Weighted average cost of capital (WACC) is commonly used in practice to value businesses and underlying assets. Unfortunately, it is often misapplied or misunderstood. *Greg Beech* and *Dave Thayser* explain

The concept of weighted average cost of capital (WACC) is widely used in practice and taught at most tertiary institutions. The underlying thinking is that using debt instead of shareholder money to fund the operations of a company, venture or project has numerous benefits. The key benefit to a company is that the interest payments associated with debt are deductible for income tax purposes (assuming the debt is used to fund income-generating pursuits). This is often referred to as the ‘tax shield’.

There are many distracting arguments around using debt as opposed to equity to fund a company’s operations, however claims that the cost of debt is generally cheaper than that of equity are true, but the source of the additional value created in this way is often misunderstood. The only source of new value arising from the introduction of debt is the tax shield on interest, which introduces a new cash flow into the valuation calculation.

Similarly, the argument that using debt to fund operations instead of their own money leverages returns to shareholders has significant merit. However, it is a mistake to believe that the underlying value of the company’s operations is increased in this way. As seen above, the new value arises from a financial source – the newly introduced tax shield. Thus, while leverage enhances returns for shareholders it does so by introducing the potentially higher financial risk associated with having external competing claims on capital.

MISCONCEPTIONS ABOUT WACC

WACC, unfortunately, is widely misunderstood, misapplied and abused. Hearing investment bankers, company directors and financial alchemists state that introducing debt onto the balance sheet ‘will lower the cost of capital and increase company and/or underlying asset value’ should leave finance academics with severe heartburn. If generating value were that easy, we would all be billionaires!

As mentioned, introducing debt into the capital structure of a corporate delivers real value through the deductibility of the concomitant interest expense associated with debt. This benefit can be measured when valuing a company using the free cash flow valuation method by either discounting the expected tax shield or adjusting the discount rate when present valuing expected future free cash flows. The most common approach is to adjust the discount rate by determining WACC.

WACC is the blended cost of capital after taking into account the relative weightings of equity and debt in a company’s capital structure. The formula generally used to estimate WACC is:

WACC = (Ce x E/EV) + (Cd x D/EV)

Where:

Cd = after tax cost of debt

Ce = cost of equity

D = market value of debt

E = equity value of company

EV = enterprise value of company

The common errors made in estimating WACC include:

• Using the debt/equity ratio instead of the weighting of debt relative to enterprise value

• Using book values of debt and equity to derive relative weightings in the formula

• Using short-term debt rates instead of estimating long-term rates, and

• Using an unsustainable target debt to enterprise value ratio

The weightings should be based on market values and not book values. Aswath Damodaran (in Investment evaluation, 2012) emphasises this point by stating that ‘every textbook is categorical that the weights in the cost of capital calculation be market value weights’.

The long-term cost of debt is far more appropriate than short-term rates. The value of a business is based on its free cash flows into perpetuity in terms of the free cash flow (FCF) valuation method. Hence, it makes sense to use a sustainable debt rate into the future as opposed to, say, the bank overdraft rate. Many corporates do not have access to long-term (ten year+) finance from banks in South Africa to fund operations, and there are not many actively traded corporate bonds locally. Certain of our larger listed entities actively raise longer-term debt capital offshore and locally. However, the vast majority of South African companies do not share this privilege. It follows that in many instances we have to estimate the long-term cost of debt for companies on the assumption that they could raise such finance.

It is common practice to use the entity’s target capital structure to determine relative weights. This is certainly more practical than estimating future weightings, as debt levels often vary from year to year depending on the business life-cycle. However, often these target capital structures bear little resemblance to reality. A review of cash flow forecasts in an FCF valuation model may reveal that the business is expected to be cash generative and repay all debt within five years. Using a target debt/EV ratio of 30% into infinity in those circumstances would be inappropriate. To do so would artificially raise the enterprise value of the business.

WORKED EXAMPLE

Let’s illustrate the above common errors by use of a simplified example. Assume that XYZ (Proprietary) Limited is a newly formed business that has raised R1 million from its shareholders to purchase income-generating assets and:

• Free cash flows of R120 000 will be generated annually by the business into infinity

• There is no inflation

• XYZ’s cost of equity is 12,0%

• XYZ’s long-term cost of debt is 8,0%

• The company’s income tax rate is 28,0%

• All free cash flows generated by XYZ will be distributed to shareholders, and the distributions to shareholders will incur no taxation consequences (no dividend-withholding tax)

Given that there is currently no debt in the capital structure of XYZ, the value of the business is simple to determine:

FCF value = Future free cash flows ÷ cost of equity

= R120 000 ÷12%

= R1 000 000

There is no inflation and XYZ expects consistently to generate R120 000 of free cash flow annually. Hence both the enterprise and equity value of XYZ are estimated to be R1 million today.

On reflection, the board of directors and shareholders of XYZ decide that it would be more advantageous to introduce R300 000 of long-term debt into the business than for shareholders to exclusively fund the business. What impact will this have on the enterprise value and equity value of XYZ?

**Error 1: Using debt/equity in the WACC calculation instead of debt/enterprise value**

The example below illustrates the rare error (hopefully) of using debt/equity ratios to estimate WACC.

**Example 1 Using the debt/equity ratio**

Debt = R300 000

Equity = R700 000

Debt/equity ratio = 42,9%

WACC = [12% x 57,1%] + [((8,0% x (1 – 28%) x 42,9%]

= 9,32%

Enterprise value = R120 000 ÷ 9,32%

= R1 287 133

Equity value = Enterprise value – Debt

= R1 287133 – R300 000

= R987 133

The calculations above are clearly erroneous, as we know that WACC should be estimated using market values relative to enterprise value. The impact of the error on the value is significant – implying that the value of XYZ shareholders’ interests increased from R700 000 to R987 133, an increase of 41%. Creating shareholder value just isn’t that easy!

**Error 2: Using a debt/enterprise ratio based on book values in the WACC calculation, rather than the market values**

In example 2 below, the error made in example 1 is corrected; however, we will discover shortly that this solution is imperfect, too!

**Example 2 Debt and equity book values relative to EV**

Debt = R300 000

Equity = R700 000

Debt/EV ratio = 30%

Equity/EV ratio = 70%

WACC = [12% x 70%] + [((8,0% x (1 – 28%) x 30%]

= 10,128%

Enterprise value = R120 000 ÷ 10,128%

= R1 184 834

Equity value = Enterprise value – Debt

= R1 184 834 – R300 000

= R884 834

At face value, the results in example 2 seem plausible. However, the theory clearly states that we should use market values of debt, equity and enterprise value to determine relative weightings in deriving WACC. A quick reasonability check in example 2 reveals that the market value of debt-to-EV is actually 25,3% and not 30% as we estimated.

**Valuation results per example 2 **

Market value of debt = R300 000

= 25,3%

Market value of equity = R884 834

= 74,7%

Enterprise value = R1 184 834

= 100,0%

**The nearly right answer: calculating WACC in an iterative manner**

The calculation of WACC is an iterative process, as at the start of the valuation we do not know the enterprise value and, hence, the equity value of XYZ. It follows that we are not able to determine relative weights until the conclusion of the valuation process. Fortunately, we have access to spreadsheet software such as Excel to do this relatively easily. Refer to example 3 below for the correct answer.

**Example 3 WACC iteration**

*Guess weights *

Debt-to-EV = 25,9516%

Equity-to-EV = 74,0484%

Resultant WACC = [12% x 74,0484%] + [5,76% x 25,9516%]

= 10,381%

Enterprise value = R120 000 ÷ 10,381%

= R1 156 000

*Actual weights *

Debt = R300 000

= 25,9516%

Equity = R856 000

= 74,0484%

Enterprise value = R1 156 000

= 100,0000%

Shareholders contributed R700 000 to XYZ, and this has increased to R856 000 according to the calculations in example 3. This is a significant uplift in value for simply introducing debt into the capital structure.

*Sanity check*

If we assume that XYZ will never have to repay the R300 000 of debt or be able to keep renewing this obligation, we can estimate the value of the tax shield.

**Example 4 Present value of the tax shield**

Annual interest cost = R300 000 x 8%

= R24 000

Annual tax saving = 28% x R24 000

= R6 720

PV of the tax shield discounted at:

Cost of equity = R6 720 ÷ 12%

= R56 000

= R56 000

Cost of debt = R6 720 ÷ 8%

= R84 000

XYZ will derive real benefit by paying R6 720 less income tax annually than it would have if it had no debt on its balance sheet. Finance literature is divided on whether to discount this benefit at the cost of equity or whether to use the cost of debt (8%).

The approach of valuing a business and then adding the present value of future tax benefits associated with debt is referred to as the adjusted present value (APV) method. This method usually provides a much lower enhancement in value for shareholders than using WACC – between R56 000 and R84 000 in our example, depending on the discount rate used.

**The final twist in the tale: adjusting the cost of equity to reflect financial risk**

There is a strong argument that following the introduction of debt into the capital structure; the cost of equity should increase to compensate for the higher financial risk faced by the business. The theories surrounding how to adjust the cost of equity in these circumstances are numerous and difficult for us mere mortals to comprehend and mathematically follow. In practice, the APV approach is least likely to result in a valuation error. However, should you enjoy financial alchemy, read Hamada’s formula for adjusting the cost of equity, or the 20-odd other alternatives.

**CONCLUSION**

In summary, WACC should be treated with great caution in practice. There are multiple paths to error from following this approach and hopefully you have been alerted to some of them. The ultimate reality check is to adopt the APV approach and double check your valuation results. Valuations, like beauty, are often a matter of opinion.

**Author: **Greg Beech (CA)SA is a self-employed mergers and acquisition adviser, and also chairs the APC Examco at SAICA. Dave Thayser CA(SA) lectures and consults on corporate finance issues since retiring as a corporate finance partner at EY