Asset Valuation

P.V. Viswanath

Class Notes for EDHEC course on Mergers and Acquisitions

P.V. Viswanath 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

Value = CFt

(1+ r)tt =1

t = n

P.V. Viswanath 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.

P.V. Viswanath 4

Equity Valuation

Assets Liabilities

Assets in Place Debt

Equity

Discount rate reflects only the cost of raising equity financingGrowth Assets

Figure 5.5: Equity Valuation

Cash flows considered are cashflows from assets, after debt payments and after making reinvestments needed for future growth

Present value is value of just the equity claims on the firm

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

P.V. Viswanath 5

Firm Valuation

Assets Liabilities

Assets in Place Debt

Equity

Discount rate reflects the cost of raising both debt and equity financing, in proportion to their use

Growth Assets

Figure 5.6: Firm Valuation

Cash flows considered are cashflows from assets, prior to any debt paymentsbut after firm has reinvested to create growth assets

Present value is value of the entire firm, and reflects the value of all claims on the firm.

Free Cash Flow to the Firm = Earnings before Interest and Taxes (1-tax rate) – Net ReinvestmentNet 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 firm’s cost of capital.

P.V. Viswanath 6

Valuation with Infinite Life

Cash flowsFirm: Pre-debt cash flowEquity: After debt cash flows

Expected GrowthFirm: Growth in Operating EarningsEquity: Growth in Net Income/EPS

CF1 CF2 CF3 CF4 CF5

Forever

Firm is in stable growth:Grows at constant rateforever

Terminal Value

CFn.........

Discount RateFirm:Cost of Capital

Equity: Cost of Equity

ValueFirm: Value of Firm

Equity: Value of Equity

DISCOUNTED CASHFLOW VALUATION

Length of Period of High Growth

P.V. Viswanath 7

Valuing the Home Depot’s 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.

P.V. Viswanath 8

Estimating cash flows to equity: The Home Depot

Year Net I ncome Reinvestment Needs Net Debt Paid FCFE PV of FCFE

1 $ 1,856 $ 1,392 $ (139) $ 603 $ 549

2 $ 2,135 $ 1,601 $ (160) $ 694 $ 576

3 $ 2,455 $ 1,841 $ (184) $ 798 $ 603

4 $ 2,823 $ 2,117 $ (212) $ 917 $ 632

5 $ 3,246 $ 2,435 $ (243) $ 1,055 $ 662

6 $ 3,733 $ 2,800 $ (280) $ 1,213 $ 693

7 $ 4,293 $ 3,220 $ (322) $ 1,395 $ 726

8 $ 4,937 $ 3,703 $ (370) $ 1,605 $ 761

9 $ 5,678 $ 4,258 $ (426) $ 1,845 $ 797

10 $ 6,530 $ 4,897 $ (490) $ 2,122 $ 835

Sum of PV of FCFE = $6,833

P.V. Viswanath 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

P.V. Viswanath 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%.

P.V. Viswanath 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 = $32,743

P.V. Viswanath 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?

P.V. Viswanath 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 + (Risk Premium) Works as well as the next best alternative in most cases.

P.V. Viswanath 14

Inputs required to use the CAPM

According to the CAPM, the required rate of return on an asset will be:

Required ROR = Rf + (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.

P.V. Viswanath 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.

P.V. Viswanath 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

P.V. Viswanath 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.

P.V. Viswanath 18

Historical Average Premiums for the United States

Historical period Stocks - T.Bills Stocks - T.Bonds Arith Geom Arith Geom

1926-1999 9.41% 8.14% 7.64% 6.60%1962-1999 7.07% 6.46% 5.96% 5.74%1981-1999 13.24% 11.62% 16.08% 14.17%

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%

P.V. Viswanath 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.

P.V. Viswanath 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.

P.V. Viswanath 21

Choosing the Parameters: Boeing

Period used: 5 years Return Interval = Monthly Market Index: S&P 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 =(533.4-514.7+1.84)/ 514.7 = 3.99%

P.V. Viswanath 22

Boeing’s Historical Beta

Boeing versus S&P 500: 10/93-9/98

-20.00%

-15.00%

-10.00%

-5.00%

0.00%

5.00%

10.00%

-25.00% -20.00% -15.00% -10.00% -5.00% 0.00% 5.00% 10.00% 15.00% 20.00%

Returns on Boeing

Beta is slope of this line

Each point represents a monthof data.

Regressionline

Returns on S&P 500

P.V. Viswanath 23

The Regression Output

ReturnsBoeing = -0.09% + 0.96 ReturnsS & P 500

R squared=29.57% Intercept = -0.09% Slope = 0.96

P.V. Viswanath 24

Estimating Expected Returns: December 31, 1998

Boeing’s 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%

P.V. Viswanath 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.

P.V. Viswanath 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

P.V. Viswanath 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.

P.V. Viswanath 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

P.V. Viswanath 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 rateD = Market Value of DebtE = 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.

P.V. Viswanath 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

P.V. Viswanath 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.

P.V. Viswanath 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

P.V. Viswanath 33

Beta Estimation: Step 1

Calculate the unlevered betas for both firms

Boeing = 0.95/(1+0.65*(3980/32438)) = 0.88

McDonnell Douglas = 0.90/(1+0.65*(2143/12555)) = 0.81

Calculate the unlevered beta for the combined firmUnlevered Beta for combined firm

= 0.88 (36,418/51,116) + 0.81 (14,698/51,116)

= 0.86

P.V. Viswanath 34

Beta Estimation: Step 2

Boeing’s acquisition of McDonnell Douglas was accomplished by issuing new stock in Boeing to cover the value of McDonnell Douglas’s equity of $12,555 million. Debt = McDonnell Douglas Old Debt + Boeing’s Old Debt

= $3,980 + $2,143 = $6,123 millionEquity = Boeing’s Old Equity + New Equity used for Acquisition

= $ 32,438 + $ 12,555 = $44,993 millionD/E Ratio = $ 6,123/44,993 = 13.61%New Beta = 0.86 (1 + 0.65 (.1361)) = 0.94

P.V. Viswanath 35

The Home Depot’s Comparable Firms

Company Name Beta Market Cap $ (Mil) Debt Due 1-Yr Out Long-Term DebtBuilding Materials 1.05 $136 $1 $113Catalina Lighting 1 $16 $7 $19Cont'l Materials Corp 0.55 $32 $2 $7Eagle Hardware 0.95 $612 $6 $146Emco Limited 0.65 $187 $39 $119Fastenal Co. 1.25 $1,157 $16 $ - HomeBase Inc. 1.1 $227 $116Hughes Supply 1 $610 $1 $335Lowe's Cos. 1.2 $12,554 $111 $1,046Waxman Industries 1.25 $18 $6 $121Westburne Inc. 0.65 $607 $9 $34Wolohan Lumber 0.55 $76 $2 $20

Sum $16,232 $200 $2,076Average 0.93

P.V. Viswanath 36

Estimating The Home Depot’s Bottom-up Beta

Average Beta of comparable firms = 0.93 D/E ratio of comparable firms =

(200+2076)/16,232 = 14.01% Unlevered Beta for comparable firms =

0.93/(1+(1-.35)(.1401)) = 0.86 If the Home Depot’s D/E ratio is 20%, our bottom-

up estimate of Home Depot’s beta is 0.86[1+(1-.35)(.2)] = 0.9718

P.V. Viswanath 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

P.V. Viswanath 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.

P.V. Viswanath 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.

P.V. Viswanath 40

Interest Coverage Ratios, Ratings and Default Spreads

Interest Coverage Ratio Rating Default Spread> 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%

< 0.65 D 10.00%

P.V. Viswanath 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 = 453

(1 1

(1.055)13.76

.055

6, 972

(1.055)13.76 $7, 631

P.V. Viswanath 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/(Debt+Equity ) = 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%

P.V. Viswanath 43

Estimating the Expected Growth Rate

Expected Growth

Net Income Operating Income

Retention Ratio=1 - Dividends/Net Income

Return on EquityNet Income/Book Value of Equity

X

Reinvestment Rate = (Net Cap Ex + Chg in WC/EBIT(1-t)

Return on Capital =EBIT(1-t)/Book Value of Capital

X

P.V. Viswanath 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.

P.V. Viswanath 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.

P.V. Viswanath 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:

Value = CF

t

(1+ r)tt = 1

t =

Value = CFt

(1 + r)t

Terminal Value

(1 + r)N

t = 1

t = N

P.V. Viswanath 47

Stable Growth and Terminal Value

When a firm’s 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.

P.V. Viswanath 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.

P.V. Viswanath 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.

P.V. Viswanath 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

P.V. Viswanath 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,

P 0 DPS1

r gn

P0

EPS0PE =

Payout Ratio * (1 gn )

r-gn

P 0

BV0PBV =

ROE - gn

r-gn

P 0

BV0PBV =

ROE * Payout Ratio * (1 gn )

r-gn

P 0

Sales 0PS =

Profit Margin * Payout Ratio * (1 gn )

r-gn