Firm Valuation Models

Approaches for valuing a firm

The cost of capital approach

Adjusted present value approach

Excess Return approach

Cost of Capital approach – FCFF is discounted with the weighted average cost of capital. Implicit in this is the tax benefit of debt (after tax cost of debt) and additional risk associated with debt (in the form of higher cost of equity and debt at higher debt ratios). The cost of capital captures both the tax benefits of borrowing and the expected bankruptcy cost. The cash flows discounted are the cash flows to the firm, computed as if the firm had no debt and no tax benefits from the interest expenses.

In this method changes in the financing mix i.e. varying debt equity ratio is captured in the cost of capital and not in the FCFF

For stable growth firms – Value of firm is FCFF*(1+g)/ (WACC-g), where g growth rate has to be less than or equal to the growth rate of economy and growth rate has to be consistent with the reinvestment rate i.e. Reinvestment rate = g/ROC with reinvestment rate we can forecast the capital expenditure and compare it with the actual capital expenditure calculated with the industry average reinvestment rate.

The cost of capital that is used for discounting the cash flows should reflect only the operating risk of the company. Also the firm value calculated by discounting the operating income with cost of capital measures the value of only the operating assets of the firm (which contribute to the operating income). Any assets whose earnings are not part of operating income have not been valued yet.

To calculate the value of the equity we have to make some adjustments

Add the non-operating assets like cash and marketable securities, the operating income from minority holdings in other companies is not included in the operating income and FCFF thus these need to be valued and added back to the value of the operating assets. Also if the firm has some idle and non-operating assets then value of these also need to be added

Subtract the non-equity claims like interest-bearing debt, present value of operating lease commitments, minority interest in consolidated companies, other potential claims against the firm like unfunded pension plans and health care obligations (these two are not included in debt in cost of capital calculation as these are not interest bearing liabilities). Also of the firm has any lawsuit which would result in potential payout that also needs to be subtracted.

The final adjustment relates to management options outstanding, we subtract the value of options outstanding currently and then divide it by the basic shares outstanding to calculate the value of equity per share

The main advantage of using the cost of capital approach is that the cash flows are unlevered i.e. independent of the level of leverage

Adjusted Present Value Approach – In APV we value the firm without debt, we add debt to the firm wherein we consider the net effect on value by considering both the benefits (tax benefits) and costs of borrowing (added cost of bankruptcy)

Value the firm without any leverage – Discount the FCFF with the unlevered cost of equity

Then calculate the expected tax benefit from a given level of debt which is equal to tax*cost of debt*debt/cost of debt = tax*debt. Tax * interest is discounted with the cost of debt to reflect the riskiness of this cash flow. Tax rate used is marginal tax rate

Final step is to evaluate the effect of the given level of debt on the default risk of the firm and on expected bankruptcy cost. This requires the probability of default with the additional debt and the direct and indirect cost of debt. PV of expected bankruptcy cost = Probability of bankruptcy (pie) * PV of bankruptcy cost (BC). Both these inputs are difficult to estimate. Probability of bankruptcy can be estimated from the rating of the firm and bankruptcy cost is estimated to be 20-30% of the firm value as per some studies.

Value of levered firm = FCFF*(1+g)/(unlevered cost of equity – g) + t*D – Pie*BC

The value of the firm by cost of capital approach and adjusted present value approach can be different because

In cost of capital approach bankruptcy cost is implicit in the cost of equity and cost of debt whereas in APV approach there is more flexibility in indirect cost of bankruptcy

APV approach considers the tax benefit from a dollar debt value, usually based on existing debt whereas the cost of capital approach estimates the tax benefit from a debt ratio that may require the firm to borrow increasing amounts in the future

Excess Returns Model – This approach computes the value of a firm as a function of expected excess returns. Economic Value Added (EVA) is one of the most widely used variant of excess return models which was popularized by Stern Stewart, a value consulting firm.

EVA = (Return on capital invested – Cost of capital) * Capital invested = EBIT *(1-t) – cost of capital * capital invested. Three inputs are required for EVA calculation ROC, Cost of capital and capital invested. We need to make three adjustment for capital invested one is R&D has to be capitalized and added back to assets, second is to treat operating leases as debt and third eliminate the effect of one time charges. Same adjustments we have to make for calculating the operating income for ROC calculation

Value of the firm = Value of assets in place + Value of expected future growth = Capital invested (assets in place) + NPV of EVA of assets in place + sum of NPV of EVA of all future assets. Thus the value of the firm can be written as the sum of three components: the capital invested in assets in place, the present value of the economic value added by these assets, and the expected present value of the economic value that will be added by future investments.

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