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Firm Valuation: A Summary . P.V. Viswanath Class Notes for Corporate Finance and Equity Valuation. Discounted Cashflow Valuation. where, n = life of the asset CF t = cashflow in period t r = discount rate reflecting the riskiness of the estimated cashflows.

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firm valuation a summary

Firm Valuation: A Summary

P.V. Viswanath

Class Notes for Corporate Finance and Equity Valuation

discounted cashflow valuation
Discounted Cashflow Valuation


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

P.V. Viswanath

two measures of discount rates
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

equity valuation
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)

P.V. Viswanath

firm valuation
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 firm’s cost of capital.

P.V. Viswanath

valuing the home depot s equity
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

terminal value and value of equity today
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

valuing boeing as a firm
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

expected cash flows and firm value
Expected Cash Flows and Firm Value
  • Terminal Value = $ 1710 (1.05)/(.0917-.05) = $ 43,049 million

P.V. Viswanath

what discount rate to use
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

the capital asset pricing model
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.

P.V. Viswanath

from cost of equity to cost of capital
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

estimating the cost of debt
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

estimating cost of capital boeing
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

expected growth in eps
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

expected growth in ebit and fundamentals
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

getting closure in valuation
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:

P.V. Viswanath

stable growth and terminal value
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

relative valuation
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

multiples and dcf valuation
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.V. Viswanath