Wesimann Co. issued 13-year bonds a year ago at a coupon rate of 8.5 percent. The bonds make semiannual payments and have a par value of $1,000. If the YTM on these bonds is 6.8 percent, what is the current bond price?

$1,137.94

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 Wesimann Co be worked out as follows:

Step 1

PV of interest payments

Semi annul interest payment

= 8.5% × 1000 × 1/2

= $42.5

Semi-annual yield = 6.8/2 = 3.4 % per six months

Total period to maturity (in months)

= (2 × 12) = 24 periods (Note it was issued a year ago)

PV of interest =

PV = A × (1-(1+r)^(-n))/r

r-3.4 %- n- 24

42.5 × (1- (1+0.034)^(-2× 12)/0.034)

=$689.70

Step 2

PV of Redemption Value

= 1,000 × (1.034)^(-2× 12)

= 448.236

Step 3

Price of bond

= 689.70 + 448.23

= $1,137.94

Current Price of the bond is $1,137.94

Explanation:

Price of a bond equals present value of coupon payments and the present value of face value at maturity

Face value = $1000

years to maturity equals to 12 years since the bond was issued a year ago and had 13 years to mature and payments are made semiannual = 12*2 =24

coupon payment since coupons are paid semiannual

1000*8.5/2=$40.25

YTM = 6.8%/2 = 3.4%

bond price = C * [1-(1+r)^-n / r) + FV/ (1+r)^n

                  =42.5 * [ 1-(1+0.034)^-24/0.034] + 1000/(1+0.034)^24

                  =689.7046 + 448.2363

                  =$1,137.94

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