A model is a simplified representation of reality that helps us to understand how something works.
Capital budgeting has a rich history and sometimes employs some pretty sophisticated procedures. Fortunately, capital budgeting relies on just a few basic principles. Capital budgeting usually uses the following assumptions:
Decisions are based on cash flows. The decisions are not based on accounting concepts, such as net income. Furthermore, intangible costs and benefits are often ignored because, if they are real, they should result in cash flows at some other time.
Timing of cash flows is crucial. Analysts make an extraordinary effort to detail precisely when cash flows occur.
Cash flows are based on opportunity costs. What are the incremental cash flows that occur with an investment compared to what they would have been without the investment?
Cash flows are analyzed on an after-tax basis. Taxes must be fully reflected in all capital budgeting decisions.
Financing costs are ignored. This may seem unrealistic, but it is not. Most of the time, analysts want to know the after-tax operating cash flows that result from a capital investment. Then, these after-tax cash flows and the investment outlays are discounted at the “required rate of return” to find the net present value (NPV). Financing costs are reflected in the required rate of return. If we included financing costs in the cash flows and in the discount rate, we would be double-counting the financing costs. So even though a project may be financed with some combination of debt and equity, we ignore these costs, focusing on the operating cash flows and capturing the costs of debt (and other capital) in the discount rate.
Capital budgeting cash flows are not accounting net income. Accounting net income is reduced by noncash charges such as accounting depreciation. Furthermore, to reflect the cost of debt financing, interest expenses are also subtracted from accounting net income. (No subtraction is made for the cost of equity financing in arriving at accounting net income.) Accounting net income also differs from economic income, which is the cash inflow plus the change in the market value of the company. Economic income does not subtract the cost of debt financing, and it is based on the changes in the market value of the company, not changes in its book value (accounting depreciation). We will further consider cash flows, accounting income, economic income, and other income measures at the end of this reading.
In assumption 5 above, we referred to the rate used in discounting the cash flows as the “required rate of return.” The required rate of return is the discount rate that investors should require given the riskiness of the project. This discount rate is frequently called the “opportunity cost of funds” or the “cost of capital.” If the company can invest elsewhere and earn a return of r, or if the company can repay its sources of capital and save a cost of r, then r is the company’s opportunity cost of funds. If the company cannot earn more than its opportunity cost of funds on an investment, it should not undertake that investment. Unless an investment earns more than the cost of funds from its suppliers of capital, the investment should not be undertaken. The cost-of-capital concept is discussed more extensively elsewhere. Regardless of what it is called, an economically sound discount rate is essential for making capital budgeting decisions.
Although the principles of capital budgeting are simple, they are easily confused in practice, leading to unfortunate decisions. Some important capital budgeting concepts that managers find very useful are given below.
A sunk cost is one that has already been incurred. You cannot change a sunk cost. Today’s decisions, on the other hand, should be based on current and future cash flows and should not be affected by prior, or sunk, costs.
An opportunity cost is what a resource is worth in its next-best use. For example, if a company uses some idle property, what should it record as the investment outlay: the purchase price several years ago, the current market value, or nothing? If you replace an old machine with a new one, what is the opportunity cost? If you invest $10 million, what is the opportunity cost? The answers to these three questions are, respectively: the current market value, the cash flows the old machine would generate, and $10 million (which you could invest elsewhere).
An incremental cash flow is the cash flow that is realized because of a decision: the cash flow with a decision minus the cash flow without that decision. If opportunity costs are correctly assessed, the incremental cash flows provide a sound basis for capital budgeting.
An externality is the effect of an investment on other things besides the investment itself. Frequently, an investment affects the cash flows of other parts of the company, and these externalities can be positive or negative. If possible, these should be part of the investment decision. Sometimes externalities occur outside of the company. An investment might benefit (or harm) other companies or society at large, and yet the company is not compensated for these benefits (or charged for the costs). Cannibalization is one externality. Cannibalization occurs when an investment takes customers and sales away from another part of the company.
Conventional versus nonconventional cash flows—A conventional cash flow pattern is one with an initial outflow followed by a series of inflows. In a nonconventional cash flow pattern, the initial outflow is not followed by inflows only, but the cash flows can flip from positive to negative again (or even change signs several times). An investment that involved outlays (negative cash flows) for the first couple of years that were then followed by positive cash flows would be considered to have a conventional pattern. If cash flows change signs once, the pattern is conventional. If cash flows change signs two or more times, the pattern is nonconventional.
Several types of project interactions make the incremental cash flow analysis challenging. The following are some of these interactions:
Independent versus mutually exclusive projects. Independent projects are projects whose cash flows are independent of each other. Mutually exclusive projects compete directly with each other. For example, if Projects A and B are mutually exclusive, you can choose A or B, but you cannot choose both. Sometimes there are several mutually exclusive projects, and you can choose only one from the group.
Project sequencing. Many projects are sequenced through time, so that investing in a project creates the option to invest in future projects. For example, you might invest in a project today and then in one year invest in a second project if the financial results of the first project or new economic conditions are favorable. If the results of the first project or new economic conditions are not favorable, you do not invest in the second project.
Unlimited funds versus capital rationing. An unlimited funds environment assumes that the company can raise the funds it wants for all profitable projects simply by paying the required rate of return. Capital rationing exists when the company has a fixed amount of funds to invest. If the company has more profitable projects than it has funds for, it must allocate the funds to achieve the maximum shareholder value subject to the funding constraints.
Source: Institute, CFA. 2018 CFA Program Level II Volume 3 Corporate Finance. CFA Institute, 07/2017. VitalBook file.
A conertible bond is a bond with an embedded conversion option that gives the bondholder the right to convert their bonds into the issuer’s common stock during a pre-determined period at a pre-determined price.
A convertible bond is a hybrid security. In its traditional form, it presents the characteristics of an option-free bond and an embedded conversion option. The conversion option is a call option on the issuer’s common stock, which gives bondholders the right to convert their debt into equity during a pre-determined period (known as the conversion period) at a pre-determined price (known as the conversion price).
Convertible bonds have been issued and traded since the 1880s. They offer benefits to both the issuer and the investors. Investors usually accept a lower coupon for convertible bonds than for otherwise identical non-convertible bonds because they can participate in the potential upside through the conversion mechanism—that is, if the share price of the issuer’s common stock (underlying share price) exceeds the conversion price, the bondholders can convert their bonds into shares at a cost lower than market value. The issuer benefits from paying a lower coupon. In case of conversion, an added benefit for the issuer is that it no longer has to repay the debt that was converted into equity.
However, what might appear as a win–win situation for both the issuer and the investors is not a “free lunch” because the issuer’s existing shareholders face dilution in case of conversion. In addition, if the underlying share price remains below the conversion price and the bond is not converted, the issuer must repay the debt or refinance it, potentially at a higher cost. If conversion is not achieved, the bondholders will have lost interest income relative to an otherwise identical non-convertible bond that would have been issued with a higher coupon and would have thus offered investors an additional spread.
Another type of embedded option that resembles a put option is an extension option: At maturity, the holder of an extendible bond has the right to keep the bond for a number of years after maturity, possibly with a different coupon. In this case, the terms of the bond’s indenture or offering circular are modified, but the bond remains outstanding. Examples of extendible bonds can be found among Canadian issuers such as Royal Bank of Canada, which, as of July 2013, has a 1.125% semi-annual coupon bond outstanding that matures on 22 July 2016 but is extendible to 21 July 2017.
A putable bond is a bond that includes an embedded put option. The put option is an investor option—that is, the right to exercise the option is at the discretion of the bondholder. The put provision allows the bondholders to put back the bonds to the issuer prior to maturity, usually at par. This usually happens when interest rates have risen and higher-yielding bonds are available.
Similar to callable bonds, most putable bonds include lockout periods. They can be European or, rarely, Bermudan style, but there are no American-style putable bonds.
2018 CFA Program Level II Volume 5 Fixed Income and Derivatives.
There are two methods commonly used to estimate volatility.
The first method is by estimating historical volatility; volatility is calculated by using data from the recent past with the assumption that what has happened recently is indicative of the future.
A second method to estimate volatility is based on observed market prices of interest rate derivatives (e.g., swaptions, caps, floors). This approach is called implied volatility.
The central idea of financial economics is that market prices will adjust until there are no opportunities for arbitrage. We will define shortly what is meant by an arbitrage opportunity, but for now think of it as “free money.” Prices will adjust until there is no free money to be acquired. Arbitrage opportunities arise as a result of violations of the law of one price. The law of one price states that two goods that are perfect substitutes must sell for the same current price in the absence of transaction costs. Two goods that are identical, trading side by side, are priced the same. Otherwise, if it were costless to trade, one would simultaneously buy at the lower price and sell at the higher price. The riskless profit is the difference in the prices. An individual would repeat this transaction without limit until the two prices converge. An implication of these market forces is deceptively straightforward and basic. If you do not put up any of your own money and take no risk, your expected return should be zero.
The preferred habitat theory is similar to the segmented markets theory in proposing that many borrowers and lenders have strong preferences for particular maturities but it does not assert that yields at different maturities are determined independently of each other.
However, the theory contends that if the expected additional returns to be gained become large enough, institutions will be willing to deviate from their preferred maturities or habitats. For example, if the expected returns on longer-term securities exceed those on short-term securities by a large enough margin, money market funds will lengthen the maturities of their assets. And if the excess returns expected from buying short-term securities become large enough, life insurance companies might stop limiting themselves to long-term securities and place a larger part of their portfolios in shorter-term investments.
The preferred habitat theory is based on the realistic notion that agents and institutions will accept additional risk in return for additional expected returns. In accepting elements of both the segmented markets theory and the unbiased expectations theory, yet rejecting their extreme polar positions, the preferred habitat theory moves closer to explaining real-world phenomena. In this theory, both market expectations and the institutional factors emphasized in the segmented markets theory influence the term structure of interest rates.
Unlike expectations theory and liquidity preference theory, segmented markets theory allows for lender and borrower preferences to influence the shape of the yield curve. The result is that yields are not a reflection of expected spot rates or liquidity premiums. Rather, they are solely a function of the supply and demand for funds of a particular maturity. That is, each maturity sector can be thought of as a segmented market in which yield is determined independently from the yields that prevail in other maturity segments.
The theory is consistent with a world where there are asset/liability management constraints, either regulatory or self-imposed. In such a world, investors might restrict their investment activity to a maturity sector that provides the best match for the maturity of their liabilities. Doing so avoids the risks associated with an asset/liability mismatch.
For example, because life insurers sell long-term liabilities against themselves in the form of life insurance contracts, they tend to be most active as buyers in the long end of the bond market. Similarly, because the liabilities of pension plans are long term, they typically invest in long-term securities. Why would they invest short term given that those returns might decline while the cost of their liabilities stays fixed? In contrast, money market funds would be limited to investing in debt with maturity of one year or less, in general.
In summary, the segmented markets theory assumes that market participants are either unwilling or unable to invest in anything other than securities of their preferred maturity. It follows that the yield of securities of a particular maturity is determined entirely by the supply and demand for funds of that particular maturity.
Liquidity preference theory is a theory that explains the term structure of interest rates. The theory asserts that liquidity premiums exist to compensate investors for the added interest rate risk they face when lending long term and that these premiums increase with maturity. Thus, given an expectation of unchanging short-term spot rates, liquidity preference theory predicts an upward-sloping yield curve. The forward rate provides an estimate of the expected spot rate that is biased upward by the amount of the liquidity premium, which invalidates the unbiased expectations theory.
Compare to the unbiased expectations theory which leaves no room for risk aversion, liquidity preference theory attempts to account for it.
For example, the US Treasury offers bonds that mature in 30 years. However, the majority of investors have an investment horizon that is shorter than 30 years. For investors to hold these bonds, they would demand a higher return for taking the risk that the yield curve changes and that they must sell the bond prior to maturity at an uncertain price. That incrementally higher return is the liquidity premium. Note that this premium is not to be confused with a yield premium for the lack of liquidity that thinly traded bonds may bear. Rather, it is a premium applying to all long-term bonds, including those with deep markets.
Liquidity preference theory fails to offer a complete explanation of the term structure. Rather, it simply argues for the existence of liquidity premiums. For example, a downward-sloping yield curve could still be consistent with the existence of liquidity premiums if one of the factors underlying the shape of the curve is an expectation of deflation (i.e., a negative rate of inflation due to monetary or fiscal policy actions). Expectations of sharply declining spot rates may also result in a downward-sloping yield curve if the expected decline in interest rates is severe enough to offset the effect of the liquidity premiums.
In summary, liquidity preference theory claims that lenders require a liquidity premium as an incentive to lend long term. Thus, forward rates derived from the current yield curve provide an upwardly biased estimate of expected future spot rates. Although downward-sloping or hump-shaped yield curves may sometimes occur, the existence of liquidity premiums implies that the yield curve will typically be upward sloping.