Tutorials › VEE Accounting and Finance › Including Preferred Stock in WACC

VEE Accounting and Finance · Weighted Average Cost of Capital · Tutorial 656 of 996

Including Preferred Stock in WACC

Calculate WACC when preferred stock is present by weighting its required return by market value without applying the interest tax adjustment.

Advanced 10 min read

What You'll Learn

  • Identify preferred stock’s market value as a separate WACC capital weight.
  • Apply the corporate tax adjustment to debt interest, not to preferred stock’s required return.
  • Calculate WACC from source-specific costs and market-value weights.
  • Check that capital weights sum to one and contributions use consistent units.
  • Diagnose how incorrectly tax-adjusting preferred stock changes the result.

Why Preferred Stock Needs Its Own WACC Term

A company can finance its operations with debt, preferred stock, and common equity. Each source has a required return: the return expected by the investors who provide that capital. When preferred stock is part of the financing mix, its market value and required return belong in the weighted average cost of capital (WACC) as a distinct component.

The key distinction is tax treatment. Under the standard corporate-finance convention, interest on debt is deductible when calculating corporate taxable income, so the cost of debt is adjusted for the interest tax shield. Preferred dividends are not treated as deductible interest in this convention. Therefore, the preferred-stock term uses the preferred required return as given, without multiplying it by one minus the tax rate.

Definition: Let \(D\), \(P\), and \(E\) be the market values of debt, preferred stock, and common equity, respectively, and let \(V=D+P+E\) be total market-value capital. Let \(k_d\), \(k_p\), and \(k_e\) be their required returns, and let \(T_c\) be the corporate tax rate. With deductible debt interest and nondeductible preferred dividends, the standard WACC is
$$ \mathrm{WACC} = \frac{D}{V}k_d(1-T_c) + \frac{P}{V}k_p + \frac{E}{V}k_e. $$
The market-value weights are \(D/V\), \(P/V\), and \(E/V\); they sum to one when these are the capital sources included in the calculation.

This expression assumes that the required returns and capital values refer to the same financing basis and that the debt interest tax deduction is available at the stated tax rate. It also uses the standard convention that preferred distributions do not receive the corporate interest deduction. Actual tax rules can differ by jurisdiction and instrument; if a problem specifies a different tax treatment, use that stated treatment rather than silently applying this convention.

How the Preferred-Stock Term Fits

The preferred-stock contribution is its market-value weight multiplied by its required return: \((P/V)k_p\). The relevant weight is not the preferred stock’s book value, par value, or dividend amount; it is the market value of the preferred stock included in the capital structure. The relevant return is the required return specified or otherwise established for that preferred financing.

The debt term is different because the standard formula recognizes the tax saving from deductible interest. If a firm pays \(k_d\) per dollar of debt before tax and can deduct the interest at rate \(T_c\), the effective after-tax cost is \(k_d(1-T_c)\). No parallel adjustment is made to \(k_p\) under the stated convention. Preferred stock may have a stated dividend, but that does not make the dividend deductible interest.

Why the Formula Is a Weighted Average

The weights allocate total market-value capital among its sources. To see why each source contributes in this way, consider the financing charge on a total capital base \(V\). Debt has an after-tax cost per dollar of \(k_d(1-T_c)\), preferred stock has a cost per dollar of \(k_p\), and common equity has a cost per dollar of \(k_e\). Multiplying each per-dollar cost by the dollars supplied by that source gives the total charge per period represented by the model:

$$ Dk_d(1-T_c)+Pk_p+Ek_e. $$

Dividing this amount by total capital \(V\) converts the total financing charge into a rate per dollar of capital. Separating the terms after division gives

$$ \frac{Dk_d(1-T_c)+Pk_p+Ek_e}{V} = \frac{D}{V}k_d(1-T_c) + \frac{P}{V}k_p + \frac{E}{V}k_e. $$

This derivation also shows the role of the preferred-stock weight: preferred investors supply \(P\) of the total \(V\), so their required return contributes in proportion to \(P/V\). Applying the debt tax adjustment to that term would change the assumed tax treatment, not merely rearrange the weighted average.

Calculating WACC with Preferred Stock

A reliable calculation keeps market values, weights, component returns, and weighted contributions separate until the final sum. The sequence below is useful when all three sources are present.

1
Find total market-value capital.
Add the market values of debt, preferred stock, and common equity: \(V=D+P+E\).
2
Calculate each source’s weight.
Divide each market value by \(V\), then check that the weights sum to one.
3
Adjust the debt return only.
Use \(k_d(1-T_c)\) for debt under the standard deductible-interest assumption. Keep \(k_p\) unchanged.
4
Weight and add the returns.
Multiply each source’s weight by its applicable return and add the three contributions.

Worked Example: Three Capital Sources at Given Market Values

A hypothetical firm has market-value debt of $24 million, preferred stock of $6 million, and common equity of $30 million. The required returns are 6.0% on debt, 8.0% on preferred stock, and 12.0% on common equity. The corporate tax rate is 25%, and debt interest is deductible. Find WACC. The values and rates are hypothetical.

Method. Find total market capital, compute each weight, adjust only the debt return, and sum the weighted contributions.

Total capital is

$$ V=24+6+30=60\text{ million dollars}. $$

The weights are \(24/60=0.40\) for debt, \(6/60=0.10\) for preferred stock, and \(30/60=0.50\) for common equity. They check: \(0.40+0.10+0.50=1.00\).

The after-tax debt cost is \(6.0\%(1-0.25)=6.0\%(0.75)=4.5\%\). The weighted contributions are:

  • Debt: \(0.40(4.5\%)=1.80\%\).
  • Preferred stock: \(0.10(8.0\%)=0.80\%\).
  • Common equity: \(0.50(12.0\%)=6.00\%\).

Thus, \(\mathrm{WACC}=1.80\%+0.80\%+6.00\%=8.60\%\). As a check, the preferred contribution is its 10% share of total capital multiplied by its full 8.0% required return; it has not been reduced for taxes.

Common Trap: Tax-Adjusting Preferred Stock

A frequent error is to apply the factor \(1-T_c\) to every financing return. That incorrectly treats preferred dividends like deductible interest. The following example isolates the effect of that mistake.

Worked Example: Correcting an Incorrect Preferred Tax Adjustment

A hypothetical company has $18 million of debt, $12 million of preferred stock, and $30 million of common equity. The debt, preferred, and common-equity required returns are 7.5%, 9.0%, and 13.0%, respectively. Debt interest is deductible, and the corporate tax rate is 20%. Calculate WACC and identify the result of incorrectly tax-adjusting preferred stock.

Method. Use market-value weights and adjust only the debt cost. The total capital is \(18+12+30=60\) million dollars, so the weights are \(18/60=0.30\), \(12/60=0.20\), and \(30/60=0.50\). They sum to \(1.00\).

The after-tax debt return is \(7.5\%(1-0.20)=7.5\%(0.80)=6.0\%\). Correct weighted contributions are:

  • Debt: \(0.30(6.0\%)=1.80\%\).
  • Preferred stock: \(0.20(9.0\%)=1.80\%\).
  • Common equity: \(0.50(13.0\%)=6.50\%\).

Therefore, the correct WACC is \(1.80\%+1.80\%+6.50\%=10.10\%\).

Wrong calculation and correction. If preferred stock is incorrectly treated as tax-deductible, its adjusted return would be \(9.0\%(0.80)=7.2\%\), and its contribution would be \(0.20(7.2\%)=1.44\%\). That produces a mistaken WACC of \(1.80\%+1.44\%+6.50\%=9.74\%\). The correction is to restore the preferred contribution to \(0.20(9.0\%)=1.80\%\), giving 10.10%. The error understates WACC by \(10.10\%-9.74\%=0.36\) percentage points.

Market Values, Units, and Checks

Preferred stock may be quoted per share while other capital values are supplied as totals. Convert share counts and prices into a market value before calculating weights. Use consistent units throughout: all dollars, all thousands of dollars, or all millions of dollars. Dividing a value in dollars by a total in millions without conversion will produce a meaningless weight.

The following example combines share-based market values with a debt market value stated directly. It also illustrates why the weight check is useful: the preferred value must be included in the denominator, not added after the other sources’ weights have already been calculated.

Worked Example: Converting Preferred Shares into a WACC Weight

A hypothetical firm has 80,000 preferred shares trading at $25 per share, $4.2 million of market-value debt, and 300,000 common shares trading at $40 per share. The required returns are 5.5% on debt, 7.2% on preferred stock, and 11.0% on common equity. Debt interest is deductible, and the corporate tax rate is 30%. Find WACC, rounding the final rate to two decimal places.

Method. First calculate both share-based market values, then find total capital and the weighted costs. The preferred-stock market value is \(80{,}000\times \$25=\$2{,}000{,}000\), or $2.0 million. Common-equity market value is \(300{,}000\times \$40=\$12{,}000{,}000\), or $12.0 million. Thus,

$$ V=4.2+2.0+12.0=18.2\text{ million dollars}. $$

The weights are \(4.2/18.2=0.230769\) for debt, \(2.0/18.2=0.109890\) for preferred stock, and \(12.0/18.2=0.659341\) for common equity. Their sum is \(1.000000\), subject to displayed rounding.

The after-tax debt return is \(5.5\%(1-0.30)=5.5\%(0.70)=3.85\%\). Using values in millions, the weighted cost amounts are:

  • Debt: \(4.2(0.0385)=0.1617\) million dollars.
  • Preferred stock: \(2.0(0.072)=0.1440\) million dollars.
  • Common equity: \(12.0(0.11)=1.3200\) million dollars.

Their sum is \(0.1617+0.1440+1.3200=1.6257\) million dollars. Divide by total capital: \(1.6257/18.2=0.089324\), or 8.9324%. Rounded only at the final step to two decimal places, WACC is 8.93%. The same result follows by multiplying the three weights by their applicable rates and adding; any small difference from that route would be due only to rounding intermediate weights.

Interpretation and Exam Checks

Including preferred stock matters because omitting its market value changes both its own contribution and the weights assigned to the other capital sources. A correct calculation treats all included sources consistently: determine market values first, form weights using the same total, then apply the correct return treatment to each source.

  • Do not omit preferred stock from total capital. If \(P\) is included as a financing claim, it belongs in \(V\) and has its own weight.
  • Do not tax-adjust the preferred return under the standard convention. The factor \(1-T_c\) applies to deductible debt interest, not to preferred dividends.
  • Do not confuse a stated dividend with the required return. Use the preferred required return given in the problem; a dividend amount alone is not automatically that return.
  • Check the weights. The weights should add to one, apart from rounding. If not, inspect for a missing source, an inconsistent denominator, or a unit conversion error.
  • Keep weighted contributions in rate units. For example, use either 0.08 or 8%, consistently; do not mix decimal and percentage forms in the same sum.

These checks are especially useful in a multi-source calculation: a plausible-looking final percentage can still be wrong if the preferred stock was omitted from the denominator or incorrectly given an interest tax shield. The method here is aligned with the SOA VEE Accounting and Finance syllabus.

Check Your Understanding

For each hypothetical firm, calculate WACC using the standard assumption that debt interest is deductible and preferred dividends are not. Round only as requested.

  1. A firm has $10 million of debt, $4 million of preferred stock, and $6 million of common equity. Required returns are 6.0%, 8.0%, and 10.0%, respectively, and the tax rate is 25%. (Answer: 6.85%)
  2. A firm has $5 million of debt, 50,000 preferred shares trading at $40 each, and $8 million of common equity. Required returns are 6.4% on debt, 7.5% on preferred stock, and 12.0% on common equity; the tax rate is 25%. (Answer: 9.00%)
  3. A firm’s market-value capital is $12 million of debt, $3 million of preferred stock, and $15 million of common equity. The required returns are 8.0%, 9.0%, and 14.0%, and the corporate tax rate is 30%. A calculation applies the tax adjustment to both debt and preferred stock. What is the correct WACC, and by how many percentage points does that calculation understate it? (Answer: Correct WACC 10.14%; understatement 0.27 percentage points.)
  4. A firm has $7.5 million of debt, 120,000 preferred shares at $32 each, and 240,000 common shares at $40 each. Required returns are 5.2% on debt, 6.5% on preferred stock, and 10.5% on common equity; the tax rate is 25%. Calculate WACC to two decimal places. (Answer: 7.40%)
Clinical Biostats