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Review

Review. Review Item. An firm has a project with NPV>0 that costs a lot of money. It pays off after the owner dies. Should she invest? In the project? In financial assets? How?. Invest to here. Finance to here. An investment opportunity that increases value. Time one cash flow.

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Review

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  1. Review

  2. Review Item • An firm has a project with NPV>0 that costs a lot of money. • It pays off after the owner dies. • Should she invest? In the project? In financial assets? How?

  3. Invest to here Finance to here An investment opportunity that increases value. Time one cash flow NPV Time zero cash flow

  4. Review item • What is the interest rate?

  5. Don’t write • The interest rate is the time value of money.

  6. Do write: • The interest rate is the premium for current delivery of money. • P0 is the price of current money in current money, namely 1. • P1 is the price of time-one money in terms of current money, something <1. • P

  7. Office hours • Anderson • Monday 10:30 – 12:30 • Tuesday 10-11 • Seo • Monday 2-4 • Tuesday 9-10 • Marshall • Monday 4-6 • Tuesday 11-12

  8. Review item • When a firm creates value through a financial transaction, who gets the increase?

  9. Answer • Old equity means the shareholders at the time the decision is made. • Old equity gets the gains. • Why? Old equity has no competitors. Everyone else is competitive and must accept a market return.

  10. Review item • Two assets have the same expected return. • Each has a standard deviation of 2%. • The correlation coefficient is .5. • What is the standard deviation of an equally weighted portfolio?

  11. Answer • Var P = .5x.5x4+.5x.5x4+2x.5x.5x.5x2x2 • = 3 • Standard deviation = sq. root of 3 • =1.732

  12. Review item • A firm has a project with positive NPV. • The project costs 100M to start. • The firm has only 50M. • What should it do?

  13. Answer • Raise the money in the capital market. • It can because NPV is market valuation.

  14. EPS and ROE under Proposed Capital Structure Shares Outstanding = 240 Recession Expected Expansion EBIT $1,000 $2,000 $3,000 Interest 640 640 640 Net income $360 $1,360 $2,360 EPS $1.50 $5.67 $9.83 ROA 5% 10% 15% ROE 3% 11% 20%

  15. Proposition II of M-M • rB is the interest rate • rs is the return on (levered) equity r0 is the return on unlevered equity • B is value of debt • SL is value of levered equity • rs = r0 + (B / SL) (r0 - rB)

  16. rWACC MM Proposition II no tax Cost of capital: r(%) rS . r0 rB Debt-to-equityratio (B/S)

  17. MM II (with taxes) • Corporate taxes, not personal • rB = interest rate • rS = return on equity • r0 = return on unlevered equity • B = value of debt • SL = value of levered equity • Previously, without taxes rS = r0 + (B/SL)(r0 - rB)

  18. Effect of tax shield • Increase of equity risk is partly offset by the tax shield • rS = r0 + (1-TC)(r0 - rB)(B/SL) • Leverage raises the required return less because of the tax shield.

  19. . rS 0.2351 . rWACC 200 370 MM II and WACC Cost of capital: r(%) . 0.200= r0 . rB 0.100 Debt-to-equityratio (B/S)

  20. Optimal Debt and Value Present value offinancial distress costs Value of firm (V) Present value of taxshield on debt VL=VU+TCB= Value of firm underMM with corporatetaxes and debt Maximumfirm value V=Actual value of firm VU=Value of firm with no debt 0 Debt (B) B* Optimal amount of debt

  21. D e b t E q u i t y c h a n n e l c h a n n e l Channels O p e r a t i n g C a s h F l o w s = $ 1 TC TB TS 1 - TB (1-TC)(1-TS)

  22. Value as debt Value as equity D of rich investors D of Institutions V* = 1/RS V* = 1/RB as debt as equity Operating C.F.’s of the whole economy Miller: Tax-class clienteles

  23. Value as debt Value as equity tax reform increased debt Operating C.F.’s of the whole economy ...

  24. L o w - d i v i d e n d f i r m s l o p e = - ( 1 + r ) F u t u r e r e t u r n o r H i g h - d i v i d e n d f i r m d i v i d e n d n o w Separation theorem interpreted for dividends (Figure 18.4) C1 C0

  25. L o D i v H i D i v v a l u e v a l u e p e r $ 1 p e r $ 1 V * = 1 / Rh V * = 1 / RL E q u i l i b r i u m E q u i l i b r i u m H i D i v L o D i v $ o f o p e r a t i n g c a s h f l o w s Dividend equilibrium ...

  26. Review item • What is the weighted average cost of capital?

  27. Answer • Give the definitions and the formula. • rB = bond rate • rS = expected return on shares • B = market value of bonds • S = market value of shares • TC = corporate tax rate

  28. Pay-off pitch • rWACC =(S/(S+B))rS + (B/(S+B))(1-TC)rB • Now say that it applies when • (1) the physical project has the same risk as the firm • (2) it is financed like the firm.

  29. Review item • Does a good project have IRR greater than the hurdle rate, or less?

  30. Answer • IRR is the discount rate that makes NPV(IRR) = 0. • The hurdle rate is the market rate for the risk-class. • Investing means cash flows are first negative, then positive. • Financing (in this context) means cash flows are first positive, then negative.

  31. More answer • Other sign patterns, IRR is not useful. • Investing, a good project has IRR > hurdle rate. • Financing, a good project has hurdle rate > IRR.

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