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Part 5 Chapter 20 The valuation of a project under different financing strategies.

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

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Part 5 Chapter 20 The valuation of a project under different financing strategies.

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

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

  3. 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 yearsand Rd = 8%. Question: PV tax shield? APV = -58 + 141 = 83 > 0!

  4. 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 Rd = 8%. Question: PV tax shield? APV = -58 + 223.6 = 165.58 > 0!

  5. 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 RD only. As long as future tax shields are tied to uncertain future cash flows, discount with Ru.

  6. WACC method (textbook) NPVWACC ME = -I + EBITt (1-tc)/(1+WACCME)t 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. NPV = 4,090.34 – 4,000 = 90.34

  7. Check with APV method; using Ru and Rd! 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)]

  8. CFE method CFE1 = (EBIT-Rd D)(1-tc) – redemption = (1600 – 163.61)(1-0.35) – 344.65 = 589.01Market value of E at t=0: 2,045.17Equity holders invested: 4,000 – D0 = 4,000 – 2,045.17 = 1,954.83NPV = 2,045.17 – 1,954.83 = 90.34

  9. 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 RU (see Part 5 note B) NPVWACC Ruback = -I + EBITt (1-tc)/(1+WACCRuback)t

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

  11. Check with APV method; using Ru only! NPV = 4,087.57 - 4,000 = 87.57

  12. CFE method CFE1 = (EBIT-Rd D)(1-tc) – redemption = (1600 – 163.50)(1-0.35) – 344.23 = 589.49 Market value of E at t=0: 2,043.79Equity holders invested: 4,000 – D0 = 4,000 – 2,043.79 = 1,956.21NPV = 2,043.79 – 1,956.21 = 87.57

  13. Summary example Financing Rule 1 2 3a 3bMiles HarrisPringle/ Ezzell Ruback APV 83,4 166,0 90,3 87,6 - Base case -57,6 -57,6 - 57,6 - 57,6 - tax shield 141,0 223,6 147,9 145,2 WACC ME, CFE ME 90,3 87,6 Financing rule 1 equal principlal repayments (2,000; 1,600; 1,200; 800; 400) 2 balloon repayment (2,000; 2,000; 2000; 2000; 2000) 3 target 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)

  14. Levering and Unlevering betas, some formulas MM1963, PVTS discounted at RD, g = 0 and HP1985, PVTS discounted at RU and

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

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

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

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

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