Estimating the cost of Cost of Capital

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Estimating the cost of Cost of Capital

• Presented by Ken Lo

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Overview

• Introduction--The definition of WACC
• Formula for estimating the WACC
• Three related steps involving in developing WACC
• 1. Developing market value weights for the
  capital structure.
• 2. Estimating the opportunity cost of non-equity
  financing.
• 3.Estimating the opportunity cost of equity
  financing.

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Introduction

• The WACC is the discount rate, or time value of
  money used to convert expected future cash flow
  into present value for all investors
• Value of firm CF(1)/(1 wacc) CF(2)/(1wacc)2
  . CF(n)/(1wacc)n. ...
• The WACC must be consistent with the overall
  valuation approach and with the definition of
  cash flow to be discounted.

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The estimate of the cost of capital must

• i. comprise a weighted average of all the costs
  of sources of capital since the free cash flow
  represents cash available to all providers of
  capital
• ii. be computed after corporate taxes since FCF
  is after tax
• iii. use nominal rates of return because the FCF
  is expressed in nominal terms

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The estimate of the cost of capital must

• iv. adjust for the systematic risk borne by each
  provider of capital, since each expects a return
  that compensates for the risk taken
• v. employ market value weights for each financing
  element because market values reflect the true
  economic claim of each type of financing
  outstanding, whereas book values usually do not
• vi. be subject to change across the cash flow
  forecast period because of expected changes in
  inflation, systematic risk, or capital structure.

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Formula for estimating the WACC

• The general formula is as follows
• WACC kb(1-Tc)(B/V) kp(P/V) Ks(S/V)
• BPSV
• The cost of equity should reflect the riskiness
  of an equity investment in the company
• The cost of debt should reflect the default risk
  of the firm and the tax advantage
• The cost of preferred stock reflect the preferred
  dividend

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Step 1 Develop Target market Value

• A. The capital structure of the firm for which
  the WACC is being calculated is reflected in the
  market value weights attached to each source of
  financing.
• Target capital structure weights are used rather
  than actual weights for two reasons
• I. At any point in time the firms actual capital
  structure may not equal its ideal or target.
• II. Calculating the market value weights and the
  WACC involves circularity. WACC depends on market
  value weights the market value of the firm,v,
  depends on WACC

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Three approaches in developing target capital
structure weights

• I. Estimate, to extent possible, the current
  market value based capital structure of the firm
• II.Review the capital structure of comparable
  companies.
• III. Review managements explicit or implicit
  approach to financing the business and its
  implications for the target capital structure.

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Types of financing forms

• I. Debt-type financing
• II. Equity linked/hybrid financing including
  warrants and convertible securities.
• III. Minority interest-these represent claims by
  outside shareholders on a portion of a companys
  business.
• IV. Common equity

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Reviewing the capital structures of comparable
companies

• I. To determine if the firms financial structure
  is unusual
• II.If the firm is privately held, we may want to
  use comparable firms to determine the target
  proportion of equity.

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Step 2 Estimate the cost of non-equity financing

• A. Straight investment grade debt (not
  convertible into other securities, not callable
  and the risk of bankruptcy is low)
• Use DCF analysis to estimate the market rate of
  return
• PV ? CFt/(1 i)t FV / (1 i)t
• t1.N

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Estimate the cost of non-equity financing

• B. Below investment grade debt (ex Junk Bonds)--
  Use DCF model as above except the coupon payments
  and principal should be set equal to their
  expected values.
• The promised payments are higher than the
  expected payments since there is low default risk.

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Estimate the cost of non-equity financing-Example

• A three-year bond promises to pay a 10 percent
  coupon at the end of each year, plus a face value
  of 1,000 at the end of third year. The current
  market value of the bond is 951.96.
• Bo ? Coupon t Face
• t1 (1y) (1y)

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The solution is y 12
t
3
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Estimate the cost of non-equity financing-Example

• The solution is 12 , which is promised yield to
  maturity assumes that the debt is default-free.
• Suppose that there is 5 chance that the bond
  will default and pay only 400. If we were
  rewrite the formula, putting the bonds expected
  payments rather than its promised payments in the
  numerator. The market expected rate of return on
  the risky debt would be 11.9 .
• The rate of return that the market expects to
  earn is 91 basis points lower than the promised
  YTM.

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Estimate the cost of non-equity financing

• C. Subsidized debt (e.g. industrial revenue
  bonds)-the coupon rate on these bonds is below
  the market rate on similar taxable bonds because
  they are tax-free to investors.
• They should enter into the wacc at their current
  market YTM.
• D. Leases- since operating and financial leases
  are basically substitutes for other types of
  debt, their opportunity cost is the same as for
  the companys other long-term debt.

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Estimate the cost of non-equity financing

• E. Foreign currency denominated debt-- we must
  measure the cost of debt in terms of the local
  currency
• the all-in cost of borrowing in foreign currency
  will be close to the cost of borrowing in
  domestic markets due to the interest rate parity
  relationship enforced by the active arbitrage
  engaged in the cash, forward exchange, and
  currency swap markets.

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Estimate the cost of non-equity financing

• The interest-rate parity relationship (leaving
  minor transaction costs and temporary, small
  arbitrage opportunities aside) guarantees the
  following relationship
• 1 Kb (X0/ Xf) (1 r0)
• Kb The domestic pretax cost of N-year debt
• Xo The Spot foreign exchange rate
• Xf The N-year forward foreign exchange rate
• r0 The foreign interest rate on an N-year bond

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Estimate the cost of non-equity financing

• Suppose that the domestic borrowing rate is 7.25
  and that the the rate on a one-year loan
  denominated in Swiss francs is 4 . How would
  these rates compare? If the spot exchange rate is
  1.543 francs per dollar, and the one-year forward
  rate is 1.4977 francs per dollar, then the
  equivalent domestic one-year borrowing rate is
  7.15 percent for the Swiss franc loan.
• 1 Kb (1.543/1.4977) (10.04), Kb7.15

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Estimate the cost of non-equity financing

• F. Straight preferred stock
• Cost of preferred, kp div/P

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Step 3 Estimate the cost of equity financing

• A.Using the CAPM E(Rj) Ks RfE (Rm)-Rf)
  (beta)
• B. The Arbitrage Pricing model
• (I). Determining the risk-free rate-- the author
  recommend using the 10 year Treasury rate for
  several reasons
• (a). It is a long-term rate that usually comes
  close to matching the duration of the cash flow
  of the company being valued.
• (b). The ten-year rate approximates the duration
  of a stock market index or portfolio.
• (c). Ten-year rate has a smaller beta than
  thirty-year rate because it is less sensitive to
  unexpected changes in inflation.

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Determining the market risk premium

• The market risk premium is the difference between
  the expected rate of return on market portfolio
  and the risk free rate.
• The market risk premium is one of the most vexing
  issues in finance.
• It can be based on historical data, assuming the
  future will be like the past

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Geometric Versus arithmetic average

• An arithmetic average of rates of return is the
  simple average of the single period rates of
  return. The geometric average is the compound
  rate of return that equates the beginning and
  ending value.
• The difference between the both averages is that
  the former treats the observed historical path
  as the single best estimate of the future, the
  latter infers expected returns by assuming
  independence.

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Geometric Versus arithmetic average

• The arithmetic average is the best estimate of
  future expected returns because all possible
  paths are given equal weighting. The geometric
  return is the correct measure of historical
  performance, it is not forward looking.
• The arithmetic average depends on interval
  chosen, the geometric average, is the same
  regardless of the interval chosen.
• Ex. an average of monthly returns will be higher
  than an average of annual return.

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Geometric Versus arithmetic average

• Determining the market premium-- The authors
  recommend the use of a long-run geometric average
  of the market risk premium for the following
  arguments
• (a). The use of a very long time frame eliminates
  the effects of short-term anomalies in
  measurement.
• (b). A geometric average is used because the
  arithmetic averages are biased by the measurement
  period.
• (c.) the premium is calculated over long-term
  government bond returns to be consistent with the
  risk free rate we use to calculate the cost of
  equity.

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Estimating the systematic risk (beta)

• Betas can be calculated solely using historical
  stock and market return data
• Another alternative is to use published beta
  estimates.

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Estimating the Beta Coefficient

• If we know the securitys correlation with the
  market, its standard deviation, and the standard
  deviation of the market, we can use the
  definition of beta

• Generally, these quantities are not known.
• We therefore rely on their historical values to
  provide us with an estimate of beta.

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Estimating the Beta Coefficient
Using historical values , we can run the linear
regression to estimate the b
Once the regression line has been drawn, we can
estimate its intercept and slope, the a and b
values in Y abX. The intercept, a, is where the
line cuts the vertical axis. The slope
coefficient, b, can be estimated by the rise
over run method.
bj Rise ?Y Run ?X
This equation is called the Characteristic Line
of security j
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The Arbitrage Pricing Model
Let rj be asset js required rate of return. Let
rf be the riskless rate of return. For each
factor f (f 1, ..., K), let mf be the expected
return to factor f. Let bjf denote the asset
returns sensitivity to factor j.
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CAMP vs. APT

• Similarities
• Both breaking risk down into firm specific and
  market risk components.
• Contrast
• In the CAPM, an assets return depends on a
  single risk factor the market portfolios
  expected return.
• The CAPM assumes that the market risk is captured
  in the market portfolio, whereas APT sticks with
  fundamentals, allowing for multiple sources
  market wide risk such as changes in interest
  rates or inflation.
• In CAPM, b is the weighted average of the betas
  of the assets in the portfolio. However in APT,
  the expected returns should be linearly related
  to betas.