Estimating the cost of Cost of Capital

Estimating the cost of Cost of Capital

Presented by Ken Lo

OverviewOverview

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.

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)/(1+wacc)^2 +…. CF(n)/(1+wacc)^n. ...

The WACC must be consistent with the overall valuation approach and with the definition of cash flow to be discounted.

The estimate of the cost of The estimate of the cost of capital must 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;

The estimate of the cost The estimate of the cost of capital mustof 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.

Formula for estimating the Formula for estimating the WACCWACC

The general formula is as follows:

WACC = kb(1-Tc)(B/V) + kp(P/V) + Ks(S/V)

B+P+S=VThe cost of equity should reflect the riskiness of an equity

investment in the companyThe cost of debt should reflect the default risk of the firm

and the tax advantageThe cost of preferred stock reflect the preferred dividend

Step 1: Develop Target Step 1: Develop Target market Valuemarket 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 firm’s 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

Three approaches in developing Three approaches in developing target capital structure weightstarget capital structure weightsI. Estimate, to extent possible, the current

market value based capital structure of the firmII.Review the capital structure of comparable

companies.III. Review management’s explicit or implicit

approach to financing the business and its implications for the target capital structure.

Types of financing formsTypes of financing forms

I. Debt-type financingII. Equity linked/hybrid financing including

warrants and convertible securities.III. Minority interest-these represent claims

by outside shareholders on a portion of a company’s business.

IV. Common equity

Reviewing the capital structures Reviewing the capital structures of comparable companiesof comparable companies

I. To determine if the firm’s 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.

Step 2: Estimate the cost of non-Step 2: Estimate the cost of non-equity financingequity 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]

t=1….N

Estimate the cost of non-Estimate the cost of non-equity financingequity 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.

Estimate the cost of non-Estimate the cost of non-equity financing-Exampleequity 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

t=1 (1+y) (1+y)t 3

3The solution is y= 12%

Estimate the cost of non-Estimate the cost of non-equity financing-Exampleequity 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 bond’s 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.

Estimate the cost of non-equity Estimate the cost of non-equity financingfinancing

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 company’s other long-term debt.


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.


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


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) (1+0.04), Kb=7.15%


F. Straight preferred stock

Cost of preferred, kp = div/P

Step 3: Estimate the cost of equity Step 3: Estimate the cost of equity financingfinancing A.Using the CAPM E(Rj) Ks= Rf+[E (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.

Determining the market risk Determining the market risk premiumpremium

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

Geometric Versus arithmetic averageGeometric 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.


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.


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.

Estimating the systematic risk Estimating the systematic risk (beta)(beta)

Betas can be calculated solely using historical stock and market return data

Another alternative is to use published beta estimates.

Estimating the Beta Estimating the Beta CoefficientCoefficient

Generally, these quantities are not known.

We therefore rely on their historical values to provide us with an estimate of beta.

If we know the security’s correlation with the market, its standard deviation, and the standard deviation of the market, we can use the definition of beta:

m

jmj

,

jm

j m j m

m

j m j

m

COV j M

( , ) , ,2 2

Estimating the Beta CoefficientEstimating the Beta CoefficientUsing historical values , we can run the linear regression to estimate the :

This equation is called the Characteristic Line of security j

Once the regression line has been drawn, we can estimate its intercept and slope, the a and b values in Y= a+bX. 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

The Arbitrage Pricing ModelThe Arbitrage Pricing Model

fKjK

fjfjfj

r

rrrr

2211

Let rj be asset j’s required rate of return.Let rf be the riskless rate of return.For each factor f (f = 1, ..., K), let f be the expected return to factor f.Let jf denote the asset returns’ sensitivity to factor j.

CAMP vs. APTCAMP vs. APTSimilarities: Both breaking risk down into firm specific and market risk components.

Contrast In the CAPM, an asset’s return depends on a single risk factor: the market

portfolio’s 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, 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.

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Estimating the cost of Cost of Capital