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Chapter 3: WACC
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Weighted Average Cost of Capital, WACC
Risk-adjusted discount rate for the firm’s free cash flows (FCF)
Average cost of funds for the company
rE is the return expected by shareholders
rD is the return expected by bondholders
TC is firm’s tax rate—cost of debt is a tax-deductible expense
Determination requires a good deal of judgement
Mid-year discounting
Mid-year discounting – assumes that FCFs occur on average in the middle of the year
Enterprise Value formula:
Five Problems in WACC determination
Determine market value of equity, E
Determine market value of debt, D
Determine corporate tax rate, TC
Find cost of debt, rD
Find cost of equity, rE
Increasing
difficulty
Finding market value of equity, E
In Finance, “cost” often means “rate of return” i.e rate of return expected by a firm’s shareholders
Other names for cost of equity
Required rate of equity return
Expected rate of equity return (used in CAPM)
Opportunity cost
Discount rate for equity cash flows
Market value of equity, E = No. of shares * Market price per share
Finding market value of debt, D
Market price of firm’s debts
However, almost always replaced by book value of firm’s debts
Some reasons why:
Most firms have many kinds of debt
Much debt (most?) is not listed on a market
Difficult to value debt
Maybe it doesn’t matter much!
For WACC, Debt = net debt = Debt – cash & marketable securities
Exception: where cash needed for production; banks and financial companies
Finding market value of debt, D
Should be marginal tax rate paid on additional $ of Profit before Taxes
In practice, TC often estimated by average historic tax rate
TC sometimes estimated by ballpark figure
Finding tax rate, TC
rD should be the marginal borrowing cost of the firm, but hard to determine!
Plausible alternatives:
rD = current interest payments ÷ Average debt (most common)
rD imputed from rating-adjusted yield curve
rD = expected return on firm’s bonds (complicated! See Chapter 23)
Finding cost of debt, rD
Finding the cost of debt, rD
Finding the cost of debt, rD
Finding the cost of debt, rD
Two leading models
Gordon dividend model: rE derived from shareholder anticipations of future dividends
CAPM/SML: rE derived from firm’s equity beta
Gordon model:
Finding the cost of equity, rE
Finding the cost of equity, rE
Finding the cost of equity, rE
Note hidden rows
Implementation issues: growth rate differ based on period used
Finding the cost of equity, rE
Choice of period: 5 years’ or 10 years’ growth rate?
Finding the cost of equity, rE
Gordon derivation:
Variation on Gordon model: use all equity payouts instead of dividends, essentially dividends + repurchases
Finding the cost of equity, rE
Finding the cost of equity, rE
Cash flow to equity is necessary for Gordon model
Dividends are much less important
“Apart from those firms that continue to pay dividends and make regular repurchases, dividend payers are no longer economically important.”
“Over the period from 1980 to 2005, firms that only pay dividends decline from 13% to 7% of firms and from 8% to 2% of all payouts.”
Repurchases are taking over
Finding the cost of equity, rE
Source: Skinner, ., “The Evolving Relation Between Earnings, Dividends, and Stock Repurchases”. Journal of Financial Economics, Forthcoming . Available at SSRN: http://ssrn.com/abstract=1027059
Source: Skinner, ., “The Evolving Relation Between Earnings, Dividends, and Stock Repurchases”. Journal of Financial Economics, Forthcoming . Available at SSRN: http://ssrn.com/abstract=1027059
Finding the cost of equity, rE
Finding the cost of equity, rE
Variation on Gordon model: two dividend growth rates
High dividend growth rate (typically in coming years)
Lower dividend growth rate (long-term)
rE is IRR of future anticipated dividends wrt to current stock price
Use of historical average 28.28% leads to very high cost of equity!
Implausibly high / sustainable growth rates?
Finding the cost of equity, rE
Given two growth rates g1 and g2, find rE to make P0 equal to last line.
rE has to make these two equal
Finding the cost of equity, rE – Two stage Gordon model
TwoStageGordon is a VBA function on the Excel file accompanying this chapter (details on next slide)
Finding the cost of equity, rE – Two stage Gordon model
Function TwoStageGordon(P0, Div0, Highgrowth, Highgrowthyrs, Normalgrowth)
Do While (High – Low) > 0.0000001
Estimate = (High + Low) / 2
factor = (1 + Highgrowth) / (1 + Estimate)
Term1 = Div0 * factor * (1 – factor ^ Highgrowthyrs) / _
(1 – factor)
Term2 = Div0 * factor ^ Highgrowthyrs * _
(1 + Normalgrowth) / (Estimate – Normalgrowth)
If (Term1 + Term2) > P0 Then
Low = (High + Low) / 2
Else: High = (High + Low) / 2
TwoStageGordon = Estimate
End Function
See Chapter 0 for how to add this function to your spreadsheet.
Or: Read Chapter 36 in Financial Modeling.
Variation on Gordon: Use P/E
We will use this model as one way to determine
E(rM) for the CAPM
CAPM – Classic &Tax-adjusted
CAPM issues
rf : short-term or long-term
Short-term
Historical average of market returns
Forward-looking using (rM) P/E formula
Incorporating taxes into SML
Why rf short-term?
SML should apply to all risky assets
This includes bonds
This means that rf has to be short-term (otherwise, non-risky short-term bond would have long-term interest rate)
Another way of saying this: The b incorporates the time risk of the asset
Measuring E(rM): Historical average
Variation on historical approach:
Estimating E(rM) – rf directly
Market risk premium of 4.40% estimated from previous slide
Measuring E(rM): /E model
Application to Companies
Whole Foods
Caterpillar
rfirm’scostofequity
rfirm’scostofdebt
Tfirmscorporatetaxrate
EnterprisevaluePVFutureFCFsdiscountedWAC
Can be computed with
Excel’s NPV formula
EnterprisevaluePVFutureFCFsdiscountedWAC
Cash 825,000188,000
Marketable securities 00
Short-term and current
portion of long-term debt
588,0001,315,000
Long-term debt 7,304,0006,850,000
Net debt 7,067,0007,977,000<-- =SUM(C6:C7)-SUM(C3:C4)
KROGER, COMPUTING NET DEBT
(thousand $)
Cash 5,4985,065
Marketable securities 16,3879,772
Short-term debt and
current portion of long-
Long-term debt 2,0777,084
Net debt -19,770-7,506
<-- =SUM(C6:C7)-SUM(C3:C4)
Cash 218,798303,960
Marketable securities 329,738442,320
Short-term debt and
current portion of long-
Long-term debt 508,28817,439
Net debt -39,838-728,375
<-- =SUM(C15:C16)-SUM(C12:C13)
INTEL HAS NEGATIVE NET DEBT
(million $)
WHOLE FOODS HAS NEGATIVE NET DEBT
(thousand $)
200920102011
Income before tax 250,942411,781551,712
Income tax expense 104,138165,948209,100
Tax rate, T
41.50%40.30%37.90%
<-- =D4/D3
WHOLE FOODS MARKET TAX RATE
200920102011
Income before taxes15,290,0001,653,0007,334,000
Income tax expense2,268,000671,000942,000
Tax rate, T
14.83%40.59%12.84%
<-- =J4/J3
MERCK TAX RATE
200920102011
Cash 9,311,00010,900,00013,531,000
Short-term investments 293,0001,301,0001,441,000
Total liquid assets 9,604,00012,201,00014,972,000<-- =D4+D3
Short-term debt and current
portion of long-term debt
1,379,0002,400,0001,990,000
Long-term debt 16,095,00015,482,00015,525,000
Total financial debt 17,474,00017,882,00017,515,000<-- =D7+D8
Net debt 7,870,0005,681,0002,543,000<-- =D9-D5
Interest income 210,00083,000199,000
Interest expense 460,000715,000749,000
Net interest 250,000632,000550,000<-- =D13-D12
Implied cost of debt, r
9.33%13.38%<-- =D14/AVERAGE(C11:D11)
Interest rate earned 0.76%1.46%<-- =D12/AVERAGE(SUM(D3:D4),SUM(C3:C4))
Interest rate paid 4.04%4.23%<-- =D13/AVERAGE(SUM(D7:D8),SUM(C7:C8))
MERCK, COST OF DEBT r
200920102011
Cash 1,218,000578,000408,000
Short-term investments 000
Short-term debt and current
portion of long-term debt
19,000216,000400,000
Long-term debt 3,345,0003,517,0003,828,000
Net debt 2,146,0003,155,0003,820,000<-- =SUM(D6:D7)-SUM(D3:D4)
Interest 190,000195,000159,000
Implied cost of debt, r
7.36%4.56%
<-- =D10/AVERAGE(C9:D9)
UNITED STATES STEEL, COST OF DEBT
Divcurrentfirmdividend
ganticipatedfuturedividendgrowth
Pcurrentfirmshareprice
Current share price, P
Current dividend, D
Anticipated dividend growth rate
Gordon model cost of equity, r
<-- =B3*(1+B4)/B2+B4
THE GORDON MODEL COST OF EQUITY
4-Sep-020.36
4-Dec-020.36Quarterly growth0.39%<-- =(B43/B3)^(1/40)-1
5-Mar-030.36Annual growth1.55%<-- =(1+E4)^4-1
4-Jun-030.36
20-Aug-032.88
3-Sep-030.37Quarterly growth0.50%<-- =(B43/B23)^(1/20)-1
3-Dec-030.37Annual growth2.02%<-- =(1+E8)^4-1
3-Mar-040.37
2-Jun-040.37
1-Sep-040.38
13-Sep-110.38
13-Dec-110.42
13-Mar-120.42
13-Jun-120.42
Dividend growth
Whole period
Last 5 years
MERCK DIVIDEND HISTORY
Merck stock price P
, 29 June 2012
Current dividend
Quarterly 0.42
Annualized dividend, Div
1.68<-- =4*B4
Dividend growth rate, g
Last 5 years 1.55%
Last 10 years 2.02%
Gordon model cost of equity, r
Using last 5 years' growth 5.64%<-- =$B$5/$B$2*(1+B7)+B7
Using last 10 years' growth 6.13%<-- =$B$5/$B$2*(1+B8)+B8
COMPUTING MERCK'S r
WITH THE GORDON MODEL
DivgDivgDivgDivg
TakePandsolveforr
Cashflowtoequityg
Marketvalueofequity
repurchases
from stock
29-Jun-053,3071,4308993,838<-- =B3+C3-D3
30-Jun-053,2792,7251025,901
1-Jul-053,21501863,029
2-Jul-054,7341,5933635,964
3-Jul-054,8181,9213216,418
Growth 13.71%<-- =(E7/E3)^(1/4)-1
Computing the Gordon model cost of equity r
based on total equity payouts
Shares outstanding
Price per share 41.75
Market value of equity 126,955<-- =B12*B13, $ million
Gordon model cost of
19.46%<-- =E7*(1+B9)/B14+B9
GORDON MODEL FOR MERCK'S EQUITY PAYOUTS
stock issued
repurchased
Total equity
16,462,000
150,730,000
135,483,000
<-- =D3+C3-B3
29,717,000
170,756,000
31,197,000
172,236,000
<-- =D4+C4-B4
24,961,000
191,488,000
98,804,000
265,331,000
25,339,000
210,503,000
52,908,000
238,072,000
24,115,000
235,495,000
65,032,000
276,412,000
25,826,000
254,458,000
376,716,000
605,348,000
59,281,000
327,303,000
532,682,000
800,704,000
80,375,000
381,798,000
531,122,000
832,545,000
59,478,000
418,447,000
634,623,000
993,592,000
Compound growth rate
<-- =(E11/E3)^(1/8)-1
End 1999 stock price
Number of shares
outstanding, end 1999
202,795,000
Future dividend growth, g?
End 1999 equity value, P
13,790,060,000
<-- =B16*B17
Projected next total
equity cash flow, D
1,274,598,774
<-- =E11*(1+B18)
Gordon model cost
of equity, r
<-- =B20/B19+B18
WACHOVIA BANK--DIVIDENDS, STOCK ISSUED AND STOCK REPURCHASED
Does historical growth overstate the cost of equity?
Cost of capital using the
Using total equity payout and total equity value
PV of m yearsPV of remaining
of high-growth gnormal-growthg
dividendsdividends
144424443144424443
End-1999 equity value, P
13,790,060,000
End 1999 total equity payout
993,592,000
High growth rate, g
Number of high-growth years, m
Normal growth rate, g
Cost of equity, r
using the function
twostagegordon
<-- =twostagegordon(B2,B3,B5,B6,B7)
WACHOVIA, 2-STAGE GORDON MODEL
adividendpayoutratio
PEPSisfirmspriceearningsratio
Merck beta,
Risk-free rate, r
Expected market return, E(r
Merck cost of equity, r
5.86%<-- =B3+B2*(B4-B3)
COMPUTING THE COST OF EQUITY FOR MERCK
Classic CAPM: r
Merck beta,
Merck tax rate, T
12.84%<-- ='Page 76'!D5
Risk-free rate, r
Expected market return, E(r
Merck tax-adjusted cost of equity, r
6.06%<-- =B4*(1-B3)+B2*(B5-B4*(1-B3))
COMPUTING THE COST OF EQUITY FOR MERCK
Tax-adjusted CAPM: r
Alpha -0.0029<-- =INTERCEPT(E13:E72,F13:F72)
Using Excel's
2.2516<-- =SLOPE(E13:E72,F13:F72)
Using Cov/Var 2.2516<-- =COVAR(E13:E72,F13:F72)/VARP(F13:F72)
R-squared 0.5304<-- =RSQ(E13:E72,F13:F72)
t-statistic for alpha -0.2438<-- =tintercept(E13:E72,F13:F72)
t-statistic for beta 8.0942<-- =tslope(E13:E72,F13:F72)
DateIntelSP500IntelSP500
9-Jan-01 35.381366.01
1-Feb-01 27.321239.94-25.85%-9.68%<-- =LN(C13/C12)
1-Mar-01 25.171160.33-8.20%-6.64%<-- =LN(C14/C13)
2-Apr-01 29.571249.4616.11%7.40%<-- =LN(C15/C14)
1-May-01 25.861255.82-13.41%0.51%
1-Jun-01 281224.387.95%-2.54%
2-Jul-01 28.541211.231.91%-1.08%
1-Aug-01 26.781133.58-6.37%-6.63%
4-Sep-01 19.581040.94-31.31%-8.53%
1-Oct-01 23.391059.7817.78%1.79%
1-Nov-01 31.311139.4529.16%7.25%
3-Dec-01 30.151148.08-3.78%0.75%
2-Jan-02 33.591130.210.80%-1.57%
1-Feb-02 27.381106.73-20.44%-2.10%
1-Mar-02 29.171147.396.33%3.61%
1-Apr-02 27.441076.92-6.11%-6.34%
1-May-02 26.511067.14-3.45%-0.91%
3-Jun-02 17.54989.82-41.30%-7.52%
1-Jul-02 18.04911.622.81%-8.23%
1-Aug-02 16.02916.07-11.88%0.49%
3-Sep-02 13.35815.28-18.23%-11.66%
1-Oct-02 16.62885.7621.91%8.29%
1-Nov-02 20.09936.3118.96%5.55%
2-Dec-02 14.98879.82-29.35%-6.22%
ReturnsPrices
COMPUTING THE BETA FOR INTEL
monthly returns for Intel and S&P 500, 2001-2006
y = 2.2516x -0.0029R
-45%-35%-25%-15%-5%5%15%25%-13%-11%-9%-7%-5%-3%-1%1%3%5%7%Intel returnsSP500 returns
Intel Returns vs SP500, 2001 -2006
BondfBondMf
Average monthly return 0.69%<-- =AVERAGE(C10:C311)
Monthly standard deviation
<-- =STDEV(C10:C311)
Annualized return
<-- =12*B2
Annualized standard deviation
<-- =SQRT(12)*B3
DatePriceReturn
1-Apr-8715.66
1-May-8715.821.02%
<-- =LN(B10/B9)
1-Jun-8716.624.93%
<-- =LN(B11/B10)
1-Jul-8717.444.82%
<-- =LN(B12/B11)
3-Aug-8718.113.77%
<-- =LN(B13/B12)
1-Dec-10113.116.46%
3-Jan-11115.772.32%
1-Feb-11119.733.36%
1-Mar-11119.760.03%
1-Apr-11123.292.90%
2-May-11121.88-1.15%
1-Jun-11119.84-1.69%
1-Jul-11117.39-2.07%
1-Aug-11110.99-5.61%
1-Sep-11103.16-7.32%
3-Oct-11114.4210.36%
1-Nov-11114.15-0.24%
1-Dec-11115.321.02%
3-Jan-12120.474.37%
1-Feb-12125.664.22%
1-Mar-12129.783.23%
2-Apr-12128.95-0.64%
1-May-12121.19-6.21%
1-Jun-12125.553.53%
MEASURING E(r
) USING HISTORICAL DATA
erived from prices for the Vanguard 500 Index Fund (symbol: VFINX)
These prices include dividends; April 1987 - June 2012
Average monthly risk premium 0.37%<-- =AVERAGE(E10:E311)
Monthly standard deviation 4.58%<-- =STDEV(E10:E311)
Annualized risk premium 4.40%<-- =12*B2
Annualized standard deviation 15.85%<-- =SQRT(12)*B3
DatePriceReturn
1-Apr-87 15.66
1-May-87 15.821.02%0.48%0.53%
<-- =C10-D10
1-Jun-87 16.624.93%0.49%4.45%
<-- =C11-D11
1-Jul-87 17.444.82%0.49%4.33%
3-Aug-87 18.113.77%0.49%3.28%
1-Feb-11 119.733.36%0.01%3.35%
1-Mar-11 119.760.03%0.01%0.01%
1-Apr-11123.292.90%0.01%2.90%
MEASURING THE MARKET RISK PREMIUM E(r
USING HISTORICAL DATA
Vanguard 500 Index Fund (symbol: VFINX) minus Treasury Bills
April 1987 - June 2012
All measurements relate to monthly returns on SP500, r
, and the Treasury bill rate r
Methodological note: I have used the St. RED data for 3-month Treasury Bills; this data is annualized, and I have divided it by 12 to get the monthly returns. Since the data can be taken as an ex-ante return, the April 1987 rate is attributed to May 1987.I've used 3-month instead of 1-month, because there are lots of data problems with the latter.
Merck beta,
0.6435<-- ='Page 96'!B2
) derived from SP price/earnings
4.40%<-- ='Page 100'!B5
Merck tax rate, T
12.84%<-- ='Page 98'!B3
Risk free rate, r
2.00%<-- Still to be discussed
Intel cost of equity, r
Classic CAPM 4.83%<-- =B5+B2*B3
Tax-adjusted CAPM 4.74%<-- =B5*(1-B4)+B2*(B3+B4*B5)
COMPUTING THE COST OF EQUITY FOR MERCK USING THE
MARKET RISK PREMIUM E(r
: The tax-adjusted model in cell B8 uses the equivalence:
For the low levels of taxes and low r
in this example, there is virtually no difference between
the two approaches.
Market price/earnings multiple, June 2012
Equity cash flow payout ratio
<-- Approx. U.S.: Dividends + repurchases
Anticipated growth of market equity cash flow
<-- Analyst's estimate
Expected market return, E(r
<-- =B3*(1+B4)/B2+B4
COMPUTING E(r
) USING MARKET MULTIPLE
Shares outstanding 3.04<-- Billions
Share price, 29 June 2012 41.75
Equity value, E 126.92<-- =B2*B3
Net debt, D 2.59<-- Billions
Tax rate, T
12.84%<-- ='Page 98'!B3
Cost of debt, r
4.23%<-- 0.0423
Expected market return, E(r
8.45%<-- ='Page 102'!B5
Risk-free rate, r
Equity beta,
0.6435<-- ='Pages 91,93'!B3
WACC based on Gordon per-share dividends
Current dividend/share 1.68<-- =4*'Page 84, bottom'!B43
Growth rate 2.02%<-- ='Page 84, bottom'!E9
Cost of equity, r
6.13%<-- =B13*(1+B14)/B3+B14
WACC 6.08%<-- =B15*$B$4/($B$4+$B$5)+$B$7*(1-$B$6)*$B$5/($B$4+$B$5)
WACC based on Gordon equity payouts
Current equity payout 6,418<-- ='Page 86'!E7
Growth rate 13.71%<-- ='Page 86'!B9
Cost of equity, r
11.20%<-- ='Page 88, bottom'!B20
WACC 11.05%<
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