Time Value of Money

The basic premise of time value of money is that you would rather receive $1 today than $1 tomorrow, so to forego $1 today you will have to be induced to receive more that $1 in the future. How much more would it take to make you indifferent from receiving the $1 today and waiting? Let's assume that you expect to earn a 5% annual return on a comparable investment, we can use that rate to calculate the value today of receiving $1 one year from now. We can then easily extend this calculation to receiving $1 two years from now and so on. For this exercise, the variables future value fv, which equals $100, and the expected return r, which equals 5%, are stored in memory. Use these variables to calculate the present value of $100 one year from now and $100 two years from now. You will see that the farther out we go, that same $100 is worth less and less today.

This exercise is part of the course

Equity Valuation in R

Exercise instructions

Calculate the present value of $100 one year from now.
Calculate the present value of $100 two years from now.

Hands-on interactive exercise

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

# Calculate PV of $100 one year from now
pv_1 <- ___
pv_1

# Calculate PV of $100 two years from now
pv_2 <- ___
pv_2

Edit and Run Code

This exercise is part of the course

Equity Valuation in R

IntermediateSkill Level

4.9+

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Many individuals and institutions invest in equities. To do so effectively, the investor must have a solid understanding of how the value of the equity compares to the stock price. In this course, we focus on fundamental concepts of equity valuation. We begin with a discussion of time value of money and then move on to the first of two discounted cash flow methods we will discuss - the free cash flow to equity valuation model.

Exercise 1: Course Intro and Fundamental Valuation Exercise 2: Time Value of Money

Current Exercise

Exercise 3: Difference Between Valuing Enterprise and Equity Cash Flows Exercise 4: The Free Cash Flow to Equity Model Exercise 5: Calculating Operating Profit Exercise 6: Calculate Free Cash Flow to Equity Exercise 7: Calculating Terminal Value Exercise 8: Calculating Equity Value Exercise 9: Calculating Present Value of Free Cash Flow to Equity Exercise 10: Calculate Present Value of Terminal Value Exercise 11: Calculate Equity Value

One of the critical components of free cash flow to equity valuation is using reliable projections. In the first part of this chapter, we will discuss ways to analyze the projections to help us identify the right questions to ask. In the second part of this chapter, we will go through the second of our discounted cash flow models - the dividend discount model. In this approach, we discount expected dividends instead of free cash flows.

Exercise 1: Analyzing the Projections Exercise 2: Analyze Revenue Trends - Bar Chart Exercise 3: Analyze Revenue Trends - Regression Exercise 4: Perpetuity Growth Rate Exercise 5: Calculate Retention Ratio Exercise 6: Perpetuity Growth Rate Calculation Exercise 7: Dividend Discount Model Exercise 8: Valuing Preferred Stock Exercise 9: Valuation Assuming No Dividends For First Few Years Exercise 10: Valuation Assuming 2-Stages of Dividends

To be able to discount cash flows, we need a discount rate. For the free cash flow to equity and dividend discount model, the cost of equity is the appropriate discount rate. In this chapter, we will discuss how each of the components of the cost of equity are calculated.

Exercise 1: What is a discount rate?Exercise 2: Risk and Return Exercise 3: Calculating Returns Exercise 4: Estimating Beta Exercise 5: Unlevering Betas Exercise 6: Hamada vs. Fernandez Formula Exercise 7: Beta Unlevering Exercise Exercise 8: Beta Relevering Exercise Exercise 9: Risk-Free Rate and Equity Risk Premium Exercise 10: Obtain Risk-Free Rate Data Exercise 11: Calculate Historical Equity Risk Premium Exercise 12: Calculate the Cost of Equity

Relative valuation allows us to use the valuation of comparable companies to infer the value of our subject firm. In this chapter, we discuss how to identify comparable companies and how to calculate valuation multiples. We also show how to analyze the determinants of multiples.

Exercise 1: Relative Valuation Exercise 2: Identifying Comparable Firms Exercise 3: Valuation Multiples Exercise 4: Calculating Valuation Multiples Exercise 5: Calculating the Relevant Multiple Exercise 6: Implied Price Exercise 7: Analyzing Determinants of Multiples Exercise 8: Calculate ROE and P/B Exercise 9: Plot P/B vs. ROE Exercise 10: Strength of Relationship Exercise 11: Implied Price Using Regression Exercise 12: Difference in Implied Values

This chapter combines the lessons from Chapters 1 to 4 in a series of exercises. You will be asked to inspect the data and to value the firm using discounted cash flow and relative valuation approaches. At the end, you will combine the results in a summary table.

Exercise 1: Fundamental Valuation: Analyzing Projections Exercise 2: Visually Inspecting the Data Exercise 3: Using Regression to Test the Projections Exercise 4: Fundamental Valuation: Implementation Exercise 5: Cost of Equity Exercise 6: Calculate Value During Projection Period Exercise 7: Calculate the Terminal Value Exercise 8: Equity Value Per Free Cash Flow to Equity Model Exercise 9: Equity Value per Dividend Discount Model Exercise 10: Relative Valuation Exercise 11: Equity Value Per Price-to-Earnings Multiples Exercise 12: Combine valuation into a summary table Exercise 13: Congratulations!