NPV CRITERION FOR CAPITAL EXPENDITURE ANALYSIS

1
NPV CRITERION FOR CAPITAL EXPENDITURE ANALYSIS

• Discount incremental after-tax cash flows at the
  cost of capital
• e.g., if initial investment 100, cash flow in
  years 1 and 2 70, cost of capital 10, NPV
  -100 70/(1.1) 70/(1.1)2 21.49
• Since NPV gt 0, project is worthwhile

2
NPV AND SHAREHOLDER WEALTH

• Firm has no debt
• Existing assets generate cash flows of 100 per
  year forever
• Discount rate 10
• Firm has 20 mil shares currently selling at 50
  per share

3
NPV AND S/H WEALTH (CONT.)

• Now firm plans to invest 120 in new project
• Project will generate 20 CF per year forever
• Firm will issue ?n new shares at price P to
  finance project

4
NPV AND S/H WEALTH (CONT.)

• Equating sides of post-project bal. sheet
• 100/.10 20/.10 20P ?nP
• But from original bal. Sheet
• 100/.10 20x50 nP
• And since we need to raise 120 for project
• 120 ?nP
• Thus
• 20x50 20/.10 20P 120

5
NPV AND S/H WEALTH (CONT.)

• Rearranging
• 20/.10 - 120 20 x (P - 50)
• Or
• 20/.10 - 120/20 (P - 50)
• Or
• ? ? ? ? NPV per share change in wealth
• for original shareholders ? ? ? ?

6
COST OF CAPITAL

• What is it?
• Appropriate discount rate
• Minimum acceptable rate of return for investors
• Investors opportunity cost
• Required compensation for risk borne by investors

7
COST OF CAPITAL (all-equity financing)

• What rate of return will shareholders demand? Two
  possible answers from stock market
• Capital Asset Pricing Model
• rE rf ?(rM - rf)
• (shareholders demand compensation for systematic
  risk)
• Dividend Discount Model
• rE D1/P0 g

8
COST OF CAPITAL (with debt and equity)

• E equity mkt. value
• ATOCF after-tax operating cash flow
• rD cost of debt
• rE cost of equity
• D value of debt
• T corporate tax rate

9
COST OF CAPITAL (debt and equity cont.)

• Cross-multiplying by V, we derive a discount rate
  for the company as a whole
• Note that debt ratio is measured at market value

10
COST OF CAPITAL FOR A PROJECT

• For a project, the cost of capital is project
  specific, not company-specific (Would a risky
  project be any less risky if undertaken by a
  currently safe company?)
• Cost of capital should reflect business risk of
  this project
• Cost of capital should reflect long-run financing
  mix for this project