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Part 5 Chapter 20 The valuation of a project under different financing strategies. Marc B.J. Schauten

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Example Consider a project to produce product SMART. I = 4000. Cash flow is $ 1600 pre-tax per year for 5 years. R U = 10%. Tax rate = 35%. NPV base case = -I + [EBIT x (1- C )] /(1+R U ) t NPV base case = -I + [EBIT x (1- C )] /(1+R U ) t = -4000 + 3942 = -58

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Financing rule 1: Equal principal repayments Suppose that because of the value of the expected CF’s of this project, the firm can borrow 2000 more, the loan is repaid in equal installments during 5 years and R d = 8%. Question: PV tax shield? APV = -58 + 141 = 83 > 0!

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Financing rule 2: Balloon repayment Suppose that because of the value of the expected CF’s of this project, the firm can borrow 2000 more, the loan is repaid at the end of year 5 and R d = 8%. Question: PV tax shield? APV = -58 + 223.6 = 165.58 > 0!

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Financing rule 3: Target capital structure Assume that the project will be financed for 50% with debt, Rd = 8%. Use the WACC MM? Assumptions (a.o.) of WACC MM: -PVTS = tc D Alternatives are: 3a) Miles Ezzell WACC and 3b) Harris Pringle / Ruback WACC Ad 3a) Assumptions WACC Miles Ezzell: -debt as a proportion of the total market value is remains constant during the life of the project; -the project generates stable/unstable CFs that could be finite and/or variable. -ME do not discount the tax shield with R D only. As long as future tax shields are tied to uncertain future cash flows, discount with R u.

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NPV WACC ME = -I + EBIT t (1-t c )/(1+WACC ME ) t NPV = 4,090.34 – 4,000 = 90.34 WACC method (textbook) Inselbag, I. and H. Kaufold, 1997, Two DFF approaches for Valuing Companies under alternative financing strategies (and how to choose between them), Journal of Applied Corporate Finance, 114-122.

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NB explanation column 5: 53.02 = 57.26 / (1.08) 40.08 = 47.61 / [(1.10)(1.08)] 28.42 = 37.14 / [(1.10) 2 (1.08)] 17.92 = 25.76 / [(1.10) 3 (1.08)] 8.48 = 13.41 / [(1.10) 4 (1.08)] Check with APV method; using R u and R d !

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CFE method CFE 1 = (EBIT-Rd D)(1-tc) – redemption = (1600 – 163.61)(1-0.35) – 344.65 = 589.01 Market value of E at t=0: 2,045.17 Equity holders invested: 4,000 – D 0 = 4,000 – 2,045.17 = 1,954.83 NPV = 2,045.17 – 1,954.83 = 90.34

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Financing rule 3: Target capital structure Assume that the project will be financed for 50% with debt, Rd = 8%. Ad 3b)Harris and Pringle (1985) and Ruback (2002) assume tax shields are discounted at R U (see Part 5 note B) NPV WACC Ruback = -I + EBIT t (1-t c )/(1+WACC Ruback ) t

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NPV = 4,087.57 - 4,000 = 87.57 WACC method (textbook)

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NPV = 4,087.57 - 4,000 = 87.57 Check with APV method; using R u only!

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CFE method CFE 1 = (EBIT-Rd D)(1-tc) – redemption = (1600 – 163.50)(1-0.35) – 344.23 = 589.49 Market value of E at t=0: 2,043.79 Equity holders invested: 4,000 – D 0 = 4,000 – 2,043.79 = 1,956.21 NPV = 2,043.79 – 1,956.21 = 87.57

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Financing Rule 1 2 3a3b Miles Harris Pringle/ Ezzell Ruback APV 83,4166,0 90,3 87,6 - Base case -57,6 -57,6 - 57,6 - 57,6 - tax shield141,0223,6 147,9 145,2 WACC ME, CFE ME 90,3 87,6 Financing rule 1equal principlal repayments (2,000; 1,600; 1,200; 800; 400) 2balloon repayment (2,000; 2,000; 2000; 2000; 2000) 3target capital structure / debt rebalanced (50% of project value) a) ME: (2,045; 1,701; 1,326; 920; 479) b) HP/R:(2,044; 1,700; 1,326; 920; 479) Summary example

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MM1963, PVTS discounted at R D, g = 0 Levering and Unlevering betas, some formulas HP1985, PVTS discounted at R U and

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MM1963: Discount rate tax shield is r d, g = 0 The expected economic income for the providers of capital is: Rewriting gives: → MM63 tells us that: and, this results in: (1) (2) If we insert (2) in (1) we find: Relation WACC and r d (3) Remark: (3) = Proposition II MM63! (4) If we insert (3) in (4) we find: Since (5) We can rewrite (5) into: (6)

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Relation E en D Following the CAPM: (3) (7) (8) (9) Inserting (7)-(9) in (3) gives: and

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HP1985: Discount rate tax shield is r u The expected economic income for the providers of capital is: → Substitute V U = E+D - PVTS → → → Note that (1) is the same as proposition II of Miller and Modigliani (1958) (1) When substituting (1) in the equation in order to calculate the WACC, by taking the weighted average of R D after taxes and R E, we find (2)

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Relation E en D Following the CAPM: (3) (4) (5) (6) Inserting (4)-(6) in (3) gives: → and

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