interest payment =( 4.75%×$1000)= $47.5

Semi annual yield = 8%/2 = 4%

PV of interest payment

= A ×(1- (1+r)^(-n))/r

A- interest payment, r- yield - 4%, n- no of periods- 2 × 7 = 14 periods

= 47.5× (1-(1.04)^(-7×2))/0.04)

= 501.748

Step 2

PV of redemption value (RV)

PV = RV × (1+r)^(-n)

RV - redemption value- $1000, n- 7, r- 4.5%

= 1,000 × (1+0.04)^(-2×7)

= 577.475

Step 3

Price of bond = PV of interest payment + PV of RV

$ 501.7483391 + 577.4750828

=$1,079.22

Crane will pay =$1,079.22

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