11.8Computing Certainty Equivalents from Prices in Financial Markets

In some cases, prices from financial markets provide information that analysts can use

to project future cash flows.

Forward Prices

Forward prices are related to estimates of the future spot prices of different currencies

and commodities. As Chapter 7 pointed out, the forward price represents the certainty

equivalent of the uncertain future price rather than its expected value. Whenever for-

ward prices are available for future cash flows, use the certainty equivalent method for

valuation. Such forward prices effectively translate data from the complex world of

risky cash flows to the much simpler world of riskless cash flows, which were con-

sidered in Chapter 10.

Example 11.11 illustrates how to value cattle using this method.

²⁷The analyst, however, might also want to consider the possibility that the managers may have a

tendency to be overly optimistic. This could offset the bias towards conservative estimates and justify a

higher discount rate.

Grinblatt842Titman: Financial	III. Valuing Real Assets	11. Investing in Risky	© The McGraw842Hill
Markets and Corporate		Projects	Companies, 2002
Strategy, Second Edition

414Part IIIValuing Real Assets

Example 11.11:Present Values with Certainty Equivalents from Futures Prices

Farmer John is considering the purchase of live cattle that will be ready for slaughter six

months from now, at which point their aggregate weight will be 100,000 pounds.The asking

price for the cattle is $50,000 and it will cost $10,000 to buy feed and medication for all the

cattle.The (unannualized) risk-free interest rate over this six-month period is 3 percent, and

the only source of uncertainty associated with this transaction is the future market price of

cattle.However, on the Chicago Mercantile Exchange, we observe a six-month forward price

for cattle of $0.70 per pound.Should Farmer John buy the cattle?

Answer:$70,000 is the certainty equivalent for the cattle revenue produced by the farm

in six months.A comparison of the present value of that amount, $67,961 $70,000/1.03,

with the cost of the cattle, the feed, and the medication, $60,000, implies that Farmer John

should purchase the cattle because the project has a positive NPVof $7,961.

Tracking Portfolios That Contain Forward Contracts

It would be difficult to calculate an expected cash flow and to apply the risk-adjusted

discount rate approach in Example 11.11. In this case, the tracking portfolio approach

provides an equivalent answer; the appropriate tracking portfolio would be a forward

contract to sell 100,000 pounds of live cattle along with $70,000/1.03 in a risk-free

investment with a return of 3 percent. Since the forward contract has zero value (see

Chapter 7), the value of that tracking portfolio is $70,000/1.03, which is the present

value of the future cash flows.²⁸