## Models Based in Discounted Cash Flow (DCF)

The discounted cashflow-based method (DCF valuation method), as the traditional fundamental valuation technique, relies on the capital asset pricing model (CAPM) to compute the cost of capital.

## DCF Valuation

There are four variants of discounted cash flow models in practice and theorists have long argued about their advantages and disadvantages.

- In the first, the expected cash flows on an asset (or a business) are discounted at a risk-adjusted discount rate to arrive at the value of the asset
- In the second, the expected cash flow is first adjusted for risk to obtain the risk-adjusted or certainty equivalent cashflows, which is then discounted at the risk free rate to estimate the value of the risky asset
- The third is termed the adjusted present value (APV) approach in which the business is first valued, without the effects of debt, the marginal effects on value is then considered
- Finally, a business can be valued as a function of the excess returns that it is expected to generate on its investments. However, there are common assumptions that bind these approaches together, but there are variants in assumptions in practice that result in different values

### Discount Rate Adjustment and Cash flows Adjustment Models

Amongst others, the risk adjusted discount rate approach is the most common, where a higher discount rate is used to discount expected cash flows when valuing riskier assets, and a lower discount rate is used when valuing safer assets.

Some companies assess all projects using a single discount rate; however, this method can work only when all the projects under analysis have the same level of risk, but this is usually not the case. There are two ways in which dcf valuation can be approached. “The first is to value the entire business, with both assets-in-place and growth assets; this is often termed firm or enterprise valuation.

The second way is to value just the equity stake in the business, and this is called equity valuation. The cash flows after debt payments and reinvestment needs are called free cash flows to equity, and the discount rate that reflects just the cost of equity financing is the cost of equity. It is also important to note that one can always get from the former (firm value) to the latter (equity value) by netting out the value of all non-equity claims from firm value. Done right, the value of equity should be the same whether it is valued directly (by discounting cash flows to equity at the cost of equity) or indirectly (by valuing the firm and subtracting out the value of all non-equity claims)”.

In cash flow adjustment, cash flows for each alternative are adjusted before the comparison, based on its probability of occurrence. The present value of each alternative is estimated using value scenarios as follows: Optimistic, Expected or Pessimistic. However, in practice, analysts and investors find these probabilities challenging, since they do not have a magical way to determine which one of the probabilities will occur for every cash flow.

Corporate risk is still debatable in investment valuation. This is because it is conceived differently in decision theory, which uses probabilities, and in financial economics, which adjusts the discount rate of the cash flows instead.

### The Hybrid Method

Some practitioners use a method that simultaneously adjusts both the cash flow and discount rates. The cash flows are first discounted for each state at a rate higher than the risk-free rate, but lower than the rate used in a pure rate adjustment model after which a probability weighted, single economic value is found for the scenarios. This procedure is controversial because it is difficult to say which portion of risk corresponds to each adjustment. However, the method is still in use.

### Adjusted Present Value (APV) or Weighted Average Cost of Capital (WACC)

The cost of equity (Ce), which is usually computed by using the capital asset pricing model (CAPM), is used for discounting free cash flows of equity (FCFE). With CAPM, expected risk premium on stock = beta x expected risk premium on market.

r = rf + β(rm – rf)

Where:

r is expected risk premium (expected return on asset)

rf is the risk-free rate of interest

rm is the return on the market β (Beta) = Cov(Ri Rm)/σ m (that is – covariance between the market and stock i, divided by the corresponding market variance. σ m = Market Variance

Beta can be estimated by regression analysis. Based on CAPM, Ce is equal to the risk-free rate plus a risk premium. This premium is the product of the sensitivity of returns of the company’s shares to the market return (the beta factor) and the so-called systematic risk premium (the difference between the average market return and the risk-free rate).

The entire mass of assets invested in the company in economic terms reflected by free cash flows for the firm (FCFF) is usually discounted at a cost of capital, which reflects the costs of both equity and debt as the weighted average cost of capital (WACC).

WACC captures in a single figure the combined costs of equity and debt and the cost is reduced whenever the tax rate generates a tax shield, because debt interests are (at least partially) deductible as an expense in the income statement; interest expenses reduce reported income and therefore total tax payments”. The need to recalculate the cost of capital for each and every year is a disadvantage with the use of WACC and may impel the analyst to directly apply the adjusted present value (APV) method.

WACC = rdebt (1-Tc)D/V+requity(E/V)

Where:

r = cost of capital

Tc = Company tax rate

D = Market value of debt

E = Market value of equity

V = Market value of company

The APV method involves putting apart the operating cash flow of the business from all the effects of financial leverage and each APV cash flows need to be discounted at a proper rate. The business cash flow, composed of operating inflows and outflows, must be discounted with the cost of equity, as if the whole project were financed exclusively by equity. The tax shield cash flow is discounted with the cost of debt, the true cost at which the company can issue debt in the market. The first attempt to isolate the effect of tax benefits from borrowing was by Modigliani and Miller, where they valued the present value of the tax savings in debt as a perpetuity using the cost of debt as the discount rate. The adjusted present value approach, in its current form, was first presented in 1974 in the context of examining the interrelationship between investments and financing decisions.

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