Weighted Average Cost of Capital : Clearing the Confusion for Users

I got a question from my friend which I believe this question might be relevant to be shared for bigger audience.

He asked me about the Weighted Average Cost of Capital (or abbreviated as WACC) formula, which to him, this has raised a bit confusion.

From his googling WACC formula, the WACC is shown as follows (note: I took this from https://corporatefinanceinstitute.com/resources/valuation/what-is-wacc-formula/, accessed on 2 April 2023)

WACC?=?(E/V x Re)?+?((D/V x Rd)?x?(1 – T))

Where:

E = market value of the firm’s equity (market cap)

D = market value of the firm’s debt

V = total value of capital (equity plus debt)

E/V = percentage of capital that is equity

D/V = percentage of capital that is debt

Re = cost of equity (required rate of return)

Rd = cost of debt (yield to maturity on existing debt)

T = tax rate

That site gave a good picture of the components of WACC as depicted below.

Image Source: CFI’s?Business Valuation Modeling Course.

I guess, there is no new about this WACC formula, as this formula is shown in all corporate finance textbooks.

The WACC formula above shows that cost of debt is multiplied with (1 minus corporate income tax), which means that the cost of debt has considered that the interest expense arising from the leverage has lowered the income tax expense of the company, as it is deductible expense.

However, his consultants do not follow this post-tax cost of debt, instead, they just use WACC formula :

WACC?=?(E/V x Re)?+?((D/V x Rd)?[without (1-Tax)]

This has baffled him as he has tried to get confirmation from his certification in finance holder about the WACC formula and he said it is confirmed that WACC is always shown as that in many website, including CFI’s website, that it, cost of debt will always be multiplied with (1-Tax).

Upon bringing up this to me, I said, WACC formula is not always written as post-tax cost of debt. It is possible to have pre-tax cost of debt to calculate the present value of the cash flows.

Either it is post-tax or pre-tax cost of debt being used in the WACC formula, it comes back to what Cash Flows it is discounting.

I asked him to better check the calculation of the Cash Flows being used by his consultants instead of being confused with the post-tax or pre-tax cost of debt. Both could be correct and could be used in the determination of the present value of the cash flows, that is WACC could be calculated as:

Post-tax :

WACC?=?(E/V x Re)?+?((D/V x Rd)?x?(1 – T))

Pre-tax :

WACC?=?(E/V x Re)?+?((D/V x Rd)?[without (1-Tax)]

He is a bit surprised to my statement above.

Post-tax WACC becomes so familiar in many books and websites, and it is quite rare to see that the authors will show at the same time, what they meant with the Cash Flows that they are going to discount it.

Post-tax WACC has an underlying assumption, that the Cash Flows are Unlevered after-tax Free Cash Flows, in which the Project Cash Flows are not taken into account the Debt financing. Here we will not see the Interest Expense in the Income Statement of the Project, and accordingly, there is no tax advantage coming from the Debt. The Project income tax will be higher, as a result.

Let me give a simple table to show the effect of leverage (using Debt) on the Project’s Income Statement.

?

As we can see from the above table, Project’s net income is lower by 80 if we put the Interest Expense of 100 (with Leverage), than it would have been without Leverage.

Interestingly, we could see that by using the Debt, this has reduced the cash flows being available to the equity investor (720 with Leverage vs 800 without Leverage). However, the total cash flows available to all investors is even higher if the Leverage is used.

We could have two observations from above table:

First, where does this 20 come from? If we are looking into the first table, we could find easily this 20, which is the lower income tax that the Project has to accrue, that is:

Interest expense x Income Tax Rate = 100 x 20% = 20

This “gain” to the equity holders arises from the tax deductibility of the interest expense, and this is generally speaking, referred to as “interest tax shield”, that additional amount of income tax that the Project would have to accrue and pay to Tax Office, if the Project does not have the Debt financing.

Second, which investors will enjoy this Lower Income Tax? As we could see from the above table, it is the Equity Holder, which now instead of receiving 800, they could get 820, instead.

Nonetheless, my friend is still confused, as he said if the Project’s Cash Flows doesn’t reflect the Interest Expense, yet, the Project is financed both with Equity and Debt.

The question is now, how to put this Debt financing if we can’t find it in the Project’s Cash Flows?

The answer lies in the WACC calculation, and here we are going to use the famous version of WACC, that is:

WACC?=?(E/V x Re)?+?((D/V x Rd)?x?(1 – T))

I could re-write the WACC formula to show that the Interest Tax Shield will flow to the equity holders:

WACC = (1) (E/V x Re) + (2) (D/V x Rd) – (3) (D/V x Rd x T)

If we add (1) with (2) – this is what we call Pre-Tax WACC, or theoretically, it is a world without tax (the assumptions under a perfect capital market). In other words, in a perfect capital market, though the use of Debt or Leverage would increase the risk, and accordingly the cost of capital of the Project’s equity, the Project’s WACC and the total value will stay the same by any change in the Debt or Leverage. As MM Propositions proved it, the Project’s choice of the capital structure (using Equity, or both Equity and Debt) is irrelevant.

In a nut shell, in the WACC formula, we will only use Post-tax Cost of Debt only for the case in which the Free Cash Flows does not include the interest payments and debt payment. In other words, there is no Leverage being reflected in the Project’s Cash Flows being discounted at. As the Project is financed by Equity and Debt, then the Debt will be included in the calculation of WACC by using post-tax Cost of Debt. As the post-tax Cost of Debt will be lowering the WACC (to certain limit, in which the Project should have positive EBIT and the limit of interest expense advantage will be limited by its EBIT amount), the value of the Project’s Cash Flows will go higher. ?Or, the cost of the interest it must pay will be partially offset to some extent by the tax savings coming from the Interest Tax Shield.

In the Second Part of this article, I will show that Pre-Tax WACC in which Cost of Debt is not multiplied with (1-Tax) is possible to be used. We will talk about the Interest Tax Shield is being reflected into the Cash Flows being discounted at. Also we will talk about why Post-Tax WACC has strong assumptions, that in certain situation, is not appropriate to be used.

#Cost of Capital #Corporate Finance #Debt Financing #Cash Flows #WACC #Discount Rate #Project Finance #Leverage #Equity #Tax Savings #Modigliani-Miller #Equity Holder #Debt Holder #Interest Expense #Income Tax #EBIT #Net Income #Pre-tax Income #Income Statements

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