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


 Rudolf Dorsey
 4 years ago
 Views:
Transcription
1 Discounted Cash Flow Valuation Literature Review and Direction for Research Composed by Ngo Manh Duy
2 TABLE OF CONTENTS Acronyms DCF Valuation: definition and core theories DCF Valuation: Main Objective and Basic Steps Theories and gaps in each step: Methods Cash Flows Discount Rates Implementation Research objective and research questions Method and research value Reference
3 Acronyms DCF: Discounted Cash Flow Vbv: Book value of the firm Dbv: Book value of debt Ebv: Book value of equity APV: Adjusted Present Value method CCF: Capital Cash Flow method FCFF: Free Cash Flow to Firm method FCFE: Free Cash Flow to Equity method EVA: Economic Valued Added method RI: Residual Income method BRadj FCF: Business riskadjusted Free Cash Flow method BRadj ECF: Business riskadjusted Equity Cash Flow method BRadj CCF: Business riskadjusted Capital Cash Flow method RFadj FCF: Risk freeadjusted Free Cash Flow method RFadj ECF: Risk freeadjusted Equity Cash Flow method RFadj CCF: Risk freeadjusted Capital Cash Flow method V: Value of the firm D: Value of debt E: Value of equity Vu: Value of unlevered equity VTS: Value of interest tax shield V[EVA]: Value of economic values added V[RI]: Value of residual incomes FCF: Free cash flow ECF: Equity cash flow CCF: Capital cash flow FCF//Ku: Business riskadjusted Free cash flow ECF//Ku: Business riskadjusted Equity cash flow CCF//Ku: Business riskadjusted Capital cash flow FCF//Rf: Risk freeadjusted Free cash flow ECF// Rf: Risk freeadjusted Equity cash flow CCF// Rf: Risk freeadjusted Capital cash flow CFd: Cash flows to debtholders CFTS: Cash flow of interest tax shield EVA: Economic value added RI: Residual income I: Interest paid on book value of debt r: Actual interest rate on book value of debt Rf: Riskfree rate Ku: cost of unlevered equity Kd: cost of debt Ke: cost of equity K: weighted average cost of capital (WACC) Kbt: beforetax weighted average cost of capital (WACCbt) T: corporate tax rate
4 Definition of DCF valuation & Application Discounted Cash Flow (DCF) valuation is: a method of evaluating an investment opportunity by discounting predicted future cash flows generated by the investment at certain discount rates to find out the present value of the investment in monetary term Application: Mostly used in valuating securities (bonds or shares), companies and business projects. Valuation of bonds using DCF is simple and straightforward while DCF valuation of shares, companies and business projects is quite complex leading several issues for debates exploration.
5 1. DCF Model (Theory of Interest) by Fisher (1930): Two core theories: 1. DCF Model = ( + ) Where: PV 0 : Present value of cash flows (at time t = 0) CF t : Cash flow at time t k i : Discount rate or required rate of return for the period i n : Number of periods generating cash flows
6 2. Value Additivity principle Two core theories: 2. Value Additivity principle The summation of present values of cash flows divided from the same original cash flow will always equal the present value of the original. This principle is first demonstrated in MM Proposition I with tax of Modigliani and Miller (1958) : Where: V t : value of the firm at time t D t : value of debt at time t E t : value of equity at time t V t = D t + E t = Vu t + VTS t (1) Vu t : value of unlevered equity at time t (value of the firm when there is no leverage, i.e. 100% equity) VTS t : value of interest tax shield at time t
7 CCF = ECF + CFd = FCF + CFTS Two core theories: 2. Value Additivity principle V = E + D = Vu + VTS Where: CCF: Capital cash flow (all cash flows available to capital providers ) CFTS: generated from tax deduction on interest expenses) ECF: Equity cash flow (free cash flows to shareholders) CFd: Debt cash flow (cash flows to debtholders) FCF: Free cash flow (cash flows generated from business operation) CFTS: Cash flow from interest tax shield
8 Main objective & basis steps Objective of DCF valuation: Calculate shareholders (or investors ) equity value of the investmen. Basic steps of DCF valuation: 1. Choose a method (METHODS) 2. Calculate cash flows (CASH FLOWS) 3. Calculate discount rates (DISCOUNT RATES) 4. Implement discounting (IMPLEMENTATION)
9 12. RFadj CCF 1. APV 2. CCF Theories and 11. RFadj ECF 10. RFadj FCF 12 methods 3. FCFF 4. FCFE METHODS 9. BRadj CCF 5. EVA 8. BRadj ECF 7. BRadj FCF 6. RI Acronyms
10 METHODS 1 to 6 No. Method Cash flows Discount rate Implementation 1 Adjusted Present FCF, CFd, Ku, Kd Vu: discount FCF at Ku Value (APV) CFTS VTS: discount CFTS (at Ku or Kd or both depending the chosen theory) V = Vu + VTS D: discount CFd at Kd E = V D 2 Capital Cash Flow (CCF) 3 Free Cash Flow to Firm (FCFF) 4 Free Cash Flow to Equity (FCFE) CCF, CFd Kbt, Kd V: discount CCF at Kbt D: discount CFd at Kd E = V D FCF, CFd K, Kd V: discount FCF at K D: discount CFd at Kd E = V D ECF Ke E: discount ECF at Ke 5 Economic Value Added (EVA) EVA, CFd K, Kd V[EVA]: discount EVA at K V = Vbv + V[EVA] D: discount CFd at Kd E = V D Acronyms 6 Residual Income (RI) RI Ke V[RI]: discount RI at Ke E = Ebv + V[RI]
11 METHODS 7 to 9 No. Method Cash flows Discount rate Implementation 7 Business riskadjusted FCF//Ku, K, Ku, Kd FCF//Ku: obtained by adjusting FCF using K and Ku Free Cash Flow (BRadj FCF) CFd so that discounting FCF//Ku at Ku will return V. V: discount FCF//Ku at Ku 8 Business riskadjusted Equity Cash Flow (BRadj ECF) 9 Business riskadjusted Capital Cash Flow (BRadj CCF) D: discount CFd at Kd E = V D ECF/Ku Ke, Ku ECF//Ku: obtained by adjusting ECF with Ke and Ku so that discounting ECF//Ku at Ku will return E. E: discount ECF//Ku at Ku CCF/Ku, CFd Kbt, Ku, Kd CCF//Ku: obtained by adjusting CCF using Kbt and Ku so that discounting CCF//Ku at Ku will return V. V: discount CCF//Ku at Ku D: discount CFd at Kd E = V D Acronyms
12 METHODS 10 to 12 No. Method Cash flows Discount rate Implementation 7 Risk freeadjusted FCF/Rf, CFd K, Rf, Kd FCF//Rf: obtained by adjusting FCF using K and Rf so Free Cash Flow (RFadj FCF) that discounting FCF//Rf at Rf will return V. V: discount FCF//Rf at Rf 8 Risk freeadjusted Equity Cash Flow (RFadj ECF) 9 Risk freeadjusted Capital Cash Flow (RFadj CCF) D: discount CFd at Kd E = V D ECF/Rf Ke, Rf ECF//Rf: obtained by adjusting ECF with Ke and Rf so that discounting ECF//Rf at Rf will return E. E: discount ECF//Rf at Rf CCF/Rf, CFd Kbt, Rf, Kd CCF//Rf: obtained by adjusting CCF using Kbt and Rf so that discounting CCF//Rf at Rf will return V. V: discount CCF//Rf at Rf D: discount CFd at Kd E = V D Acronyms
13 METHODS Summary APV and CCF were created by Myers (1974) and Arditti and Levy (1977) respectively why the rest were found by practitioners. The most popular method is FCFF which is sometimes referred as the textbook approach or the WACC approach. In the first 4 methods (APV, CCF, FCFF and FCFE), cash flows can be calculated independently of discount rates. The last 8 methods requires that discount rates and cash flows must be calculated at the same time. As long as Value Additivity principle is satisfied, there are no gaps in this literature regarding methods because all methods follow the same core theories and share the same inputs. Hence, if inconsistent results across methods in practice, it suggests that there are gaps in the last 3 steps.
14 13. RFadj CCF 1. FCF 2. CFTS Theories and CASH FLOWS 11. RFadj FCF 12. RFadj ECF 10. BRadj CCF 13 Cash Flows 3. CCF 4. CFd 5. ECF 9. BRadj ECF 6. EVA 8. BRadj FCF 7. RI
15 1. FCF t = EBIT t (1 T t ) Vbv t 2. CFTS t = T t I t = T t r t Dbv t1 3. CCF t = FCF t + CFTS t = EBIT t (1 T t ) Vbv t + T t I t Theories and CASH FLOWS Formulas 4. CFd t = I t Dbv t 5. ECF t = CCF t CFd t = EBIT t (1 T t ) Vbv t (1 T t )I t + Dbv t 6. EVA t = EBIT t (1 T t ) K t Vbv t1 7. RI t = EBIT t (1 T t ) (1 T t )I t Ke t Ebv t1 8. FCF//Ku t = FCF t + V t1 (Ku t K t ) 9. CCF//Ku t = CCF t + V t1 (Ku t Kbt t ) 10. ECF//Ku t = ECF t + E t1 (Ku t Ke t ) 11. FCF//Rf t = FCF t + V t1 (Rf t K t ) 12. CCF//Rf t = CCF t + V t1 (Rf t Kbt t ) 13. ECF//Rf t = ECF t + E t1 (Rf t Ke t )
16 CASH FLOWS 3 approaches (assumptions) There are 3 different approaches which will lead to different cash flow results: 1. Constant debt and no growth (Modigliani and Miller 1958) 2. Constant debt ratio and perpetual growth (all other researchers including big names such as Hamada (1972), Myers (1974), Miles and Ezzell (1980), Fernández (2004), Damodaran (2008)) 3. Proforma financial statements (practitioners)
17 CASH FLOWS 3 approaches (assumptions) The first approach (constant debt, no growth) was too unrealistic to be applied in practice The second approach (constant debt ratio, perpetual growth): allows having discount rate unchanged but only takes advantage of the first year forecasted financial statements and forces all financial statements to grow at the same rate. Hence, it s still very unrealistic since it almost never happens in real business. The last approach (Proforma financial statement): Applies constant debt ratio and perpetual growth in stable period Uses budgeted financial statements and releases all assumptions in dynamic period.
18 CASH FLOWS Summary The third approach (used by practitioners) filled the gaps in the first 2 approaches. However, inconsistent results still occur due to: 1. Incorrect cash flow formulas 2. Incorrect discount rate formulas (tackled in DISCOUNT RATE step) 3. Improper implementation (tackled in IMPLEMENTATION step) The gap of this literature regarding cash flow is to reformulate cash flow formulas so that they are general enough to address almost all scenarios happening due to the dynamics of financial statement in the third approach.
19 1. Rf Theories and DISCOUNT RATES 6. Ke 5. Kbt 6 DISCOUNT RATES 2. Kd 3. Ku 4. K
20 DISCOUNT RATES Rf, Kd, Ku Beta approach: CAPM module of Sharpe (1964) Ku = Rf + BetaU MRP Topdown methods: (1) Regress market returns and stock return to obtain historical equity beta; (2) Unlever historical beta to acquire unlevered equity beta (BetaU) Bottomup method: (1) Break down firm s overall operation to specific operations; (2) Find comparable BetaU for each operation; (3) Calculate weighted average BetaU of the firm Fama and French approach: Multifactor model of Fama and French (1993) Acronyms
21 DISCOUNT RATES K, Kbt, Ke These discount rates must be calculated internally using the previous three discount rates and cash flow information. Those discount rate formulas are affected by: 1. Assumption of capital structure 2. Theory on which discount rate is chosen to discount cash flow of tax shield Acronyms
22 Theory Author Modigliani and Miller (1958) Fixed debt No growth Fixed ratio Constant growth debt Discount CFTS at Kd In 1 st In all period period Discount CFTS at Ku From 2 nd In all period period DISCOUNT RATES K, Kbt, Ke Luehrman (1997) Myers (1974) Harris and Pringle (1985) Kaplan and Ruback (1995) Miles and Ezzell (1985) Lewellen Emery (1986) and
23 DISCOUNT RATES K, Kbt, Ke Summary of theories Capital Structure assumption: As stated in CASH FLOW section, dynamic capital structure is the proper assumption for dynamic period while fixed capital structure is suitable for stable period. Theory on discount rate of CFTS: Discount CFTS at Kd (MM 1958): CFTS is one part of cash flow received by debtholders, hence, it should be discounted at cost of debt Kd. Discount CFTS at Ku (Myers 1974): Fixed debt ratio assumption leads to proportional adjustment of debt to firm value, hence, CFTS which arises from debt should have the same risk as the firm Ku. Discount CFTS at Kd in period 1 and at Ku from period 2 onward (Miles and Ezzell 1985): obtained through mathematic approach under fixed debt assumption. Author s view: MM s theory is straightforward and independent of capital structure. Theories of Myers and Miles and Ezzell s will lose their veracity when fixed debt ratio assumption is released.
24 DISCOUNT RATES Ke and K Formulas and gaps Cost of equity formula calculated through Ku and Kd Ke = Ku + (Ku Kd ) by MM (1958) Use fixed debt assumption under MM s theory Gap: Reformulate Ke under dynamic debt level and dynamic growth in all 3 theories. Weighted Average Cost of Capital formula calculated through Ke and Kd (must be used with a correct Ke formula) K = Ke E + 1 T Kd D E + D Popular textbook formula with no mathematic proof The gap was filled by Fernández (2003) with the following formula: K = Ke E + Kd D T r Dbv E + D
25 DISCOUNT RATES K Formulas and gaps Weighted Average Cost of Capital formula calculated through Ku and Kd (can be used alone) Ku (E +D D T ) + Kd D T T r Dbv K = E + D Found by Fernández (2003, 2004) but was proven incorrect by Fieten, Kruschwitz et al. (2005) and Cooper and Nyborg (2006) Gap: Find correct K formula calculated through Ku and Kd in all 3 theories of CFTS discount rate.
26 DISCOUNT RATES Kbt Formulas and gaps Beforetax Weighted Average Cost of Capital formula calculated through Ke and Kd (must be used with a correct Ke formula) Kbt = Ke E E + Kd D + D Found by Arditti and Levy (1977) with no mathematic proof but correct reasoning. Beforetax Weighted Average Cost of Capital formula calculated through Ku and Kd (can be used alone) Kbt = Ku with BetaU = BetaD + BetaE Proved by Ruback (2002) through beta formula under Myers theory Gap: Find correct Kbt formula calculated through Ku and Kd in MM s theory and Miles and Ezzell s theory.
27 IMPLEMENTA TION Inconsistent results across DCF methods were experienced in common practice along with violation of Value Additivity principle. Apart from reasons due existing gaps in step 2 and step 3 which were discussed before, improper implementation is one of the key reasons. In fact, considering all methods share the same input (evaluating the same asset) and the same core theories, the method should arrive at the same result.
28 IMPLEMENTA TION Researcher Findings Limitations Taggart Jr (1989) A consistent result in 3 methods: Fixed leverage APV, FCFF, FCFE Fixed discount rates Ku, Kd Shrieves and Wachowicz Jr (2001) Fernández (2003) A consistent result in 3 methods: FCFF, EVA, CCF A consistent result in 10 methods: APV, FCFF, FCFE, BRadj FCF, BRadj ECF, RFadj FCF, RFadj ECF, CCF, EVA, RI Use textbook formula K No complex example testing Only try to prove the consistency of methods No discount rate formulas shown No testing Perpetual growth Proven errors in formula Use constant growth assumption in example Attempts and their limitation Oded and Michel (2007) A consistent result in 4 methods: APV, CCF, FCFE, FCFF Fixed leverage and rebalancing assumptions Constant growth Constant discount rates No complex example testing Massari, Roncaglio, and Zanetti (2008) Inconsistent results between APV and FCFF under perpetual growth assumptions Fixed leverage Perpetual growth Use textbook formula K
29 IMPLEMENTA TION Summary Fernández (2003) was able to filled most of the gaps in this literature by showing consistent results in 10 methods with Backward iteration method which was also applied by Miles and Ezzell (1985) However, he used incorrect formula, perpetual growth assumption and applied only his incorrectlyproven theory. Gap: Use correct cash flow formulas and discount rate formulas to demonstrate consistent results in 12 methods in 3 theories with dynamic debt and growth assumptions.
30 Research objectives Research questions Research objectives Under dynamic assumption of capital structure and growth: 1. Find generalised formulas for cash flows 2. Find generalized formulas for Ke, K and Kbt calculated through Ku and Kd under all 3 theories 3. Demonstrate consistent results in 12 methods under all 3 theories Research questions Under dynamic assumption of capital structure and growth: 1. What are the generalized formulas for cash flows? 2. What are the generalized formulas for Ke, K and Kbt calculated through Ku and Kd under all 3 theories? 3. How can one demonstrate consistent results in 12 methods under all 3 theories?
31 Method and Research value Method: Qualitative method with mathematic approach. Research value: Academic: Enhance the current literature of DCF valuation with more logical understanding, more general formulas and more suitable implementation. Practice: Allowing practitioners (investors, analyst, consultants etc) to make better investment decisions through making the popular DCF valuation much more reliable, logical and understandable/
32 References Arditti, F. D., & Levy, H. (1977). The weighted average cost of capital as a cutoff rate: a critical analysis of the classical textbook weighted average. Financial management, Cooper, I. A., & Nyborg, K. G. (2006). The value of tax shields IS equal to the present value of tax shields. Journal of Financial Economics, 81(1), Damodaran, A. (2008). Damodaran on valuation: John Wiley & Sons. Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), Fernández, P. (2003). Equivalence of ten different methods for valuing companies by cash flow discounting. Paper presented at the EFMA 2004 Basel Meetings Paper. Fernández, P. (2004). The value of tax shields is NOT equal to the present value of tax shields. Journal of Financial Economics, 73(1), Fieten, P., Kruschwitz, L., Laitenberger, J., Löffler, A., Tham, J., VélezPareja, I., & Wonder, N. (2005). Comment on The value of tax shields is NOT equal to the present value of tax shields. The Quarterly Review of Economics and Finance, 45(1), Fisher, I. (1930). The Theory of Interest New York: Macmillan. Gordon, M. J. (1962). The investment, financing, and valuation of the corporation: RD Irwin. Hamada, R. S. (1972). The effect of the firm's capital structure on the systematic risk of common stocks. The Journal of Finance, 27(2), Harris, R. S., & Pringle, J. J. (1985). Risk adjusted discount rates extensions from the average risk case. Journal of Financial Research, 8(3), Kaplan, S. N., & Ruback, R. S. (1995). The valuation of cash flow forecasts: An empirical analysis. The Journal of Finance, 50(4), Lewellen, W. G., & Emery, D. R. (1986). Corporate debt management and the value of the firm. Journal of Financial and Quantitative Analysis, 21(04), Luehrman, T. (1997). Using APV (adjusted present value): a better tool for valuing operations. Harvard business review, 75(3), 145. Massari, M., Roncaglio, F., & Zanetti, L. (2008). On the equivalence between the APV and the WACC approach in a growing leveraged firm. European financial management, 14(1), Miles, J. A., & Ezzell, J. R. (1985). Reformulating tax shield valuation: a note. The Journal of Finance, 40(5), Modigliani, F., & Miller, M. H. (1958). The cost of capital, corporation finance and the theory of investment. The American economic review, Myers, S. C. (1974). Interactions of corporate financing and investment decisions implications for capital budgeting. The Journal of Finance, 29(1), Oded, J., & Michel, A. (2007). Reconciling DCF valuation methodologies. Journal of Applied Finance, 17(2), 21. Ruback, R. S. (2002). Capital cash flows: a simple approach to valuing risky cash flows. Financial management, Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk*. The Journal of Finance, 19(3),
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 informationWorking 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 informationLEVERED AND UNLEVERED BETA. Pablo Fernández
CIIF Working Paper WP no 488 January, 2003 (Rev. May 2006) LEVERED AND UNLEVERED BETA Pablo Fernández IESE Business School Universidad de Navarra Avda. Pearson, 21 08034 Barcelona, España. Tel.: (+34)
More informationMohsen Dastgir, Vali Khodadadi and Maryam Ghayed. Abstract
2010 Mohsen Dastgir, Vali Khodadadi and Maryam Ghayed 45 CASH FLOWS VALUATION USING CAPITAL CASH FLOW METHOD COMPARING IT WITH FREE CASH FLOW METHOD AND ADJUSTED PRESENT VALUE METHOD IN COMPANIES LISTED
More informationTHE CORRECT VALUE OF TAX SHIELDS: AN ANALYSIS OF 23 THEORIES. Pablo Fernández
CIIF Working Paper WP no 628 May, 2006 THE CORRECT VALUE OF TAX SHIELDS: AN ANALYSIS OF 23 THEORIES Pablo Fernández IESE Business School Universidad de Navarra Avda. Pearson, 21 08034 Barcelona, Spain.
More informationA General Formula for the WACC: A Comment
INTRNATIONAL JOURNAL OF BUSINSS, 12(3, 2007 ISSN: 1083 4346 A General Formula for the WACC: A Comment Pablo Fernandez a a IS Business School, University of Navarra Camino del Cerro del Aguila 3, 28023
More informationTitle: Using a Simplified MilesEzzell Framework to Value Equity
Centre for Global Finance Working Paper Series (ISSN 20411596) Paper Number: 02/11 Title: Using a Simplified MilesEzzell Framework to Value Equity Author(s): David Bence Centre for Global Finance Bristol
More informationThe 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 informationAPractitionersToolkitonValuation
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 informationA MORE REALISTIC VALUATION: APV AND WACC WITH CONSTANT BOOK LEVERAGE RATIO. Pablo Fernández
CII Working Paper WP no 715 November, 27 A MORE REALISTIC VALUATION: APV AND WACC WITH CONSTANT BOOK LEVERAGE RATIO Pablo ernández IESE Business School University of Navarra Avda. Pearson, 21 834 Barcelona,
More informationISSUES ON USING THE DISCOUNTED CASH FLOWS METHODS FOR ASSET VALUATION
ISSUES ON USING THE DISCOUNTED CASH FLOWS METHODS FOR ASSET VALUATION CRISTINA AURORA BUNEABONTAŞ 1, MIHAELA COSMINA PETRE 2 CONSTANTIN BRANCOVEANU UNIVERSITY OF PITESTI, FACULTY OF MANAGEMENTMARKETING
More informationTaxadjusted discount rates with investor taxes and risky debt
Taxadjusted 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 taxadjusted discount rate formulas with
More informationIESE 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 informationSource 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
More informationWACC: DEFINITION, MISCONCEPTIONS AND ERRORS
Working Paper WP914 March, 2011 WACC: DEFINITION, MISCONCEPTIONS AND ERRORS Pablo Fernández IESE Business School University of Navarra Av. Pearson, 21 08034 Barcelona, Spain. Phone: (+34) 93 253 42 00
More informationWACC 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 informationDiscounted Cash Flow Valuation: Basics
Discounted Cash Flow Valuation: Basics Aswath Damodaran Aswath Damodaran 1 Discounted Cashflow Valuation: Basis for Approach Value = t=n CF t t =1(1+r) t where CF t is the cash flow in period t, r is the
More informationTaxadjusted discount rates with investor taxes and risky debt
Taxadjusted discount rates with investor taxes and risky debt Ian A Cooper and Kjell G Nyborg October 2004 Abstract This paper derives taxadjusted discount rate formulas with MilesEzzell leverage policy,
More informationValuing the Debt Tax Shield
INSTITUTT FOR FORETAKSØKONOMI DEPARTMENT OF FINANCE AND MANAGEMENT SCIENCE FOR 15 2007 ISSN: 15004066 MARCH 2007 Discussion paper Valuing the Debt Tax Shield BY IAN COOPER AND KJELL G. NYBORG This paper
More informationCapital 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 informationThe 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
More informationA GENERAL FORMULA FOR THE WACC: A CORRECTION. Pablo Fernández
CIIF Working Paper WP no 663 ecember, 2006 GNRL FORMUL FOR TH WCC: CORRCTION Pablo Fernández IS Business School University of Navarra vda. Pearson, 21 08034 Barcelona, Spain. Tel.: (+34 93 253 42 00 Fax:
More informationValuation Methods and Shareholder Value Creation
2008 AGIInformation Management Consultants May be used for personal purporses only or by libraries associated to dandelon.com network. Valuation Methods and Shareholder Value Creation Pablo Fernandez
More informationStock 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
More informationA 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
More informationLeverage. 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 informationNORTHWESTERN 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 informationChapter 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 informationEquity 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 informationWACC 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 EuropaUniversität Viadrina, Frankfurt, Germany, Freie
More informationCorporate 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 informationWACC 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 informationMM1  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 informationUse 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 defaultfree zerocoupon bonds (expressed as a percentage of face value): Maturity (years) 1 3 4 5 Price
More informationOn 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 informationCAPITAL 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 informationProjecting 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 postmerger
More informationDiscount 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 informationA Note on the Weighted Average Cost of Capital WACC Ignacio VélezPareja Politécnico Grancolombiano Bogotá, Colombia ivelez@poligran.edu.
A Note on the Weighted Average Cost of Capital WACC Ignacio VélezPareja Politécnico Grancolombiano Bogotá, Colombia ivelez@poligran.edu.co Joseph Tham Project Associate at the Center for Business and
More informationP&C Insurance Company Valuation Richard Goldfarb, FCAS, CFA, FRM Original Draft: 2005 (Revised: 2010)
P&C Insurance Company Valuation Richard Goldfarb, FCAS, CFA, FRM Original Draft: 2005 (Revised: 2010) Abstract This study note was prepared for use on the CAS Exam Syllabus. Its purpose is to describe
More informationDiscount 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 informationUSING 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 informationDCF and WACC calculation: Theory meets practice
www.pwc.com DCF and WACC calculation: Theory meets practice Table of contents Section 1. Fair value and company valuation page 3 Section 2. The DCF model: Basic assumptions and the expected cash flows
More informationBasics 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 informationDUKE 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 informationHHIF 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
More informationE. 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 informationBA 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 informationSome common mistakes to avoid in estimating and applying discount rates
Discount rates Some common mistakes to avoid in estimating and applying discount rates One of the most critical issues for an investor to consider in a strategic acquisition is to estimate how much the
More informationCost 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 informationCHAPTER 13 Capital Structure and Leverage
CHAPTER 13 Capital Structure and Leverage Business and financial risk Optimal capital structure Operating Leverage Capital structure theory 1 What s business risk? Uncertainty about future operating income
More informationFinancial 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 informationCost 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 informationModule 1: Corporate Finance and the Role of Venture Capital Financing TABLE OF CONTENTS
1.0 FINANCING PRINCIPLES Module 1: Corporate Finance and the Role of Venture Capital Financing Financing Principles 1.01 Introduction to Financing Principles 1.02 Capitalization of a Business 1.03 Capital
More informationNew 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
More informationGESTÃO 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 20102011 Chapter 18 Capital Budgeting and Valuation with Leverage
More informationThe AdjustedPresentValue Approach to Valuing Leveraged Buyouts 1)
IE Aufgabe 4 The AdjustedPresentValue 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 informationLecture Notes. Valuation. WS 2009 Dr. Alex Stomper
Lecture Notes WS 2009 Dr. Alex Stomper Introduction What does this course offer? Scientific tools and techniques for valuing financial assets We focus on of publicly traded firms Value of equity Value
More informationNIKE 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 information1 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 informationDiscounted Cash Flow Methodology. Table of Contents. Section 1 Discounted Cash Flow Overview CONFIDENTIAL. DCF Primer 5467729.doc
Table of Contents Section 1 Discounted Cash Flow Overview CONFIDENTIAL DCF Primer 5467729.doc Section 1 Discounted Cash Flow Overview The DCF approach values a business based on its future expected cash
More informationVALUE UNDER ACTIVE AND PASSIVE DEBT MANAGEMENT POLICY. Tony Appleyard. and. Ian M. Dobbs *
VALUE UNDER ACTIVE AND PASSIVE DEBT MANAGEMENT POLICY by Tony Appleyard and Ian M. Dobbs * * Department of Accounting and Finance, University of Newcastle upon Tyne, NE1 7RU. * Our thanks to the anonymous
More informationMergers & Acquisitions: The Case of Microsoft and Nokia
Mergers & Acquisitions: The Case of Microsoft and Nokia Luís Franco Hilário Advisor: Peter Tsvetkov Dissertation submitted in partial fulfillment of requirements for the degrees of MSc in Business Administration,
More informationJournal of Business Valuation and Economic Loss Analysis
Journal of Business Valuation and Economic Loss Analysis Volume 5, Issue 1 2010 Article 2 Valuation Methodologies and Emerging Markets Howard Qi Michigan Technological University, howardqi@mtu.edu opyright
More informationINTERVIEWS  FINANCIAL MODELING
420 W. 118th Street, Room 420 New York, NY 10027 P: 2128544613 F: 2128546190 www.sipa.columbia.edu/ocs INTERVIEWS  FINANCIAL MODELING Basic valuation concepts are among the most popular technical
More informationFirm Valuation: Free Cash Flow or Cash Flow to Equity? Ignacio VélezPareja ivelez@poligran.edu.co Politécnico Grancolombiano Bogotá, Colombia
Firm Valuation: Free Cash Flow or Cash Flow to Equity? Ignacio VélezPareja ivelez@poligran.edu.co Politécnico Grancolombiano Bogotá, Colombia Joseph Tham Fulbright Economics Teaching Program Ho Chi Minh
More informationEconomic Value Added (EVA) Valuation Tutorial
Economic Value Added (EVA) Valuation Tutorial Index 1. Introduction to valuation: valuation of bond 2. Company valuation Determing the cost of capital Calculating EVA 3. Detailed examples of EVAvaluation
More informationII. Estimating Cash Flows
II. Estimating Cash Flows DCF Valuation Aswath Damodaran 61 Steps in Cash Flow Estimation Estimate the current earnings of the firm If looking at cash flows to equity, look at earnings after interest expenses
More informationThe Adjusted Present Value Approach to Valuing Leveraged Buyouts 1
Chapter 17 Valuation and Capital Budgeting for the Levered Firm 17A1 Appendix 17A The Adjusted Present Value Approach to Valuing Leveraged Buyouts 1 Introduction A leveraged buyout (LBO) is the acquisition
More informationEquity Market Risk Premium Research Summary. 12 April 2016
Equity Market Risk Premium Research Summary 12 April 2016 Introduction welcome If you are reading this, it is likely that you are in regular contact with KPMG on the topic of valuations. The goal of this
More informationThe Adjusted Present Value Approach to Valuing Leveraged Buyouts 1 Introduction
Chapter 18 Valuation and Capital Budgeting for the Levered Firm 18A1 Appendix 18A The Adjusted Present Value Approach to Valuing Leveraged Buyouts 1 Introduction A leveraged buyout (LBO) is the acquisition
More informationEstimating Cash Flows
Estimating Cash Flows DCF Valuation 1 Steps in Cash Flow Estimation Estimate the current earnings of the firm If looking at cash flows to equity, look at earnings after interest expenses  i.e. net income
More informationChapter 9 The Cost of Capital ANSWERS TO SELEECTED ENDOFCHAPTER QUESTIONS
Chapter 9 The Cost of Capital ANSWERS TO SELEECTED ENDOFCHAPTER QUESTIONS 91 a. The weighted average cost of capital, WACC, is the weighted average of the aftertax component costs of capital debt,
More informationCATÓLICALISBON. Equity Valuation. Apple Inc intrinsic value and market price adjustment towards equilibrium
CATÓLICALISBON Equity Valuation Apple Inc intrinsic value and market price adjustment towards equilibrium Marco António Lourenço Madeira 03062013 ABSTRATC The main objective in this dissertation is
More informationChapter 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 allequity firm D) I and III only
More informationChapter 14 Capital Structure in a Perfect Market
Chapter 14 Capital Structure in a Perfect Market 141. 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 informationCompany Share Price Valuation using Free Cash Flow To Equity
Financial Modeling Templates Company Share Price Valuation using Free Cash Flow To Equity http://spreadsheetml.com/finance/valuation_freecashflowtoequity.shtml Copyright (c) 20092014, ConnectCode All
More informationForecasting 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 informationCost of Capital. Katharina Lewellen Finance Theory II April 9, 2003
Cost of Capital Katharina Lewellen Finance Theory II April 9, 2003 What Next? We want to value a project that is financed by both debt and equity Our approach: Calculate expected Free Cash Flows (FCFs)
More informationChapter 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
More informationCHAPTER 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 informationChapter 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
More informationContact Information Politécnico Grancolombiano Calle 57 N 300 E Bogota, Colombia Phone #: (571) 3468800 Fax #: (571) 3469258
Firm Valuation: Free Cash Flow or Cash Flow to Equity? Ignacio VélezPareja ivelez@poligran.edu.co Politécnico Grancolombiano Bogotá, Colombia Joseph Tham Fulbright Economics Teaching Program Ho Chi Minh
More informationCalculation of Return on Equity (Ke) Presentation to Stakeholders 8 th October 2008
Calculation of Return on Equity (Ke) Presentation to Stakeholders 8 th October 2008 1 Overview (1) Tariffs set by Energy Regulator based on Allowable Revenue Tariff 1 Tariff 2 Tariff 3 Allowable Revenue
More informationUniversity of Notre Dame Mendoza College of Business MSM Corporate Finance: Preliminary Syllabus Clements Spring 2015
Course & Contact Information: Meets Monday and Wednesday, 2:00 3:20PM Instructor: Walt Clements Office: 224 Mendoza Office Hours: regular times TBD, others by appt or stop by email: wclement@nd.edu Phone:
More informationDiscounted 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
More informationA 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 informationConsolidation in the Luxury Sector: Study of a merger between LVMH and Hermès
Consolidation in the Luxury Sector: Study of a merger between LVMH and Hermès Duarte Teixeira de Melo e Lacerda de Queiroz September 2011 Dissertation submitted in partial fulfilment of requirements for
More informationLOS 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
More informationMASTER FINANZAS DE EMPRESA
MASTER FINANZAS DE EMPRESA Subject Corporate Finance Code 607627 Mode Credits 4 Compulsory Attending 4 Nonattending Course First Year Semester 1 Language English LECTURERS 0 Department Professor Alejandro
More informationCHAPTER 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 informationExam (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
More informationQUADRANT SKEW CAPITAL Syllabus
QUADRANT SKEW CAPITAL Syllabus OVERVIEW Quadrant Skew Capital s Equity Research Program focuses on material, content and skills that are directly applicable to realworld application. Our program provides
More informationDUKE 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 information1. CFI Holdings is a conglomerate listed on the Zimbabwe Stock Exchange (ZSE) and has three operating divisions as follows:
NATIONAL UNIVERSITY OF SCIENCE AND TECHNOLOGY FACULTY OF COMMERCE DEPARTMENT OF FINANCE BACHELOR OF COMMERCE HONOURS DEGREE IN FINANCE PART II 2 ND SEMESTER FINAL EXAMINATION MAY 2005 CORPORATE FINANCE
More informationIf 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 informationa) 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 informationTest3. Pessimistic Most Likely Optimistic Total Revenues 30 50 65 Total Costs 2520 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 informationEquity Valuation Project
Equity Valuation Project Group: Mike Altman Alison Birch Erin Burns Joe Faber Santosh Lakhan Josh Sullivan Companies: Affiliated Computer Services Apple Computer Biosite Gundle Environmental Systems Infosys
More informationt = 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