# Zero Coupon Bond: Definition, Formula & Example

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• 0:04 Zero Coupon Bonds Definition
• 0:59 Pricing
• 1:45 Formula & Example
• 3:58 Lesson Summary
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Lesson Transcript
Instructor: Ian Lord

Ian has an MBA and is a real estate investor, former health professions educator, and Air Force veteran.

Zero coupon bonds are an alternative investment type compared to traditional bonds. In this lesson, we will explore what makes these investments unique and how investors can calculate a purchase price or yield of these bonds.

## Zero Coupon Bonds Definition

Most bonds make periodic interest payments to pay back bondholders for borrowing money. For some bond investors, these regular payments are an annoyance; they'd rather receive one big payday later on. Tom is looking for an investment that fits this goal and has come across zero coupon bonds. Let's take a look at what's different about these bonds and how Tom can calculate what's a good purchase price to meet his desired returns.

A zero coupon bond is a type of bond that doesn't make a periodic interest payment. In bond investing, the term 'coupon' refers to the interest rate repaid periodically to the bondholder. When Tom buys the bond, it will have a face value, which represents how much money someone receives from the bond issuer at maturity. Since Tom won't be receiving any periodic interest payments, the only time he'll receive payment from the issuer is when the bond matures. When the bond is originally issued, the purchase price is intentionally set low to motivate investors to buy.

## Pricing

Maturity dates and interest rates dictate the price of zero coupon bonds. When interest rates are higher, the purchase price is lower. A maturity date far off in the future will cause the zero coupon bond to have a lower price compared to one that's maturing sooner. The interest rate remains fixed throughout the life of the zero coupon bond, so the price to buy the bond has to change throughout its life to match equivalent yields already out there in the market.

Zero coupon bonds typically have long maturity periods and can take 10 or more years to pay out. Because of this, prices fluctuate wildly on the secondary market. Because of the discount on the original price and opportunities to buy on the secondary market, these bonds can be a good way to provide a lump sum return at a specific time for a long-term goal, like paying for a child's college.

## Formula & Example

The basic method for calculating a zero coupon bond's price is a simplification of the present value (PV) formula. The formula is price = M / (1 + i)^n where:

• M = maturity value or face value
• i = required interest yield divided by 2
• n = years until maturity times 2

Zero coupon bond prices are typically calculated using semi-annual periods (twice a year) because bonds that offer a coupon often pay interest twice a year. So calculating the price of a zero coupon bond this way allows Tom to compare investing in this zero coupon bond to investing in a traditional bond.

So because the required interest yield is a yearly figure, it has to be divided by two to make the yield semi-annual. In addition, the number of years until maturity has to be multiplied by two since, again, coupon bonds pay out twice a year.

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