Firm Valuation: A Summary

P.V. Viswanath

Class Notes for Corporate Finance and Equity Valuation

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

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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.

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Equity Valuation

Assets Liabilities

Assets in Place Debt

EquityDiscount 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)

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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.

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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 ValueCFn.........

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

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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.

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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

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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

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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%.

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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 $8952 $1,124 $9433 $1,293 $9944 $1,487 $1,0475 $1,710 $43,049 $28,864Value of Boeing as a firm = $32,743

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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?

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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.

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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

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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.

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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%

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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

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

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

X

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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.

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Expected Growth in EBIT And Fundamentals

Reinvestment Rate and Return on CapitalgEBIT = (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.

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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 = CFt

(1+ r)tt = 1

t =

Value = CFt

(1 + r)t Terminal Value

(1 + r)Nt = 1

t = N

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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.

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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

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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,

P0 DPS1r gn

P0EPS0

PE = Payout Ratio * (1 gn )

r-gn

P 0BV 0

PBV = ROE - gn

r-gn

P0BV 0

PBV = ROE * Payout Ratio * (1 gn )

r-gn

P0Sales 0

PS = Profit Margin * Payout Ratio * (1 gn )

r-gn