DCF Approach to Horizon Value
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One difficulty with relying solely on comparables when forecasting a horizon value is that we are comparing future multiples of the firm with current multiples of its competitors. In 20Y0, the multiples of Ideko and the comparables we have chosen may all be very different, especially if the industry is currently experiencing abnormal growth. To guard against such a bias, it is wise to check our estimate of the horizon value based on fundamentals using a discounted cash flow approach.
To estimate a continuation value in year T using discounted cash flows, we assume a constant expected growth rate, g, and a constant debt-equity ratio. When the debt-equity ratio is constant, the WACC valuation method is the simplest to apply:
\[\begin{align*} & \text{Enterprise Value in Year } T = V^L_T = {FCF_{T+1} \over {r_{wacc} - g}} \end{align*}\]FCF at Horizon (T + 1)
To estimate free cash flow in year T + 1, we note that free cash flow is equal to unlevered net income plus depreciation, less capital expenditures and increases in net working capital:
\[\begin{align*} \text{FCF }_{T+1} = \text{Unlevered Net Income }_{ T + 1} + \text{Depreciation }_{T + 1} - \text{Increases in NWC }_{T + 1} - \text{Capital Expenditures }_{T + 1} \end{align*}\]If the firm’s sales are expected to grow at a nominal rate g, and its operating expenses remain a fixed percentage of sales, then its unlevered net income will also grow at rate g. Similarly, the firm’s receivables, payables, and other elements of net working capital will grow at rate g.
The firm will need new capital to offset depreciation; it will also need to add capacity as its production volume grows. Given a sales growth rate g, we may expect that the firm will need to expand its investment in fixed assets at about the same rate. In that case:
\[\begin{align*} \text{Capital Expenditures }_{T + 1} = \text{Depreciation }_{T + 1} + g * \text{Fixed Assets }_{T} \end{align*}\]Thus, given a growth rate of g for the firm, we can estimate its free cash flow as:
\[\begin{align*} \text{FCF }_{T+1} = (1 + g) * \text{Unlevered Net Income }_{T} - g * \text{Net Working Capital}_{T} - g * \text{Fixed Assets }_{T} \end{align*}\]Note:
Here, fixed assets are measured according to their book value net of accumulated depreciation. This level of capital expenditures is required to maintain the firm’s ratio of sales to fixed assets (also called its fixed asset turnover ratio).
An alternative approach — which is preferable if we anticipate a change in the turnover ratio — is to estimate increases in NWC and net investment (capital expenditures in excess of depreciation), as a target percentage of the change in sales, where the target percentage is the expected long-run ratio of NWC and PP&E to sales.
Horizon Value
Assuming a future expected growth rate of 5%, a future debt-to-value ratio of 40%, and a debt cost of capital of 6.8% , Idekos Horizon value can be calculated as follows:
In 20Y0, Ideko’s unlevered net income is forecasted to be $15.849 million, with working capital of $40.425 million. It has fixed assets of $69.392 million From the earlier equation, we can estimate Ideko’s free cash flow in 20Y1: \(\text{FCF }_{2011}\) = (1.05)(15.849) - (5%)(40.425) - (5%)(69.392) = $11.151 million
With a debt-to-value ratio of 40%, Ideko’s WACC can be calculated from the equation:
\[\begin{align*} r_{wacc} = r_U - d\tau_c[r_D + \phi (r_U - r_D)] \end{align*}\]where \(d = D^s / (D^s + E)\) is the debt-to-value ratio, and \(\phi = T^s/(\tau_cD)\) is a measure of the permanence of the debt level, \(D\), \(r_u = {E \over {E + D^s}}r_E + {D^s \over {E + D^s}}r_D\), and \(D^s = D - T^s\)
Three cases which are commonly used in practice, which differ according to the frequency with which the debt is assumed to adjust to the growth of the investment.
- Continuously adjusted debt to maintain target debt ratio: \(T^s = 0, D^s = D\) and \(\phi = 0\)
- Annually adjusted debt to maintain targer debt ratio: \(T^s = {\tau_cr_DD \over {1 + r_D}}\), \(D^s = D (1 - \tau_c{r_D \over {1 + r_D}})\), and \(\phi = {r_D \over {1 + r_D}}\)
- Permanent debt: \(T^s = \tau_cD\), \(D^s = D (1 - \tau_c)\), and \(\phi = 1\)
Note that unless \(d\) and \(\phi\) remain constant over time, the WACC must be computed period by period.
As the debt to equity ratio is 40% (after the Horizon period), it is continuously adjusted, so \(\phi = 0\). The equation therefore becomes:
\[\begin{align*} r_{wacc} = r_U - d\tau_cr_D \end{align*}\]Therefore,
\[\begin{align*} r_{wacc} = 10 \text{ % } - 0.40(0.35) * 6.8 \text{ % } = 9.05 \text{ % } \end{align*}\]Given the estimate of Ideko’s free cash flow and WACC, we can estimate Ideko’s horizon value in 20Y0 as:
\[V^L_{20Y0} = {11.151 \over {9.05 \text{ % } - 5 \text{ % }}} = $275.33 \text{million}\]This horizon value represents a terminal EBITDA multiple of 275.33/32.09 = 8.6.
The full calculations are also summarised in the spreadsheet below:
Tip: Double click a cell to view its formula
Both the multiples approach (Ideko - Horizon Value with Multiples) and the discounted cash flow approach are useful in deriving a realistic continuation value estimate. Our recommendation is to combine both approaches.
As shown in the spreadsheet, our projected EBITDA multiple of 9.1 can be justified by the discounted cash flow method with a nominal long- term growth rate of about 5.34%.
Given an expected future inflation rate of 2.5%, this nominal rate represents a real growth rate of about 2.8%. This implied growth rate is another important reality check for our continuation value estimate. If it is much higher than our expectations of long-run growth for the industry as a whole, we should be more sceptical of the estimate being used.
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