1. Bond valuation
In this course,
2. Bond valuation
our exercises will focus on a particular bond that pays a fixed coupon rate once a year and has a fixed maturity with no embedded options.
3. Value of an asset
As a matter of economics, the value of any asset is equal to the present value of its expected future cash flows. These cash flows are discounted at an appropriate risk-adjusted discount rate. This is reflected mathematically in the equation on the slide.
4. Laying out a bond's cash flows
Bonds are no different.
The first step in calculating bond value is to layout the cash flows we are discounting. Prior to maturity, the bond investor receives coupon payments. At maturity, the investor receives the last coupon payment and the par value.
So we can modify the equation from the last slide to account for how these cash flows are separated from a mechanical point of view. We will revisit the inputs to this formula in more detail later. For now, it's important to understand the major components included in this formula.
5. Creating a cash flow vector
So how do we run this analysis in R?
In R, we can then create a cash flow vector "cf" by laying out the cash flows as-is and remembering that the last cash flow equals the par value plus the last coupon payment.
6. Converting to dataframe
To complete the bond valuation exercise, we have to be able to add additional variables to the cash flow vector. We do this by using the data frame command.
7. Creating a time index
Because each cash flow occurs at a particular time, the first variable we need to add is a time index. We label this variable "t."
The time index is used as the number of periods - in our example years - that we will discount each of the bond's cash flows.
8. Calculating the PV factors
Next, we need to calculate a present value factor to discount each bond's cash flow. The discount rate for bonds is called the bond's yield. We will discuss yields in more detail in Chapter 2, but for now assume that the yield is given.
The present value factor for discounting called "pv_factor" is equal to 1 over 1 plus the yield raised to the time index. So, for example, if we have a discount rate of 10%, the pv_factor for cash flows received 2 years from now is equal to 1 over 1 plus 10% raised to the second power.
9. PV of cash flows
The penultimate step is to calculate the present value of each of the bond's cash flows by multiplying each cash flow by the appropriate PV factor.
Finally, we sum the PV of the cash flows to arrive at the bond's value.
10. Let's practice!
You will now apply these steps to value a bond in the following exercises.