Asset Valuation

1
Asset Valuation

• P.V. Viswanath
• Class Notes for Corporate Finance and Mergers
  and Acquisitions

2
Discounted Cashflow Valuation

• where,
• n life of the asset
• CFt cashflow in period t
• r discount rate reflecting the riskiness
  of the estimated cashflows

3
Two Measures of Discount Rates

• Cost of Equity This is the rate of return
  required by equity investors on an investment. It
  will incorporate a premium for equity risk -the
  greater the risk, the greater the premium. This
  is used to value equity.
• Cost of capital This is a composite cost of all
  of the capital invested in an asset or business.
  It will be a weighted average of the cost of
  equity and the after-tax cost of borrowing. This
  is used to value the entire firm.

4
Equity Valuation

• Free Cash Flow to Equity Net Income Net
  Reinvestment (capex as well as change in working
  capital) Net Debt Paid (or Net Debt Issued)

5
Firm Valuation
Free Cash Flow to the Firm Earnings before
Interest and Taxes (1-tax rate) Net
Reinvestment Net Reinvestment is defined as
actual expenditures on short-term and long-term
assets less depreciation. The tax benefits of
debt are not included in FCFF because they are
taken into account in the firms cost of capital.
6
Valuation with Infinite Life
7
Valuing the Home Depots Equity

• Assume that we expect the free cash flows to
  equity at Home Depot to grow for the next 10
  years at rates much higher than the growth rate
  for the economy. To estimate the free cash flows
  to equity for the next 10 years, we make the
  following assumptions
• The net income of 1,614 million will grow 15 a
  year each year for the next 10 years.
• The firm will reinvest 75 of the net income back
  into new investments each year, and its net debt
  issued each year will be 10 of the reinvestment.
• To estimate the terminal price, we assume that
  net income will grow 6 a year forever after year
  10. Since lower growth will require less
  reinvestment, we will assume that the
  reinvestment rate after year 10 will be 40 of
  net income net debt issued will remain 10 of
  reinvestment.

8
Estimating cash flows to equity The Home Depot
9
Terminal Value and Value of Equity today

• FCFE11 Net Income11 Reinvestment11 Net Debt
  Paid (Issued)11
• 6,530 (1.06) 6,530 (1.06) (0.40) (-277)
  4,430 million
• Terminal Price10 FCFE11/(ke g)
• 4,430 / (.0978 - .06) 117,186 million
• The value per share today can be computed as the
  sum of the present values of the free cash flows
  to equity during the next 10 years and the
  present value of the terminal value at the end of
  the 10th year.
• Value of the Stock today 6,833 million
  117,186/(1.0978)10
• 52,927 million

10
Valuing Boeing as a firm

• Assume that you are valuing Boeing as a firm, and
  that Boeing has cash flows before debt payments
  but after reinvestment needs and taxes of 850
  million in the current year.
• Assume that these cash flows will grow at 15 a
  year for the next 5 years and at 5 thereafter.
• Boeing has a cost of capital of 9.17.

11
Expected Cash Flows and Firm Value

• Terminal Value 1710 (1.05)/(.0917-.05)
  43,049 million

Year Cash Flow Terminal Value Present Value
1 978 895
2 1,124 943
3 1,293 994
4 1,487 1,047
5 1,710 43,049 28,864
Value of Boeing as a firm Value of Boeing as a firm Value of Boeing as a firm 32,743
12
What discount rate to use?

• Since financial resources are finite, there is a
  hurdle that projects have to cross before being
  deemed acceptable.
• This hurdle will be higher for riskier projects
  than for safer projects.
• A simple representation of the hurdle rate is as
  follows Hurdle rate Return for postponing
  consumption
  Return for bearing
  risk Hurdle rate Riskless Rate Risk
  Premium
• The two basic questions that every risk and
  return model in finance tries to answer are
• How do you measure risk?
• How do you translate this risk measure into a
  risk premium?

13
The Capital Asset Pricing Model

• Uses variance as a measure of risk
• Specifies that a portion of variance can be
  diversified away, and that is only the
  non-diversifiable portion that is rewarded.
• Measures the non-diversifiable risk with beta,
  which is standardized around one.
• Relates beta to hurdle rate or the required rate
  of return
• Reqd. ROR Riskfree rate b (Risk Premium)
• Works as well as the next best alternative in
  most cases.

14
Inputs required to use the CAPM

• According to the CAPM, the required rate of
  return on an asset will be
• Required ROR Rf b (E(Rm) - Rf)
• The inputs required to estimate the required ROR
  are
• (a) the current risk-free rate
• (b) the expected market risk premium (the premium
  expected for investing in risky assets over the
  riskless asset)
• (c) the beta of the asset being analyzed.

15
The Riskfree Rate

• For an investment to be riskfree, i.e., to have
  an actual return be equal to the expected return,
  there must be
• No default risk this usually means a
  government-issued security but, not all
  governments are default free.
• No uncertainty about reinvestment rates.
• In practice, the riskfree rate is the rate on a
  zero coupon government bond matching the time
  horizon of the cash flow being analyzed.
• Using a long term government rate (even on a
  coupon bond) as the riskfree rate on all of the
  cash flows in a long term analysis will yield a
  close approximation of the true value.

16
Measurement of the risk premium

• The risk premium is the premium that investors
  demand for investing in an average risk
  investment, relative to the riskfree rate.
• As a general proposition, this premium should be
• greater than zero
• increase with the risk aversion of the investors
  in that market
• increase with the riskiness of the average risk
  investment

17
The Historical Premium Approach

• This is the default approach used by most to
  arrive at the premium to use in the model
• In most cases, this approach does the following
• it defines a time period for the estimation
  (1926-Present, 1962-Present....)
• it calculates average returns on a stock index
  during the period
• it calculates average returns on a riskless
  security over the period
• it calculates the difference between the two
• and uses it as a premium looking forward
• The limitations of this approach are
• it assumes that the risk aversion of investors
  has not changed in a systematic way across time.
  (The risk aversion may change from year to year,
  but it reverts back to historical averages)
• it assumes that the riskiness of the risky
  portfolio (stock index) has not changed in a
  systematic way across time.

18
Historical Average Premiums for the United States
Considering that market rates of return since
1999 have been lower, it is probably more
appropriate to use a market risk premium, which
is somewhat lower, such as 5.5
19
Estimating Beta

• The standard procedure for estimating betas is to
  regress stock returns (Rj) against market returns
  (Rm) -
• Rj a b Rm
• where a is the intercept and b is the slope of
  the regression.
• The slope of the regression corresponds to the
  beta of the stock, and measures the riskiness of
  the stock.

20
Setting up for the Estimation

• Decide on an estimation period
• Services use periods ranging from 2 to 5 years
  for the regression
• Longer estimation period provides more data, but
  firms change.
• Shorter periods can be affected more easily by
  significant firm-specific event that occurred
  during the period
• Decide on a return interval - daily, weekly,
  monthly
• Shorter intervals yield more observations, but
  suffer from more noise.
• Noise is created by stocks not trading and biases
  all betas towards one.
• Estimate returns (including dividends) on stock
• Return (PriceEnd - PriceBeginning
  DividendsPeriod)/ PriceBeginning
• Included dividends only in ex-dividend month
• Choose a market index, and estimate returns
  (inclusive of dividends) on the index for each
  interval for the period.

21
Choosing the Parameters Boeing

• Period used 5 years
• Return Interval Monthly
• Market Index SP 500 Index.
• For instance, to calculate returns on Boeing in
  May 1995,
• Price for Boeing at end of April 27.50
• Price for Boeing at end of May 29.44
• Dividends during month 0.125 (It was an
  ex-dividend month)
• Return (29.44 - 27.50 0.125)/27.50
  7.50
• To estimate returns on the index in the same
  month
• Index level (including dividends) at end of April
  514.7
• Index level (including dividends) at end of May
  533.4
• Dividends on the Index in May 1.84
• Return (533.4-514.71.84)/ 514.7 3.99

22
Boeings Historical Beta
Boeing versus SP 500 10/93-9/98
10.00
Regression
line
5.00
Returns on Boeing
0.00
-25.00
-20.00
-15.00
-10.00
-5.00
0.00
5.00
10.00
15.00
20.00
-5.00
Beta is slope of this line
-10.00
-15.00
Each point represents a month
of data.
-20.00
Returns on SP 500
23
The Regression Output

• ReturnsBoeing -0.09 0.96 ReturnsS P 500
  
• R squared29.57
• Intercept -0.09
• Slope 0.96

24
Estimating Expected Returns December 31, 1998

• Boeings Beta 0.96
• Riskfree Rate 5.00 (Long term Government Bond
  rate)
• Risk Premium 5.50 (Approximate historical
  premium)
• Expected Return 5.00 0.96 (5.50) 10.31

25
Fundamental Determinants of Betas

• Type of Business Firms in more cyclical
  businesses or that sell products that are more
  discretionary to their customers will have higher
  betas than firms that are in non-cyclical
  businesses or sell products that are necessities
  or staples.
• Operating Leverage Firms with greater fixed
  costs (as a proportion of total costs) will have
  higher betas than firms will lower fixed costs
  (as a proportion of total costs)
• Financial Leverage Firms that borrow more
  (higher debt, relative to equity) will have
  higher equity betas than firms that borrow less.

26
Determinant 1 Product Type

• Industry Effects The beta value for a firm
  depends upon the sensitivity of the demand for
  its products and services and of its costs to
  macroeconomic factors that affect the overall
  market.
• Cyclical companies have higher betas than
  non-cyclical firms
• Firms which sell more discretionary products will
  have higher betas than firms that sell less
  discretionary products

27
Determinant 2 Operating Leverage Effects

• Operating leverage refers to the proportion of
  the total costs of the firm that are fixed.
• Other things remaining equal, higher operating
  leverage results in greater earnings variability
  which in turn results in higher betas.

28
Determinant 3 Financial Leverage

• As firms borrow, they create fixed costs
  (interest payments) that make their earnings to
  equity investors more volatile.
• This increased earnings volatility which
  increases the equity beta

29
Equity Betas and Leverage

• The beta of equity alone can be written as a
  function of the unlevered beta and the
  debt-equity ratio
• ?L ?u (1 ((1-t)D/E)
• where
• ?L Levered or Equity Beta
• ?u Unlevered Beta
• t Corporate marginal tax rate
• D Market Value of Debt
• E Market Value of Equity
• The unlevered beta measures the riskiness of the
  business that a firm is in and is often called an
  asset beta.

30
Effects of leverage on betas Boeing

• The regression beta for Boeing is 0.96. This beta
  is a levered beta (because it is based on stock
  prices, which reflect leverage) and the leverage
  implicit in the beta estimate is the average
  market debt equity ratio during the period of the
  regression (1993 to 1998)
• The average debt equity ratio during this period
  was 17.88.
• The unlevered beta for Boeing can then be
  estimated(using a marginal tax rate of 35)
• Current Beta / (1 (1 - tax rate) (Average
  Debt/Equity))
• 0.96 / ( 1 (1 - 0.35) (0.1788)) 0.86

31
Betas are weighted Averages

• The beta of a portfolio is always the
  market-value weighted average of the betas of the
  individual investments in that portfolio.
• Thus,
• the beta of a mutual fund is the weighted average
  of the betas of the stocks and other investment
  in that portfolio
• the beta of a firm after a merger is the
  market-value weighted average of the betas of the
  companies involved in the merger.

32
The Boeing/McDonnell Douglas Merger

• Company Beta Debt Equity Firm Value
• Boeing 0.95 3,980 32,438 36,418
  
• McDonnell Douglas 0.90 2,143 12,555
  14,698

33
Beta Estimation Step 1

• Calculate the unlevered betas for both firms
• Boeing 0.95/(10.65(3980/32438)) 0.88
• McDonnell Douglas 0.90/(10.65(2143/12555))
  0.81
• Calculate the unlevered beta for the combined
  firm
• Unlevered Beta for combined firm
• 0.88 (36,418/51,116) 0.81 (14,698/51,116)
• 0.86

34
Beta Estimation Step 2

• Boeings acquisition of McDonnell Douglas was
  accomplished by issuing new stock in Boeing to
  cover the value of McDonnell Douglass equity of
  12,555 million.
• Debt McDonnell Douglas Old Debt Boeings Old
  Debt
• 3,980 2,143 6,123 million
• Equity Boeings Old Equity New Equity used
  for Acquisition
• 32,438 12,555 44,993 million
• D/E Ratio 6,123/44,993 13.61
• New Beta 0.86 (1 0.65 (.1361)) 0.94

35
The Home Depots Comparable Firms
36
Estimating The Home Depots Bottom-up Beta

• Average Beta of comparable firms 0.93
• D/E ratio of comparable firms
  (2002076)/16,232 14.01
• Unlevered Beta for comparable firms
  0.93/(1(1-.35)(.1401)) 0.86
• If the Home Depots D/E ratio is 20, our
  bottom-up estimate of Home Depots beta is
  0.861(1-.35)(.2) 0.9718

37
From Cost of Equity to Cost of Capital

• The cost of capital is a composite cost to the
  firm of raising financing to fund its projects.
• In addition to equity, firms can raise capital
  from debt

38
Estimating the Cost of Debt

• If the firm has bonds outstanding, and the bonds
  are traded, the yield to maturity on a long-term,
  straight (no special features) bond can be used
  as the interest rate.
• If the firm is rated, use the rating and a
  typical default spread on bonds with that rating
  to estimate the cost of debt.
• If the firm is not rated,
• and it has recently borrowed long term from a
  bank, use the interest rate on the borrowing or
• estimate a synthetic rating for the company, and
  use the synthetic rating to arrive at a default
  spread and a cost of debt
• The cost of debt has to be estimated in the same
  currency as the cost of equity and the cash flows
  in the valuation.

39
Estimating Synthetic Ratings

• The rating for a firm can be estimated using the
  financial characteristics of the firm. In its
  simplest form, the rating can be estimated from
  the interest coverage ratio
• Interest Coverage Ratio EBIT / Interest
  Expenses
• Consider InfoSoft, a firm with EBIT of 2000
  million and interest expenses of 315 million
• Interest Coverage Ratio 2,000/315 6.15
• Based upon the relationship between interest
  coverage ratios and ratings, we would estimate a
  rating of A for the firm.

40
Interest Coverage Ratios, Ratings and Default
Spreads

• Interest Coverage Ratio Rating Default Spread
• gt 12.5 AAA 0.20
• 9.50 - 12.50 AA 0.50
• 7.50 9.50 A 0.80
• 6.00 7.50 A 1.00
• 4.50 6.00 A- 1.25
• 3.50 4.50 BBB 1.50
• 3.00 3.50 BB 2.00
• 2.50 3.00 B 2.50
• 2.00 - 2.50 B 3.25
• 1.50 2.00 B- 4.25
• 1.25 1.50 CCC 5.00
• 0.80 1.25 CC 6.00
• 0.50 0.80 C 7.50
• lt 0.65 D 10.00

41
Estimating Market Value Weights

• Market Value of Equity should include the
  following
• Market Value of Shares outstanding
• Market Value of Warrants outstanding
• Market Value of Conversion Option in Convertible
  Bonds
• Market Value of Debt is more difficult to
  estimate because few firms have only publicly
  traded debt. There are two solutions
• Assume book value of debt is equal to market
  value
• Estimate the market value of debt from the book
  value for Boeing, the book value of debt is
  6,972 million, the interest expense on the debt
  is 453 million, the average maturity of the
  debt is 13.76 years and the pre-tax cost of debt
  is 5.50.
• Estimated MV of Boeing Debt

42
Estimating Cost of Capital Boeing

• Equity
• Cost of Equity 5 1.01 (5.5) 10.58
• Market Value of Equity 32.60 Billion
• Equity/(DebtEquity ) 82
• Debt
• After-tax Cost of debt 5.50 (1-.35) 3.58
• Market Value of Debt 8.2 Billion
• Debt/(Debt Equity) 18
• Cost of Capital 10.58(.80)3.58(.20) 9.17

43
Estimating the Expected Growth Rate
44
Expected Growth in EPS

• gEPS (Retained Earningst-1/ NIt-1) ROE
• Retention Ratio ROE
• b ROE
• ROE  (Net Income)/ (BV Common Equity)
• This is the right growth rate for FCFE
• Proposition The expected growth rate in earnings
  for a company cannot exceed its return on equity
  in the long term.

45
Expected Growth in EBIT And Fundamentals

• Reinvestment Rate and Return on Capital
• gEBIT (Net Capex Change in WC)/EBIT(1-t)
  ROC Reinvestment Rate ROC
• Return on Capital (EBIT(1-tax rate)) / (BV
  Debt BV Equity)
• This is the right growth rate for FCFF
• Proposition No firm can expect its operating
  income to grow over time without reinvesting some
  of the operating income in net capital
  expenditures and/or working capital.

46
Getting Closure in Valuation

• A publicly traded firm potentially has an
  infinite life. The value is therefore the present
  value of cash flows forever.
• Since we cannot estimate cash flows forever, we
  estimate cash flows for a growth period and
  then estimate a terminal value, to capture the
  value at the end of the period

47
Stable Growth and Terminal Value

• When a firms cash flows grow at a constant
  rate forever, the present value of those cash
  flows can be written as
• Value (Expected Cash Flow Next Period) / (r -
  g) where,
• r Discount rate (Cost of Equity or Cost of
  Capital)
• g Expected growth rate
• This constant growth rate is called a stable
  growth rate and cannot be higher than the growth
  rate of the economy in which the firm operates.
• While companies can maintain high growth rates
  for extended periods, they will all approach
  stable growth at some point in time.
• When they do approach stable growth, the
  valuation formula above can be used to estimate
  the terminal value of all cash flows beyond.

48
Estimating Stable Growth Inputs

• Start with the fundamentals
• Profitability measures such as return on equity
  and capital, in stable growth, can be estimated
  by looking at
• industry averages for these measure, in which
  case we assume that this firm in stable growth
  will look like the average firm in the industry
• cost of equity and capital, in which case we
  assume that the firm will stop earning excess
  returns on its projects as a result of
  competition.
• Leverage is a tougher call. While industry
  averages can be used here as well, it depends
  upon how entrenched current management is and
  whether they are stubborn about their policy on
  leverage (If they are, use current leverage if
  they are not use industry averages)
• Use the relationship between growth and
  fundamentals to estimate payout and net capital
  expenditures.

49
Estimating Stable Period Net Cap Ex

• gEBIT (Net Capex Change in WC)/EBIT(1-t)
  ROC Reinvestment Rate ROC
• Therefore, Reinvestment Rate gEBIT / Return on
  Capital
• For instance, assume that Disney in stable growth
  will grow 5 and that its return on capital in
  stable growth will be 16. The reinvestment rate
  will then be
• Reinvestment Rate for Disney in Stable Growth
  5/16 31.25
• In other words,
• the net capital expenditures and working capital
  investment each year during the stable growth
  period will be 31.25 of after-tax operating
  income.

50
Relative Valuation

• In relative valuation, the value of an asset is
  derived from the pricing of 'comparable' assets,
  standardized using a common variable such as
  earnings, cashflows, book value or revenues.
  Examples include --
• Price/Earnings (P/E) ratios
• and variants (EBIT multiples, EBITDA multiples,
  Cash Flow multiples)
• Price/Book (P/BV) ratios
• and variants (Tobin's Q)
• Price/Sales ratios

51
Multiples and DCF Valuation

• Gordon Growth Model
• Dividing both sides by the earnings,
• Dividing both sides by the book value of equity,
• If the return on equity is written in terms of
  the retention ratio and the expected growth rate
• Dividing by the Sales per share,