## Forecast Cash Flow in the Subsidiarys Home Currency

As mentioned at the beginning of this chapter, it is best to value a foreign subsidiary in its home currency. But first, you should forecast the components of cash flow in their most relevant currency. This means forecasting the British pound cash flows in British pounds, the Swiss franc cash flows in Swiss francs, and so on, before combining them into a set of financials for the foreign subsidiary. In practice, this is an iterative process: you cannot forecast the individual line items without considering how they affect the other line items in the forecast. You need a coherent integrated forecast that reflects the competitive dynamics of the business unit.

Once all cash flow has been forecasted in terms of its most relevant currency, it should be converted into the currency of the subsidiary before discounting using the forward-rate method. In our example, forward foreign exchange rates are used to convert forecasted French Euro revenues to British pound cash flow on a year-by-year basis. Then it combines this with other pound-equivalent cash flow received by the English subsidiary, and discounts it at the English subsidiary's weighted average cost of capital. As a practical matter, for most currencies forward exchange rates are not available beyond 18 months. Using this method means forecasting long-term foreign exchange rates, a task that will be explained shortly.

A mathematically equivalent alternative to the forward-rate method is the spot-rate method. We will employ it in step 3 to discount all of the subsidiary's cash flow that has been restated in pounds sterling at the English subsidiary's cost of capital to translate its present value to U.S. dollars at the spot exchange rate.

The spot-rate method is not generally used to convert partial cash flow, such as a revenue stream denominated in Euros, because no practical way exists to estimate a risk-adjusted Euro discount rate for the revenue stream alone. Estimating the appropriate discount rate for total cash flow from operations is difficult enough.

To do the forward-rate method, you must use interest-rate parity to forecast future spot foreign exchange rates, and then use the future spot foreign exchange rates to convert predicted foreign currency cash flow into the subsidiary's domestic currency. We will focus on a stream of revenue

Exhibit 17.6 English Subsidiary's Forecasted French Revenues

Exhibit 17.6 English Subsidiary's Forecasted French Revenues

received from France by the English subsidiary. The forecasted Euro revenues are shown in Exhibit 17.6.

The interest-rate parity theory is based on the idea that changes in foreign exchange rates are related to the ratio of expected inflation rates between two countries. Exhibit 17.7 plots the relationship between domestic inflation and domestic interest rates for 47 countries from 1977 to 1981. Inflation often explains most of the difference in nominal interest rates.

Across countries, the interest-rate parity theory is expressed as follows: the expected spot foreign exchange rate in year t, Xft, is equal to the current Exhibit 17.7 Relationship between Inflation and Interest Rates

Average of banks' lending rate at start of year (pertent)

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Average of banks' lending rate at start of year (pertent)

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spot rate, X0, multiplied by the ratio of nominal rates of return in the two countries over the forecast interval, t (for a derivation, see Copeland and Weston, pp. 790-8033):

Where, f = The foreign currency d = The domestic currency

To illustrate the theory for a single year, suppose that our English subsidiary can borrow one-year money in Switzerland at a 4 percent nominal interest rate, N, while the borrowing rate in England is 7.1 percent. The spot exchange rate, X0, is 2.673 Swiss francs per pound sterling and the one-year forward rate, X, is 2.5944 Swiss francs per dollar. We can use interest-rate parity to estimate what English borrowing rate a 4 percent borrowing rate in Switzerland is equivalent to:

No practical difference exists between borrowing in England at 7.15 percent or in Switzerland at 4 percent, because the Swiss rate is equivalent to 7.15 percent in England. The foreign borrowing rate, when converted to a domestic equivalent rate, is usually close to the domestic rate (unless there are tax implications).

Next, we show how to use interest-rate parity to forecast future spot rates and use that information to convert the French Euro revenues in Exhibit 17.6 to English pounds. Exhibit 17.8 uses U.K. and French data to illustrate. The first two rows are the term structures of interest rates on government debt for England and France. The third row is the ratio of nominal rates. We know from the interest-rate parity theory that the ratio of nominal rates multiplied by the current spot rate (pounds/Euros) provides an estimate of the forward exchange rate.

As indicated in the fifth row, the market is forecasting that the pound will strengthen versus the Euro. The French Euro revenues in line 6 of Exhibit 17.8 are converted to pound revenues (line 7) by using the interest-rate

3 T.E. Copeland and J.F. Weston, Financial Theory and Corporate Policy, 3rd ed. (Reading, MA: Addison-Wesley, 1988).

Exhibit 17.8 Example of Forecasting Forward Exchange Rates ^-

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