Choosing the discount rate

When we discount the cash flow of a project at a rate $i$, we compare the project with another way to use the same money: investing it at $i$ a year. If the NPV at this rate is positive, the project earns more than $i$. If it is negative, the project earns less (Net present value (NPV)). So the question “which rate should we take?” is really the question “what is money worth to the one who invests it?” Three ideas shape the answer.

• The cost of raising capital. A company's money belongs to its shareholders and its lenders, and every unit of it has a price. Lenders get interest. Shareholders get dividends (a share of the profit paid out) and a rising share price. A project that earns less than this price, the cost of capital, makes the owners poorer.
• Opportunity cost. Money, specialists and drilling rigs are limited. By putting them into one project, the company gives up another. The return of the best project that is turned down is the price of the choice.
• Risk. The less predictable the result of an investment, the higher the return that the investor asks for. The starting point is the return on safe government bonds in the same currency (the risk-free rate). For the risk on top of that, investors ask for an extra return, called a premium.

State the rate together with the period and the kind of money. “10% a year, real” is a rate for a cash flow in constant prices (real terms, with inflation taken out) and with yearly amounts. The lesson Inflation: nominal and real money shows how the same rate looks in nominal money (the money of each year).

A company pays for its investments from two sources. Equity is the money of the shareholders: what they paid in when the shares were issued, plus the profit of past years that was left in the company. There is no contract to pay it back. But a shareholder always has a choice: keep the shares, or sell them and put the money somewhere else. A shareholder stays only as long as the company is expected to give at least as much as the money would earn elsewhere at the same risk. The company gives it as dividends and as a rising share price. This expected return is called the cost of equity ($r_e$). A company that does not provide it finds it harder to raise new money from shareholders.

Debt means bank loans and bonds. Interest and repayment are a duty under a contract, whatever the success of the project. The cost of debt ($r_d$) is the full price of new borrowing: the interest rate together with fees, converted into a yearly rate. What matters is the price at which the company can borrow now, not the rate on old loans. In many tax systems, interest reduces the taxable profit. So debt in fact costs less: $r_d(1 - T)$, where $T$ is the income tax rate.

Equity costs more than debt. Lenders are paid first and under a contract. Shareholders get what is left, so their risk is higher. But cheap debt cannot replace all the equity. The larger the share of debt (it is called gearing, or leverage), the more fixed payments there are. Then the risk grows for both lenders and shareholders, and both rates rise. The weighted average cost of capital gives the average price of money for a company.

The cost of capital is the lower limit of the rate. A project that earns exactly WACC adds nothing to the wealth of the owners, but takes nothing away. A rate equal to the cost of capital lets through every project that at least earns the price of its money. If money, people and equipment were unlimited, this would be enough. In reality resources are short, and accepting a weak project means turning down a stronger one.

Then the opportunity cost of capital fits better. It is the return of the best project that has to be given up. Discounting at this rate compares the project with the alternative right away: NPV > 0 means that the project is better, and NPV < 0 means that it is worse. But this value is unstable. The set of available projects, the oil prices and the project estimates keep changing. So the opportunity cost is used as a guide when the hurdle rate is set. It is not recalculated for every decision.

Risk. An investor accepts more risk only for a higher expected return. The starting point is the risk-free rate: the return on government bonds of a reliable borrower in the same currency. For flows in dollars, we usually take the bonds of the US government. Everything that investors ask for above this rate is a risk premium. We measure risk by the spread of the possible results of the investment. The spread is often expressed as the standard deviation of the return (a number that shows how widely the results scatter around the average). The wider the range of outcomes, the higher the premium. That is why investors accept a lower return on the bonds of an oil company than on its shares: a bondholder gets the money earlier than a shareholder, and with more certainty.

It matters which risk the rate should cover. Part of the risk is common to the whole economy and the whole industry: the oil price, demand, interest rates, taxes. It cannot be removed by combining many projects, and investors ask for a premium for it. Another part belongs to the single project: whether the reserves will be confirmed, what the platform will cost, whether an exploration well turns out dry. In a large portfolio (many projects held together), such deviations largely cancel each other. So in theory we take them into account not with a premium on the rate, but with probabilities and scenarios (Expected monetary value and preference theory, Geological and technical uncertainty of a project). In practice, companies often add premiums for such risks too. So it is important to understand what a premium does to the cash flow (see the section on the hurdle rate).

None of the ingredients of the rate can be measured once and for all. Interest rates and exchange rates change, the expectations of shareholders follow the oil price, and the set of projects is renewed. So companies do not work out a “true” rate for every decision. They set a hurdle rate: the lowest return that they accept. It is the same for similar projects, and it is reviewed, for example, once a year.

• One rate for the whole company. Usually it is not lower than WACC, and often it is set higher, to leave a margin. There is not enough money and there are not enough specialists for all projects, and project estimates are on average too optimistic. A single rate is simple and makes projects comparable.
• Rates by risk class. These are separate rates or premiums for countries, for exploration and for development, and for new technology. One rate for projects of very different risk distorts the picture: risky projects look better than they are, and safe ones look worse.
• Prescribed rates. To make reports comparable, rules sometimes set the rate. In the US reporting of proved reserves (the volumes that can be recovered with high confidence), the future cash flows are discounted at a fixed rate of 10%. Hence the name common in the industry, PV-10 (the present value at 10%). It is an agreed rule for comparing companies, not the cost of capital of any particular company.
• Calculation at several rates. Even when a rate has been approved, it is useful to show the NPV at several values, for example 8, 10, 12 and 15%. Then you can see how much the decision depends on this assumption.

A risk premium on the rate looks like a simple and cautious decision. But it acts not on the risk but on time. A flow $t$ years ahead is reduced by a factor of $\left((1 + i + \Delta)/(1 + i)\right)^{t}$, where $\Delta$ is the premium. Near flows hardly suffer, and distant flows suffer a lot, however uncertain they really are.

The present value of a flow $t$ years ahead is proportional to $(1+i)^{-t}$. So when the rate changes a little, the present value changes by a fraction of about $-t\,\Delta i/(1+i)$. This fraction grows with the time to the flow. Long projects with late income lose much more from a rise in the rate than quick projects that pay back in a year or two. Examples of long projects are gas fields with a long production plateau (a period of steady, high output) and projects that recover a larger share of the oil (enhanced oil recovery).

The rate also changes the order of the options. The lesson Internal rate of return (IRR) compares two ways to restore the production of a well: hydraulic fracturing (A) and a sidetrack (B). Hydraulic fracturing cracks the rock around the well to help oil flow. A sidetrack is a new branch drilled from the existing well. At 10%, B has the larger NPV: 1.70 against 1.03 million dollars. At 15%, A wins: 0.73 against 0.59 million dollars. The profiles cross at about 14.1%. A high rate favours fast options that pay early, and a low rate favours long ones.

The rate and the cash flow come as a pair. One project can be valued in different consistent ways, but you cannot take the cash flow from one way and the rate from another.