I’m gonna show you how to do bond valuation.
When we say valuation, it means we are calculating the price or value of an investment. Basic Bond Valuation Model
This is a basic model or formula we use to calculate the price or the value of a bond. V0 is the bond price. Here we have to include two components. The first is coupon interest payment. The second is the par value or the principal value of a bond, which is usually equal to $1000.
To get the price of a bond, we are basically converting all
the future cashflows back to current year, year 0.
In other words, the price of a bond is the same as the present value of all future cashflows.
i is the discount rate, required rate, or market interest rate.
n is the number of time period until maturity. Bond Pricing: Annual Compounding
Let’s take an example. What is the market price of a $1,000 par value
20-year bond that pays 9.5% compounded annually when the market rate is 10%?
Before I show you how to do the calculation, let’s understand the meaning of this question first. $1,000 par value, this is the future value that you will receive at the end of the maturity
date after 20 years of investment. This is also called the face value. The 20-year bond represents the maximum period of this investment. After 20 years, this investment will come to maturity. 9.5% is the coupon interest rate. You will have to convert it into dollars by multiplying it with the par value. Therefore, your coupon interest payment is $95. Market interest rate is the current interest rate
people receive in the market from similar investments.
And this question is asking you to calculate the market price of this bond. Market price means the present value, PV. To calculate the market price of the bond,
you need to use an app called financial calculator. You may download it from Google Play Store or Apple App Store. Just search “financial calculator”, you will find it. After downloading it, look for bond calculator, and click to open it.
By using financial calculator,
first, you need to set the compounding to annually. It means when you invest in this bond, you will receive the coupon interest payment once a year.
Now, key in the face value or par value, FV, $1,000.
Annual coupon payment, PMT, taking 9.5% times $1000 face value, equals to 95.
Annual yield, this is the market interest rate, I/Y, equals to 10.
Years to maturity, N, equals to 20.
Last step, just press Price button, you will get the bond price, PV, negative $957.43.
Negative sign means this is a payment. You pay $957.43 to purchase this bond investment. So that, every year you will receive coupon payment of $95 for 20 years. At the end of 20 years, you will get back $1,000 face value.
Bond Pricing: Semi-annual Compounding
Let’s look at the next example, which is about semi-annual compounding.
What is the market price of a $1,000 par value 20-year bond that pays
9.5% compounded semi-annually when the market rate is 10%?
Using financial calculator, set compounding to semiannually. FV, the future value is the face
value or par value, equals to $1000. PMT, annual coupon payment, taking 9.5% times $1000 par value,
you will get $95. I/Y, the market interest rate = 10%. N, years to maturity = 20.
Last step, press Price. You will get the PV, which is the bond price = negative $957.10. Negative means this is a payment.
Ways to Measure Bond Yield
In fact, there are many ways to measure bond yield or bond return, such as current yield,
yield-to-maturity, yield-to-call, and expected return. We will cover these in the following part. Current Yield
First, current yield.
The current yield measures the annual return to an investor based on the current price. This is the return you can earn by holding the bond for one year. As the market price of a bond
will constantly change, the current yield of a bond is also different at varying period of time. Take an example, a 10% coupon bond which is currently selling at $1,150,
how much would be the current yield?
By taking 10% times $1,000 par value, over $1,150, you will get a current yield, 8.7%.
Yield-to-Maturity: Annual Compounding
Yield to maturity is another measure of bond’s return. Compared to current yield which measures bond’s return for one year,
yield to maturity measures the average return of a bond for the whole holding period. Take an example. There is a 7.5%, $1,000 par value bond that has 15 years remaining to maturity,
and is currently trading in the market at $809.50 with annual coupon payments. 7.5% is annual coupon interest rate, multiplying with $1,000 par value,
you will get $75 coupon interest. $75 over $809.50, current yield is 9.26%. This is the return for the bond in current year.
To calculate the yield to maturity, YTM, it is basically the market interest
rate or annual yield, I/Y. Using Finance
