Discounting bond cash flows with a known yield

After laying out the bond's cash flows, we can now go through the steps of calculating the present value of each cash flow and value the bond. Recall that the value of the bond is the sum of the present value of its cash flows.

In this exercise, you will calculate the appropriate present value factor, pv_factor, for each cash flow, so we can calculate each cash flow's present value pv. You will then sum the pv to find the value of the bond.

Recall that this bond has a yield of 6%, which acts as the discount rate. The data frame you created in the prior exercise, cf, is present in your workspace.

This exercise is part of the course

Bond Valuation and Analysis in R

Exercise instructions

Create a new column, t, in your cf data frame to indicate the year in which cash flow is received. Note that for your purposes, the year is equivalent to the name of the rows in your data frame (1, 2, 3, etc.). This means you can simply use rownames() to name t. Use as.numeric() to make sure the values of t are numeric.
Create another new column, pv_factor in your cf object to store each year's present value factor. Recall that each year's present value factor is calculated as 1 divided by 1 + the yield rate (in this case 6%, or 0.06) set to the power of your time variable (t).
Create a pv column in cf to store the present value of each year's cash flow. The present value is calculated as cash flow (cf) multiplied by the year's present value factor (pv_factor).
Finally, use sum() to sum the values in pv to find the value of the bond.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Add column t to cf
cf$t <- as.numeric(___(___))

# Calculate pv_factor
cf$pv_factor <- 1 / (1 + ___)^___

# Calculate pv
cf$pv <- ___ * ___

# Calculate the bond price
sum(___$___)

Edit and Run Code

This exercise is part of the course

Bond Valuation and Analysis in R

IntermediateSkill Level

5.0+

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The fixed income market is large and filled with complex instruments. In this course, we focus on plain vanilla bonds to build solid fundamentals you will need to tackle more complex fixed income instruments. In this chapter, we demonstrate the mechanics of valuing bonds by focusing on an annual coupon, fixed rate, fixed maturity, and option-free bond.

Exercise 1: Introduction Exercise 2: Price vs. value Exercise 3: Time value of money Exercise 4: Computing a bond's future value Exercise 5: Computing a bond's present value Exercise 6: Bond valuation Exercise 7: Laying out the bond's cash flows Exercise 8: Discounting bond cash flows with a known yield

Current Exercise

Exercise 9: Convert your code into a function Exercise 10: Convert your code into a bond valuation function

Estimating Yield To Maturity - The YTM measures the expected return to bond investors if they hold the bond until maturity. This number summarizes the compensation investors demand for the risk they are bearing by investing in a particular bond. We will discuss how one can estimate YTM of a bond.

Exercise 1: Price-yield relationship Exercise 2: Credit ratings Exercise 3: The yield on the Moody's Baa index Exercise 4: Value the 5% bond using the Baa yield you found Exercise 5: Plotting the price/yield relationship Exercise 6: Components of yield Exercise 7: Risk-free yield Exercise 8: Plotting US Treasury yields Exercise 9: Plotting the investment grade spread Exercise 10: Estimating the yield of a bond Exercise 11: Finding a bond's yield Exercise 12: Use uniroot function to find YTM

Interest rate risk is the biggest risk that bond investors face. When interest rates rise, bond prices fall. Because of this, much attention is paid to how sensitive a particular bond's price is to changes in interest rates. In this chapter, we start the discussion with a simple measure of bond price volatility - the Price Value of a Basis Point. Then, we discuss duration and convexity, which are two common measures that are used to manage interest rate risk.

Exercise 1: Bond price volatility and the price value of a basis point Exercise 2: Price value of a basis point Exercise 3: Calculate PV01 of a 10% bond Exercise 4: Duration Exercise 5: Duration of a zero-coupon bond Exercise 6: Calculate approximate duration for a bond Exercise 7: Estimating effect on bond price using duration Exercise 8: Convexity Exercise 9: Calculate approximate convexity for a bond Exercise 10: Estimating effect of convexity on bond price Exercise 11: Estimating the bond price using duration and convexity

We will put all of the techniques that the student has learned from Chapters One through Three into one comprehensive example. The student will be asked to value a bond by using the yield on a comparable bond and estimate the bond's duration and convexity.

Exercise 1: Summarizing the main lessons Exercise 2: Find AAA bond yields as of September 30, 2016 Exercise 3: Bond valuation Exercise 4: Alternative cash flow vector code Exercise 5: Duration and convexity Exercise 6: Direction of price change Exercise 7: Calculate duration Exercise 8: Calculate convexity measure Exercise 9: The estimated price change using duration and convexity Exercise 10: Congratulations!