Question

Wine and Roses, Inc., offers a bond with a coupon of 7.0 percent with semiannual payments and a yield to maturity of 7.75 percent. The bonds mature in 14 years. What is the market price of a $1,000 face value bond?

Answer 1

Answer:

P = 9359.8

Explanation:

Given:

• n = 14

• YTM = 7.75% = 0.0775
• F = 1000

• Coupon rate = 7.0 percent => Coupon payment is: 1000*7% = 70

As we know that, the formula to find out YTM is:

       YTM = [C + (F-P/n) ] / (F+ P) / 2

<=> 0.0775 = [ 70 + (1000 - P/14)] / (1000+P)/2

<=> 0.0775(1000+P) /2 =  70 + (1000 - P/14)

<=> 0.0775(1000+P)  = 140 + 2(1000 - P/14)  

<=> P = 9359.8

So the price of the $1,000 face value bond is 9359.8  

Answer 2

Answer:

$936.60

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.

The price of the bond can be calculated as follows:

Step 1

PV of interest payment

Semi-annual coupon rate = 7.0%/2 = 3.5%

Interest payment =( 3.5%×$1000)=

= $35

Semi annual yield = 7.75%/2 = 3.875%

PV of interest payment

= A ×(1- (1+r)^(-n))/r

A- interest payment = $35

n- time to maturity - 14× 2= 28 periods

= 35× (1-(1.03875)^(-14×2))/0.03875)

= 35× 16.91567435

=$ 591.7048215

Step 2

PV of redemption value  (RV)

PV = RV× (1+r)^(-n)

= 1,000 × (1+0.03875)^(-2× 14)

= 344.89

Step 3

Price of bond =

$591.70 + 344.89

$936.60