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Discount Nominal Cash Flows by the Nominal Cost of Capital

The distinction between nominal and real cash flows and interest rates is crucial in capital budgeting. Interest rates are usually quoted in nominal terms. If you invest $100 in a bank deposit offering 6 percent interest, then the bank promises to pay you $106 at the end of the year. It makes no promises about what that $106 will buy. The real rate of interest on the bank deposit depends on inflation. If inflation is 2 percent, that $106 will buy you only 4 percent more goods at the end of the year than your $100 could buy today. The real rate of interest is therefore about 4 percent.3

If the discount rate is nominal, consistency requires that cash flows be estimated in nominal terms as well, taking account of trends in selling price, labor and materials costs, and so on. This calls for more than simply applying a single assumed inflation rate to all components of cash flow. Some costs or prices increase faster than inflation, some slower. For example, perhaps you have entered into a 5-year fixed-price contract

with a supplier. No matter what happens to inflation over this period, this part of your costs is fixed in nominal terms.

Of course, there is nothing wrong with discounting real cash flows at the real interest rate, although this is not commonly done. We saw earlier that real cash flows discounted at the real discount rate give exactly the same present values as nominal cash flows discounted at the nominal rate.

It should go without saying that you cannot mix and match real and nominal quantities. Real cash flows must be discounted at a real discount rate, nominal cash flows at a nominal rate. Discounting real cash flows at a nominal rate is a big mistake.

While the need to maintain consistency may seem like an obvious point, analysts sometimes forget to account for the effects of inflation when forecasting future cash flows. As a result, they end up discounting real cash flows at a nominal interest rate. This can grossly understate project values.

Cash Flows and Inflation

City Consulting Services is considering moving into a new office building. The cost of a 1-year lease is $8,000, but this cost will increase in future years at the annual inflation rate of 3 percent. The firm believes that it will remain in the building for 4 years. What is the present value of its rental costs if the discount rate is 10 percent? The present value can be obtained by discounting the nominal cash flows at the 10 percent discount rate as follows:

Alternatively, the real discount rate can be calculated as 1.10/1.03 1 = .067961 = 6.7961%. The present value of the cash flows can also be computed by discounting the real cash flows at the real discount rate as follows:

Notice the real cash flow is a constant, since the lease payment increases at the rate of inflation. The present value of each cash flow is the same regardless of the method used to discount. The sum of the present values is, of course, also identical.

Separate Investment and Financing Decisions

When we calculate the cash flows from a project, we ignore how that project is financed. The company may decide to finance partly by debt but, even if it did, we would neither subtract the debt proceeds from the required investment nor recognize the interest and principal payments as cash outflows. Regardless of the actual financing, we should view the project as if it were all equity-financed, treating all cash outflows required for the project as coming from stockholders and all cash inflows as going to them.

We do this to separate the analysis of the investment decision from the financing decision. We first measure whether the project has a positive net present value, assuming all-equity financing. Then we can undertake a separate analysis of the financing decision. We discuss financing decisions later.

Nasty Industries is closing down an outmoded factory and throwing all of its workers out on the street. Nasty s CEO, Cruella DeLuxe, is enraged to learn that it must continue to pay for workers health insurance for 4 years. The cost per worker next year will be $2,400 per year, but the inflation rate is 4 percent, and health costs have been increasing at three percentage points faster than inflation. What is the present value of this obligation? The (nominal) discount rate is 10 percent.