Comparing APV, FTE, and WACC continued from lecture 4

1
Comparing APV, FTE, and WACC (continued from
lecture 4)

• The APV approach
• The FTE approach
• The WACC approach

2
What cash flows to use?

• Both APV and WACC use unlevered after tax cash
  flows EBIT(1-Tc), i.e. NOT actual after tax cash
  flows (EBIT-i)(1-Tc)i !!!
• Thats why in WACC the cost of debt for the firm
  is kd(1-Tc)
• For the shareholders paying i out of EBIT and
  then being taxed is the same as simply paying
  i(1-Tc) out of EBIT(1-Tc) they get
  (EBIT-i)(1-Tc) anyway.

3
What are the discount rates?

• For APV use the cost of equity for the unlevered
  firm r0.
• For FTE and WACC use the cost of equity for the
  levered firm rS.

4
Which capital structure?

• Always use target weights in WACC.
• When computing weights in WACC and B/S for rs use
  market values market values are closer to actual
  amounts of money that can be raised by issuing
  securities.
• Ideally, the resulting capital structure (in
  terms of market values) should coincide with the
  target.
• If you choose an arbitrary B/S mix as a target,
  compute WACC based on it, calculate the projects
  PV and then calculate the actual B/S in market
  values it may be the same as the initial target!
• Example at the previous lecture (WACC for
  Pearson). The assumed target ratio was 1.5, but
  the actual one turned out to be 600/406.68
• (Here 406.68 is the market value of equity PV
  Debt 106.68 600)

5
Which method is better?

• In theory they are equivalent (at least for the
  case when debt is perpetuity)
• In practice
• Use WACC and FTE when you target the constant
  debt ratio. Otherwise computations become
  complex.
• Use APV when the level of debt is supposed to be
  constant. APV does not care about B/S, it only
  cares about the PV of Tax Shield.
• In the real world, WACC is the most widely used

6
Determining rs. Pure play technique

• We know that
• What if we dont know r0? We can use
• But how to determine ?S if the project has a risk
  different from the one of the firm? (otherwise we
  could use firm beta)
• Answer look at a firm whose whole business is
  similar to your project (pure-play firm).

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• The problem pure-play firm may have a leverage
  that differs from your project
• Solution unlever the pure-play firm, calculate
  its beta and then relever it with your
  projects leverage.

In a world with corporate taxes, and riskless
debt, it can be shown that the relationship
between the beta of the unlevered firm and the
beta of levered equity is
8
Applying the Pure-Play Technique -Time Warners
Cable Division

• Pure-Play Equity or
  Debt To Debt To
• Firm Market Beta MV
  of Capital MV of Equity
• Cablevision Systems 1.20 68.2
  214.5
• Century 1.01
  64.8 184.1
• Comcast 1.18
  48.5 94.8
  
• Jones Intercable 1.07
  60.7 154.5
• TCI Group 1.17
  50.0 100.0

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• Unlevered beta ?U ?L /1 (1 - TC) B/S

Pure-Play Equity or Debt
To Debt To Asset or Firm
Market Beta Capital
Equity Unlevered
Beta Cablevision Systems
1.20 68.2 214.5
0.501 Century 1.01
64.8 184.1 0.460 Comcast
1.18 48.5
94.8 0.730 Jones Intercable
1.07 60.7 154.5
0.534 TCI Group 1.17
50.0 100.0 0.705
Average Asset
Beta 0.586
10
Releveraging Asset Betas - Time Warners Cable
Division
- values for your project
Calculating the Cost of Equity - Time Warners
Cable Division
11
Common Errors in Calculating the WACC Using the
CAPM

• Using different capital structure assumptions in
  computing the cost of equity than are used in
  calculating the WACC.
• Using a different maturity for the risk-free rate
  in the CAPM than the one used in calculating the
  market risk premium.
• Estimating the market risk premium based on the
  most recent returns rather than a long-term time
  series.

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• Using the historical average T-bond or T-bill
  rate instead of the current rate.
• Failing to releverage asset betas.
• Failing to include taxes in unleveraging and
  leveraging betas.
• Using the historical market return instead of the
  market risk premium.

13
Other ways to deal with uncertainty

• Sensitivity analysis
• How sensitive NPV is to changes in parameters
• Identifies the most important variables that can
  alter NPV in a drastic way
• Scenario analysis identifies the most important
  scenarios (i.e. combinations of variables
  values) rather than considering each variable
  separately

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• Traditional simulation
• Estimate the probability distributions of the
  variables that affect cash flows.
• Simulate NPV to get a distribution of NPV.
• To calculate NPV for each realization of cash
  flows discount at the risk-free rate.
• Problem what is the meaning of the resulting
  distribution? Shall we accept or reject the
  project?
• Decision trees
• Allows to account for managerial flexibility!
• But the problem at what rate to discount???

15
Failure of traditional capital budgeting

• Option to defer investment
• The manager has an option to defer undertaking a
  project (building a plant) for a year.
• If he chooses to defer, after a year he either
  may or may not find it profitable to build a
  plant
• What is the value of this flexibility?

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Setup

• At t 0 investment outlay (required inv-t) I0
  104
• At t 1
• If the market moves up (prob. q) the project
  generates V 180
• If the market moves down (prob. 1-q) the project
  generates V 60
• The manager has a choice
• To invest at t 0 and get 180 with prob. q and
  60 with prob 1-q, or
• To wait until t 1 and build a plant only in the
  good state of nature (i.e. if the market has
  moved up). But then the required investment is I1
  112.32. Thus, then he gets
• E 180 I1 67.68 in the good state
• E 0 in the bad state.

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• Assume q 1/2
• Risk free rate r 8
• There exist a risky security (twin security),
  which payoffs are perfectly correlated with the
  payoffs of the project.
• Payoffs S 36, S 12
• Price S 20
• ? rate of return k (½ S ½ S)/S 20
• How much a manager would pay for this investment
  opportunity (what is the value of the project)?

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No flexibility case

• Assume theres no option to defer
• The traditional DCF technique yields
• V0 (qV (1-q)V-)/(1k) (0.5180
  0.5160)/(1 0.2) 100
• NPVpassive V0 - I0 100 104 - 4
• Reject the project!

19
When the option to defer is present

• Consider a strategy
• Buying N shares of the twin security S, partly
  financed by borrowing of amount B at the riskless
  rate r 8
• We can always pick such N and B that
• E NS - (1r)B
• E- NS- - (1r)B
• Thus, we can replicate the payoffs from the
  project with this portfolio ? the arbitrage
  argument tells us that the project value must be
  the same as the price of the portfolio E0 NS -
  B

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• N (E - E-)/(S - S-)
• B (NS- E-)/(1r)
• We obtain the risk-neutral valuation!
• E0 NS B (pE (1-p)E-)/(1r)
• where p ((1 r)S S-)/(S - S-)
• Notice q does not enter the expression for E0!
  Why? Because q is already incorporated in the
  price of the twin security S.
• pE (1-p)E- can be viewed as Certainty
  Equivalent of the random payoff at t 1.

21

• For our project
• p 0.4, E0 25.07
• The value of the option
• E0 NPVpassive 25.07 (-4) 29.07
• What if we use traditional capital budgeting,
  i.e. the actual probabilities q and the rate of
  return on the twin security k 20 to discount
  cash flows?
• E0 (qE (1-q)E-)/(1k) 28.20 gt 25.07
• Overestimation! One should not pay more than
  25.07 for this option!