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Session 9: Valuation. C15.0008 Corporate Finance Topics. Outline. Valuation with leverage WACC APV FTE Valuation using multiples. Approaches to Valuation. There are 3 equivalent (but not identical) approaches to valuation (of projects or firms) WACC: weighted average cost of capital

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session 9 valuation

Session 9: Valuation

C15.0008 Corporate Finance Topics

outline
Outline
  • Valuation with leverage
    • WACC
    • APV
    • FTE
  • Valuation using multiples
approaches to valuation
Approaches to Valuation

There are 3 equivalent (but not identical) approaches to valuation (of projects or firms)

  • WACC: weighted average cost of capital
  • APV: adjusted present value
  • FTE: flow to equity
formulas
Formulas

WACC:

V = t UCFt / (1+rWACC)t

APV:

V = t UCFt / (1+r0)t + PV(financing effects)

FTE:

S = t LCFt / (1+rS)t

cash flows
Cash Flows
  • UCF--unlevered cash flows
    • Cash flows available to all security holders (equity, debt, etc.)
    • UCF = EBIT(1-T) + depr - capex - NWC = (1-b)EBIT(1-T)
    • Gives V
  • LCF--levered cash flows
    • Cash flows available to equity holders (dividends)
    • LCF = UCF - int exp(after-tax) - pref divLCF = (EBIT-int exp)(1-T) - pref div + depr - capex - NWC = (1-b)[(EBIT-int exp)(1-T) – pref div]
    • Gives S
discount rates
Discount Rates
  • WACC--weighted average cost of capital
    • Market value weights of permanent financing
    • After-tax
  • r0--required return on (cost of) unlevered equity
    • Asset required return
    • Can be backed out of rS
  • rS--required return on (cost of) equity
    • Dependent on financing
the problem
The Problem

Firm

- No growth, UCF of 60 in perpetuity

- Debt and equity financed

0 1 2 3 …

60 60 60 …

What is the value of the firm?

wacc approach
WACC Approach

V = t UCFt / (1+rWACC)t

UCF -- expected, after-tax, unlevered cash flow

rWACC = wB rB(1-T)+wS rS

Key assumption -- the weights are constant

Inputs: (1) leverage ratio (weights), (2) component costs of capital, (3) cash flows

wacc valuation
WACC Valuation

0 1 2 3 …

60 60 60 …

rS = 11.2%, rB = 8%, wB = wS = 0.5, T = 40%

rWACC = 0.5(8%)(1-0.4) + 0.5(11.2%) = 8%

V = 60/0.08 = 750

apv approach
APV Approach

V = t UCFt / (1+r0)t + PV(financing effects)

PV(financing effects) = PV(tax shield) + PV(subsidies) - PV(fin. distress/agency costs) – PV (other side-effects)

UCF -- expected, after-tax, unlevered cash flow

r0 -- required return on unlevered equity

Key assumption -- $ amount of debt known

Inputs: (1) financing effects, (2) cost of unlevered equity, (3) cash flows

apv valuation
APV Valuation

0 1 2 3 …

60 60 60 …

r0 = 10%, B = 375 (perpetual), rB = 8%

V = 60/0.1 + 0.4(375) = 750

wacc and apv
WACC and APV

Why did the WACC approach and APV approach yield the same answer?

B = 375, V = 750  wB= 0.5

r0 = 10%, rS = 11.2%, rB = 8%

Because rS = r0 + (1- TC)(B/S)(r0 - rB)

MM w/ corporate taxes!

fte approach
FTE Approach

S = t LCFt / (1+rS)t

LCF -- expected, after-tax, levered cash flow

rS -- required return on levered equity

Key assumptions -- debt cash flows known, rS constant

Inputs: (1) cost of levered equity, (2) cash flows

fte cash flows
FTE Cash Flows

0 1 2 3 …

UCF 60 60 60 …

Int. exp. -30 -30 -30 …

After-tax -18 -18 -18 …

LCF 42 42 42 …

Or reconstruct income statement!

fte valuation
FTE Valuation

0 1 2 3 …

42 42 42 …

rS = 11.2%, B = 375

S = 42/0.112 = 375

V = B + S = 375 + 375 = 750

issues
Issues
  • Theoretically equivalent
  • Assumptions/inputs determine applicability
    • Constant leverage ratio  WACC
    • $ value of debt  APV
    • Both  WACC, APV, FTE
  • In practice all methods are approximations
wacc approach17
WACC Approach

Consider a firm with expected EBIT next year of 100, a payout ratio of 75%, an expected perpetual growth rate of 5%, a tax rate of 40%, a WACC of 10%, and current market value of debt of 250.

What is the value of the equity?

the solution
The Solution

V = [(1-b)EBIT(1-T)]/(WACC-g)

= [(0.75)100(1-0.4)]/(10%-5%) = 900

S = V - B = 900 - 250 = 650

Assumptions

  • Fixed leverage ratio, i.e., the debt will grow with firm value
  • b(EBIT) = capex + NWC - depr
apv approach19
APV Approach

Consider a firm with a single 1 year project, that requires 1000 in financing, will generate expected UCF of 2200, and has a required return of 10%. The financing will come from equity and 400 in subsidized debt. The cost of debt is 6%, but the government is offering a low interest loan of 2% in return for an origination fee of 5. Assume a tax rate of 40%.

What is the NPV of the project?

the solution20
The Solution

NPVU = -1000 + 2200/1.1 = 1000

Financing:01

400 -400

Int .exp -8

After-tax -4.8

CF 400 -404.8

PV(financing effects) = PV(tax shield) + PV(subsidy) – PV(financing costs) =

0.4(8)/1.06 + (24-8)/1.06 – 5 = 13.11

NPV = 1000 + 13.11 = 1013.11

fte approach21
FTE Approach

Consider a firm with expected EBIT next year of 100, interest expense of 25, a payout ratio of 40%, an expected perpetual growth rate of 3%, a tax rate of 40%, and a cost of equity of 13%.

What is the value of the equity?

the solution22
The Solution

S = [(1-b)(EBIT-Int. Exp.)(1-T)]/(rS-g)

= [(0.40)(100-25)(1-0.4)]/(13%-3%)

= 180

Assumptions

  • Fixed leverage ratio
  • Interest expense growing with value
terminal values
Terminal Values
  • Usually, cash flows and tax shields can be forecasted only for a certain number of years into the future.
  • Beyond that, you have to consider some terminal value of cash-flows and tax-shields, usually at a fixed or zero growth rate
  • Applicable to all DCF methods
example
Example
  • Spreadsheet..
multiple based valuation
Multiple-Based Valuation
  • Value target as a multiple of earnings, cash flows, revenues (sales), etc.
  • Multiple from comparable companies
  • Choice of multiple depends on industry and motivation
logic
Logic
  • DCF is truth!
  • Multiple-based valuation will give the correct answer if
    • The variable (e.g., sales) translates into cash flows (current and future) the same way in both companies
    • The discount rate (risk, capital structure) is the same for both companies
implicit assumptions
Implicit Assumptions
  • UCF = EBIT(1-T) + depr – cap ex. – NWC
  • Sales
    • Same margin
    • Same WC management
    • Same growth (reinvestment rate, ROE)
    • Same WACC (risk, leverage)
  • EBITDA
    • No margin assumption needed but more calculations required
advantages
Advantages
  • Easy
  • Correct if required assumptions are valid
  • Uses market-based expectations
  • Works even if firms are (consistently) mispriced
an example p e ratios
An Example: P/E Ratios
  • Valuing the equity
  • For comparable firms, P/E = 15  For firm to be valued P = 15  EPS
  • Assumptions:P/E = (1-b)/(rS-g) g = b ROE
    • Same cost of equity (risk, leverage)
    • Same growth (reinvestment rate, investment opportunities, ROE)
multiples
Multiples

SalesP/SalesP/EM/B

Wal-Mart 256 0.86 23.97 5.33

H.D. 65 1.35 19.56 3.99

Lowes 31 1.25 21.92 4.00

Target 48 0.96 23.07 3.70

Sears 41 0.31 21.12 1.98

Kmart 17 0.43 20.52 2.85

assignments
Assignments
  • Chapter 29.1-29.10
  • Case: USG