Present Value (Issue Price) of a Bond

Present value is one of the core ideas behind how we value things in corporate finance—especially when it comes to figuring out how much a bond is really worth when it's issued.

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What Is Present Value?

Put simply, it tells us what a future cash inflow is really worth today.

The basic formula is:

Present Value = Future Value / (1 + r)^n

Where:

r is the discount rate per period
n is the number of periods

For bonds, since they pay interest over time and return the principal at the end, we just calculate the present value of each payment and add them up.

Components of a Bond

Let’s recap the key parts of a bond...

Face Value (Par Value): The amount repaid at maturity, usually $1,000
Coupon Rate: The annual interest rate based on the face value
Maturity Date: When the bond’s principal is repaid
Coupon Payment: The periodic interest amount (typically annual or semiannual)

So, a 5-year bond with a 6% annual coupon and $1,000 face value pays $60 per year.

Determining the Issue Price of a Bond

The issue price of a bond is simply what investors are ready to pay when the company puts it on the market.

This depends on how the bond’s coupon compares to the current market interest rate.

The Issue Price Is the Present Value of Future Cash Flows

To find the issue price, we take all the bond’s future payments—interest and principal—and discount them back to today using the market rate.

Here’s the basic approach:

Issue Price = sum of (Coupon / (1 + r)^t) + (Face Value / (1 + r)^n)

Where:

t is each period until maturity
n is the total number of periods
r is the market interest rate per period

Three Common Scenarios

Par Bond – Coupon rate equals market rate → Issue price equals face value
Premium Bond – Coupon rate is higher than market rate → Issue price is above face value
Discount Bond – Coupon rate is lower than market rate → Issue price is below face value

It’s basic investor logic: if the bond pays more than what’s out there, people will pay a premium; if it pays less, they’ll only buy it at a discount.

Example: Pricing a Bond

Let’s say a company issues a 3-year bond with a $1,000 face value, a 5% annual coupon, and the current market rate is 6%.

What’s the fair price?

Step 1: List the Cash Flows

Annual interest = $50
Final principal = $1,000
Discount rate = 6%

Step 2: Discount Each Cash Flow

$50 / (1.06)^1 = $47.17$50 / (1.06)^2 = $44.50$50 / (1.06)^3 = $41.98

Total PV of coupons = $133.65

$1,000 / (1.06)^3 = $839.62

Total Issue Price = $133.65 + $839.62 = $973.27

Since the bond offers less than the market, it gets issued at a discount.

Why It Matters

Knowing how to value a bond using present value is about pricing a financial instrument but also about understanding how interest rates, cash flow timing, and investor expectations all play into your financing or investment strategy.

Using present value helps us put a fair price on a bond, based on what it pays and what the market expects in return.