# Coupon Rate Bond

The coupon rate bond is the annual interest rate the issuer pays to the bondholder. The rate is expressed as a percentage of the bond’s face value. Bond coupon rates are quoted as annual rates, but the bond coupons are typically paid semi-annually.

For example, an investor holding a bond with a \$1,000 face value and a 10% annual bond coupon will receive \$100 in interest yearly until the bond matures. At maturity the investor will receive the principal, also called the face value or the par value, plus the final coupon payment. Similarly, an investor holding a bond with a \$1,000 face value and a 10% semi-annual coupon will receive \$50 in interest every six months until maturity.

## Bond Coupon Definition

A bond coupon refers to the interest payments the bond issuer pays to the bondholder periodically until the bond matures. Bond coupon rates are quoted as annual rates, but the coupons are typically paid semi-annually. The term “coupon” stems from the days when bondholders would actually tear detachable coupons from the bond certificate and turn them in to the bond issuer on certain dates to redeem the interest payments.

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## Basis Points

A basis point is one hundredth of a percentage point. A single basis point would look like this: 0.01%. Fifty basis points is a half a percentage point: 0.50%. 100 basis points equal one percentage point: 1.00%.

## When To Use Basis Points

In finance, changes in the values of financial instruments or interest rates may be denoted in basis point. They are used to describe quantities less than one percent. When the Federal Reserve lowers its fed funds rate by a half a percent, the media may report that the fed funds rate was lowered by 50 basis points.

Similarly, the interest rate on a loan or debt instrument that is based on a reference rate, such as LIBOR or the Prime Rate, may have a spread quoted using the term basis point. The rate may be described as Prime Rate plus 50 basis point. If Prime Rate is 5%, then the rate on that loan or debt instrument would be 5.5%.

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# Annual Interest Rate Definition

The Annual percentage rate (APR) of a loan is the yearly interest rate expressed as a simple percentage. A bank or lender quotes the rate or APR. The annual percent rate does not incorporate the effects of compounding.

The federal Truth in Lending Act requires all consumer loan agreements to show the APR in large bold type. This is to make it easier for consumers to compare borrowing costs from different lenders. However, the annual percentage rate may not be the most accurate representation of the cost of the loan.

If interest on the loan compounds more than once per year, then the annual percent rate will be less than the actual interest rate on the loan, which is called the effective interest rate or the effective annual rate (EAR). In order to see the true cost of the loan, it is necessary to convert the annual percentage rate into the effective annual rate.

## Annual Interest Rate Equation

If the lender offers a loan at 1% per month and it compounds monthly, then the annual percentage rate (APR) on that loan would be quoted as 12%. The annual percentage rate does not include the effects of compounding, so it is less than what the borrower would actually pay. Below is the annual interest equation for APR.

12% = 1% per month x 12 months

APR = Rate per period x Periods per year

## Effective Annual Rate Formula

If the lender offers a loan at 1% per month, and the loan compounds monthly, the effective annual rate (EAR) on that loan would be 12.68%. The effective annual rate does include the effects of compounding, so it is higher than the APR. The EAR reflects what the borrower actually pays in interest on the loan. Below is the effective annual rate formula.

12.68% = (1 + 1%)12

EAR = ( 1 + (APR/N)N ) – 1

(Where N = the number of compounding periods per year.)

## Convert APR to Monthly Interest

To convert annual rate to monthly rate, when using APR, simply divide the annual percent rate by 12.

Monthly Rate = APR / 12

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# Binomial Options Pricing Model

The binomial options pricing model is a tool for valuing stock options. Starting with certain given values, and making certain assumptions, the model uses a binomial distribution to calculate the price of an option. The binomial method is considered as accurate, if not more accurate than the Black Scholes method of valuing options.

Calculating the value of an option using the binomial method requires certain givens and certain assumption. Start with the current price of the stock and the strike price of the option. You must also know the expiration date of the stock option. The necessary assumptions required for this method of options valuation include two possible stock prices for the end of the period as well as the probability for each of the two stock prices at the end of the period. You must also have an appropriate interest rate or borrowing cost to calculate the price of an option using the binomial method.

Once all of these pieces of information are in place, using the binomial options pricing model, you can compute the value of an option for a single period, or for a multi-period span of time. For example, you can compute the value of an option that expires in one year based on two assumed stock prices at the end of the year. Or, to get a more accurate option valuation, you can split the year into finer segments of time and calculate values for the option based on smaller intervals of time and narrower ranges of stock price outcomes.

## Example of the Binomial Options Pricing Model – One Period

Here is a simple example of the binomial options pricing model for a single period. Let’s say the current stock price is \$100. The strike price of the option is also \$100. The option expires in one year. At the end of the year, the stock price will either rise to \$130 or fall to \$80. We assume there is a 60% chance it will rise to \$130 and a 40% chance it will fall to \$80. The interest rate is 10%.

If the stock rises to \$130, then the value of the option will be \$30. This is because option value equals stock price minus strike price. There is a 60% chance the option will be worth \$30 at the end of the year. If the stock falls to \$80, then the value of the option will be \$0. This is because option value cannot be negative. They are either positive, or they are zero. There is a 40% chance the option will be worth nothing at the end of the year. Using this data, let’s compute the value of the stock using the appropriate formula.

```Option Value = (Chance of Rising x Up Value) x (Chance of Falling x Down Value)
1 + Interest Rate

\$16.36 = (.60 x \$30) x (.40 x \$0)
1.10```

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## Libor vs Prime Rate

Interesting article in the April 23rd Wall Street Journal on page C1 highlighting the divergence of Libor from U.S. Prime Rate. Let’s dive into what the difference between Libor vs Prime Rate is.

## What’s the Difference Between Libor vs Prime Rate?

Libor has been increasing while the Prime Rate has been dropping.

You need to check your loan agreement to see what is the index for setting your loan rate. Now is also a good time to see if there is a floor on your interest rate. I have had clients in the past who woke up to find that the prime rate had fallen significantly but their interest rate had a floor on it. You can often negotiate that floor away.

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