Review

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Review
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Review Item

• An firm has a project with NPVgt0 that costs a lot
  of money.
• It pays off after the owner dies.
• Should she invest? In the project? In financial
  assets? How?

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An investment opportunity that increases value.
Time one cash flow
NPV
Time zero cash flow
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Review item

• What is the interest rate?

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Dont write

• The interest rate is the time value of money.

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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 lt1.
• P

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Office hours

• Anderson
• Monday 1030 1230
• Tuesday 10-11
• Seo
• Monday 2-4
• Tuesday 9-10
• Marshall
• Monday 4-6
• Tuesday 11-12

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Review item

• When a firm creates value through a financial
  transaction, who gets the increase?

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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.

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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?

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Answer

• Var P .5x.5x4.5x.5x42x.5x.5x.5x2x2
• 3
• Standard deviation sq. root of 3
• 1.732

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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?

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Answer

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

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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

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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)

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

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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.

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MM II and WACC
Cost of capital r()
.
0.200
r0
.
rB
0.100
Debt-to-equityratio (B/S)
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Optimal Debt and Value
Value of firm (V)
Present value offinancial distress costs
Present value of taxshield on debt
Value of firm underMM with corporatetaxes and
debt
VLVUTCB
Maximumfirm value

VActual value of firm
VUValue of firm with no debt
0
Debt (B)
B
Optimal amount of debt
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Channels
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TC
TB
TS
1 - TB
(1-TC)(1-TS)
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Miller Tax-class clienteles
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...
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Separation theorem interpreted for dividends
(Figure 18.4)
C1
C0
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Dividend equilibrium
...
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Review item

• What is the weighted average cost of capital?

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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

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Pay-off pitch

• rWACC (S/(SB))rS (B/(SB))(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.

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Review item

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

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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.

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More answer

• Other sign patterns, IRR is not useful.
• Investing, a good project has IRR gt hurdle rate.
• Financing, a good project has hurdle rate gt IRR.

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