Banking Chapter 4 The Time Value Money Outline The Following Outline Correlated

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Chapter 4

The Time Value of Money

I. Chapter Outline

The following chapter outline is correlated to the PowerPoint Lecture Slides. The PowerPoint slides

are referenced in bold. Alternative Examples to selected textbook examples are also available in the

PowerPoint Lecture Slides and are also referenced in bold.

4.1 The Timeline (Slides 8–11)

• Example 4.1 Constructing a Timeline (Slides 12–13)

• PowerPoint Alternative Example 4.1 (Slides 14–15)

4.2 The Three Rules of Time Travel (Slide 16)

• Rule 1: Comparing and Combining Values (Slide 17)

• Rule 2: Moving Cash Flows Forward in Time (Slides 18-19)

• Figure 4.1 The Composition of Interest over Time (Slide 25)

• Example 4.2 The Power of Compounding (Slides 26–28)

• PowerPoint Alternative Example 4.2 (Slides 29–31)

• Rule 3: Moving Cash Flows Back in Time (Slide 32)

• Example 4.3 Present Value of a Single Future Cash Flow (Slides 33–35)

• PowerPoint Alternative Example 4.3 (Slides 36-38)

4.3 Valuing a Stream of Cash Flows (Slides 52–53)

• Example 4.5 Present Value of a Stream of Cash Flows (Slides 54–56)

• PowerPoint Alternative Example 4.5 (Slides 57–58)

4.4 Calculating the Net Present Value (Slide 60)

• Example 4.6 Net Present Value of an Investment Opportunity (Slides 61–63)

• PowerPoint Alternative Example 4.6 (Slides 64–66)

4.5 Perpetuities and Annuities (Slides 67–68)

• Perpetuities (Slides 67–68)

• Example 4.7 Endowing a Perpetuity (Slides 69–70)

• PowerPoint Alternative Example 4.7 (Slides 71–72)

14 Berk/DeMarzo • Corporate Finance, Fourth Edition, Global Edition

• Example 4.8 Present Value of an Annuity Due (Slides 77–80)

– Future Value of an Annuity (Slide 81)

• Example 4.9 Retirement Savings Plan Annuity (Slides 82–85)

• Growing Cash Flows (Slide 86)

– Growing Perpetuity (Slide 86)

• Example 4.10 Endowing a Growing Perpetuity (Slides 87–88)

• PowerPoint Alternative Example 4.10 (Slides 89–90)

– Growing Annuity (Slide 91)

• Example 4.11 Retirement Savings with a Growing Annuity (Slides 92–93)

• PowerPoint Alternative Example 4.11 (Slides 94–95)

4.6 Using an Annuity Spreadsheet or Calculator (Slide 96)

• Example 4.12 Computing the Future Value in Excel (Slides 97–98)

• Example 4.13 Using the Annuity Spreadsheet (Slides 99–100)

4.7 Non-Annual Cash Flows (Slide 101)

• Example 4.14 Evaluating an Annuity with Monthly Cash Flows (Slides 102–103)

4.8 Solving for the Cash Payments (Slides 104–105)

4.9 The Internal Rate of Return (Slide 110)

• Example 4.16 Computing the IRR for a Perpetuity

(Slides 111–112)

• Example 4.17 Computing the Internal Rate of Return for an Annuity (Slides 113–114)

II. Learning Objectives

4-1 Draw a timeline illustrating a given set of cash flows.

4-3 Calculate the future value of

a. A single sum

4-4 Calculate the present value of

a. A single sum

4-5 Given four out of the following five inputs for an annuity, compute the fifth: (a) present value,

(b) future value, (c) number of periods, (d) periodic interest rate, and (e) periodic payment.

4-7 Given cash flows and present or future value, compute the internal rate of return for a series of

cash flows.

III. Chapter Overview

The introduction to Chapter 4 draws on the discussion of NPV in Chapter 3. The text puts a great deal

of emphasis on drawing a timeline when approaching every problem, so that students may better

visualize the problems they are solving. Another distinguishing feature of this text is that this chapter

4.1 The Timeline

Drawing a timeline as the first step in solving a problem will often clarify any confusion about

amount or timing of cash flows, making problems much clearer. The timeline is a very important part

of calculating the time value of money.

4.2 The Three Rules of Time Travel

Following are the three rules of time travel:

1. It is only possible to compare or combine values at the same point in time.

To compound cash flows, multiply the amount by (1 + r)n (Equation 4.1), where r is the periodic

4.3 Valuing a Stream of Cash Flows

This section shows how to calculate the present value or future value of an uneven cash flow stream.

16 Berk/DeMarzo • Corporate Finance, Fourth Edition, Global Edition

Future Value of a Cash Flow Stream with a Present Value of PV

4.4 Calculating the Net Present Value

The logic developed in Chapter 3 is reexamined here in the context of the time value of money.

4.5 Perpetuities and Annuities

Several alternatives to the formulas developed earlier are addressed at this point in the chapter. In

every case, the formula is derived using algebra:

1. Present value of a perpetuity

2. If we have several cash flows of the same size occurring at regular intervals, starting either

now or sometime in the future, this is a present value or future value of an annuity. Annuities

due are treated as ordinary annuities with one extra period of interest.

3. The authors introduce the concept of valuing an infinite stream of cash flows that grow at a

constant rate each period, using the formula for present value of a growing perpetuity. This

development is particularly useful in later chapters.

Berk/DeMarzo • Corporate Finance, Fourth Edition, Global Edition 17

4. Sometimes several cash flows occur at regular intervals, which grow at a constant rate each

period. Present value or future value of a growing annuity is used.

4.6 Using an Annuity Spreadsheet or Calculator

4.7 Non-Annual Cash Flows

4.8 Solving for Cash Payments

This section explains how to solve for the annuity payment.

4.9 The Internal Rate of Return

IV. Spreadsheet Solutions in Excel