# Cost of Capital. Katharina Lewellen Finance Theory II April 9, 2003

Save this PDF as:

Size: px
Start display at page:

Download "Cost of Capital. Katharina Lewellen Finance Theory II April 9, 2003"

## Transcription

1 Cost of Capital Katharina Lewellen Finance Theory II April 9, 2003

2 What Next? We want to value a project that is financed by both debt and equity Our approach: Calculate expected Free Cash Flows (FCFs) from the project iscount FCFs at a rate that reflects opportunity costs of capital of all capital suppliers Incorporate the interest tax shields Adjust the discount rate (WACC) Adjust cash flows (APV) Recall: Free Cash Flows are cash flows available to be paid to all capital suppliers ignoring interest rate tax shields (i.e., as if the project were 100% equity financed). 2

3 Two Approaches Weighted Average Cost of Capital (WACC): iscount the FCF using the weighted average of after-tax debt costs and equity costs WACC = k ( 1 t) + + k + Adjusted Present Value (APV): Value the project as if it were all-equity financed Add the PV of the tax shield of debt and other side effects 3

4 1. WACC

5 Weighted Average Cost of Capital (WACC) Step 1: Generate the Free Cash Flows (FCFs) Step 2: iscount the FCFs using the WACC WACC = k( 1 t) + + k + 5

6 WACC - xample You are evaluating a new project. The project requires an initial outlay of \$100 million and you forecast before-tax profits of \$25 million in perpetuity. The tax rate is 40%, the firm has a target debt-to-value ratio of 25%, the interest rate on the firm s debt is 7%, and the cost of equity is 12%. After-tax CFs = \$ = \$15 million After-tax WACC= /V (1 τ) r d + /V r e = = 10.05% NPV = / = \$49.25 million 6

7 WARNING!!! The common intuition for using WACC is: To be valuable, a project should return more than what it costs us to raise the necessary financing, i.e., our WACC This intuition is wrong. Using WACC this way is OK sometimes... but by accident. Sometimes, this is plain wrong: conceptually, i.e., the logic may be flawed practically, i.e., gives you a result far off the mark Need to understand this concept (more tricky than it appears). 7

8 Weighted Average Cost of Capital (WACC) Recall: iscount rates are project-specific ==> Imagine the project is a stand alone, i.e., financed as a separate firm. ebt worth (i.e. market value) and with expected return k (i.e., cost of debt) if against that project only quity worth (i.e. market value) and with expected return k (i.e., cost of equity) if against that project only t is the marginal tax rate of the firm undertaking the project 8

9 Why WACC? Consider a one-year project (stand-alone) such that: expected cash-flow at the end of year 1 (BIT) = X Today (year 0) the projects has: debt outstanding with market value 0 equity outstanding with market value 0 project s total value is V 0 = We are looking for the discount rate r such that: Aftertax CFs (if all equity financed) 1+ r ( 1 t) X 1+ r 1 V0 = = r = ( 1 t) X V 1 0 V 0 9

10 Why WACC? (cont.) The expected increase in value from year 0 to year 1 is: k 0 + k0 = k 0 + (1 t)(x 1 k 0 ) V 0 CF to debt- holders CF to share- holders k 0 + (1 t)k 0 = (1 t)x 1 V 0 k V (1 t)k V 0 0 = ( 1 t)x1 V V 0 0 r = WACC 10

11 Leverage Ratio /(+) /(+) should be the target capital structure (in market values) for the particular project under consideration. Common mistake 1: Using a priori /(+) of the firm undertaking the project. Common mistake 2: Use /(+) of the project s financing xample: Using 100% if project is all debt financed. Caveat: We will assume that the target for A+B is the result of combining target for A and target for B. It s OK most of the time. 11

12 Leverage Ratio (cont.) So how do we get that ratio? Comparables to the project: Pure plays in the same business as the project Trade-off: Number vs. quality of comps The firm undertaking the project if the project is very much like the rest of the firm (i.e., if the firm is a comp for the project). Introspection, improved by checklist,... 12

13 Important Remark If the project maintains a relatively stable /V over time, then WACC is also stable over time. If not, then WACC should vary over time as well so you should compute/forecast a different WACC for each year. In practice, firms tend to use a constant WACC. So, in practice, WACC method is not great when capital structure is expected to vary substantially over time. 13

14 Cost of ebt Capital: k When default probability is low We can estimate k using CAPM (empirical evidence suggests using debt betas between 0.2 and 0.3) k should be close to the interest rate that lenders would charge to finance the project with the chosen capital structure When default probability is high We would need default probabilities to estimate expected cash flows to debtholders 14

15 Marginal Tax Rate: t It s the marginal tax rate of the firm undertaking the project (or to be more precise, of the firm + project). Indeed, this is the rate that is going to determine the tax savings associated with debt. Marginal as opposed to average tax rate t 15

16 Cost of quity Capital: k Need to estimate k from comparables to the project: Pure Plays, i.e. firms operating only in the project s industry The firm undertaking the project (if the firm is a pure play) Problem: A firm s capital structure has an impact on k Unless we have comparables with same capital structure, we need to work on their k before using it. 16

17 Using CAPM to stimate k 1) Finds comps for the project under consideration. 2) Unlever each comp s β (using the comp s /(+)) to estimate its β A : β A = β + β V V 3) Use the comps β A to estimate the project s β A (e.g. take the average). 4) Relever the project s estimated β A (using the project s /(+)) to estimate its β under the assumed capital structure: β = β A + (β A β ) 5) Use the estimated β to calculate the project s cost of equity k : k = r f + β * Market Risk Premium 17

18 Remarks Formulas: Relevering formulas are reversed unlevering formulas. The appendix shows where they come from. Most of the time: Unlever each comp, i.e., one unlevering per comp. stimate one β A by taking the average over all comps β A possibly putting more weight on those we like best. This is our estimate of the project s β A Relever that β A only, i.e., just one relevering. In the course, we use mostly the formula for a constant /V. 18

19 More on Business Risk and Financial Risk Comparable firms have similar Business Risk Similar asset beta β A and, consequently, similar unlevered cost of capital k A Comparable firms can have different Financial Risk (β -β A ) if they have different capital structures ifferent equity beta β and thus different required return on equity k In general, equity beta β increases with / Consequently the cost of equity k increases with leverage 19

20 Leverage, returns, and risk Asset risk is determined by the type of projects, not how the projects are financed Changes in leverage do not affect r A or β A Leverage affects r and β A V V β + β = β ) ( A A β β + = β β A r V r V r + = ) r (r r r A A + = 20

21 Leverage and beta 4 β 3 Beta 2 β A 1 β ebt to equity ratio 21

22 Leverage and required returns r required return r A r ebt to equity ratio 22

23 Business Risk and Financial Risk: Intuition Consider a project with β A >0 Its cash flows can be decomposed into: Safe cash-flows Risky cash-flows that are positively correlated with the market. As the level of debt increases (but remains relatively safe): A larger part of the safe cash-flows goes to debtholders; The residual left to equityholders is increasingly correlated with the market. Note: If cash-flows were negatively correlated with the market (β A <0), increasing debt would make equity more negatively correlated with the market and would reduce the required return on equity. 23

24 General lectric s WACC Assume r f = 6% We can get G s β =1.10 which implies k = 7.5% k = 6% * 8% = 14.8% /(+) =.06 t = 35% WACC =.06 * 7.5% * (1-35%) * 14.8% = 14.2% 24

25 When Can G Use This WACC in CF? When the project under consideration has the same basic risk as the rest of the company (i.e., when the company is a good comp for its project). And, the project will be financed in the same way as the rest of the company. For example, if G is expanding the scale of entire operations then it should use its own WACC. But, if planning to expand in only one of its many different businesses then it s not the right cost of capital. In that case: Find publicly-traded comps and do unlevering / levering. 25

26 Important Warning Cost of capital is an attribute of an investment, not the company Few companies have a single WACC that they can use for all of their businesses. G s businesses: Financial services Power systems Aircraft engines Industrial ngineered plastics Technical products Appliances Broadcasting 26

27 How Firms Tend to Use WACC They calculate their WACC using: Their current cost of debt k Their own current capital structure /(+) Their own current cost of equity capital k (more on this soon). The marginal tax rate they are facing They discount all future FCF with: this (single) discount rate maybe adjusted for other things (e.g., project s strategic value ) 27

28 Selected Industry Capital Structures, Betas, and WACCs Industry ebt ratio (%) quity beta Asset beta WACC (%) lectric and Gas % Food production % Paper and plastic % quipment % Retailers % Chemicals % Computer software % Average of all industries % Assumptions: Risk-free rate 6%; market risk premium 8%; cost of debt 7.5%; tax rate 35% 28

29 Relation to MM: W/o taxes, WACC is independent of leverage 20% 18% r 16% 14% 12% r A = WACC 10% 8% 6% ebt-to-equity r 29

30 The WACC Fallacy (Revisited) The cost of debt is lower than the cost of equity (true). oes this mean that projects should be financed with debt? WACC = k + + k + No: WACC is independent of leverage As you are tapping into cheap debt, you are increasing the cost of equity (its financial risk increases). 30

31 With taxes, WACC declines with leverage r r A WACC ebt-to-equity r 31

32 2. APV

33 Adjusted Present Value Separates the effects of financial structure from the others. Step 1: Value the project/firm as if it were 100% equity financed. Step 2: Add the value of the tax shield of debt. Note: This is simply applying MM-Theorem with taxes APV = Valuation by Components = ANPV 33

34 Step 1: Value if 100% quity Financed Cash-flows: Free Cash Flows are exactly what you need. You need the rate that would be appropriate to discount the firm s cash flows if the firm were 100% equity financed. This rate is the expected return on equity if the firm were 100% equity financed. To get it, you need to: Find comps, i.e., publicly traded firms in same business. stimate their expected return on equity if they were 100% equity financed. 34

35 Step1: Value if 100% quity Financed (cont.) Unlever each comp s β to estimate its asset beta (or all equity or unlevered beta) β A using the appropriate unlevering formula β A = β + V V β Use the comps β A to estimate the project s β A (e.g. average). Use the estimated β A to calculate the all-equity cost of capital k A k A = r f + β A * Market Risk Premium Use k A to discount the project s FCF 35

36 xample Johnson and Johnson operate in several lines of business: Pharmaceuticals, consumer products and medical devices. To estimate the all-equity cost of capital for the medical devices division, we need a comparable, i.e., a pure play in medical devices (we should really have several). ata for Boston Scientific: quity beta = 0.98 ebt = \$1.3b quity = \$9.1b. 36

37 xample (cont.) Compute Boston Scientific s asset beta: 9.1 βa = β = 0.98 = Let this be our estimate of the asset beta for the medical devices business Use CAPM to calculate the all-equity cost of capital for that business (assuming 6% risk-free rate, 8% market risk premium): k A = 6% +.86 *8% = 12.9% 37

38 Step 2: Add PV(Tax Shield of ebt) Cash-flow: The expected tax saving is tk where k is the cost of debt capital (discussed earlier). If is expected to remain stable, then discount tk using k PVTS = tk / k = t If /V is expected to remain stable, then discount tk using k A PVTS = tk / k A Intuition: If /V is constant, (tk ) moves up/down with V The risk of tk is similar to that of the firm s assets: use k A 38

39 Step 2: Add PVTS (cont.) For many projects, neither nor /V is expected to be stable. For instance, LBO debt levels are expected to decline. In general you can estimate debt levels using: repayment schedule if one is available, financial forecasting and discount by a rate between k and k A. 39

40 xtending the APV Method One good feature of the APV method is that it is easy to extend to take other effects of financing into account. For instance, one can value an interest rate subsidy separately as the PV of interest savings. APV= NPV(all-equity) + PV(Tax Shield) + PV(other stuff) 40

41 WACC vs. APV Pros of WACC: Most widely used Less computations needed (before computers). More literal, easier to understand and explain (?) Cons of WACC: Mixes up effects of assets and liabilities. rrors/approximations in effect of liabilities contaminate the whole valuation. Not very flexible: What if debt is risky? Cost of hybrid securities (e.g., convertibles)? Other effects of financing (e.g., costs of distress)? Nonconstant debt ratios? Note: For non-constant debt ratios, could use different WACC for each year (see appendix) but this is heavy and defeats the purpose. 41

42 WACC vs. APV (cont.) Advantages of APV: No contamination. Clearer: asier to track down where value comes from. More flexible: Just add other effects as separate terms. Cons of APV: Almost nobody uses it. Overall: For complex, changing or highly leveraged capital structure (e.g., LBO), APV is much better. Otherwise, it doesn t matter much which method you use. 42

43 Appendix

44 Appendix A: Unlevering Formula for a Constant ebt Ratio /V Consider a firm with perpetual expected cash-flows, X. Capital structure: ebt worth and equity worth + = V all -equity + PVTS By definition, the all-equity cost of capital is the rate k A that is appropriate for discounting the project s FCF, (1-t)X. Moreover, since the firm s /V is stable, PVTS= tk / k A + = ( 1 t) X t ( 1 t) k k k X + t k + or ka = A A + 44

45 Appendix A: Unlevering Formula for a Constant ebt Ratio /V (cont.) ebt- and equity-holders share each year s (expected) cash-flows xpected after-tax cashflow if 100% equity financed 1 X + tk = k + ( t) Annual tax shield of debt xpected payment todebt xpected payment toequity k liminating X, we get: k A = k + + k + Translating into betas (all relationships being linear) yields: β A = β and so if + β + β + 0 we have β A = β + 45

46 Appendix B: Unlevering Formula for a Constant ebt Level Consider a firm with perpetual expected cash-flows, X. Capital structure: ebt worth and equity worth + = V all -equity + PVTS Since the firm s is constant over time, PVTS= t + = ( 1 t) X ( 1 t) X + t or ka = + ( 1 t) k A 46

47 Appendix B: Unlevering Formula for a Constant ebt Level (cont.) ebt- and equity-holders share each year s (expected) cash-flows xpected after-tax cashflow if 100% equity financed 1 X + tk = k + ( t) ividing both sides by (+), we get (see formula for k A above): = k Translating into betas yields: k A Annual tax shield of debt 1 + xpected payment todebt ( t) + k ( 1 t) + ( 1 t) xpected payment toequity k β A = β and so if 1 + ( t) + β ( 1 t) + ( 1 t) β 0 we have β A = β + 1 ( t) 47

48 Appendix C: WACC vs. APV: xample Objective of the example: See APV and WACC in action. Show that, when correctly implemented, APV and WACC give identical results. Correctly implementing WACC in an environment of changing leverage. Convince you that APV is the way to go. 48

49 WACC vs. APV: xample (cont.) Anttoz Inc., a Fortune 500 widget company, is planning to set up a new factory in New Orleans with cash flows as presented on the next slide: The new plant will require an initial investment in PP of \$75 million, plus an infusion of \$10 million of working capital (equal to 8% of first-year sales). Sales are projected to be \$125 million in the first year of operation. Sales are projected to rise a whopping 10% over the next two years, with growth stabilizing at a 5% rate indefinitely thereafter. Anttoz s army of financial analysts estimate that cash costs (COGS, GS&A expenses, etc.) will constitute 50% of revenues. New investment in PP will match depreciation each year, starting at 10% of the initial \$75 million investment and growing in tandem with sales thereafter. The firm plans to maintain working capital at 8% of the following year s projected sales. 49

50 WACC vs. APV: xample (cont.) With Anttoz Widgets Inc. in the 35% tax bracket, FCF would approach \$45 million in three years, and grow 5% per year thereafter. The required rate of return on the project s assets, k A, is 20%. The project supports a bank loan of \$80 million initially with \$5 million principal repayments at the end of the first three years of operation, bringing debt outstanding at the end of the third year to \$65 million. From that point on, the project s debt capacity will increase by 5% per year, in line with the expected growth of operating cash flows. Because of the firm s highly leveraged position in the early years, the borrowing rate is 10% initially, falling to 8% once it achieves a stable capital structure (after year 3). 50

51 WACC vs. APV: xample (cont.) Year 0 Year 1 Year 2 Year 3 Year 4 Sales 125, , , ,813 Cash Costs 62,500 68,750 75,625 79,406 epreciation 7,500 8,250 9,075 9,529 BIT 55,000 60,500 66,550 69,878 Corporate Tax 19,250 21,175 23,293 24,457 arnings Before Interest After Taxes 35,750 39,325 43,258 45,420 + epreciation 7,500 8,250 9,075 9,529 Gross Cash Flow 43,250 47,575 52,333 54,949 Investments into Fixed Assets 75,000 7,500 8,250 9,075 9,529 Net Working Capital 10,000 1,000 1, Unlevered Free Cash Flow (85,000) 34,750 38,225 42,653 44,785 ebt Level 80,000 75,000 70,000 65,000 68,250 51

52 WACC vs. APV: xample (cont.) Year 0 Year 1 Year 2 Year 3 Year 4 APV Unlevered FCF (85,000) 34,750 38,225 42,653 44,785 Unlevered Value 252, , , , ,496 Interest Tax Shield 2,800 2,625 2,450 1,820 iscounted Value of TS 52,135 54,549 57,379 60,667 63,700 Levered Value 305, , , , ,196 52

53 WACC vs. APV: xample (cont.) Year 0 Year 1 Year 2 Year 3 Year 4 APV Unlevered Value 252, , , , ,496 iscounted Value of Tax Shields 52,135 54,549 57,379 60,667 63,700 Levered Value 305, , , , ,196 WACC Value of ebt 80,000 75,000 70,000 65,000 68,250 Value of quity 225, , , , ,946 Required quity Return 21.2% 20.8% 20.5% 20.2% 20.2% WACC 17.4% 17.5% 17.6% 17.5% 17.5% WACC iscounted FCF 305, , , , ,196 53

### WACC and APV. The Big Picture: Part II - Valuation

WACC and APV 1 The Big Picture: Part II - Valuation A. Valuation: Free Cash Flow and Risk April 1 April 3 Lecture: Valuation of Free Cash Flows Case: Ameritrade B. Valuation: WACC and APV April 8 April

### EMBA in Management & Finance. Corporate Finance. Eric Jondeau

EMBA in Management & Finance Corporate Finance EMBA in Management & Finance Lecture 5: Capital Budgeting For the Levered Firm Prospectus Recall that there are three questions in corporate finance. The

Chapter 17 Valuation and Capital Budgeting for the Levered Firm 17A-1 Appendix 17A The Adjusted Present Value Approach to Valuing Leveraged Buyouts 1 Introduction A leveraged buyout (LBO) is the acquisition

### The Adjusted Present Value Approach to Valuing Leveraged Buyouts 1 Introduction

Chapter 18 Valuation and Capital Budgeting for the Levered Firm 18A-1 Appendix 18A The Adjusted Present Value Approach to Valuing Leveraged Buyouts 1 Introduction A leveraged buyout (LBO) is the acquisition

### Corporate Finance & Options: MGT 891 Homework #6 Answers

Corporate Finance & Options: MGT 891 Homework #6 Answers Question 1 A. The APV rule states that the present value of the firm equals it all equity value plus the present value of the tax shield. In this

### Financial Markets and Valuation - Tutorial 6: SOLUTIONS. Capital Structure and Cost of Funds

Financial Markets and Valuation - Tutorial 6: SOLUTIONS Capital Structure and Cost of Funds (*) denotes those problems to be covered in detail during the tutorial session (*) Problem 1. (Ross, Westerfield

### Cost of Capital and Project Valuation

Cost of Capital and Project Valuation 1 Background Firm organization There are four types: sole proprietorships partnerships limited liability companies corporations Each organizational form has different

IE Aufgabe 4 The Adjusted-Present-Value Approach to Valuing Leveraged Buyouts 1) Introduction A leveraged buyout (LBO) is the acquisition by a small group of equity investors of a public or private company

### DUKE UNIVERSITY Fuqua School of Business. FINANCE 351 - CORPORATE FINANCE Problem Set #4 Prof. Simon Gervais Fall 2011 Term 2.

DUK UNIRSITY Fuqua School of Business FINANC 351 - CORPORAT FINANC Problem Set #4 Prof. Simon Gervais Fall 2011 Term 2 Questions 1. Suppose the corporate tax rate is 40%. Consider a firm that earns \$1,000

### Practice Exam (Solutions)

Practice Exam (Solutions) June 6, 2008 Course: Finance for AEO Length: 2 hours Lecturer: Paul Sengmüller Students are expected to conduct themselves properly during examinations and to obey any instructions

### t = 1 2 3 1. Calculate the implied interest rates and graph the term structure of interest rates. t = 1 2 3 X t = 100 100 100 t = 1 2 3

MØA 155 PROBLEM SET: Summarizing Exercise 1. Present Value [3] You are given the following prices P t today for receiving risk free payments t periods from now. t = 1 2 3 P t = 0.95 0.9 0.85 1. Calculate

### GESTÃO FINANCEIRA II PROBLEM SET 5 SOLUTIONS (FROM BERK AND DEMARZO S CORPORATE FINANCE ) LICENCIATURA UNDERGRADUATE COURSE

GESTÃO FINANCEIRA II PROBLEM SET 5 SOLUTIONS (FROM BERK AND DEMARZO S CORPORATE FINANCE ) LICENCIATURA UNDERGRADUATE COURSE 1 ST SEMESTER 2010-2011 Chapter 18 Capital Budgeting and Valuation with Leverage

### Leverage. FINANCE 350 Global Financial Management. Professor Alon Brav Fuqua School of Business Duke University. Overview

Leverage FINANCE 35 Global Financial Management Professor Alon Brav Fuqua School of Business Duke University Overview Capital Structure does not matter! Modigliani & Miller propositions Implications for

### Use the table for the questions 18 and 19 below.

Use the table for the questions 18 and 19 below. The following table summarizes prices of various default-free zero-coupon bonds (expressed as a percentage of face value): Maturity (years) 1 3 4 5 Price

### Projecting Consistent Debt and Interest Expenses

WEB EXTENSION26A Projecting Consistent Debt and Interest Expenses Projecting financial statements for a merger analysis requires explicit assumptions regarding the capital structure in the post-merger

### DUKE UNIVERSITY Fuqua School of Business. FINANCE 351 - CORPORATE FINANCE Problem Set #7 Prof. Simon Gervais Fall 2011 Term 2.

DUKE UNIVERSITY Fuqua School of Business FINANCE 351 - CORPORATE FINANCE Problem Set #7 Prof. Simon Gervais Fall 2011 Term 2 Questions 1. Suppose the corporate tax rate is 40%, and investors pay a tax

### Equity Analysis and Capital Structure. A New Venture s Perspective

Equity Analysis and Capital Structure A New Venture s Perspective 1 Venture s Capital Structure ASSETS Short- term Assets Cash A/R Inventories Long- term Assets Plant and Equipment Intellectual Property

### CHAPTER 12 RISK, COST OF CAPITAL, AND CAPITAL BUDGETING

CHAPTER 12 RISK, COST OF CAPITAL, AND CAPITAL BUDGETING Answers to Concepts Review and Critical Thinking Questions 1. No. The cost of capital depends on the risk of the project, not the source of the money.

### ENTREPRENEURIAL FINANCE: Strategy Valuation and Deal Structure

ENTREPRENEURIAL FINANCE: Strategy Valuation and Deal Structure Chapter 9 Valuation Questions and Problems 1. You are considering purchasing shares of DeltaCad Inc. for \$40/share. Your analysis of the company

### BA 351 CORPORATE FINANCE. John R. Graham Adapted from S. Viswanathan LECTURE 10 THE ADJUSTED NET PRESENT VALUE METHOD

BA 351 CORPORATE FINANCE John R. Graham Adapted from S. Viswanathan LECTURE 10 THE ADJUSTED NET PRESENT VALUE METHOD FUQUA SCHOOL OF BUSINESS DUKE UNIVERSITY 1 THE ADJUSTED NET PRESENT VALUE METHOD COPING

### Capital Cash Flows: A Simple Approach to Valuing Risky Cash Flows

Capital Cash Flows: A Simple Approach to Valuing Risky Cash Flows Richard S. Ruback Graduate School of Business Administration Harvard University Boston, MA 02163 email: rruback@hbs.edu ABSTRACT This paper

### CHAPTER 8. Problems and Questions

CHAPTER 8 Problems and Questions 1. Plastico, a manufacturer of consumer plastic products, is evaluating its capital structure. The balance sheet of the company is as follows (in millions): Assets Liabilities

### Discount rates for project appraisal

Discount rates for project appraisal We know that we have to discount cash flows in order to value projects We can identify the cash flows BUT What discount rate should we use? 1 The Discount Rate and

### Valuing Companies. Katharina Lewellen Finance Theory II May 5, 2003

Valuing Companies Katharina Lewellen Finance Theory II May 5, 2003 Valuing companies Familiar valuation methods Discounted Cash Flow Analysis Comparables Real Options Some new issues Do we value assets

### Chapter 17 Corporate Capital Structure Foundations (Sections 17.1 and 17.2. Skim section 17.3.)

Chapter 17 Corporate Capital Structure Foundations (Sections 17.1 and 17.2. Skim section 17.3.) The primary focus of the next two chapters will be to examine the debt/equity choice by firms. In particular,

### CAPITAL STRUCTURE [Chapter 15 and Chapter 16]

Capital Structure [CHAP. 15 & 16] -1 CAPITAL STRUCTURE [Chapter 15 and Chapter 16] CONTENTS I. Introduction II. Capital Structure & Firm Value WITHOUT Taxes III. Capital Structure & Firm Value WITH Corporate

### ( ) ( )( ) ( ) 2 ( ) 3. n n = 100 000 1+ 0.10 = 100 000 1.331 = 133100

Mariusz Próchniak Chair of Economics II Warsaw School of Economics CAPITAL BUDGETING Managerial Economics 1 2 1 Future value (FV) r annual interest rate B the amount of money held today Interest is compounded

### Valuing Companies. The Big Picture: Part II - Valuation

Valuing Companies The Big Picture: Part II - Valuation A. Valuation: Free Cash Flow and Risk April 1 April 3 Lecture: Valuation of Free Cash Flows Case: Ameritrade B. Valuation: WACC and APV April 8 April

### Chapter 14 Capital Structure in a Perfect Market

Chapter 14 Capital Structure in a Perfect Market 14-1. Consider a project with free cash flows in one year of \$130,000 or \$180,000, with each outcome being equally likely. The initial investment required

### NORTHWESTERN UNIVERSITY J.L. KELLOGG GRADUATE SCHOOL OF MANAGEMENT

NORTHWESTERN UNIVERSITY J.L. KELLOGG GRADUATE SCHOOL OF MANAGEMENT Tim Thompson Finance D42 Fall, 1997 Teaching Note: Valuation Using the Adjusted Present Value (APV) Method vs. Adjusted Discount Rate

### COST OF CAPITAL. Please note that in finance, we are concerned with MARKET VALUES (unlike accounting, which is concerned with book values).

COST OF CAPITAL Cost of capital calculations are a very important part of finance. To value a project, it is important to discount the cash flows using a discount rate that incorporates the debt-equity

### Finance 2 for IBA (30J201) F. Feriozzi Re-sit exam June 18 th, 2012. Part One: Multiple-Choice Questions (45 points)

Finance 2 for IBA (30J201) F. Feriozzi Re-sit exam June 18 th, 2012 Part One: Multiple-Choice Questions (45 points) Question 1 Assume that capital markets are perfect. Which of the following statements

### APractitionersToolkitonValuation

APractitionersToolkitonValuation Part I: (Un)Levering the Cost of Equity and Financing Policy with Constant Expected Free Cash Flows: APV, WACC and CFE Frans de Roon, Joy van der Veer 1 Introduction Valuation

### Wrap-up of Financing. Katharina Lewellen Finance Theory II March 11, 2003

Wrap-up of Financing Katharina Lewellen Finance Theory II March 11, 2003 Overview of Financing Financial forecasting Short-run forecasting General dynamics: Sustainable growth. Capital structure Describing

### NIKE Case Study Solutions

NIKE Case Study Solutions Professor Corwin This case study includes several problems related to the valuation of Nike. We will work through these problems throughout the course to demonstrate some of the

### The Assumptions and Math Behind WACC and APV Calculations

The Assumptions and Math Behind WACC and APV Calculations Richard Stanton U.C. Berkeley Mark S. Seasholes U.C. Berkeley This Version October 27, 2005 Abstract We outline the math and assumptions behind

### INTERVIEWS - FINANCIAL MODELING

420 W. 118th Street, Room 420 New York, NY 10027 P: 212-854-4613 F: 212-854-6190 www.sipa.columbia.edu/ocs INTERVIEWS - FINANCIAL MODELING Basic valuation concepts are among the most popular technical

### Estimating Beta. Aswath Damodaran

Estimating Beta The standard procedure for estimating betas is to regress stock returns (R j ) against market returns (R m ) - R j = a + b R m where a is the intercept and b is the slope of the regression.

### Chapter 9. Year Revenue COGS Depreciation S&A Taxable Income After-tax Operating Income 1 \$20.60 \$12.36 \$1.00 \$2.06 \$5.18 \$3.11

Chapter 9 9-1 We assume that revenues and selling & administrative expenses will increase at the rate of inflation. Year Revenue COGS Depreciation S&A Taxable Income After-tax Operating Income 1 \$20.60

### LECTURES ON REAL OPTIONS: PART I BASIC CONCEPTS

LECTURES ON REAL OPTIONS: PART I BASIC CONCEPTS Robert S. Pindyck Massachusetts Institute of Technology Cambridge, MA 02142 Robert Pindyck (MIT) LECTURES ON REAL OPTIONS PART I August, 2008 1 / 44 Introduction

### New Venture Valuation

New Venture Valuation Antoinette Schoar MIT Sloan School of Management 15.431 Spring 2011 What is Different About Valuing New Ventures? Higher risks and higher uncertainty Potential rewards higher? Option

### Capital Structure: Informational and Agency Considerations

Capital Structure: Informational and Agency Considerations The Big Picture: Part I - Financing A. Identifying Funding Needs Feb 6 Feb 11 Case: Wilson Lumber 1 Case: Wilson Lumber 2 B. Optimal Capital Structure:

### USING THE EQUITY RESIDUAL APPROACH TO VALUATION: AN EXAMPLE

Graduate School of Business Administration - University of Virginia USING THE EQUITY RESIDUAL APPROACH TO VALUATION: AN EXAMPLE Planned changes in capital structure over time increase the complexity of

### FIN 413 Corporate Finance. Capital Structure, Taxes, and Bankruptcy

FIN 413 Corporate Finance Capital Structure, Taxes, and Bankruptcy Evgeny Lyandres Fall 2003 1 Relaxing the M-M Assumptions E D T Interest payments to bondholders are deductible for tax purposes while

### Chapter 17 Does Debt Policy Matter?

Chapter 17 Does Debt Policy Matter? Multiple Choice Questions 1. When a firm has no debt, then such a firm is known as: (I) an unlevered firm (II) a levered firm (III) an all-equity firm D) I and III only

### The Tangent or Efficient Portfolio

The Tangent or Efficient Portfolio 1 2 Identifying the Tangent Portfolio Sharpe Ratio: Measures the ratio of reward-to-volatility provided by a portfolio Sharpe Ratio Portfolio Excess Return E[ RP ] r

### Forecasting and Valuation of Enterprise Cash Flows 1. Dan Gode and James Ohlson

Forecasting and Valuation of Enterprise Cash Flows 1 1. Overview FORECASTING AND VALUATION OF ENTERPRISE CASH FLOWS Dan Gode and James Ohlson A decision to invest in a stock proceeds in two major steps

### E. V. Bulyatkin CAPITAL STRUCTURE

E. V. Bulyatkin Graduate Student Edinburgh University Business School CAPITAL STRUCTURE Abstract. This paper aims to analyze the current capital structure of Lufthansa in order to increase market value

### Choice of Discount Rate

Choice of Discount Rate Discussion Plan Basic Theory and Practice A common practical approach: WACC = Weighted Average Cost of Capital Look ahead: CAPM = Capital Asset Pricing Model Massachusetts Institute

### The value of tax shields is NOT equal to the present value of tax shields

The value of tax shields is NOT equal to the present value of tax shields Pablo Fernández * IESE Business School. University of Navarra. Madrid, Spain ABSTRACT We show that the value of tax shields is

### Tax-adjusted discount rates with investor taxes and risky debt

Tax-adjusted discount rates with investor taxes and risky debt Ian A Cooper and Kjell G Nyborg October 2005, first version October 2004 Abstract This paper derives tax-adjusted discount rate formulas with

### MM1 - The value of the firm is independent of its capital structure (the proportion of debt and equity used to finance the firm s operations).

Teaching Note Miller Modigliani Consider an economy for which the Efficient Market Hypothesis holds and in which all financial assets are possibly traded (abusing words we call this The Complete Markets

### Chapter 7. . 1. component of the convertible can be estimated as 1100-796.15 = 303.85.

Chapter 7 7-1 Income bonds do share some characteristics with preferred stock. The primary difference is that interest paid on income bonds is tax deductible while preferred dividends are not. Income bondholders

### Tax-adjusted discount rates with investor taxes and risky debt

Tax-adjusted discount rates with investor taxes and risky debt Ian A Cooper and Kjell G Nyborg October 2004 Abstract This paper derives tax-adjusted discount rate formulas with Miles-Ezzell leverage policy,

### Chapter 15: Debt Policy

FIN 302 Class Notes Chapter 15: Debt Policy Two Cases: Case one: NO TAX All Equity Half Debt Number of shares 100,000 50,000 Price per share \$10 \$10 Equity Value \$1,000,000 \$500,000 Debt Value \$0 \$500,000

### Stock Valuation: Gordon Growth Model. Week 2

Stock Valuation: Gordon Growth Model Week 2 Approaches to Valuation 1. Discounted Cash Flow Valuation The value of an asset is the sum of the discounted cash flows. 2. Contingent Claim Valuation A contingent

### The cost of capital. A reading prepared by Pamela Peterson Drake. 1. Introduction

The cost of capital A reading prepared by Pamela Peterson Drake O U T L I N E 1. Introduction... 1 2. Determining the proportions of each source of capital that will be raised... 3 3. Estimating the marginal

### LOS 42.a: Define and interpret free cash flow to the firm (FCFF) and free cash flow to equity (FCFE).

The following is a review of the Equity Investments principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in: Free Cash Flow Valuation This

### IESE UNIVERSITY OF NAVARRA OPTIMAL CAPITAL STRUCTURE: PROBLEMS WITH THE HARVARD AND DAMODARAN APPROACHES. Pablo Fernández*

IESE UNIVERSITY OF NAVARRA OPTIMAL CAPITAL STRUCTURE: PROBLEMS WITH THE HARVARD AND DAMODARAN APPROACHES Pablo Fernández* RESEARCH PAPER No 454 January, 2002 * Professor of Financial Management, IESE Research

### If you ignore taxes in this problem and there is no debt outstanding: EPS = EBIT/shares outstanding = \$14,000/2,500 = \$5.60

Problems Relating to Capital Structure and Leverage 1. EBIT and Leverage Money Inc., has no debt outstanding and a total market value of \$150,000. Earnings before interest and taxes [EBIT] are projected

### Option Pricing Applications in Valuation!

Option Pricing Applications in Valuation! Equity Value in Deeply Troubled Firms Value of Undeveloped Reserves for Natural Resource Firm Value of Patent/License 73 Option Pricing Applications in Equity

### Discount Rates and Tax

Discount Rates and Tax Ian A Cooper and Kjell G Nyborg London Business School First version: March 1998 This version: August 2004 Abstract This note summarises the relationships between values, rates of

### On the Applicability of WACC for Investment Decisions

On the Applicability of WACC for Investment Decisions Jaime Sabal Department of Financial Management and Control ESADE. Universitat Ramon Llull Received: December, 2004 Abstract Although WACC is appropriate

### Discounted Cash Flow. Alessandro Macrì. Legal Counsel, GMAC Financial Services

Discounted Cash Flow Alessandro Macrì Legal Counsel, GMAC Financial Services History The idea that the value of an asset is the present value of the cash flows that you expect to generate by holding it

### CHAPTER 14 COST OF CAPITAL

CHAPTER 14 COST OF CAPITAL Answers to Concepts Review and Critical Thinking Questions 1. It is the minimum rate of return the firm must earn overall on its existing assets. If it earns more than this,

### Homework Solutions - Lecture 2

Homework Solutions - Lecture 2 1. The value of the S&P 500 index is 1286.12 and the treasury rate is 3.43%. In a typical year, stock repurchases increase the average payout ratio on S&P 500 stocks to over

### A Basic Introduction to the Methodology Used to Determine a Discount Rate

A Basic Introduction to the Methodology Used to Determine a Discount Rate By Dubravka Tosic, Ph.D. The term discount rate is one of the most fundamental, widely used terms in finance and economics. Whether

### Estimating Cost of Capital. 2. The cost of capital is an opportunity cost it depends on where the money goes, not where it comes from

Estimating Cost of Capal 1. Vocabulary the following all mean the same thing: a. Required return b. Appropriate discount rate c. Cost of capal (or cost of money) 2. The cost of capal is an opportuny cost

### CHAPTER 15 Capital Structure: Basic Concepts

Multiple Choice Questions: CHAPTER 15 Capital Structure: Basic Concepts I. DEFINITIONS HOMEMADE LEVERAGE a 1. The use of personal borrowing to change the overall amount of financial leverage to which an

### Part 9. The Basics of Corporate Finance

Part 9. The Basics of Corporate Finance The essence of business is to raise money from investors to fund projects that will return more money to the investors. To do this, there are three financial questions

### Exam (Correction) Exercise 1: Market efficiency

Executive MA Program Pr. Eric Jondeau orporate Finance Exam (orrection) Exercise 1: Market efficiency (10 points) Answer the following questions in a few lines. a) TransTrust orp. has changed how it accounts

### Appendix B Weighted Average Cost of Capital

Appendix B Weighted Average Cost of Capital The inclusion of cost of money within cash flow analyses in engineering economics and life-cycle costing is a very important (and in many cases dominate) contributing

### Chapter 13, ROIC and WACC

Chapter 13, ROIC and WACC Lakehead University Winter 2005 Role of the CFO The Chief Financial Officer (CFO) is involved in the following decisions: Management Decisions Financing Decisions Investment Decisions

### Problem 1 Problem 2 Problem 3

Problem 1 (1) Book Value Debt/Equity Ratio = 2500/2500 = 100% Market Value of Equity = 50 million * \$ 80 = \$4,000 Market Value of Debt =.80 * 2500 = \$2,000 Debt/Equity Ratio in market value terms = 2000/4000

The consequence of failing to adjust the discount rate for the risk implicit in projects is that the firm will accept high-risk projects, which usually have higher IRR due to their high-risk nature, and

### Chapter 1: The Modigliani-Miller Propositions, Taxes and Bankruptcy Costs

Chapter 1: The Modigliani-Miller Propositions, Taxes and Bankruptcy Costs Corporate Finance - MSc in Finance (BGSE) Albert Banal-Estañol Universitat Pompeu Fabra and Barcelona GSE Albert Banal-Estañol

### Chapter 14 Multinational Capital Structure and Cost of Capital

Sample Exam: Part IV Chapters 12-17 Butler / Multinational Finance (5e) Multiple Choice Choose the best answer Chapter 12 Foreign Market Entry and Country Risk Management 1. Much of the 1990 s growth in

### CHAPTER 15 FIRM VALUATION: COST OF CAPITAL AND APV APPROACHES

0 CHAPTER 15 FIRM VALUATION: COST OF CAPITAL AND APV APPROACHES In the last two chapters, we examined two approaches to valuing the equity in the firm -- the dividend discount model and the FCFE valuation

### Contact Information Politécnico Grancolombiano Calle 57 N 3-00 E Bogota, Colombia Phone #: (571) 3468800 Fax #: (571) 3469258

Firm Valuation: Free Cash Flow or Cash Flow to Equity? Ignacio Vélez-Pareja ivelez@poligran.edu.co Politécnico Grancolombiano Bogotá, Colombia Joseph Tham Fulbright Economics Teaching Program Ho Chi Minh

### ] (3.3) ] (1 + r)t (3.4)

Present value = future value after t periods (3.1) (1 + r) t PV of perpetuity = C = cash payment (3.2) r interest rate Present value of t-year annuity = C [ 1 1 ] (3.3) r r(1 + r) t Future value of annuity

### HHIF Lecture Series: Discounted Cash Flow Model

HHIF Lecture Series: Discounted Cash Flow Model Alexander Remorov University of Toronto November 19, 2010 Alexander Remorov (University of Toronto) HHIF Lecture Series: Discounted Cash Flow Model 1 / 18

### SOLUTIONS. Practice questions. Multiple Choice

Practice questions Multiple Choice 1. XYZ has \$25,000 of debt outstanding and a book value of equity of \$25,000. The company has 10,000 shares outstanding and a stock price of \$10. If the unlevered beta

### Chapter 8. Stock Valuation Process. Stock Valuation

Stock Valuation Process Chapter 8 Stock Valuation: Investors use risk and return concept to determine the worth of a security. In the valuation process: The intrinsic value of any investment equals the

### Asymmetry and the Cost of Capital

Asymmetry and the Cost of Capital Javier García Sánchez, IAE Business School Lorenzo Preve, IAE Business School Virginia Sarria Allende, IAE Business School Abstract The expected cost of capital is a crucial

### Source of Finance and their Relative Costs F. COST OF CAPITAL

F. COST OF CAPITAL 1. Source of Finance and their Relative Costs 2. Estimating the Cost of Equity 3. Estimating the Cost of Debt and Other Capital Instruments 4. Estimating the Overall Cost of Capital

### CHAPTER 5. Interest Rates. Chapter Synopsis

CHAPTER 5 Interest Rates Chapter Synopsis 5.1 Interest Rate Quotes and Adjustments Interest rates can compound more than once per year, such as monthly or semiannually. An annual percentage rate (APR)

### EMBA in Management & Finance. Corporate Finance. Eric Jondeau

EMBA in Management & Finance Corporate Finance EMBA in Management & Finance Lecture 4: Capital Structure Limits to the Use of Debt Outline 1. Costs of Financial Distress 2. Description of Costs 3. Can

### Financial Statement Analysis!

Financial Statement Analysis! The raw data for investing Aswath Damodaran! 1! Questions we would like answered! Assets Liabilities What are the assets in place? How valuable are these assets? How risky

### Fundamentals Level Skills Module, Paper F9. Section A. Mean growth in earnings per share = 100 x [(35 7/30 0) 1/3 1] = 5 97% or 6%

Answers Fundamentals Level Skills Module, Paper F9 Financial Management June 2015 Answers Section A 1 A 2 D 3 D Mean growth in earnings per share = 100 x [(35 7/30 0) 1/3 1] = 5 97% or 6% 4 A 5 D 6 B 7

### Fundamentals Level Skills Module, Paper F9

Answers Fundamentals Level Skills Module, Paper F9 Financial Management June 2008 Answers 1 (a) Calculation of weighted average cost of capital (WACC) Cost of equity Cost of equity using capital asset

### Evaluation of Google and Apple

Xing Chen & Yuanyuan Pan FIN 5190---Special Topics: Financial Modeling Prof. Michael D. Boldin Final Project Evaluation of Google and Apple Overview of project and modeling objectives The objective of

### CHAPTER FOUR Cash Accounting, Accrual Accounting, and Discounted Cash Flow Valuation

CHAPTER FOUR Cash Accounting, Accrual Accounting, and Discounted Cash Flow Valuation Concept Questions C4.1. There are difficulties in comparing multiples of earnings and book values - the old techniques

### Kicking The Tires: Determining the Cost of Capital

- 1 - Kicking The Tires: Determining the Cost of Capital Howard E. Johnson The cost of capital refers to the discount rate or capitalization rate that is used by corporate acquirers in assessing the value

### Discounted Cash Flow Valuation. Literature Review and Direction for Research Composed by Ngo Manh Duy

Discounted Cash Flow Valuation Literature Review and Direction for Research Composed by Ngo Manh Duy TABLE OF CONTENTS Acronyms DCF Valuation: definition and core theories DCF Valuation: Main Objective

### Chapter 11 The Cost of Capital ANSWERS TO SELECTED END-OF-CHAPTER QUESTIONS

Chapter 11 The Cost of Capital ANSWERS TO SELECTED END-OF-CHAPTER QUESTIONS 11-1 a. The weighted average cost of capital, WACC, is the weighted average of the after-tax component costs of capital -debt,

### Chapter 9 The Cost of Capital ANSWERS TO SELEECTED END-OF-CHAPTER QUESTIONS

Chapter 9 The Cost of Capital ANSWERS TO SELEECTED END-OF-CHAPTER QUESTIONS 9-1 a. The weighted average cost of capital, WACC, is the weighted average of the after-tax component costs of capital -debt,

### CHAPTER 9 Stocks and Their Valuation

CHAPTER 9 Stocks and Their Valuation Preferred stock Features of common stock etermining common stock values Efficient markets 1 Preferred Stock Hybrid security. Similar to bonds in that preferred stockholders