# Is the Growth Potential of Stock Prices Underestimated? A Real Option Approach

By Levyne, Olivier; Heller, David | International Journal of Business, Fall 2014 | Go to article overview

# Is the Growth Potential of Stock Prices Underestimated? A Real Option Approach

Levyne, Olivier, Heller, David, International Journal of Business

I. INTRODUCTION: LIMITS OF THE DISCOUNTED CASH FLOW (DCF) VALUATION METHOD

From a DCF point of view, the value of the firm (EV) corresponds to the present value of the future free cash flows (FCF), the discount rate used being the weighted average cost of capital or WACC (K):

EV = [+[infinity].summation over (t=1)] [FCF.sub.t]/[(1 + K).sup.t]

with

K = k E/E + D + i.(1-[tau]) D/E + D

where E is the equity value and D is the net debt. The embedded WACC in the firm value calculation is based on the equity value which is looked for in the DCF approach. For that reason, practitioners include a loop in their DCF model.

Assuming a perpetuity growth rate g of FCF from year 1 onwards and a WACC equal to K:

EV = FCF.(1 + g)/K - g

and

K = k E/EV + i.(1 - [tau])D/EV

The reference to the Modigliani and Miller's adjusted cost of capital enables to get rid of the loop. Indeed, as

K = [rho].(1 - D.[tau]/EV)

where [rho] is the cost of capital of the unleveraged firm with the same sector risk. In other words, thanks to the Capital Asset Pricing Model, CAPM,

[rho] = r + [[beta].sup.*].[E([R.sub.M]) - r]

where r is the risk free rate. Then

EV = FCF.(1 + g)/[rho].(1 - D.[tau]/EV) - g

and

EV = FCF.(1 + g) + D.[tau].p/[rho] - g

D.[tau] is the tax shield which is justified by the tax deductibility of interests which are due on the assumed perpetual financial debt. Indeed, in the Modigliani and Miller's theory, D.[tau] results from the simplification of i.D.[tau]/i where i. D.[tau] is the tax saving on interests and i the corresponding capitalization rate. In that case, D is obviously the outstanding debt which can be found in the last available financial statements.

When practitioners deduct D from the EV to obtain the equity value, a closed form of E can be obtained:

E = FCF.(1 + g) + D.[g - [rho].(1-x)]/[rho] - g

The Modigliani and Miller's theory evidences that the spread on the risky debt has no impact on the WACC and therefore on the equity value: the cost of debt does not appear in the two previous formulas and any increase of the spread of the debt corresponds to an increase of the risk which is borne by the bondholders and banks. It is therefore consistent with a decrease of the risk which is borne by the shareholders. The Table below uses a simple example to show the risk transfer between stakeholders and the unchanged WACC:

```Table 1

The unchanged WACC according to Modigliani and Miller's theory

FCF                              100      100
Perpetuity growth = g          3.00%    3.00%
Risk free rate = r             2.00%    2.00%
Unleveraged beta = [beta] *     0.90     0.90
Cost of debt
Pretax cost of debt            3.40%    5.50%
Post tax @ 36.1%               2.17%    3.51%
Beta of the debt                0.20     0.50
Leveraged beta = [beta]         1.20     1.07
Cost of equity = k            10.38%    9.49%
WACC = K                       7.11%    7.11%
P                              8.30%    8.30%
Adjusted cost of capital       7.11%    7.11%
EV                             2,509    2,509
Debt                           1,000    1,000
Equity                         1,509    1,509
```

For a FCF which is equal to 100, a risk free rate of 2%, a market risk premium of 7% and an unleveraged beta of 0.9, 2 assumptions regarding the pretax cost of debt are taken into account: 3.40%, based on a debt's beta of 0.20 and 5.50% based on debt's beta of 0.50. The corresponding leveraged betas, based on the Hamada's formula, are respectively 1.20 and 1.07 and the implied costs of equity are respectively 10.38% and 9.49%. Then both WACC and adjusted costs of capital are 7.11%. Then the enterprise value is the same in both cases: 2509.

A. Discount Rates

The WACC calculation is a bit subjective as a lot of assumptions have to be taken into account: the market risk premium depends on a assumption regarding the perpetuity growth rate of the listed firms' dividends; when the firm is listed, the cost of equity can either include its beta (which is different according to the data provider) or a leveraged beta based on the industry's unleveraged beta, which depends on the peers which have been included in the sample; the weighting coefficients can correspond to a target--or normative--financial structure or be based on an iterative calculation. …

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