# Valuing businesses

The value of a business is equal to the present value of all future (free) cash flows using the after-tax WACC as the discount rate. A project's free cash flows generally fall into three categories

1. Initial investment

- Initial outlay including installation and training costs

- After-tax gain if replacing old machine

2. Annual free cash flow

- Profits, interest, and taxes

- Working capital

3. Terminal cash flow

- Salvage value

- Taxable gains or losses associated with the sale

For long-term projects or stocks (which last forever) a common method to estimate the present value is to forecast the free cash flows until a valuation horizon and predict the value of the project at the horizon. Both cash flows and the horizon values are discounted back to the present using the after-tax WACC as the discount rate:

Where FCFi denotes free cash flows in year i, WACC the after-tax weighted average cost of capital and PVt the horizon value at time t.

There exist two common methods of how to estimate the horizon value

1. Apply the constant growth discounted cash flow model, which requires a forecast of the free cash flow in year t+1 as well as a long-run growth rate (g):

2. Apply multiples of earnings, which assumes that the value of the firm can be estimated as a multiple on earnings before interest, taxes (EBIT) or earnings before interest, taxes, depreciation, and amortization (EBITDA):

**PVt = EBIT Multiple • EBIT**

**PVt = EBITDA Multiple • EBITDA**

**Example:**

- If other firms within the industry trade at 6 times EBIT and the firm's EBIT is forecasted to be €10 million, the terminal value at time t is equal to 6-10 = €60 million.

**Capital budgeting in practice**

Firms should invest in projects that are worth more than they costs. Investment projects are only worth more than they cost when the net present value is positive. The net present value of a project is calculated by discounting future cash flows, which are forecasted. Thus, projects may appear to have positive NPV because of errors in the forecasting. To evaluate the influence of forecasting errors on the estimated net present value of the projects several tools exists:

- Sensitivity analysis

- Analysis of the effect on estimated NPV when a underlying assumption changes, e.g. market size, market share or opportunity cost of capital.

- Sensitivity analysis uncovers how sensitive NPV is to changes in key variables.

- Scenario analysis

- Analyses the impact on NPV under a particular combination of assumptions. Scenario analysis is particular helpful if variables are interrelated, e.g. if the economy enters a recession due to high oil prices, both the firms cost structure, the demand for the product and the inflation might change. Thus, rather than analysing the effect on NPV of a single variable (as sensitivity analysis) scenario analysis considers the effect on NPV of a consistent combination of variables.

- Scenario analysis calculates NPV in different states, e.g. pessimistic, normal, and optimistic.

- Break even analysis

- Analysis of the level at which the company breaks even, i.e. at which point the present value of revenues are exactly equal to the present value of total costs. Thus, break-even analysis asks the question how much should be sold before the production turns profitable.

- Simulation analysis

- Monte Carlo simulation considers all possible combinations of outcomes by modeling the project. Monte Carlo simulation involves four steps:

1. Modeling the project by specifying the project's cash flows as a function of revenues, costs, depreciation and revenues and costs as a function of market size, market shares, unit prices and costs.

2. Specifying probabilities for each of the underlying variables, i.e. specifying a range for e.g. the expected market share as well as all other variables in the model

3. Simulate cash flows using the model and probabilities assumed above and calculate the net present value

## Why projects have positive NPV

In addition to performing a careful analysis of the investment project's sensitivity to the underlying assumptions, one should always strive to understand why the project earns economic rent and whether the rents can be sustained.

Economic rents are profits than more than cover the cost of capital. Economic rents only occur if one has

- Better product

- Lower costs

- Another competitive edge

Even with a competitive edge one should not assume that other firms will watch passively. Rather one should try to identify:

- How long can the competitive edge be sustained?

- What will happen to profits when the edge disappears?

- How will rivals react to my move in the meantime?

- Will they cut prices? o Imitate the product?

Sooner or later competition is likely to eliminate economic rents.