Lecture 15 - Capital Budgeting and Valuation with Leverage
Revisiting the Free Cash Flow
(+) Revenues
(-) Costs
(-) Depreciation
(=) EBIT
(-) Tax Expenses
(=) Unlevered Net Income
(+) Depreciation
(-) CAPEX
(-) \(\Delta\) NWC
(=) Free Cash Flow
- This is the standard estimate of a Free Cash Flow, which is the amount of incremental cash that a project can actually bring to the firm!
Introducing different Financing Decisions
So far, we’ve assumed that this project was financed only through equity.
How the financing decision of the firm can affect both the cost of capital and the set of cash flows that we ultimately discount?
In this lecture, we’ll revisit the three main methods that can consider leverage decisions and market imperfections:
- The Weighted-Average Cost of Capital (WACC) method
- The Adjusted Present Value (APV) method
- The flow-to-equity (FTE) method
While their details differ, when appropriately applied each method produces the same estimate of an investment’s (or firm’s) value
Underlying assumptions
To illustrate these methods most clearly, we begin the chapter by applying each method to a single example in which we have made a number of simplifying assumptions:
The project has average risk: in essence, the market risk of the project is equivalent to the average market risk of the firm’s investments. In that case, the project’s cost of capital can be assessed based on the risk of the firm.
The firm’s debt-equity ratio is constant: we consider a firm that adjusts its leverage to maintain a constant debt-equity ratio in terms of market values.
Corporate taxes are the only imperfection: we assume that the main effect of leverage on valuation is due to the corporate tax shield. Other effects, such as issuance costs, personal costs, and bankruptcy costs, are abstracted away
While these assumptions are restrictive, they are also a reasonable approximation for many projects and firms
Method #1: the WACC
Recall that our definition of free cash flow measures the after-tax cash flow of a project before regardless how it is financed
In a perfect capital markets, choosing debt of equity shouldn’t change the value of the firm. However, because interest expenses are tax deductible, leverage reduces the firm’s total tax liability, enhancing its value!
We can directly incorporate market imperfections using the WACC method:
\[ r_{\text{WACC}}=\underbrace{\dfrac{E}{D+E}}_{\text{% of Equity}}\times r_e+ \underbrace{\dfrac{D}{D+E}}_{\text{% of Debt}}\times r_{D}\times (1-\tau) \]
where \(E\) is the market-value of Equity, \(D\) is the market-value of debt, \(r_e\) is the cost of equity, \(r_d\) is the cost of debt, and \(\tau\) is the marginal tax rate
Method #1: the WACC (continued)
- Because the WACC incorporates the tax savings from debt, we can compute the levered value of an investment by looking at its stream of cash flows discounted by \(r_{\text{WACC}}\):
\[ V^{L}= \dfrac{FCF_1}{(1+r_{\text{WACC}})}+ \dfrac{FCF_2}{(1+r_{\text{WACC}})^2}+...+\dfrac{FCF_n}{(1+r_{\text{WACC}})^n} \]
- In what follows, we’ll be using an example taken from (Berk and DeMarzo 2019), Chapter 18, to see how the WACC and the other methods can be applied in practice for the RFX project that is being studied by AVCO’s company
Practical Application: WACC
Practical Application: WACC (continued)
As said before, we’ll be assuming that the market risk of the RFX project is expected to be similar to that for the company’s other lines of business
Because of that, we can use Avco’s equity and debt to determine the weighted average cost of capital for the new project:
\(\rightarrow\) Important: because market values reflect the true economic claim of each type of financing, while calculating the WACC, market value weights for each financing element (equity, debt, etc.) must be used, and not historical, book values
Practical Application: WACC (continued)
- Using our example, we can calculate the WACC as:
\[ \small r_{\text{WACC}}=\underbrace{\dfrac{300}{300+300}}_{\text{% of Equity}}\times 10\%+ \underbrace{\dfrac{320}{300+300}}_{\text{% of Debt}}\times 6\%\times (1-25\%)=7.25\% \]
- Now, using \(\small r_{\text{WACC}}=7.25\%\), we can calculate the value of the project, including the tax shield from debt, by calculating the present value of its future free cash flows. Note that we’re using Net Debt \(\small (320-20)\) to weight-in the debt potion in the capital structure:
\[ \small V^{L}=\sum_{T=1}^{T=4}\dfrac{21}{(1+7.25\%)^t}=70.73 \]
- Because the investment in \(\small t=0\) is \(\small 29\), \(\small NPV=70.73-29=41.73\) million.
General thoughts on the WACC method
This is the method that is most commonly used in practice for capital budgeting purposes
After calculating \(r_{\text{WACC}}\), the rate can then be used throughout the firm assuming that:
- This rate represents the company-wide cost of capital for new investments that are of comparable risk to the rest of the firm
- Pursuing the project will not alter the firm’s debt-equity ratio
Question: how to ensure that the Debt-to-Equity will remain constant when implementing new projects?
Thus far, we have simply assumed the firm adopted a policy of keeping its debt-equity ratio constant. An important advantage of the WACC method is that you do not need to know how this leverage policy is implemented in order to make the capital budgeting decision
Nevertheless, keeping the Debt-to-Equity ratio constant has implications for how the firm’s total debt will change with new investment - we’ll refer to this as Debt-Capacity
Debt Capacity
- Debt Capacity refers to the the amount of debt that a firm needs to raise in order to keep its debt-to-equity ratio constant. Why is that important?
WACC is a weighted average based on the proportions of Equity and Debt
Because of that, any changes in these proportions affect the WACC
Therefore, after calculating \(r_\text{WACC}\), to ensure that you can use it over the years, you need to ensure that the firm maintains the same debt-to-equity ratio
- You can find the the debt capacity for a given period \(t\) by:
\[ D_t=d\times V^L_t \]
Where \(d\) is the debt-to-value ratio, which is the proportion of (market-value) debt over the market value of the firm or project (debt + equity)
Debt Capacity
- You can estimate the value of the levered firm, \(V^L_t\), over each period \(t\) by summing up the discounted stream of cash-flows remaining:
\[ V^L_t=\dfrac{FCF_{t+1}+V^L_{t+1}}{(1+r_{\text{WACC}})} \] where \(V^L_{t+1}\) refers to the continuation value – see the accompanying Excel spreadsheet for a comprehensive example
- While the WACC does not require you to know exactly the debt capacity of the project, this component is essential when calculating the value of the project using other methods, such as the APV, as we’ll see in the next set of slides
The APV Adjusted Present Value (APV) method
Our previous method estimated the value of a levered firm, \(\small V^L\), by considering the interest-tax shields into the cost of capital calculation, \(r_{\text{WACC}}\)
What if we wanted to gauge the impact of the interest tax-shields separately from the actual value of the unlevered project?
The Adjusted Present Value (APV) method does it so by calculating two components: \(V^U\), which is the present value of the unlevered project (i.e, no debt) and the present value of the interest tax-shields stemming from the financing decision:
\[ \small V^{L}_{APV}=V^U+ PV(\text{Interest Tax Shield}) \]
- The APV method incorporates the value of the interest tax shield directly, rather than by adjusting the discount rate as in the WACC method
The APV method in practice
The first step in the APV method is to calculate the value of these free cash flows using the project’s cost of capital if it were financed without leverage \(\rightarrow V^U\)
What is the project’s unlevered cost of capital?
Because the RFX project has similar risk to Avco’s other investments, its unlevered cost of capital is the same as for the firm as a whole
We can calculate the unlevered cost of capital using Avco’s pre-tax WACC, the average return the firm’s investors expect to earn
\[ r_U = \dfrac{E}{E+D}\times r_e + \dfrac{D}{E+D}\times r_d=\text{Pre-Tax WACC} \]
- Note that this formula is the same as of the \(r_{WACC}\), but we’re not including the tax-shield effect, \((1-\tau)\), into account!
The APV method in practice (continued)
To understand why the firm’s unlevered cost of capital equals its pre-tax WACC, note that the pre-tax WACC represents investors’ required return for holding the entire firm (equity and debt)
So long as the firm’s leverage choice does not change the overall risk of the firm, the pre-tax WACC must be the same whether the firm is levered or unlevered!
Applying it to our case, we have:
\[ r_U = 0.5\times 10\% + 0.5\times 6\% = 8\% \]
- With that, our estimate for \(V^U\) is:
\[ \small V^{U}=\sum_{T=1}^{T=4}\dfrac{21}{(1+8\%)^t}=69.55 \]
The APV method in practice (continued)
The value of the unlevered project, \(V^U\), does not include the value of the tax shield provided by the interest payments on debt
Knowing the project’s debt capacity for the future, we can explicitly calculate the the present value of the interest tax-shields. First, determine the amount of interest expenses at each period \(t\):
\[ \text{Interest Expenses}_t= r_D\times D_{t-1} \]
- After that, assuming a corporate tax rate of \(\tau\), the interest tax-shield is just:
\[ \text{Interest Tax-Shield}= \text{Interest Expenses}_t\times \tau \]
The APV method in practice (continued)
To compute the present value of the interest tax shield, we need to determine the appropriate cost of capital. Which rate shall we use? Note that:
- If the project does well, its value will be higher \(\rightarrow\) more debt \(\rightarrow\) more interest tax-shield
- If the project performs poorly, its value will be lower \(\rightarrow\) less debt \(\rightarrow\) less interest tax-shield
Because the interest tax-shield fluctuates with the risk of the project, we should discount it using the same same, \(r_U\)!
The APV method in practice (continued)
- Using \(\small r_U=8\%\) and evaluating the present value of the interest tax-shield, we have:
\[ \small PV(\text{Interest Tax-Shield})=\dfrac{0.53}{(1+8\%)}+\dfrac{0.41}{(1+8\%)^2}+\dfrac{0.28}{(1+8\%)^3}+\dfrac{0.15}{(1+8\%)^4}=1.18 \]
- Now, to determine the value of the levered firm, \(V^L\), we add the value of the interest tax shield to the unlevered value of the project:
\[ \small V^L=V^U+PV(\text{Interest Tax-Shield})= 69.55+1.18=70.73 \]
- Which is exactly the same value that we’ve found using the WACC method!
General thoughts on the APV method
In the APV method, we separately calculated the value of the unlevered firm and the value stemming from the tax-shields
In this case, the APV method is more complicated than the WACC method because we must compute two separate valuations
Notwithstanding, the APV method has some advantages:
It can be easier to apply than the WACC method when the firm does not maintain a constant debt-equity ratio
It also provides managers with an explicit valuation of the tax shield itself
There could be cases where the value of the project heavily depends on the tax-shield, and not on the operating gains themselves \(\rightarrow\) if taxes change, the value of the project may be severely affected!
Exercise: APV
Consider again Avco’s acquisition from Examples 18.1 and 18.2. The acquisition will contribute $4.25 million in free cash flows the first year, which will grow by 3% per year thereafter. The acquisition cost of $80 million will be financed with $50 million in new debt initially. Compute the value of the acquisition using the APV method, assuming Avco will maintain a constant debt-equity ratio for the acquisition.
\(\rightarrow\) Taken from (Berk and DeMarzo 2019), p. 689
Solution Rationale: proceed in the following steps to compute the value using the APV method:
- Calculate \(V^U\) - the value of the unlevered project
- Calculate the present value of the tax-shields
- Sum them up
- Note that, because the project will grow at a 3% rate, debt capacity will also grow at the same rate. Therefore, the growth-rate of the interest tax-shield is also 3% - see details
Exercise: APV
- Calculating \(V^U\): this is just the value of a growing perpetuity for the unlevered cash-flows:
\[ \small V^U= \dfrac{FCFC}{r-g}=\dfrac{4.25}{8\%-3\%}= 85 \]
- Now, if the firm will start with $50MM in debt, interest expenses are \(50\times6\%=3\) millions. The present value of the interest tax-shield is:
\[ \small \dfrac{25\%\times 3}{8\%-3\%}=\dfrac{0.75}{5\%}=15 \]
- Therefore, \(\small V^L=V^U+PV(\text{Tax-Shield})=85+15=100\)
References
Presented by Lucas S. Macoris (FGV-EAESP)