Ian Lord

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

Steven Scalia

Steven completed a Graduate Degree is Chartered Accountancy at Concordia University. He has performed as Teachers Assistant and Assistant Lecturer in University.

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. Updated: 05/09/2020

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

A zero coupon bond is a type of bond that doesnt 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 wont be receiving any periodic interest payments, the only time hell 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 thats 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 childs college.

## Formula & Example

The basic method for calculating a zero coupon bonds 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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## Zero Coupon Bonds - A Practical Exercise:

The following practical exercise is designed to enable students to apply their knowledge of Zero Coupon Bonds in a real-life situation.

### Scenario:

You just finished college and received a graduation gift of \$10,000 from your family. Having majored in Finance, you want to put this money to work so that it can grow over time. You give yourself the objective of investing the money over 5 years and then use the proceeds towards the down payment of your first home. You have two options, both with the same amount of risk:

1. Invest in a reputable bond mutual fund that provides annual returns of 3%. You deem this to be an acceptable rate of return.
2. Purchase a \$10,000 Zero Coupon Bond from Company X that matures in 5 years.

According to the latest quote, the \$10,000 Zero Coupon Bond of Company X is trading at \$9,110. You thus have a decision to make. Should you invest in the Zero Coupon Bond or in the bond mutual fund?

### Exercise:

1. What is the principal value, interest rate, and maturity of the Zero Coupon Bond of Company X?

2. What is the value of the bond for your purposes? (Hint: Compute the present value!)

3. Given the bonds current price, should you purchase it or not?

### Solution:

1.

Principal: \$10,000

Interest rate: 3%

Maturity: 5 years

2.

Present value = Principal / (1 + Rate)^{Term}

= 10,000 / (1.03^5)

= \$8,626.09

3.

The answer is No.

• This is because the current market price is greater than the present value that you computed. This means that, if you were to invest in the Zero Coupon Bond, you would earn an annual rate of return below 3%.

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