## Project and component cash flow procedure

In this post I want to give some remarks on the component cash flow procedure. I am using this approach in my DCF analysis. It is the only correct way to discount the cash flows of complex investments, projects or diversified firms. In investment valuation many analysts take the WACC of the company, the business unit or the investment project to discount the cash flows. Taking only one single discount rate in a valuation is called **project cash flow procedure** (PCFP)

But most projects consist of a **mixture **of cash flows with **different risks**. To take this into account the present value of each cash flow should be calculated using a discount rate appropriate for its risk. The present values of all of the cash flow components should then be summed up. Projects should hence be selected using the present value criterion applied to its total present values. This approach is called **component cash flow procedure** (CCFP).

## Disadvantages of using a single discount rate

In general, it is possible to find a composite discount rate for a project that gives the same NPV for the project as the NPV derived from the component cash flow procedure. The net cash flows can be determined that gives the same present value as the sum of the present values of its components. But there are at least three problems in applying one discount rate to the sum of the cash flows (Bierman, Smidt / Advanced Capital Budgeting, 2007).

- Any
**change in assumptions**about the project will tend to lead to a**change in the composite discount rate**. Changing the life of the project or the proportion of any of its cash flow components would likely require a different composite discount rate for the total cash flows. - If the correct composite discount rate is applied to the net cash flows of a project, then although the NPV of the project will be correct, the
**present values**assigned to the**cash flow components**using this rate**will be inaccurate**. For example, the present value of the depreciation tax shields will usually be underestimated. In addition, the present value of the total cash flows in a particular year or a particular period will usually be inaccurate. This may lead to**errors in decisions**, such as estimating the value of the project at various future dates. - If the
**cash flow mixture is changed**, the present value calculated using the previous**composite discount rate would not produce accurate present values**. This is particularly important in making choice between mutually exclusive alternatives that frequently involve a change in the mixture of cash flows, for example, the substitution of capital for labor.

If the project life is finite and greater than one year, then finding the composite discount rate of a project requires finding an IRR. There may be projects for which an IRR does not exist, or is not unique. For those projects, there may be **no composite rate**, or the composite rate may **not be unique**.

## My proposal for appropriate discount rates

I propose the following way to discount the cash flows in a DCF analysis:

**Market related (contribution) cash flows**that depend on the overall market development should be discounted with their appropriate risk adjusted WACC. For that I take the CAPM (including additional country risk premiums for non-diversifiable country specific risks) and the APT. These WACC should include appropriate default free interest rates, market and country risk premiums, the appropriate debt to equity ratios, equity betas and marginal tax rates.**Revenues**,**variable costs**,**taxes**and expenses for**working capital**are mainly part of these market contribution cash flows. If you have a project with revenues in various markets with different currencies and risks, you have to discount each cash flow with its appropriate discount rate. If you do not take the specific appropriate discount rate for each market cash flow, you can get wrong results in your calculation.**Capex / investment**cash flows should be discounted with the risk-free rate of the corresponding currency. These cash flows are not related to any market development.**One time payments and expenses**should be discounted with the risk-free rate of the corresponding currency. These cash flows are not related to any market development.**Fixed costs**should be discounted with the risk-free rate of the corresponding currency. In some real options, e.g. switch options, savings in fixed costs are part of the option value. Option values are discounted with the risk-free rate, which is close to the WACC with a CAPM beta of 0. In this way DCF and ROA concepts fit together.**Leasing revenues and expenses**should be discounted with the risk-free rate of the corresponding currency. The buy versus lease decision illustrates well the desirability of using different discount rates for cash flows with different characteristics. The use of different discount rates for different cash flow components is a widely accepted practice in analyzing buy vs lease problems.**Interests**and**Tax shield savings**depend on the leverage strategy of the company. If the amount of debt is fixed over time, the discount rate should be the risk-free rate of the corresponding currency. If the share of debt is kept constant over time, the discount rate should be the specific risk-adjusted market WACC.

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