08-01-2010

Business Valuation: The Problem with Capitalization Formula

and

Weighted Average Cost of Capital (WACC)

By

(MBA, MSEE, MSME, CBI, CM&A)

# Introduction

Capitalization formula with weighted average cost of capital (WACC) is universally used in business valuation. It is quick and convenient. It is used by itself to value 100% of the business, or as part of the excess earnings method, or to calculate the Terminal Value in a DCF (Discounted Cash Flow) analysis. In DCF approach a large portion of the total value is usually based on the Terminal Value, which is calculated using the capitalization formula. However, there are certain, and potentially serious, problems in using the capitalization formula. This article discusses one such problem in detail i.e. the use of WACC. Other problems with the capitalization formula are also briefly discussed.

The capitalization formula has an implicit assumption that only the interest cost of debt is relevant to valuation. It ignores the impact of debt repayments to equity holder’s cash flow. Valuation textbooks and literature do not appear to have explicit discussion on this subject. Many in the industry believe that debt repayment’s impact can be ignored because a typical business has a perpetual ability to continuously refinance the debt at no transaction cost, and that a constant debt to equity ratio can be maintained through additional borrowing as the business grows. Even if one were to assume unconstrained and perpetual access to debt refinancing, capitalization formula implicitly assumes that such debt refinancing proceeds are distributable, and are distributed, to the equity holder as dividend, such that each period’s cash flow is distributed to each investor in proportion to their investment. Such luxury of perpetual debt, perpetual debt/equity ratio, and the option to distribute the refinancing proceeds as dividend, is not realistic for most situations. Therefore, this article analyses the impact of the preferential distribution of the debt interest and the debt principal repayment on the results of the capitalization formula. The analysis quantifies impact on value and impact on equity return as-if debt has to be repaid without new borrowing.

Debt service causes deferral of dividend distribution to the equity holder compared to the proportional distribution implicit in WACC. As a result the actual return to the equity holder is lower than the cost of equity used in calculating the WACC. In the example shown here the cost of equity is 30% and the cost of debt is 10%, debt/equity ratio is 50%, and hence WACC is 20%. Servicing of debt at the expense of distribution to the equity holder reduces the actual return to the equity holders to 23.6% from the 30% cost of equity used in calculating WACC. The difference of 6.4% is a 20% reduction in the expected equity return of 30%. Reduction in equity return is equivalent to overvaluation. In the example shown here, 20% reduction in equity return is equivalent to approximate 25% overvaluation by the capitalization formula.

## Analysis

The capitalization formula is,

V0 = x1 / (k - g) (1)

where

V0 is the value of the firm at the beginning of year-1

x1 is the Net Cash Flow (NCFi) to investors in year-1

k is the WACC to the recipients of x1 cash flow

g is the projected growth of x1, and

k = we * re + wd * rd * (1-tc) (2)

where

we is the weight of the equity

re is the cost of the equity

wd is the weight of the debt

rd is the cost of the debt (pre-tax)

tc is the corporate tax rate

In order to understand the impact of debt service on equity return, assume following simplifying scenario.

1)     Growth is zero

2)     EBITDA = \$200, it does not change because g = 0

3)     Working capital change = 0, because g = 0.

4)     Company has no fixed assets, hence depreciation = 0

5)     No capital expenditure.

6)     All of the available cash is used to pay down the debt. In real life debt usually has a fixed pay down schedule. This leaves some cash in the company, but lenders restrict it from being distributed to the equity holders

7)     All of the available cash flow is distributed to the equity holder if there is no debt outstanding.

8)     Business is liquidated at the end of the planning period (2 and 5 years in the example). Liquidation value of the business is equal to the original acquisition value. This is a reasonable assumption considering the business is not growing.

9)     There are no corporate level taxes on liquidation.

10) Proceeds of liquidation are first used to retire existing debt; excess is distributed to the equity holder.

11) Business is acquired in a stock purchase rather than in an Asset purchase. Hence, the tax benefits of tax-deductible goodwill amortization and asset step-up are absent.

Let us also assume the following.

Corporate tax rate = tc = 0

Equity weight = we = 50%

Debt weight = wd = 50%

Cost of equity = re = 30%

Pre-tax cost of debt = rd = 10%

The weighted average cost of capital k is 20%, calculated as follows.

k = we * re + wd * rd * (1-tc)

= 0.5 * 30% + 0.5 * 10% * (1-0)

= 20%

The Net Cash Flow (NCFi) available to investors, x1, is equal to EBITDA, because there are no taxes, no capital expenditures and no working capital changes. Therefore, the value of the firm V0 is \$1000, calculated as follows.

= \$200/(0.2 - 0)

= \$1000

Debt is 50% of the purchase price of \$1000. Hence, debt equals \$500, and Equity is also \$500.

Company’s EBITDA is \$200, the interest cost is \$50 (= \$500 * 10%), there are no other expenses; hence taxable income is \$150 (= \$200 – \$50). There are no taxes hence Net Income is \$150. (See Table – 1)

Free Cash Flow to Equity (FCFE) is equal to net income minus capital expenditures and working capital changes, plus non-cash expenses. It is \$150 in our example because there are no capital expenditures, no working capital changes, and no non-cash expenses. (Note: If we were to capitalize FCFE of \$150 using cost of equity of 30% in our example, we will get equity value of \$500 (= \$150/0.3). This equity value when added to debt of \$500 gives us the Invested Capital value of \$1000, which is the same value as calculated above.)

The capitalization formula assumes that the FCFE will be distributed to the investors in proportion to their investment. However, in real life FCFE is not available for distribution to the equity holder due to lender restrictions. We are assuming, for the sake of simplicity, that all of the FCFE of \$150 is used to pay down the debt. Hence, at the end of year-1, debt will reduce by \$150, from \$500 to \$350 (= \$500 –\$150). In year-2 EBITDA is still \$200 (no growth), the interest will reduce, due to lower debt, to \$35 (= \$350 * 10%) and hence, the FCFE in year-2 is \$165 (= \$200 – \$35). All of the FCFE is used to pay down the debt. This will reduce the outstanding debt at the end of year-2 to \$185 (= \$500 – \$150 – \$165).

Business is liquidated at the end of year-2 for the same price as the original price of \$1000 at the beginning of period-1 (This is a result of zero growth assumption, and it further assumes that the capital markets at the end of year-2 will be the same as that at the beginning of period-1). We are assuming no liquidation taxes. Therefore, cash available to the equity holder is the liquidation proceeds of \$1000 less the outstanding debt of \$185, which equals \$815 (= \$1000 – \$185).

Table –1 provides above analysis in a tabular form.

Based on the above cash flows, let us look at the return to the investors.

The debt holder is investing \$500 and expects a 10% return. Actual cash flow to him delivers his expected return as shown below.

Debt Holder Cash Flow - Actual

Year-0 Year-1 Year-2

Investment (debt) -\$500

Principal Return \$150 \$165

Liquidation Proceeds \$185

------------------------------------------

-\$500 \$200 \$385

IRR of above cash flow stream is IRR = 10%

(For the debt holder actual return equals expected return).

The equity holder is investing \$500 and expects a 30% return. His expected cash flow stream is as shown below.

Equity Holder Cash Flow - Expected

Year-0 Year-1 Year-2

Investment -\$500

Expected Interest \$150 \$150

Principal Return \$500

--------------------------------------------

-\$500 \$150 \$650

IRR of above cash flow stream is IRR = 30%

(This is the expected return by the equity holder).

The actual cash flow to the equity holder is deferred due to the priority of debt interest and debt principal repayments as shown below.

Equity Holder Cash Flow – Actual

Year-0 Year-1 Year-2

Investment -\$500

Liquidation Proceeds 0 \$1000

Debt retirement -\$185

--------------------------------------------

-\$500 0 \$815

IRR of above cash flow stream is IRR = 27.7%

As shown in the IRR calculations above, the actual return to the equity holder is 27.7% even though 30% was used in calculating WACC.

In real life the liquidation event generally occurs at 5 years (primarily driven by the debt terms). Table – 2 shows the results of stretching the above example to 5 years. In this case, the equity holder’s actual ROI will be 23.6 %… 6.4% less than the expected equity return of 30%.

In the above example the actual equity return is approximately 20% (= 6.4/30) lower than the expected equity return. Essentially the equity holder is overpaying at a value of \$1000. The equity holder can increase the return back to 30% by lowering the price. At a reduced price of \$800 (see note at the end of this paragraph) the equity holder’s return will be 30%. The \$200 difference in the valuation (= \$1000 – \$800) is the amount of overvaluation by the capitalization approach. Thus, in the example here, the capitalization formula is overvaluing the business by 25% (= \$200/\$800). This is significant by any standard.

[Note: Value of \$800 is derived by trial and error. At 40% expected equity return, and 50% debt/equity ratio, WACC is 25% and V0 = \$800. The actual equity return will be 30%. See Table – 3 for details).

###### What impacts the amount of overvaluation?

Of the many factors that could affect overvaluation, two are discussed below.

The amount of overvaluation by the capitalization formula increases as the spread between the equity cost and the debt cost increases. Higher the equity cost, the more expensive it is for the equity holder to use the available cash to pay down the less expensive debt holder.

The amount of overvaluation by the capitalization formula also increases as the debt to equity ratio increases. As debt increases relative to equity, the wait time for start of the equity holder’s payday gets longer.

Does capitalization formula work in any circumstances?

The capitalization formula will work (ignoring its other limitations discussed below) under the following circumstances 1) There is no debt and hence all the free cash flow can be distributed to the equity holder, 2) If one assumes that debt is evergreen i.e. debt is perpetual never requiring repayment, and the debt holder will permit dividend distribution to cover the cost of equity, 3) If equity holder can continuously refinance the debt (in other words replace old debt with new debt of same amount) at no transaction cost, and that the lender will allow such refinanced portion of the debt to be distributed to the equity holder to cover the cost of equity, or 4) The spread between the cost of debt and the cost of equity is small such that the time value of deferring equity cash flow is insignificant. (In the above example, if debt cost is kept at 10%, and equity cost was reduced from 30% to 12%, and all other things remained the same, the actual equity return will only drop from 12% to 11.6%, which is equal to approximate 3% overvaluation).

Other limitations of the capitalization formula

The capitalization formula has many limitations. One such limitation is the use of WACC as discussed in this article. In addition, capitalization formula ignores the “circular”[2] problem, ignores the impact of tax motivated deal structures, ignores tax incentives like depreciation[3], ignores organization form… and, does not include any “willing seller” requirement. Some of these limitations have been mildly hinted in some textbooks, but have not received visibility. It is possible to address all of these limitations by combining cash flow discounting, iterative calculations and optimization methods (see footnote # 1).

Summary

The capitalization formula with WACC is the backbone of most valuation methods today. It is a simple and a quick method. However, the capitalization approach with WACC overvalues businesses. The amount of overvaluation can be significant. In a simple example presented here the overvaluation is 25%.

Such overvaluation is caused by capitalization formula yielding a lower return to the equity holder than the one used in calculating WACC. Capitalization formula assumes a proportional distribution of cash flow to each investor in each period. However, in real life debt interest payments and debt principal payments get paid first. As a result payments to the equity holder are delayed relative to what they are supposed to be per the capitalization formula. Such delay in payments to the equity holder causes the actual equity return to be lower than the one used in WACC. The capitalization formula does not recognize disproportionate distribution of the cash flow to the investors.

The capitalization formula and WACC works only if there is no debt, or if one assumes perpetual debt, perpetual debt/equity ratio and no dividend restrictions. Otherwise, its use with WACC risks overvaluation of the business.

The cost of debt is not only its interest cost, but also the cost of delayed distribution to the equity. Textbooks and valuation literature do not appear to have addressed the cost of “debt over dividend” priority in the capitalization formula, or for that matter in any other finance theory.

Table – 1

Year-0

Year-1

Year-2

EBITDA

200.0

200.0

Interest

-50.0

-35.0

Tax Inc

150.0

165.0

Taxes

0.0

0.0

Net Inc.

150.0

165.0

Free CF to Equity

150.0

165.0

Debt Payment

-150.0

-165.0

Cash to Equity

0.0

0.0

Beg Debt

500.0

350.0

Debt Payment

-150.0

-165.0

End Debt

350.0

185.0

Principal

-500.0

Interest

50.0

35.0

Repayment

150.0

165.0

@ Liquidation

185.0

-500.0

200.0

385.0

10%

### Equity holder ROI

Investment

-500.0

Distribution

0.0

0.0

@ Liquidation

1000.0

Remaining Debt

-185.0

-500.0

0.0

815.0

#### IRR

27.7%

Table – 2

Year-0

Year-1

Year-2

Year-3

Year-4

Year-5

EBITDA

200.0

200.0

200.0

200.0

200.0

Interest

-50.0

-35.0

-18.5

-0.4

0.0

Tax Inc

150.0

165.0

181.5

199.7

200.0

Taxes

0.0

0.0

0.0

0.0

0.0

Net Inc.

150.0

165.0

181.5

199.7

200.0

Free CF to Equity

150.0

165.0

181.5

199.7

200.0

Debt Payment

-150.0

-165.0

-181.5

-3.5

0.0

Cash to Equity

0.0

0.0

0.0

196.2

200.0

Beg Debt

500.0

350.0

350.0

350.0

350.0

Debt Payment

-150.0

-165.0

-165.0

-165.0

-165.0

End Debt

350.0

185.0

185.0

185.0

185.0

Principal

-500.0

Interest

50.0

35.0

18.5

0.4

0.0

Repayment

150.0

165.0

181.5

3.5

0.0

@ Liquidation

0.0

0.0

0.0

0.0

0.0

-500.0

200.0

200.0

200.0

3.9

0.0

10%

### Equity holder ROI

Investment

-500.0

Distribution

0.0

0.0

0.0

196.2

200.0

@ Liquidation

0.0

0.0

0.0

0.0

1000.0

Remaining Debt

0.0

0.0

0.0

0.0

0.0

-500.0

0.0

0.0

0.0

196.2

1200.0

#### IRR

23.6%

Table – 3

Year-0

Year-1

Year-2

Year-3

Year-4

Year-5

EBITDA

200.0

200.0

200.0

200.0

200.0

Interest

-40.0

-24.0

-6.4

0.0

0.0

Tax Inc

160.0

176.0

193.6

200.0

200.0

Taxes

0.0

0.0

0.0

0.0

0.0

Net Inc.

160.0

176.0

193.6

200.0

200.0

Free CF to Equity

160.0

176.0

193.6

200.0

200.0

Debt Payment

-160.0

-176.0

-64.0

0.0

0.0

Cash to Equity

0.0

0.0

129.6

200.0

200.0

Beg Debt

400.0

240.0

64.0

0.0

0.0

Debt Payment

-160.0

-176.0

-64.0

0.0

0.0

End Debt

240.0

64.0

0.0

0.0

0.0

Principal

-400.0

Interest

40.0

24.0

6.4

0.0

0.0

Repayment

160.0

176.0

64.0

0.0

0.0

@ Liquidation

0.0

0.0

0.0

0.0

0.0

-400.0

200.0

200.0

70.4

0.0

0.0

10%

### Equity holder ROI

Investment

-400.0

Distribution

0.0

0.0

129.6

200.0

200.0

@ Liquidation

0.0

0.0

0.0

0.0

800.0

Remaining Debt

0.0

0.0

0.0

0.0

0.0

-400.0

0.0

0.0

129.6

200.0

1000.0

#### IRR

30.0%

[1] Mike Adhikari is President and owner of Illinois Corporate Investments, Inc., an M&A advisory firm since 1986. In 2001 he developed BusinessValueXpress® (BVX®), a valuation and deal structuring software. Adhikari International, Inc., a valuation firm owned by Mike, markets BVX®. Mike has an MBA in finance from the University of Chicago (1977). Since 1994, he is a guest speaker in Entrepreneurial Finance in the MBA program at the Kellogg Business School of the Northwestern University.

BVX® uses iterative calculations and optimization technique to maximize value and determine optimal debt/equity structure. It determines enterprise value, not equity value, and discounts cash flow to equity, not to invested capital. It recognizes the impact of delayed distribution to equity due to debt service priority. BVX® is a “Real Capital Markets” model, hence it does not use any formulas based on “Perfect Capital Markets”. In BVX®, enterprise value is independent of seller’s capital structure, but is dependent on buyer’s capital structure. BVX® is interactive, non-subjective and deceptively simple.

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