The Assumptions and Math Behind WACC and APV Calculations

Size: px
Start display at page:

Download "The Assumptions and Math Behind WACC and APV Calculations"

Transcription

1 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 weighted average cost of capital WACC and adjusted present value APV calculations. We first derive a general formula for the discount rate of equity and beta of equity under minimal assumptions. We then take into consideration: i The existence or non-existence of taxes; ii Whether a firm has a constant amount of debt in dollar terms; iii Whether a firm targets a constant proportion of debt in its capital structure; and iv The frequency of debt rebalancing. These considerations give rise to well known results such as the Miles and Ezzell 1980 formula for WACC and differnt methods formulae for unlevering and re-levering betas. This document is intended for those who wish to understand the motivation behind valuing a firm with WACC and/or APV. Doctoral students and professors may find the document useful when teaching WACC and APV. In particular, this document helps answer questions like: Why does my firm use this formula to unlever beta, but you have taught us another formula? Understanding the assumptions behind both formulae turns out to be the key to answering such questions. Keywords: WACC, APV, Cost of Capital JEL Classification number: G32, A22, A23 This document is based on work titled WACC/APV Mathematical Details by Richard Stanton. Contact information: Mark S. Seasholes, U.C. Berkeley Haas School of Business, 545 Student Services Bldg., Berkeley CA 94720; Tel: ; Fax: ; mss@haas.berkeley.edu. c

2 1 Introduction This document is intended for students who wish to delve into the math behind WACC and APV calculations. The derivations in this document highlight many of the assumptions behind these valuation methods. This document can be used by students ranging from advanced undergraduates to advanced MBAs. However, only the most curious students will find it interesting and benefit from it. Doctoral students and professors may find the document useful when teaching WACC and APV. In particular, this document helps answer questions like: Why does my firm use this formula to unlever beta, but you have taught us another formula? Understanding the assumptions behind both formulae turns out to be the key to answering such questions. 2 Definitions We lay out the notation used throughout the document. There are a myriad of possible ways to denote the same economic quantity. Many are self explanatory. 2.1 Unlevered Firms We use the following notation to denote the market value of a firm and its equity without leverage in its capital structure: V U MV F,unlev Market enterprise value of an unlevered firm E U MV E,unlev Market value of the equity of an unlevered firm Notice that V U E U and we address this in Section 3. We also use the following definitions: F CF t After-tax cashflow of the unlevered firm at time t β A Beta of the FCFs could be written β U or β EU, but typically isn t r A Expected return of the unlevered firm s equity could be written r U or r EU 2

3 None of the results in this paper rely on a specific model of asset returns such as the CAPM. Section 3 only relies on the fact that the beta and return of a portfolio is the weighted average of its components. 2.2 Levered Firms For firms with leverage, we use the following notation: MV F,lev Market enterprise value of a levered firm MV E,lev Equity value of a levered firm D L MV D,lev Market value of a levered firm s debt We use β E to denote the beta of the levered firm s equity therefore it could be written β EL. We use r E to denote the expected return on the levered firm s equity could be r EL. For the levered firm s debt, β D is always used to denote the beta could be β, and r D is always used to denote the expected return of the debt could be r. If the levered firm is profitable, the existance of debt creates an interest tax shield. τ is the corporate tax rate; IT S t is the interest tax shield for year t; and S is the present value of all IT S. We discuss the correct discount rate r s,t later. For now, we simply note that it may not be constant over time. IT S t r D D L,t τ S P V IT S IT S t 1 + r s,t t t1 3 General Derivations For an unlevered firm, the value of the firm is the value of the equity: V U E U. For a levered firm, the value of the firm is the value of the equity plus debt: + D L. The 3

4 value of a levered firm can also be written as the value of an unlevered firm plus the present value of interest tax shields: V U +S. If we equate these two different ways of expressing, substitute E U for V U, and reorganize we get: + D L V U + S V U D L + S E U D L + S 1 Equation 1 tells us that we can interpret as being equivalent to a portfolio of E U, D L, and S. Next, remember the beta of a portfolio P is the weighted average of its component betas. Weights are determined by market values: V P V 1 + V 2 + V 3 V1 β P β 1 + V P V2 V P V3 β 2 + β 3 V P This fact allows us to write the beta of in terms of the betas of E U, a short position in D L, and S. Following convention, we continue to write β A instead of β U or β EU, and obtain: EU S β E β A β D + β S 1 + D L S β A S β D + β S Equation 2 gives us a general relationship between β E, β A, β D and β S for an arbitrary debt policy. Later, we make assumptions about target leverage ratios which allows us to calculate S and β S. Not only is the beta of a portfolio equal to a weighted average of the betas of its components, but so is the expected return of a portfolio equal to a weighted average of the expected returns of its components. Following exactly the same logic as above, we obtain: r E 1 + D L S S r A r D + r S 3 Note that this result holds regardless of whether or not the CAPM is true No Taxes In the case of no taxes, the present value of tax shields is zero S 0 and Equation 2 becomes a familiar expression. Thus, we get our first results. In a world with no taxes and 4

5 arbitrary debt policy: β E β A 1 + D L β A β D or 4 EL β E + β D For the returns, Equation 3 gives us a similar expression remember S 0: r E 1 + D L r A r D r A or 5 EL r E + r D 3.2 Constant Amount of Debt Having a constant dollar amount of debt is the usual assumption in many APV calculations. If there is a constant dollar amount of debt outstanding D L, constant interest rate r D, and constant tax rate τ, the interest tax shield in every year is constant and we have: IT S t IT S r D D L τ The interest tax shields are known in advance in expectation every year, forever. Thus, we can calculate their present value using the perpetuity formula. The chance risk of not getting the interest tax shield in any given year is related to the debt rate. Therefore, we discount future interest tax shields to the present using r D. Discounting the interest tax shields by r D is based on the structure of cash flows when one assumes a firm issues a constant dollar amount of debt. The cash flow structure implies β S β D as the tax shield each period is proportional to the cash flow to bond holders. r S r D β S β D S IT S 1 + r D r DD L τ t r D t1 D L τ 5

6 Substituting into Equation 2 gives: β E 1 + D L S β A 1 + D L D L τ β A 1 + D ] L 1 τ β A S β D + β D + 1 τ β S τ ] β D β D 6 Substituting into Equation 3 gives: r E 1 + D ] L 1 τ r A 1 τ ] r D 7 Notice, under the following assumptions: i A constant amount of debt; ii A debt beta of zero; iii β S β D 0 and iv r S r D, we get a common formula used to unlever relever betas: β E β A 1 + D ] L 1 τ E L ] VL β A 1 τ 3.3 Constant Proportion of Debt Having a constant proportion of debt constant leverage ratio is the usual assumption behind WACC calculations. Suppose a firm changes the amount of debt outstanding each year to keep the proportion of debt constant. Split S into two pieces. The first piece is the present value P V of the first year s period s tax shield t 1. The second piece is the P V of all remaining years periods tax shields t > 1. The first part of the tax shield is a multiple of the first period s interest payment and has a beta of β D. The second part of the tax shield goes up or down in proportion to the value of the firm, and therefore has a beta of β A. Our assumptions are: β S β D and r S r D for the first period t 1. After the first period 6

7 t > 1 we assume β S β A. Finally, S PV1 st tax shield + PVRemaining tax shields: PV1 st tax shield r DD L,t1 τ 1 + r D PVRemaining tax shields S r DD L,t1 τ 1 + r D rd D L,t1 τ Sβ S 1 + r D β D + S r DD L,t1 τ β A 1 + r D Substitute the right-hand side of the equation directly above, for the Sβ S in Equation 2. Simplify and do the same with Equation 3 to obtain the following key formulae. Since the firm targets a constant proportion of debt, it is not necessary to carry the t 1 subscripts around. In other words, D L D L,t1,t1. β E r E 1 + D L 1 r ] Dτ β A 1 r ] Dτ β D 1 + r D 1 + r D 1 + D L 1 r ] Dτ r A 1 r ] Dτ r D 1 + r D 1 + r D 8 Note: These formulae do not explicitly depend on S, which cancels out of the calculations. They depend only on the relative values of D L and, so they are valid for any pattern of cash flows from the firm. In addition, the constant proportional debt assumption plays only one role after the first period the tax shields have a beta of β A. The exact rule for how the debt is adjusted each period is not important. The same result will, therefore, hold for any rule that yields this beta. For example, if a firm adjusts its debt each period to be proportional to that period s all-equity cash flow constant debt-coverage the same result holds. 3.4 Rebalancing Frequency Suppose the firm makes interest payments and adjusts its debt level more than once a year. As the adjustment frequency increases, the relationship between equity and asset betas eventually converges to Equation 4. To see this, consider a rebalancing frequency of k periods per year. If the debt rate r D is given as an effective annual rate, then we discount 7

8 the first term by 1+r D 1/k. More importantly, the tax shield over the first fractional period of the year depends on 1 + r D 1/k 1 ] τ. As the rebalancing frequency becomes higher and higher, the value of β E becomes the closer and closer to value we obtain in the absence of taxes! lim β E k β E 1 + D L D L β A 1 + rd 1/k 1 ] ] τ β 1 + r D 1/k A D L rd 1/k 1 ] ] τ β 1 + r D 1/k D 9 β D 10 Equation 10 makes it clear that continuous rebalancing in a world with taxes gives the same result as Equation 4 which comes from a world without taxes! Thus, students who believe that Equation 10 does not consider taxes because there is no τ term are not correct. We show the effect of different rebalancing periodicity in Table 1. In practice, using Equation 4 rather than Equation 9 usually gives economically similar results. In the example in Table 1, the tax rate is 35% per year, the asset beta is , the company has $2,000 of debt outstanding, the costs of debt is 7.00%, the beta of debt is , and the market value of equity is $6, Equation 9 gives a equity beta of with annual rebalancing. The equity beta increases to if the firm rebalances daily. The equity beta as calculated from Equation 4 is which is the same to four decimals as daily rebalancing. The economic difference between using and is small. Any estimation error of equity betas is typically orders of magnitude larger than this difference. 4 Weighted Average Cost of Capital WACC Assume that a firm maintains a constant leverage ratio: D L D L D L + Constant Remember F CF t refers to the all-equity firm s expected cash flow at time t i.e. the cash flow that would have occurred had the firm been all-equity financed. From earlier, we can write: + D L. The levered firm is a portfolio with two components and D L. 8

9 The expected return on is the weighted average return of its components: EL r V r E + r D + D L + D L or 11 r V EL r E + r D Consider buying both the equity and debt of a levered firm and D L today, holding them for one period, then selling both positions. In exchange for the initial cost of this investment,, we receive next period s free cash flow F CF t+1, next period s interest tax shield r D D L τ, and next period s value of the equity plus debt,t+1. If F CF t+1 is the cash flow of an all-equity firm at time t+1, then we can define the cash flow of the levered firm at t+1 C L,t+1 as the all equity cash flow plus the interest tax shield r D D L τ: C L,t+1 F CF t+1 + r D D L τ Here C L,t+1 is the total cash flow paid to debt and equity holders combined. The price we pay today must equal the present value of the future cash flows, so: F CF t+1 + r D D L τ +,t r V 12 C L,t+1 +,t r V Substituting repeatedly for,t+1,,t+2, etc., we obtain: C L,t r V + C L,t r V 2 + C L,t r V i.e. equals the present value of all future cash flows including tax shields, discounted at r V. This is not very surprising. However, there is a problem using Equation 13 in practice. We need to know the size of the tax shields each period. These depend on the amount of debt, which in turn and by assumption is a constant multiple of. However, is what we are trying to calculate. This is a way around this problem. Instead of adding the tax shields to the all-equity cash flows, we can value the firm instead by using only the all-equity cash flows whose value we do know in expectation, and discounting by an adjusted discount rate called the WACC or Weighted Average Cost of Capital. To see this, 9

10 rewrite Equation 12 using the fact that D L D L Collecting terms in, this becomes: to obtain: F CF t+1 + r D D L τ +,t r V F CF t+1 +,t r V D L r D τ 14 From Equation 11 we can substitute for r V to get: F CF t+1 +,t r E + D L r D D L r D τ F CF t+1 +,t r W ACC 15 where: r W ACC EL + D L EL r E + r E + r D 1 τ + D L r D 1 τ 16 Substituting repeatedly for,t+1,,t+2,... etc. gives: F CF t r W ACC + F CF t r W ACC 2 + F CF t r W ACC Note: Using WACC works for any pattern of cash flows, as long as the firm maintains a constant leverage ratio. Equation 16 is the usual way WACC is defined, and is the most convenient way to calculate it given r E and r D. We can also and equivalently express WACC in terms of r A instead. To do so, start the same way as above, writing as the present value of the next period s payoff, but now write the present value of each of the pieces separately, as 1 F CF t+1 + r D D L τ +,t r A 1 + r D 1 + r A 1 r A is the correct discount rate for,t+1, since is always a constant multiple of V U. 10

11 This can be rewritten as: F CF t+1 + V L,t r A D L ] r V D τ L 1+r D Comparing this equation with Equation 15, we see that: ] D L V 1 + r W ACC 1 + r A 1 L r D τ 1 + r D r W ACC r A D Lr D τ 1 + ra 1 + r D 18 Equation 18 is the Miles and Ezzell 1980 formula for WACC. 5 Example: Valuing a Firm with Taxes In this section, we shall value one firm in a number of different ways. To highlight the robustness of our derivations, growth has been included. All results from this section are shown in Table 2. The firm has the following details: EBIT is $1,000 next year; i The expected operating income ii The growth rate of EBIT is constant g 3.00%; iii The tax rate is τ 35%; iv r A 11.00%; and v The firm rebalances its capital structure, if necessary, once a year. The firm s all-equity cash flow next year is: $1, $ and using the formula for a growing perpetuity, we get: V U $8, Now assume the firm currently has $2,000 of riskless debt r D 5.00%, and will keep a constant proportion of debt outstanding in future. 5.1 APV Using APV, we calculate the PV of the tax shields, then add this to V U. To calculate the PV of the tax shields, note that each tax shield is discounted back one year at r D, and 11

12 remaining years at r A. Why? The first year s tax shield is known today. However, all future tax shields depend on the value of the firm. Since we have assumed the firm will keep a constant proportion of debt outstanding in the future, the amount of debt outstanding scales with firm value. The growth in firm value is related to r A. Thus, the first year s tax shield is: The present value of all tax shields is: IT S t1 r D D L,t1 τ $ $2, S P V IT S $ From Equation 1, the value of equity in this levered firm is the value of unlevered firm, minus the value of debt, plus the present value of the interest tax shields: V U D L + S 8, , $6, Also from the derivation of Equation 1, the value of the levered firm is greater than the unlevered firm V U by exactly the present value of interest tax shields: + D L V U + S 6, , , $8, $8, Using Equation 9 with k 1, we can calculate r E, which will be useful later: r E 1 + D L 1 r ] Dτ r A 1 r ] Dτ r D 1 + r D 1 + r D 1 + 2, , ] , , ] % 12

13 Note: APV is easy to use in this case. Everything is growing at a constant rate which makes it easy to calculate the value of the future tax shields. APV also works well in cases where we assume the amount of debt remains constant or when the amount changes deterministically over time. However, in cases where the firm s cash flows are changing over time, it is harder to calculate the size of future tax shields. 5.2 WACC Given the results above, we can calculate WACC: r W ACC r A r DD L τ 1 + ra 1 + r D , , % The value of the entire levered firm is the growing perpetuity value of the free caseflows using r W ACC as the discount value: F CF t+1 r W ACC g $8, The value of equity in this levered firm is, again, the total firm value minus the value of debt D L : 8, , 000 $6, Note: To calculate WACC based on a known amount of debt D L, one needs the value of to calculate. This is fine if we are valuing a marginal project, but less acceptable if we are trying to value the whole firm. We can get around this problem by solving iteratively using tools such as Excel s Solver. The idea is to: 1 get the value for ; 2 calculate WACC, discount the cash flows, and calculate a new value for, 3 Have a solver try different values for until the calculated value in step 2 equals the input value in step 1. 13

14 5.3 Discounting Total After Tax Cash Flow The total after-tax cash flow in year 1, including the tax shield, is $650 + $35 $685. This is expected to grow at 3% per year. The pretax weighted average cost of capital is: EL r V r E + r D + D L EL r E + 6, , %. r D D L 2, , Note that this is slightly lower than r A since the first tax shield has been discounted at r D not r A. So, from Equation 13 we use the growing perpetuity formula to get: C L,t+1 r v g $8, Note: Discounting total, after-tax cashflows shares the disadvantages of both APV and WACC discussed above. We need to forecast future tax shields like APV, and we also need r E and before we can calculate r V like WACC. 5.4 Discounting Cash Flows to Equity Only A common valuation methodology discounts the cash flows to equity holders only using the equity rate r E. This method has the advantage of not having to calculate and then subtracting the value of the debt. It does work, but you have to be very careful. We already know that r E %. The total after tax cash flow to equity and debt holders combined in year 1 is $685, of which $2, $100 goes to debt holders, leaving $585 for equity 14

15 holders. But: $5, ??? This is not the right answer. What s wrong is that we forgot to include part of the cash flow to equity holders. Next year, we expect the amount of debt outstanding to increase by 3%, from $2,000 to $2,060. The $60 raised by issuing additional debt is paid as a dividend to shareholders, so their total cash flow is actually: $685 $100 + $60 $645. Thus we get the same value for E U as before: $6, Note: Discounting cashflows to equity only is generally harder to use in practice than APV or WACC. Not only do we need to forecast the future tax shields, but we also need to forecast the amount of new debt issued each period. 5.5 Risky Debt The valuation example above assumes the firm issues $2, 000 of riskless debt. We re-do the analysis but assume the firm issues $2, 000 of risky debt. The yield on the debt is 7.00% and it has a beta. The results of the valuation exercise with risky debt are shown in Table 3. Note the total firm value is now $8, which is higher than the total firm value of $8, from the example in Table 2. The increase in value is due to the higher tax shields that result from higher interest expense. 6 Conclusion This paper outlines the math and assumptions behind weighted average cost of capital WACC and adjusted present value APV calculations. We first derive a general formula for the discount rate of equity and beta of equity under minimal assumptions. We then take into consideration: i The existence or non-existence of taxes; ii Whether a firm has a constant amount of debt in dollar terms; iii Whether a firm targets a constant proportion of debt in its capital structure; and iv The frequency of debt rebalancing. One result shows a firm s equity beta is that same in a world with no taxes as it is in a world with taxes under the assumption the firm continuously rebalances its debt to a constant 15

16 proportion of capital structure. We highlight how changing assumptions, changes formulas for equity betas and discount rates not surprisingly. We end with a valuation example that provides consistent results for a firm with growing operating income. References 1] Miles, J. and R. Ezzel, 1980, The Weighted Average Cost of Capital, Perfect Capital Markets and Project Life: A Clarification, Journal of Financial and Quantitative Analysis, 15,

17 Table 1 Rebalancing Frequency This table shows the effect of rebalancing on the equity beta β E. The firm rebalances its capital structure periodically to maintain a constant proportion of debt. The equity beta is calculated using Equation 10 from the paper. The tax rate τ is 35%; the asset beta β A is ; the company currently has $2,000 of debt outstanding but this number is expected to change; the cost of debt r D is 7.00%; the beta of debt β D is ; and the value of the firm s equity is $6, Periods Per Year Rebalancing Frequency β E 1 Annually Semi-An Quarterly Monthly Weekly Daily ,760 Hourly

18 Table 2 Valuation Example with Riskless Debt This table shows results of a valuation exercise. The firm is expected to have an operating profit EBIT of $1,000 next year. The operating profit is expected to grow at 3% per year after that. The tax rate τ is 35%; the asset beta β A is ; the company has $2,000 of debt outstanding; the cost of debt r D is 5.00%; the beta of debt β D is and it is riskless. Section of Paper Calculations Symbols Result 5.0 Unlevered Firm V U 8, APV ITS t PVITS , r E 12.79% 8, WACC r WACC 10.57% 8, , Total A/T CF r V 10.98% 8, CF to Equity 6,

19 Table 3 Valuation Example with Risky Debt This table shows results of a valuation exercise. The firm is expected to have an operating profit EBIT of $1,000 next year. The operating profit is expected to grow at 3% per year after that. The tax rate τ is 35%; the asset beta β A is ; the company has $2,000 of debt outstanding; the cost of debt r D is 7.00%; the beta of debt β D is as this example considers risky debt. Calculations Symbols Result Unlevered Firm V U 8, APV ITS t PVITS , r E 12.16% 8, WACC r WACC 10.42% 8, , Total A/T CF r V 10.98% 8, CF to Equity 6,

APractitionersToolkitonValuation

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

More information

EMBA in Management & Finance. Corporate Finance. Eric Jondeau

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

More information

Tax-adjusted discount rates with investor taxes and risky debt

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,

More information

The value of tax shields IS equal to the present value of tax shields

The value of tax shields IS equal to the present value of tax shields The value of tax shields IS equal to the present value of tax shields Ian A. Cooper London Business School Kjell G. Nyborg UCLA Anderson and CEPR October 2004 Abstract In a recent paper, Fernandez (2004)

More information

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 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

More information

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

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

More information

Discount rates for project appraisal

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

More information

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. 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

More information

1 Pricing options using the Black Scholes formula

1 Pricing options using the Black Scholes formula Lecture 9 Pricing options using the Black Scholes formula Exercise. Consider month options with exercise prices of K = 45. The variance of the underlying security is σ 2 = 0.20. The risk free interest

More information

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

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

More information

CHAPTER 14 COST OF CAPITAL

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,

More information

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).

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

More information

Chapter 17 Does Debt Policy Matter?

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

More information

Discount Rates and Tax

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

More information

Tax-adjusted discount rates with investor taxes and risky debt

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

More information

A Test Of The M&M Capital Structure Theories Richard H. Fosberg, William Paterson University, USA

A Test Of The M&M Capital Structure Theories Richard H. Fosberg, William Paterson University, USA A Test Of The M&M Capital Structure Theories Richard H. Fosberg, William Paterson University, USA ABSTRACT Modigliani and Miller (1958, 1963) predict two very specific relationships between firm value

More information

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

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

More information

Leverage and Capital Structure

Leverage and Capital Structure Leverage and Capital Structure Ross Chapter 16 Spring 2005 10.1 Leverage Financial Leverage Financial leverage is the use of fixed financial costs to magnify the effect of changes in EBIT on EPS. Fixed

More information

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 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

More information

The Adjusted Present Value Approach to Valuing Leveraged Buyouts 1

The Adjusted Present Value Approach to Valuing Leveraged Buyouts 1 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

More information

The Adjusted Present Value Approach to Valuing Leveraged Buyouts 1 Introduction

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

More information

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

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

More information

Corporate Finance & Options: MGT 891 Homework #6 Answers

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

More information

WACC and a Generalized Tax Code

WACC and a Generalized Tax Code WACC and a Generalized Tax Code Sven Husmann, Lutz Kruschwitz and Andreas Löffler version from 10/06/2001 ISSN 0949 9962 Abstract We extend the WACC approach to a tax system having a firm income tax and

More information

The Adjusted-Present-Value Approach to Valuing Leveraged Buyouts 1)

The Adjusted-Present-Value Approach to Valuing Leveraged Buyouts 1) 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

More information

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 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

More information

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

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

More information

Chapter 14 Capital Structure in a Perfect Market

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

More information

Cost of Capital and Project Valuation

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

More information

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 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

More information

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.) 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,

More information

CAPITAL STRUCTURE [Chapter 15 and Chapter 16]

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

More information

Homework Assignment #1: Answer Key

Homework Assignment #1: Answer Key Econ 497 Economics of the Financial Crisis Professor Ickes Spring 2012 Homework Assignment #1: Answer Key 1. Consider a firm that has future payoff.supposethefirm is unlevered, call the firm and its shares

More information

TPPE17 Corporate Finance 1(5) SOLUTIONS RE-EXAMS 2014 II + III

TPPE17 Corporate Finance 1(5) SOLUTIONS RE-EXAMS 2014 II + III TPPE17 Corporate Finance 1(5) SOLUTIONS RE-EXAMS 2014 II III Instructions 1. Only one problem should be treated on each sheet of paper and only one side of the sheet should be used. 2. The solutions folder

More information

Practice Exam (Solutions)

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

More information

Working Paper. WP No 549 March, 2004. Pablo Fernández *

Working Paper. WP No 549 March, 2004. Pablo Fernández * CIIF Working Paper WP No 549 March, 2004 EQUIVALENCE OF TEN DIFFERENT DISCOUNTED CASH FLOW VALUATION METHODS Pablo Fernández * * Professor of Financial Management, PricewaterhouseCoopers Chair of Finance,

More information

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. 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

More information

Use the table for the questions 18 and 19 below.

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

More information

TIP If you do not understand something,

TIP If you do not understand something, Valuing common stocks Application of the DCF approach TIP If you do not understand something, ask me! The plan of the lecture Review what we have accomplished in the last lecture Some terms about stocks

More information

E. V. Bulyatkin CAPITAL STRUCTURE

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

More information

SAMPLE FACT EXAM (You must score 70% to successfully clear FACT)

SAMPLE FACT EXAM (You must score 70% to successfully clear FACT) SAMPLE FACT EXAM (You must score 70% to successfully clear FACT) 1. What is the present value (PV) of $100,000 received five years from now, assuming the interest rate is 8% per year? a. $600,000.00 b.

More information

CHAPTER 12 RISK, COST OF CAPITAL, AND CAPITAL BUDGETING

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.

More information

Equity Analysis and Capital Structure. A New Venture s Perspective

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

More information

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

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

More information

Midterm Exam:Answer Sheet

Midterm Exam:Answer Sheet Econ 497 Barry W. Ickes Spring 2007 Midterm Exam:Answer Sheet 1. (25%) Consider a portfolio, c, comprised of a risk-free and risky asset, with returns given by r f and E(r p ), respectively. Let y be the

More information

DUKE UNIVERSITY Fuqua School of Business. FINANCE 351 - CORPORATE FINANCE Problem Set #8 Prof. Simon Gervais Fall 2011 Term 2

DUKE UNIVERSITY Fuqua School of Business. FINANCE 351 - CORPORATE FINANCE Problem Set #8 Prof. Simon Gervais Fall 2011 Term 2 DUKE UNIVERSITY Fuqua School of Business FINANCE 351 - CORPORATE FINANCE Problem Set #8 Prof. Simon Gervais Fall 2011 Term 2 Questions 1. Hors d Age Cheeseworks has been paying a regular cash dividend

More information

NORTHWESTERN UNIVERSITY J.L. KELLOGG GRADUATE SCHOOL OF MANAGEMENT

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

More information

CHAPTER 8 STOCK VALUATION

CHAPTER 8 STOCK VALUATION CHAPTER 8 STOCK VALUATION Answers to Concepts Review and Critical Thinking Questions 5. The common stock probably has a higher price because the dividend can grow, whereas it is fixed on the preferred.

More information

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

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

More information

ENTREPRENEURIAL FINANCE: Strategy Valuation and Deal Structure

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

More information

Equity Valuation. Lecture Notes # 8. 3 Choice of the Appropriate Discount Rate 2. 4 Future Cash Flows: the Dividend Discount Model (DDM) 3

Equity Valuation. Lecture Notes # 8. 3 Choice of the Appropriate Discount Rate 2. 4 Future Cash Flows: the Dividend Discount Model (DDM) 3 Equity Valuation Lecture Notes # 8 Contents About Valuation 2 2 Present-Values 2 3 Choice of the Appropriate Discount Rate 2 4 Future Cash Flows: the Dividend Discount Model (DDM) 3 5 The Two-Stage Dividend-Growth

More information

The Weighted Average Cost of Capital

The Weighted Average Cost of Capital The Weighted Average Cost of Capital What Does "Cost of Capital" Mean? "Cost of capital" is defined as "the opportunity cost of all capital invested in an enterprise." Let's dissect this definition: Opportunity

More information

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) 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

More information

Valuing the Debt Tax Shield

Valuing the Debt Tax Shield INSTITUTT FOR FORETAKSØKONOMI DEPARTMENT OF FINANCE AND MANAGEMENT SCIENCE FOR 15 2007 ISSN: 1500-4066 MARCH 2007 Discussion paper Valuing the Debt Tax Shield BY IAN COOPER AND KJELL G. NYBORG This paper

More information

THE FINANCING DECISIONS BY FIRMS: IMPACT OF CAPITAL STRUCTURE CHOICE ON VALUE

THE FINANCING DECISIONS BY FIRMS: IMPACT OF CAPITAL STRUCTURE CHOICE ON VALUE IX. THE FINANCING DECISIONS BY FIRMS: IMPACT OF CAPITAL STRUCTURE CHOICE ON VALUE The capital structure of a firm is defined to be the menu of the firm's liabilities (i.e, the "right-hand side" of the

More information

NIKE Case Study Solutions

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

More information

Chapter 11 Options. Main Issues. Introduction to Options. Use of Options. Properties of Option Prices. Valuation Models of Options.

Chapter 11 Options. Main Issues. Introduction to Options. Use of Options. Properties of Option Prices. Valuation Models of Options. Chapter 11 Options Road Map Part A Introduction to finance. Part B Valuation of assets, given discount rates. Part C Determination of risk-adjusted discount rate. Part D Introduction to derivatives. Forwards

More information

WACC and a Generalized Tax Code

WACC and a Generalized Tax Code The European Journal of Finance Vol. 12, No. 1, 33 40, January 2006 WACC and a Generalized Tax Code SVEN HUSMANN, LUTZ KRUSCHWITZ & ANDREAS LÖFFLER Europa-Universität Viadrina, Frankfurt, Germany, Freie

More information

CHAPTER 15 FIRM VALUATION: COST OF CAPITAL AND APV APPROACHES

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

More information

Things to Absorb, Read, and Do

Things to Absorb, Read, and Do Things to Absorb, Read, and Do Things to absorb - Everything, plus remember some material from previous chapters. This chapter applies Chapter s 6, 7, and 12, Risk and Return concepts to the market value

More information

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 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

More information

On the Applicability of WACC for Investment Decisions

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

More information

FINC 3630: Advanced Business Finance Additional Practice Problems

FINC 3630: Advanced Business Finance Additional Practice Problems FINC 3630: Advanced Business Finance Additional Practice Problems Accounting For Financial Management 1. Calculate free cash flow for Home Depot for the fiscal year-ended February 1, 2015 (the 2014 fiscal

More information

Analysis of Deterministic Cash Flows and the Term Structure of Interest Rates

Analysis of Deterministic Cash Flows and the Term Structure of Interest Rates Analysis of Deterministic Cash Flows and the Term Structure of Interest Rates Cash Flow Financial transactions and investment opportunities are described by cash flows they generate. Cash flow: payment

More information

Stock valuation. Price of a First period's dividends Second period's dividends Third period's dividends = + + +... share of stock

Stock valuation. Price of a First period's dividends Second period's dividends Third period's dividends = + + +... share of stock Stock valuation A reading prepared by Pamela Peterson Drake O U T L I N E. Valuation of common stock. Returns on stock. Summary. Valuation of common stock "[A] stock is worth the present value of all the

More information

Fundamentals Level Skills Module, Paper F9

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

More information

Problem 1 Problem 2 Problem 3

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

More information

The Binomial Option Pricing Model André Farber

The Binomial Option Pricing Model André Farber 1 Solvay Business School Université Libre de Bruxelles The Binomial Option Pricing Model André Farber January 2002 Consider a non-dividend paying stock whose price is initially S 0. Divide time into small

More information

CHAPTER 5 HOW TO VALUE STOCKS AND BONDS

CHAPTER 5 HOW TO VALUE STOCKS AND BONDS CHAPTER 5 HOW TO VALUE STOCKS AND BONDS Answers to Concepts Review and Critical Thinking Questions 1. Bond issuers look at outstanding bonds of similar maturity and risk. The yields on such bonds are used

More information

Bond valuation. Present value of a bond = present value of interest payments + present value of maturity value

Bond valuation. Present value of a bond = present value of interest payments + present value of maturity value Bond valuation A reading prepared by Pamela Peterson Drake O U T L I N E 1. Valuation of long-term debt securities 2. Issues 3. Summary 1. Valuation of long-term debt securities Debt securities are obligations

More information

Asymmetry and the Cost of Capital

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

More information

Chapter 10 Risk and Capital Budgeting

Chapter 10 Risk and Capital Budgeting Chapter 10 Risk and Capital Budgeting MULTIPLE CHOICE 1. Operating leverage describes the relationship between... a. EBIT and sales b. taxes and sales c. debt and equity d. fixed costs and variable costs

More information

Chapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams

Chapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams Chapter 6 Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams 1. Distinguish between an ordinary annuity and an annuity due, and calculate present

More information

Test3. Pessimistic Most Likely Optimistic Total Revenues 30 50 65 Total Costs -25-20 -15

Test3. Pessimistic Most Likely Optimistic Total Revenues 30 50 65 Total Costs -25-20 -15 Test3 1. The market value of Charcoal Corporation's common stock is $20 million, and the market value of its riskfree debt is $5 million. The beta of the company's common stock is 1.25, and the market

More information

Basics of Discounted Cash Flow Valuation. Aswath Damodaran

Basics of Discounted Cash Flow Valuation. Aswath Damodaran Basics of Discounted Cash Flow Valuation Aswath Damodaran 1 Discounted Cashflow Valuation: Basis for Approach t = n CF Value = t t =1(1+ r) t where, n = Life of the asset CF t = Cashflow in period t r

More information

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* 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

More information

CHAPTER 20. Hybrid Financing: Preferred Stock, Warrants, and Convertibles

CHAPTER 20. Hybrid Financing: Preferred Stock, Warrants, and Convertibles CHAPTER 20 Hybrid Financing: Preferred Stock, Warrants, and Convertibles 1 Topics in Chapter Types of hybrid securities Preferred stock Warrants Convertibles Features and risk Cost of capital to issuers

More information

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

] (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

More information

Ch. 18: Taxes + Bankruptcy cost

Ch. 18: Taxes + Bankruptcy cost Ch. 18: Taxes + Bankruptcy cost If MM1 holds, then Financial Management has little (if any) impact on value of the firm: If markets are perfect, transaction cost (TAC) and bankruptcy cost are zero, no

More information

6. Debt Valuation and the Cost of Capital

6. Debt Valuation and the Cost of Capital 6. Debt Valuation and the Cost of Capital Introduction Firms rarely finance capital projects by equity alone. They utilise long and short term funds from a variety of sources at a variety of costs. No

More information

Corporate Finance: Final Exam

Corporate Finance: Final Exam Corporate Finance: Final Exam Answer all questions and show necessary work. Please be brief. This is an open books, open notes exam. For partial credit, when discounting, please show the discount rate

More information

Value of Equity and Per Share Value when there are options and warrants outstanding. Aswath Damodaran

Value of Equity and Per Share Value when there are options and warrants outstanding. Aswath Damodaran Value of Equity and Per Share Value when there are options and warrants outstanding Aswath Damodaran 1 Equity Value and Per Share Value: A Test Assume that you have done an equity valuation of Microsoft.

More information

Lecture 21 Options Pricing

Lecture 21 Options Pricing Lecture 21 Options Pricing Readings BM, chapter 20 Reader, Lecture 21 M. Spiegel and R. Stanton, 2000 1 Outline Last lecture: Examples of options Derivatives and risk (mis)management Replication and Put-call

More information

a) The Dividend Growth Model Approach: Recall the constant dividend growth model for the price of a rm s stock:

a) The Dividend Growth Model Approach: Recall the constant dividend growth model for the price of a rm s stock: Cost of Capital Chapter 14 A) The Cost of Capital: Some Preliminaries: The Security market line (SML) and capital asset pricing model (CAPM) describe the relationship between systematic risk and expected

More information

Equity Valuation Formulas. William L. Silber and Jessica Wachter

Equity Valuation Formulas. William L. Silber and Jessica Wachter Equity Valuation Formulas William L. Silber and Jessica Wachter I. The ividend iscount Model Suppose a stoc with price pays dividend one year from now, two years from now, and so on, for the rest of time.

More information

1. What is the difference between nominal returns and real returns?

1. What is the difference between nominal returns and real returns? End of Chapter 11 Questions and Answers 1. What is the difference between nominal returns and real returns? Answer: Nominal returns include inflation while real returns have inflation netted out. For example,

More information

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

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

More information

INTERVIEWS - FINANCIAL MODELING

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

More information

Lecture 16: Capital Budgeting, Beta, and Cash Flows

Lecture 16: Capital Budgeting, Beta, and Cash Flows Lecture 16: Capital Budgeting, Beta, and Cash Flows eading: Brealey and Myers, Chapter 9 Lecture eader, Chapter 15 Topics: Final topics on basic CPM Debt, Equity, and sset Betas Leveraged Betas Operating

More information

UGBA 103 (Parlour, Spring 2015), Section 1. Raymond C. W. Leung

UGBA 103 (Parlour, Spring 2015), Section 1. Raymond C. W. Leung UGBA 103 (Parlour, Spring 2015), Section 1 Present Value, Compounding and Discounting Raymond C. W. Leung University of California, Berkeley Haas School of Business, Department of Finance Email: r_leung@haas.berkeley.edu

More information

Projecting Consistent Debt and Interest Expenses

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

More information

CHAPTER 9 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA

CHAPTER 9 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA CHAPTER 9 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA Basic 1. To calculate the payback period, we need to find the time that the project has recovered its initial investment. After two years, the

More information

Chapter 5 Valuing Stocks

Chapter 5 Valuing Stocks Chapter 5 Valuing Stocks MULTIPLE CHOICE 1. The first public sale of company stock to outside investors is called a/an a. seasoned equity offering. b. shareholders meeting. c. initial public offering.

More information

LECTURE- 4. Valuing stocks Berk, De Marzo Chapter 9

LECTURE- 4. Valuing stocks Berk, De Marzo Chapter 9 1 LECTURE- 4 Valuing stocks Berk, De Marzo Chapter 9 2 The Dividend Discount Model A One-Year Investor Potential Cash Flows Dividend Sale of Stock Timeline for One-Year Investor Since the cash flows are

More information

Capital Structure: With Corporate Income Taxes

Capital Structure: With Corporate Income Taxes 1/1 Capital Structure: With Corporate Income Taxes (Welch, Chapter 17) Ivo Welch UCLA Anderson School, Corporate Finance, Winter 2014 February 25, 2015 Did you bring your calculator? Did you read these

More information

cost of capital, 01 technical this measurement of a company s cost of equity THere are two ways of estimating the cost of equity (the return

cost of capital, 01 technical this measurement of a company s cost of equity THere are two ways of estimating the cost of equity (the return 01 technical cost of capital, THere are two ways of estimating the cost of equity (the return required by shareholders). Can this measurement of a company s cost of equity be used as the discount rate

More information

Why is Insurance Good? An Example Jon Bakija, Williams College (Revised October 2013)

Why is Insurance Good? An Example Jon Bakija, Williams College (Revised October 2013) Why is Insurance Good? An Example Jon Bakija, Williams College (Revised October 2013) Introduction The United States government is, to a rough approximation, an insurance company with an army. 1 That is

More information

USING THE EQUITY RESIDUAL APPROACH TO VALUATION: AN EXAMPLE

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

More information

Cost of Capital, Valuation and Strategic Financial Decision Making

Cost of Capital, Valuation and Strategic Financial Decision Making Cost of Capital, Valuation and Strategic Financial Decision Making By Dr. Valerio Poti, - Examiner in Professional 2 Stage Strategic Corporate Finance The financial crisis that hit financial markets in

More information