A look at the actual cost of capital of US firms

Figures & data

Figure 1. Cost of capital perspective.

Table 1. Variable definitions

Variable	Name	Definition
WACC weights
Val	Whole firm value	$(\text{AT}-\text{SEQ})+(|\text{prc}|\times \text{csho})-\text{TXDB}$. AT is total assets, SEQ is shareholder’s equity including preferred equity, prc is the closing price, csho is the number of common shares outstanding, and TXDB is deferred taxes
Lev	Leverage	$(\text{DLTT}+\text{DLC})/\text{Val}$. DLTT is total long-term debt and DLC is the debt in current liabilities. Lev is also known as the weight of debt in the capital structure. Thus, the weight of equity in the capital structure is $1-\text{Lev}$
Cost of debt
$\mathit{\tau }$	Tax rate	$\text{TXT}/\text{PI}$. TXT is total income taxes and PI is pretax income. Following Gupta and Newberry (1997) and Brown (2011), $\mathit{\tau }$ is set to zero if $\text{TXT}/\text{PI}<0$ and one if $\text{TXT}/\text{PI}>1$
$R_{}\text{debt}$	Before-tax cost of debt	$\text{XINT}/\left(\text{DLTT}+\text{DLC}\right)$. XINT is the interest and related expense for the year
Cost of equity
Repur	Repurchase of common	$\text{PRSTKC}-\text{if}\left(\mathrm{\Delta }\text{PSTKRV}>0,0,-\mathrm{\Delta }\text{PSTKRV}\right)$. PRSTKC is the total amount of common and preferred stock repurchased, and $\mathrm{\Delta }\text{PSTKRV}$ is the change in preferred stock redemption value from the previous year
$R_{}\text{firm}$	Firm cost of equity	$\left(\text{DVC}+\text{Repur}+\left({\text{RE}}_t-{\text{RE}}_{t-1}\right)\right)/\text{Equity}$. DVC is common dividends, RE is retained earnings, and the value of equity Equity is $\text{Val}-(\text{DLTT}+\text{DLC})$
$R_{\text{capm}}$	CAPM cost of equity	$R_f+\mathit{\beta }{E}_t[\text{MRP}]$. $R_f$ is the one-month Treasury Bill, $\mathit{\beta }$ is computed from calendar year daily return data by regressing excess firm returns onto value-weighted market returns in excess of the one-month Treasury Bill rate, and $E_t[\text{MRP}]$ is the average of market excess returns from the beginning of the sample to time t
$R_{}\text{mkt}$	Market cost of equity	ret. ret is the CRSP daily return including dividends

Notes: Accounting data obtained from S&P Compustat, daily stock return data from the Center for Research in Security Prices (CRSP), and daily market risk premium and risk-free rate data from the Kenneth E. French website. All variables are winsorized at the 1% tails annually. Compustat data items in the definition column are UPPERCASE, CRSP data items are lower case, and measures derived in this study are Capitalized.

Table 2. Exclusions and rationale

#	Exclusion	Rationale	Reference
(1)	Financial firms (GICS sector 40) and utilities (GICS sector 55)	Reduce the impact of highly regulated firms and balance sheet peculiarities of financial firms	Frank and Shen (2016), Kayhan and Titman (2007)
(2)	Firms incorporated outside of the US	Ensure dollar-denominated financial statements and to focus on US firms	Brown (2011, Frank and Shen (2016)
(3)	Firms with negative average operating income before depreciation	Eliminate firms that are possibly not a going-concern	Frank and Shen (2016)
(4)	Firm-year observations missing data necessary to compute repurchases	Specifically, common dividends, common and preferred stock purchases, and preferred stock redemption value	Grullon and Michaely (2002)
(5)	Firm-year observations missing retained earnings	Complete the firm cost of equity computation in Equation (6)	This study

Table 3. Descriptive statistics

	Lev	$R_{}\text{debt}$	$\mathit{\tau }$	$R_{}\text{firm}$	$R_{\text{capm}}$	$R_{}\text{mkt}$	${\text{Wacc}}_{}\text{firm}$	${\text{Wacc}}_{\text{capm}}$	${\text{Wacc}}_{}\text{mkt}$
Mean	0.1971	0.0967	0.3202	0.0695	0.1103	0.1707	0.0656	0.1008	0.1693
SD	0.1838	0.1628	0.1891	0.0542	0.0517	0.6204	0.0441	0.0455	0.5255
25%	0.0357	0.0449	0.2290	0.0347	0.0740	$-$0.2000	0.0376	0.0692	$-$0.1269
50%	0.1526	0.0769	0.3609	0.0573	0.1039	0.0744	0.0569	0.0939	0.0713
75%	0.3101	0.1069	0.4187	0.0885	0.1409	0.3913	0.0817	0.1257	0.3292

Notes: Mean, standard deviation (SD), and 25/50/75% quartiles for major variables in this study. There are a total of 101,817 firm-year observations and 8,112 firms over the 1972 to 2015 time frame. Leverage Lev is $\left(\text{DLTT}+\text{DLC}\right)/\text{Val}$ where the whole-firm value Val is $\left(\text{AT}-\text{SEQ}\right)+\left(\left|PRC\right|\times \text{CSHO}\right)-\text{TXDB}$. The before tax cost of debt $R_{}\text{debt}$ is $\text{XINT}/\text{Debt}$ where the value of debt Debt is $\text{DLTT}+\text{DLC}$. The tax rate $\mathit{\tau }$ is $\text{TXT}/\text{PI}$ and is set to zero if $\text{TXT}/\text{PI}<0$ and one if $\text{TXT}/\text{PI}>1$. The firm cost of equity $R_{}\text{firm}$ is $\left(\text{DVC}+\text{Repur}+\left({\text{RE}}_t-{\text{RE}}_{t-1}\right)\right)/\text{Equity}$ where the common stock repurchase measure Repur is $\text{PRSTKC}-\text{if}\left(\mathrm{\Delta }\text{PSTKRV}>0,0,-\mathrm{\Delta }\text{PSTKRV}\right)$ and the value of equity Equity is $\text{Val}-\text{Debt}$. The CAPM-based cost of equity $R_{\text{capm}}$ is $R_f+\mathit{\beta }{E}_t[\text{MRP}]$ where $R_f$ is the one-month Treasury Bill, $\mathit{\beta }$ is computed from calendar year daily return data by regressing excess firm returns onto value-weighted market returns in excess of the one-month Treasury Bill rate, and $E_t[\text{MRP}]$ is the average of market excess returns from the beginning of the sample to time t. The market cost of equity $R_{}\text{mkt}$ is the CRSP return ret. ${\text{Wacc}}_x=\text{Lev}{R}_{}\text{debt}\left(1-\mathit{\tau }\right)+\left(1-\text{Lev}\right)R_x,x=\left\{\text{firm},\text{capm},\text{mkt}\right\}$. Compustat data items are UPPERCASE, CRSP data items are lower case, and measures derived in this study are Capitalized.

Table 4. Cross section summary statistics

	All	Discret	Staples	Energy	Health	Indust	Infotech	Materi	Telecom
N	8,112	2,186	470	530	903	1,729	1,628	522	144
Leverage Lev
mean	0.1856	0.2473	0.1521	0.1796	0.0958	0.2412	0.0873	0.2234	0.2829
SD	0.0315	0.0490	0.0285	0.0484	0.0294	0.0407	0.0369	0.0365	0.0981
25%	0.1581	0.2148	0.1316	0.1398	0.0709	0.2136	0.0646	0.1931	0.2211
50%	0.1881	0.2497	0.1561	0.1820	0.0944	0.2325	0.0819	0.2248	0.2561
75%	0.2060	0.2806	0.1701	0.2070	0.1241	0.2747	0.0985	0.2519	0.3180
Before-tax cost of debt $R_{}\text{debt}$
mean	0.0821	0.0862	0.0781	0.0849	0.0793	0.0812	0.0881	0.0824	0.0730
SD	0.0240	0.0249	0.0261	0.0250	0.0271	0.0290	0.0387	0.0198	0.0171
25%	0.0660	0.0681	0.0547	0.0708	0.0628	0.0590	0.0656	0.0690	0.0619
50%	0.0783	0.0808	0.0774	0.0810	0.0775	0.0716	0.0919	0.0778	0.0688
75%	0.1007	0.1043	0.0976	0.0984	0.0960	0.0968	0.1041	0.0994	0.0848
Tax rate $\mathit{\tau }$
mean	0.3530	0.3538	0.3738	0.4163	0.3112	0.3367	0.3424	0.3346	0.3416
SD	0.0562	0.0454	0.0565	0.0722	0.0564	0.0588	0.0793	0.0447	0.0793
25%	0.2971	0.3211	0.3201	0.3653	0.2614	0.2912	0.2730	0.2962	0.2866
50%	0.3495	0.3539	0.3772	0.3857	0.3027	0.3391	0.3386	0.3379	0.3482
75%	0.3967	0.3820	0.4184	0.4583	0.3564	0.3880	0.3971	0.3656	0.4082
Firm cost of equity $R_{}\text{firm}$
mean	0.0642	0.0661	0.0628	0.0759	0.0563	0.0615	0.0573	0.0672	0.0629
SD	0.0150	0.0156	0.0145	0.0232	0.0141	0.0147	0.0163	0.0228	0.0243
25%	0.0514	0.0573	0.0506	0.0554	0.0457	0.0499	0.0436	0.0506	0.0433
50%	0.0643	0.0651	0.0624	0.0767	0.0603	0.0597	0.0588	0.0607	0.0650
75%	0.0736	0.0752	0.0733	0.0934	0.0669	0.0735	0.0709	0.0843	0.0806
CAPM cost of equity $R_{\text{capm}}$
mean	0.1279	0.1315	0.1112	0.1217	0.1225	0.1293	0.1478	0.1274	0.1110
SD	0.0390	0.0355	0.0450	0.0453	0.0445	0.0371	0.0442	0.0356	0.0415
25%	0.1010	0.1055	0.0644	0.0851	0.0771	0.0968	0.1214	0.0995	0.0845
50%	0.1291	0.1300	0.1133	0.1208	0.1277	0.1289	0.1504	0.1248	0.1118
75%	0.1545	0.1587	0.1448	0.1396	0.1612	0.1586	0.1718	0.1481	0.1305
Market cost of equity $R_{}\text{mkt}$
mean	0.1313	0.1353	0.1437	0.1380	0.1392	0.1386	0.1256	0.1215	0.1379
SD	0.1826	0.2577	0.1706	0.2168	0.2011	0.2042	0.2632	0.2114	0.2214
25%	0.0153	-0.0191	0.0522	0.0189	0.0204	0.0062	$-$0.0316	$-$0.0245	0.0153
50%	0.1548	0.1302	0.1371	0.1804	0.1151	0.1580	0.1196	0.1364	0.1446
75%	0.2741	0.3072	0.2263	0.2707	0.2613	0.2886	0.2699	0.2477	0.2313
Firm WACC ${\text{Wacc}}_{}\text{firm}$
mean	0.0609	0.0630	0.0596	0.0717	0.0548	0.0582	0.0563	0.0635	0.0563
SD	0.0130	0.0127	0.0130	0.0199	0.0132	0.0130	0.0151	0.0180	0.0170
25%	0.0500	0.0545	0.0503	0.0525	0.0440	0.0474	0.0475	0.0497	0.0438
50%	0.0615	0.0625	0.0586	0.0709	0.0582	0.0551	0.0592	0.0607	0.0575
75%	0.0718	0.0701	0.0691	0.0867	0.0652	0.0704	0.0683	0.0776	0.0684
CAPM WACC ${\text{Wacc}}_{\text{capm}}$
mean	0.1131	0.1118	0.1013	0.1076	0.1155	0.1099	0.1394	0.1098	0.0924
SD	0.0330	0.0298	0.0388	0.0374	0.0411	0.0329	0.0415	0.0278	0.0324
25%	0.0903	0.0902	0.0618	0.0773	0.0738	0.0771	0.1165	0.0872	0.0716
50%	0.1145	0.1085	0.1052	0.1069	0.1222	0.1096	0.1431	0.1091	0.0913
75%	0.1333	0.1304	0.1314	0.1271	0.1498	0.1271	0.1615	0.1281	0.1114
Market WACC ${\text{Wacc}}_{}\text{mkt}$
mean	0.1229	0.1261	0.1314	0.1299	0.1342	0.1251	0.1257	0.1142	0.1187
SD	0.1466	0.1866	0.1474	0.1748	0.1857	0.1468	0.2453	0.1596	0.1650
25%	0.0317	0.0048	0.0573	0.0312	0.0243	0.0167	$-$0.0020	$-$0.0013	0.0236
50%	0.1373	0.1248	0.1248	0.1609	0.1139	0.1323	0.1212	0.1292	0.1279
75%	0.2388	0.2318	0.2167	0.2355	0.2387	0.2317	0.2477	0.2263	0.1652

Notes: Mean, standard deviation (SD), and 25/50/75% quartiles for annual value-weighted means by sector from 1972 to 2015. Leverage Lev is $\left(\text{DLTT}+\text{DLC}\right)/\text{Val}$ where the whole-firm value Val is $\left(\text{AT}-\text{SEQ}\right)+\left(\left|\text{PRC}\right|\times \text{CSHO}\right)-\text{TXDB}$. The before tax cost of debt $R_{}\text{debt}$ is $\text{XINT}/\text{Debt}$ where the value of debt Debt is $\text{DLTT}+\text{DLC}$. The tax rate $\mathit{\tau }$ is $\text{TXT}/\text{PI}$ and is set to zero if $\text{TXT}/\text{PI}<0$ and one if $\text{TXT}/\text{PI}>1$. The firm cost of equity $R_{}\text{firm}$ is $\left(\text{DVC}+\text{Repur}+\left({\text{RE}}_t-{\text{RE}}_{t-1}\right)\right)/\text{Equity}$ where the common stock repurchase measure Repur is $\text{PRSTKC}-\text{if}\left(\mathrm{\Delta }\text{PSTKRV}>0,0,-\mathrm{\Delta }\text{PSTKRV}\right)$ and the value of equity Equity is $\text{Val}-\text{Debt}$. The CAPM-based cost of equity $R_{\text{capm}}$ is $R_f+\mathit{\beta }{E}_t[\text{MRP}]$ where $R_f$ is the one-month Treasury Bill, $\mathit{\beta }$ is computed from calendar year daily return data by regressing excess firm returns onto value-weighted market returns in excess of the one month Treasury Bill rate, and $E_t[\text{MRP}]$ is the average of market excess returns from the beginning of the sample to time t. The market cost of equity $R_{}\text{mkt}$ is the CRSP return ret. ${\text{Wacc}}_x=\text{Lev}{R}_{}\text{debt}(1-\mathit{\tau })+\left(1-\text{Lev}\right)R_x,x=\left\{\text{firm},\text{capm},\text{mkt}\right\}$. Compustat data items are UPPERCASE, CRSP data items are lower case, and measures derived in this study are Capitalized.

Figure 2. Leverage and cost of debt over time for all sectors.

Figure 3. Leverage and cost of debt cross section box plot. Note: the middle of the box plot represents the median value. Notes: The left and right box “hinges” represent the lower 25% and upper 75% quartile, respectively. The upper and lower notch edges represent the median $\pm 1.58\times IQR/\sqrt{n}$ where IQR is the inter-quartile range (difference between 75 and 25% quartile) and n is the number of observations. The upper “whisker” extends to the minimum of the largest value and the $75\%\text{quartile}+1.5\times \text{IQR}$. The lower “whisker” extends to the maximum of the smallest value and the $25\%\text{quartile}-1.5\times \text{IQR}$. Observations beyond whisker ends are outliers and plotted as points.

Figure 4. Cost of equity cross section box plot. Note: The middle of the box plot represents the median value. The left and right box “hinges” represent the lower 25% and upper 75% quartile, respectively. The upper and lower notch edges represent the median $+/-1.58\times \text{IQR}/\sqrt{n}$ where IQR is the inter-quartile range (difference between 75 and 25% quartile) and n is the number of observations. The upper “whisker” extends to the minimum of the largest value and the $75\%quartile+1.5\times \text{IQR}$. The lower “whisker” extends to the maximum of the smallest value and the $25\%quartile-1.5\times \text{IQR}$. Observations beyond whisker ends are outliers and plotted as points.

Figure 5. WACC cross section summary.

Figure 6. WACC cross section box plot. Note: The middle of the box plot represents the median value. The left and right box “hinges” represent the lower 25% and upper 75% quartile, respectively. The upper and lower notch edges represent the median $+/-1.58\times \text{IQR}/\sqrt{n}$ where IQR is the inter-quartile range (difference between 75 and 25% quartile) and n is the number of observations. The upper “whisker” extends to the minimum of the largest value and the $75\%quartile+1.5\times \text{IQR}$. The lower “whisker” extends to the maximum of the smallest value and the $25\%quartile-1.5\times \text{IQR}$. Observations beyond whisker ends are outliers and plotted as points.

Figure 7. Firm weighted average cost of capital over time.

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