Potter Industries has a bond issue outstanding with an annual coupon of 6% and a 10-year maturity. The par value of the bond is $1,000. If the going annual interest rate is 8.6%, what is the value of the bond

Value of the bond = $767.70

Explanation:

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

Value of Bond = PV of interest + PV of RV

The value of bond for Potter Industries can be worked out as follows:

Step 1

Calculate the PV of Interest payment

Present value of the interest payment

PV = Interest payment ×  (1- (1+r)^(-n))/r

Interest payment = 6% × $1,000 = $60

PV = 60 × (1 - (1.0.086)^(-10)/0.086)

      = 60 × 5.4912

      = 329.47

Step 2

PV of redemption Value

PV of RV = RV × (1+r)^(-n)

= 1000 × (1.086)^(-10)

= 438.229

Step 3

Calculate Value of the bond

=329.47 + 438.229

=767.7066285

Value of the bond = $767.70

$830.16

Explanation:

Tenor: 10 years

Coupon rate: 6% annually -> coupon received annual (PMT) = $1,000 * 6% = $60

Face value (FV): $1,000

Yield To Date (YTD): 8.6% annually  

Bond’s price = present value of bond + present value of total coupon received semiannual

Present value of bond = FV/(1+ YTD) ^tenor = 1000/(1+8.6%)^10 = $438.23

Present value of total coupon received semiannual = 60/(1+8.6%)^10 +60/(1+8.6%)^9+….+ 60/(1+8.6%)^1 = $391.93

(we can use excel to calculate the PV of coupon received = PV(rate,tenor,-PMT) = PV(8.6%,10,-60) = 391.93)

⇒ Bond’s price = $438.23+ $391.93 =  $830.16

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