Adding Value: The General Contractor Challenge

Can small private general construction contractors add value to their business?

If one is to believe in US construction industry averages, the answer is no!

We say, no, but contractors will state, "we make a lot of money". That might be true but making money and adding value is not the same.

So, let's see how the numbers work out.

Value. What is it and why should you care?

The Project

Here are the assumptions and project details:

* We used static tables and workbooks throughout this analysis. Here is a link where you can make changes to Capital Construction Excel Spreadsheets. You'll see, based on U.S. construction industry averages and the paper thin profit margins, adding value is difficult.

• Assume it's a one year self-storage construction contract.
• Project cost is $3.5 million (including profit).
• Operating margin: 5.18% (US Industry Average).
• No Depreciation, working capital, capital expenditure or salvage value.
• General contractor will contribute his own equity for months 1 to 6.
• Short term debt is used for months 7 to 12.
• Owner pays general contractor three times: 25% at the end of month 5, 25% at the end of month 9, and 50% at the end of month 12.
• All cash inflows will be contributed back to the general contractor and then debt.
• All interest costs and debt will be paid at the end of month 12.
• We will use a bottom-up beta to compute a total beta.
• The cost of debt is 6.99% (We added a five percent small contractor premium).
• The effective U.S. tax rate is 25%.
• The current equity risk premium is 4.31%.
• The median industry average debt to equity ratio is 25%.
• The current 10-year risk-free rate is 1.29%.

Borrowing Risk: Default Risk and the Cost of Debt

When a bank lends to an individual or a company, there is the chance that the borrower will not make interest and principal payments on the borrowing. This prospect of default is called the default risk. In general, borrowers with higher default risk ought to pay higher interest rates on their borrowing than those with lower default risk. This section looks at the extent of default risk, and the association of default risk to interest rates on borrowing.

The default risk of a company is a function of its ability to produce cashflows from everyday operations and its financial responsibilities - including interest and principal payments. It is also a function of how liquid a company's assets are since companies with more liquid investments should have an easier time liquidating them, in a crisis, to meet debt requirements. Consequently, the following propositions relate to default risk:

• Companies that generate high cashflows relative to their financial debt requirements generally have lower default risk than do companies that generate low cashflows relative to their debt obligations. Thus, companies with large current investments that generate significant cashflows, will generally have lower default risk than will companies that do not.
• The more stable the cashflows, the lower is the default risk in the company. Companies that operate in conventional and predictable businesses will have lower default risk than will otherwise similar companies that operate in cyclical and/or unstable businesses, for the same level of indebtedness.
• The more liquid a company's assets, for any known amount of operating cashflows and financial obligations, the less default risk in the company.

When banks did much of the lending to companies, it made sense for banks to expend the resources to make their own assessments of default risk, and they still do for most lenders. The arrival of the corporate bond market produced a need for third party estimations of default risk on behalf of the bondholders. This demand came from the need for economies of scale, since few individual bondholders had the means to do the estimations themselves. In the United States, this led to the expansion of ratings agencies like Standard and Poor's and Moody's which formulated conclusions of the default risk of corporations, using a mix of private and public information, transformed these conclusions into measures of default risk (bond rating) and made these ratings public. Investors buying corporate bonds today use the bond ratings as a shorthand assessment of default risk.

The method of rating a bond begins when a company asks for a rating from the ratings agency. This request is typically carried out by a company wanting to issue bonds. While ratings are not a legal pre-requisite for bond issues, it is unlikely that investors in the bond market will be willing to buy bonds issued by a company that is not well known and has shown itself to be unwilling to put itself through the rigor of a bond rating process. It is not surprising, therefore, that the largest number of rated companies are in the United States, which has the most active corporate bond markets, and that there are relatively few rated companies in Europe, where bank lending remains the norm for all but the largest companies.

The ratings agency then gathers information from both publicly available data, such as financial statements, and the company itself, and makes a judgment on the rating. If it disagrees with the rating, the company is given the chance to submit additional supporting documentation. This bond rating process is shown schematically for one ratings agency, Standard and Poor's (S&P), in Image 1.1:

Image 1.1: The Rating Process

The ratings assigned by these agencies are letter ratings. A rating of AAA from Standard and Poor's and Aaa from Moody's is the highest rating granted to companies deemed as having the lowest default risk. As the default risk increases, the ratings decrease toward D for companies in default (Standard and Poor's). Worksheet 1.1 provides a description of the bond ratings assigned by the two agencies.

Worksheet 1.1: List of Bond Ratings

Investment Grade and Junk Bonds

While ratings can range from AAA (safest) to D (in default), a rating at or above BBB by Standard and Poor's (Baa for Moody's) is labeled as investment grade, suggesting the opinion of the ratings agency that there is comparatively modest default risk in investing in bonds issued by these companies. Bonds rated below BBB are generally identified as junk bonds or as high-yield bonds. While it is a subjective dividing line, it is a critical one for two reasons. First, different bond investment portfolios are constrained from investing in bonds below investment grade. So, the demand for investment grade bonds tends to be greater and deeper than that for bonds below that grade. Second, companies that are not rated investment grade have a tougher time when they try to raise new funding and they also pay much higher issuance costs when they do. In fact, until the early 1980s, companies below investment grade often could not issue new bonds. The view that they are exposed to default risk also creates a lot of other costs including tighter supplier credit and debt covenants.

There is a solid correlation connecting the bond rating a company receives and its performance on these financial ratios. Worksheet 1.2 gives a review of the median ratios from 2015 to 2021 for different S&P ratings classes for manufacturing companies.

Bond Ratings and Interest Rates

The interest rate on a corporate bond should be a measure of its default risk. If the rating is a good assessment of the default risk, higher rated bonds should be priced to yield lower interest rates than would lower rated bonds. The difference between the interest rate on a bond with default risk and a default-free government bond is called the default spread. This default spread will differ by maturity of the bond and may vary from time to time, depending on economic factors. Worksheet 1.3 summarizes default spreads in early 2021 for ten-year bonds in each ratings class (using S&P ratings) and the market interest rates on these bonds, based upon a treasury bond rate of 1.29%.

Worksheet 1.3: Bond Default Spreads: July 2021

Source: https://fred.stlouisfed.org

Worksheet 1.3 shows default spreads at a point in time, but default spreads not only fluctuate over time but they can change for bonds with an identical rating but different maturities. For the bonds with higher ratings, the default spread usually widens for the longer maturities. For bonds with lower ratings, the spreads can decrease as we go to longer maturities, suggesting the truth that near term default risk is greater than long term default risk. Historically, default spreads for all ratings categories have increased during recessions and decreased during economic booms. In Image 1.2, we take a look at the changes of default spreads for different bond rating classes through 2021:

Image 1.2: Default Spreads on Rating Classes

Note how much default spreads changed through 2021. This suggests that default spreads for bonds must be re-estimated at regular intervals, particularly if the economy shifts from low to high growth or vice versa.

Risk Measurement And Hurdle Rates In Practice

Cost of Equity

The cost of equity is the rate of return that investors demand to invest in the equity of a company. All of the risk and return models talked about previously require a risk- free rate and a risk premium (in the CAPM). We start by talking about those familiar inputs before directing our attention to the evaluation of risk parameters.

I. Risk-Free Rate

The majority of risk and return models in finance begin with an investment that is identified as risk- free and use the expected return on that investment as the risk-free rate. The expected returns on risky investments are then evaluated relative to the risk-free rate, with the risk generating an expected risk premium that is added on to the risk-free rate.

Table 1.1 Levered Beta and Cost of Equity (Industry Average)

II. Risk Premium

The risk premium(s) is definitely an important input in all of the asset pricing models. In the next section, we will start by investigating the supporting determinants of risk premiums and then look at a number of useful method to estimating these premiums.

What Is the Risk Premium Supposed to Measure?

The risk premium in the CAPM measures the extra return that would be required by investors for moving their money from a riskless investment to the market portfolio or risky investments, on average. It should be a function of two variables:

1. Risk Aversion of Investors: As investors become more risk-averse, they should insist on a larger premium for changing from the riskless asset. Although a few of this risk aversion may be clear, some of it is also a function of economic prosperity (when the economy is doing great, investors are likely to be more enthusiastic about taking on more risk) and recent events in the market (risk premiums tend to surge after large market drops).

2. Riskiness of the Average Risk Investment: As the riskiness of the average risk investment rise, so should the premium. This will depend on what companies are actually traded in the market, their economic fundamentals, and how involved they are in dealing with risk.

3. Implied Equity Premiums

There is an alternative way to projecting risk premiums that does not need past statistics or changes for country risk but does assume that the overall stock market is accurately priced. Think about, for example, a very straight forward valuation model for stocks

Value = Expected Dividends Next Period / (Required Return on Equity - Expected Growth Rate in Dividends)

This is basically the present value of dividends growing at a stable rate. Three of the four variables in this model can be obtained simply-the current level of the stock market (i.e., value), the estimated dividends next period, and the estimated growth rate in earnings and dividends in the long term. The one unknown is then the required return on equity; when we solve for it, we get an implied expected return on stocks. Subtracting out the risk-free rate will produce an implied equity risk premium.

To demonstrate, suppose that the current level of the S&P 500 Index is 4,400, the expected dividend yield on the index for the next period is 2.4 percent, and the expected growth rate in earnings and dividends in the long run is 3.5 percent. Solving for the required return on equity yields the following:

4,400 = 4,400 *(0.024) / r - .035

Solving for r,

r - 0.035 = 0.024

r = 0.059 = 5.90%

If the current risk-free rate is 1.29 percent, this will yield a premium of 4.61 percent.

This calculation can be simplified to allow for high growth for a period and widened to deal with cash flow-based rather than dividend-based, models. To explain this, look at the S&P 500 Index on January 1, 2020. On December 31, 2019, the S&P 500 Index closed at 3140, and the dividend yield on the index was roughly 4.56%. In addition, the universal estimate of growth in earnings for companies in the index was about 9.7% for the next 5 years. Since the companies in the index have bought back enormous amounts of their own stock over the last few years, we included buybacks as part of the cash flows to equity investors. Worksheet 1.5 shows dividends and stock buybacks on the index, going back to 2014.

Worksheet 1.5: Dividends and Stock Buybacks on S&P 500 Index: 2014-2021

In 2020, for instance, companies collectively returned 3.16% of the index in the form of dividends (1.52%) and stock buybacks (1.64%). Buybacks are volatile, and dropped about 40% in the last quarter of 2020, relative to the last quarter of 2019, in the face of a market crisis and a slowing economy. Since this slowdown is likely to continue into 2021, we reduced the buybacks in 2021 by 16% to compute a normalized cash yield of 1.38% for the year (resulting in a total cash to equity of 116.17 for the year). In Worksheet 1.6, we estimate the cash flows to investors in the S&P 500 index from 2014-2021 by growing the normalized cash flow at 4% a year for the first five years and 1.25% (set equal to the risk-free rate) thereafter.

Worksheet 1.6 Cashflows on S&P 500 Index

Using these cash flows to compute the expected return on stocks, we get the following:

$4,297.50 = 153.16/(1+ r) + 167.85/(1+ r)² + 183.94/(1+ r)³ + 201.58/(1+ r)⁴ + 220.91/(1+ r)⁵ + 223.49/(r -.0125)(1+ r)⁵

Solving for the required return and the implied premium with the higher cash flows: Required Return on Equity = 5.678%

Implied Equity Risk Premium = Required Return on Equity - Risk-free Rate

= 5.678% - 1.29% = 4.388%

We think that this estimate of risk premium (4.21%) is a more realistic value for August 1, 2021 than the historical risk premium of 5.50%. What makes this approach better is that it is market-driven and forward-looking and does not need historical data. Also, it will adjust in response to changes in market movements. Note that the S&P 500 a year prior was trading at 3100.36 and the implied equity risk premium on July 1, 2020 was 4.72%. The unusual movements are best viewed by graphing out implied premiums from the S& P 500 from 1960 in Image 1.3:

Image 1.3: Equity Risk Premiums US Equity Mkt 1960-2020

3. Determinants of Betas

The beta of a company is determined by three inputs: (1) the type of business or businesses the firm is in, (2) the degree of operating leverage in the firm, and (3) the firm's financial leverage.

Type of Business Since betas gauge the risk of a company relative to a market index, the more sensitive a business is to market conditions, the higher its beta. Thus, other things remaining equal, cyclical firms can be expected to have higher betas than noncyclical firms. Other things remaining equal, then, companies involved in housing and automobiles, two sectors of the economy that are very sensitive to economic conditions, will have higher betas than companies involved in food processing and tobacco, which are generally insensitive to business cycles.

Building on this point, we would also reason that the degree to which a product's purchase is, or is not necessary (discretionary or not) will change the beta of the company making the product. So, the betas of discount retailers, such as Wal-Mart, should be lower than the betas of high- end specialty retailers, such as Tiffany's or Gucci, since shoppers can hold off the purchase of the latter's products during dire economic times.

It is true that firms have only limited control over how discretionary a product or service is to their customers. There are firms, however, that have used this limited control to maximum effect to make their products less discretionary to buyers and by extension lowered their business risk. One approach is to make the product or service a much more integral and necessary part of everyday life, thus making its purchase more of a requirement. A second approach is to effectively use advertising and marketing to build brand loyalty. The objective in good advertising, as we see it, is to make discretionary products or services seem like necessities to the target audience. Thus corporate strategy, advertising, and marketing acumen can, at the margin, alter business risk and betas over time.

Degree of Financial Leverage Other things remaining equal, an increase in financial leverage will increase the equity beta of a firm. Naturally, we would think that the fixed interest payments on debt to enhance earnings per share in good times and to drive it lower in bad times. Higher leverage amplifies the variance in earnings per share and makes equity investment in the firm riskier. If all of the firm's risk is borne by the stockholders (i.e., the beta of debt is zero), and debt creates a tax benefit to the firm, then

β_L = β_u (1 + (1 - t)(D/E))

where

β_L = Levered beta for equity in the firm
β_u = Unlevered beta of the firm (i.e., the beta of the assets of the firm)
t = Marginal tax rate for the firm
D /E = Debt/equity ratio

The marginal tax rate is the tax rate on the last dollar of income generated by the company and usually will not be equal to the effective or average rates; it is used because interest expenses save taxes on the marginal income. Intuitively, we see that as leverage increases (as calculated by the debt to equity ratio), equity investors bear higher levels of market risk in the company, leading to higher betas. The tax factor in the equation captures the benefit created by the tax deductibility of interest payments.

The unlevered beta of a company is identified by the kinds of businesses in which it operates and its operating leverage. This unlevered beta is sometimes defined as the asset beta because its value is recognized by the assets (or businesses) owned by the company. Consequently, the equity beta of a company is determined both by the riskiness of the business it operates in as well as the amount of financial leverage risk it has taken on. Because financial leverage multiplies the underlying business risk, it stands to reason that companies with elevated business risk should be hesitant to take on financial leverage. It also stands to reason that companies operating in somewhat established businesses should be better prepared to take on financial leverage. Utilities, for example, have traditionally maintained high debt ratios but not high betas, mostly because their fundamental businesses have been well established and rather predictable.

Breaking risk down into pieces - business and financial leverage, can give us some insight into why companies have high betas. Those companies with high betas generally operate in a risky business, or they take on too much financial leverage in a relatively stable business.

Should Small or High-Growth Firms Have Higher Betas than Larger and More Mature Firms?

Though the answer might appear apparent at first glance-that smaller, higher-growth companies are riskier than larger firms-it is not a simple question to answer. If the question were posed in terms of total risk, smaller and higher-growth companies will generally be riskier simply because they have more unstable earnings (and their market prices shows it). When it is identified in terms of betas or market risk, smaller and higher- growth firms should have higher betas only if the products and services they offer are more discretionary to their customers or if they have higher operating leverage. It is also likely that smaller companies might operate in smaller niche markets and sell products that customers can typically delay or defer buying and that the absence of economies of scales lead to elevated fixed costs for these companies. These companies should have higher betas than their larger counterparts. It is also sensible that neither condition holds for a particular small company. The answer will then depend on both the company in question and the industry in which it operates.

Table 1.2 Financial Leverage and Betas

Bottom-Up Betas

Breaking down betas into their business, operating leverage, and financial leverage components gives us another way of figuring out betas, whereby we don't need past prices on an individual company or asset to estimate its beta.

To build this improved method, we need to introduce an added feature that betas possess that proves invaluable. The beta of two assets put together is a weighted average of the individual asset betas, with the weights based on market value. So, the beta for a firm is a weighted average of the betas of all of the different businesses it is in. Thus, the bottom-up beta for a company, its asset, or its project can be estimated as follows.

1. Identify the business or businesses segments within the company whose beta we are trying to figure out. Most companies give a summary of their revenues and operating income by types of business in their annual reports and financial filings.

2. Calculate the average unlevered betas of other publicly traded firms that are primarily or only in each of these businesses. In making this assumption, we have to think about the following estimation issues:

Comparable firms : In most businesses, there are at least a few similar companies and in some businesses, there can be hundreds. Start with a narrow description of comparable companies, and broaden it if the number of comparable companies is too small.

Beta Estimation : Once a listing of comparable companies has been prepared, we need to figure out the betas of each of these companies. Optimally, the beta for each company will be estimated against a common index. If that proves unrealistic, we can use betas estimated against different indices.

Unlever First or Last : We can compute an unlevered beta for each firm in the comparable firm list, using the debt to equity ratio, and tax rate for that company, or we can compute the average beta, debt to equity ratio, and tax rate for the sector and unlever using the medians. Given the standard errors of the individual regression betas, we would suggest the latter approach.

Median Approach : The median beta across the comparable companies can be either a simple median or a weighted median, with the weights based on market capitalization. Statistically, the savings in standard error are larger if a simple median process is used.

Adjustment for Cash : Investments in cash and marketable securities have betas close to zero. So, the unlevered beta that we calculate for a business by looking at comparable companies might be changed by the cash assets of these companies. To figure out an unlevered beta cleansed of cash:

Unlevered Beta corrected for Cash = Unlevered Beta /(1 - Cash/ Firm Value)

The resulting number is sometimes called a pure play beta (total beta), indicating that it measures the risk of only the business and not any other corporate holdings.

3. To calculate the unlevered beta for the company, we take a median of the unlevered betas, using the proportion of company value derived from each business as the weights. These company values will have to be estimated because segments of a company generally do not have market values available. If these values cannot be estimated, we can use operating income or revenues as weights. This median is called the bottom-up unlevered beta. In general, it is a good exercise to compute two unlevered betas for a company, one for only the operating assets of the company, and one with cash and marketable securities treated as a separate business, with a beta of zero.

4. Calculate the current debt to equity ratio for the company, using market values if available. Otherwise, use the target debt to equity ratio specified by the management of the company or industry debt ratios.

5. Estimate the levered beta for the equity in the company (and each of its business segments) using the unlevered beta from Step 3 and the debt to equity ratio from Step 4.

Naturally, this approach rests on you being able to recognize the unlevered betas of individual businesses.

There are three benefits with using bottom-up betas, and they are important:

We can estimate betas for companies that have no previous price history because all we need to do is identify the business or businesses segments they operate in. In other words, we can estimate bottom-up betas for initial public offerings, private businesses, and divisions of companies.

• Since the beta for the business is found by computing the median value across a large number of regression betas, it will usually be more accurate than any individual company's regression beta estimate. The standard error of the median beta estimate will be a function of the number of comparable firms used in Step 2 and can be approximated as follows:

σ_{Median Beta} = Average σ _Beta / √ Number of firms

• So, the standard error of the median of the betas of 100 firms, each of which has a standard error of 0.25, will be only 0.025 (0.25/v100).
• The bottom-up beta can point out current and even impending adjustments to a company's business mix and financial leverage, because we can alter the combination of businesses and the weight on each business in making the beta estimate.

Example 1.1: Bottom-Up Beta for Capital Construction

We cannot estimate a regression beta for Capital Construction, a private firm, because it does not have a history of past prices. We can, however, estimate the beta for Capital Construction using the bottom-up approach. We list the betas of these firms as well as debt, cash, and equity values in Worksheet 1.7.

Worksheet 1.7 Betas and Leverage of Publicly Traded Engineering and Construction Firms (a complete list can be found at the end of this article)

Even though the companies in this example are very different in terms of market capitalization, the betas are consistent. To estimate the unlevered beta for the sector, we first unlevered the beta for each firm and corrected each unlevered beta for the firm's cash holdings. The median value for the unlevered beta, corrected for cash holdings, is .984.

Worksheet 1.8: Unlevered Beta Corrected for Cash

I. Estimating the Cost of Equity

Having estimated the risk-free rate, the risk premium(s), and the beta(s), we can now estimate the expected return from investing in equity at any company. In the CAPM, this expected return can be shown as:

Expected Return = Risk-Free Rate + Beta * Expected Risk Premium

where the risk-free rate would be the rate on a long-term government bond; the beta would be either the historical, fundamental, or accounting betas; and the risk premium would be either the historical premium or an implied premium.

The expected return on an equity investment in a company, given its risk, has key implications for both equity investors in the company and the managers/owners of the company. For equity investors, it is the rate they need to make to be compensated for the risk that they have taken on investing in the equity of a firm. If after evaluating a stock, they find out that they cannot generate this return, they would not buy it; instead, if they determine they can make a higher return, they would make the investment. For company managers and owners, the return that investors need to make to break even on their equity investments is the return that they need to deliver to keep these investors from becoming impatient and rebellious. In other words, it becomes the rate that they have to beat in terms of returns on their equity investments in individual projects. Thus, this is the cost of equity to the firm.

Example 1.2: Estimating the Cost of Equity

To estimate the cost of equity for Capital Construction, we will use the beta of 0.98 estimated from Worksheet 1.8 together with the risk-free rate and risk premium for the United States: Cost of Equity = 1.29% + .98 x(4.31%) = 5.51%

Inherent in the use of beta as a measure of risk is the assumption that the marginal investor in equity is a well-diversified investor. Although this is a defensible assumption when evaluating publicly traded companies, it turns out to be much more difficult to validate for private firms. The owner of a private firm usually has the majority of his or her wealth tied up in the business. Therefore, he or she carries virtually the total risk in the business rather than just the market risk. Thus, for a business like Capital Construction, the beta that we have estimated of 0.98 (leading to a cost of equity of 5.51 percent) will understate the risk carried by the owner. There are three possible answers to this problem:

1. Suppose that the business is managed with the short-term goal of selling to a large publicly traded company. In this example, it is okay to use the market beta and cost of equity that comes from it.

2. Add a premium to the cost of equity to show the elevated risk created by the owner's failure to diversify. This could help explain the excessive returns that a number of venture capitalists demand on their equity investments in fledgling businesses.

3. Change the beta to show the total risk rather than market risk. This change is rather simple, because the R² of the regression measures the proportion of the variance that is market risk. Dividing the market beta by the square root of the R² (which yields the correlation coefficient) yields a total beta. In the Capital Construction example, the regressions for the comparable firms against the market index have an average correlation with the market of 35.56% (the average R ² was 59.63%). The total beta for Capital Construction can then be computed as follows:

Total Beta = (Market Beta)/Correlation with the market = 0.98/0.3556= 2.76.

Using this total levered beta (2.77 *(1+(1 - .25)* .25) = 3.29) would yield a much higher and more realistic estimate of the cost of equity.

Cost of Equity = 1.29% + 3.29 (4.31%) = 15.45%

So, private businesses will generally have much higher costs of equity than their publicly traded counterparts, with diversified investors. Although a lot of them eventually give in by selling to publicly traded competitors or going public, a few companies elect to remain private and succeed. To do so, they must diversify on their own (as many family-run businesses in Asia and Latin America did) or acknowledge the lower value as a cost paid for retaining total control.

From Cost of Equity to Cost of Capital

Equity is clearly a vital and essential ingredient of the financing mix for every business, but it is only one ingredient. Nearly all public businesses finance some or a good deal of their operations with debt or some mix of equity and debt. The costs of using these financing sources are generally quite different from the cost of equity. Therefore, the minimum acceptable hurdle rate for a project will reflect their costs as well, in proportion to their use in the financing mix. Intuitively, the cost of capital is the weighted average of the costs of the different mix of financing-including debt, equity, and hybrid securities-used by a companies to fund their day to day operations.

Default Risk: The risk that a company might not be able to make its required debt payments, such as interest expenses or principal payments.

To estimate the cost of the funding that a company wants, we have to estimate the costs of debt. In this section, we look at the cost of debt.

The Cost of Debt

The cost of debt measures the current cost to the company if they borrow money to fund projects. In general terms, it is determined by the following variables:

1. The current level of interest rates : As market interest rates rise, the cost of debt for all companies will also rise.

2. The default risk of the company : As the default risk of a company increases, lenders will charge higher interest rates (a default spread) to compensate for the added risk.

3. The tax advantage tied to debt : Since interest is tax-deductible, the after- tax cost of debt is a function of the tax rate. The tax benefit that accrues from paying interest makes the after-tax cost of debt lower than the pretax cost. Furthermore, this benefit increases as the tax rate increases.

After-Tax Cost of Debt = (Risk-free rate + Default Spread) (1 - Marginal Tax Rate)

The challenge in estimating the cost of debt is really one of estimating the correct default spread for a company.

Estimating the Default Risk and Default Spread of a Firm

The easiest way to estimate the cost of debt is if a company has long- term bonds outstanding that are widely traded and have no special features, such as convertibility or first claim on assets, skewing interest rates. The market price of the bond, together with its coupon and maturity, can serve to calculate a yield we use as the cost of debt. For example, this approach works for companies that have a large number of outstanding bonds that are liquid and trade frequently.

Many firms have outstanding bonds that rarely trade on a regular basis. Given these firms are usually rated, we can determine their costs of debt by using their ratings and assigned default spreads. Thus, Capital Construction with a Baa rating can be expected to have a cost of debt approximately 5.00 percent higher than the Treasury bond rate, in July 2021, because this was the spread typically paid by Baa rated firms at the time.

A number of companies simply cannot get rated. Many smaller firms and most private businesses fall into this category. Ratings agencies have sprung up in many emerging markets, but there are still a number of markets in which companies are not rated on the basis of default risk. When there is no rating available to estimate the cost of debt, there are two options:

Recent Borrowing History: Countless companies that are not rated still borrow money from banks and other financial institutions. By looking at the most recent borrowings made by a company, we can get an ideal of what banks are charging this companies and the default spreads and use these information to come up with a cost of debt.

Estimate a Synthetic Rating and Default Spread : An alternative is to play the role of a ratings agency and assign a rating to a company based on its financial ratios; this rating is called a synthetic rating. To make this opinion, we start with rated firms and study the financial traits shared by companies in each ratings class. Let's look at a very simple example, using the operating income to interest expense ratio, which is, the interest coverage ratio, and we computed it for each rated firm. In Worksheet 1.9, we list the range of interest coverage ratios for manufacturing firms in each S&P ratings class, arranged by market capitalization into large (>$5 billion) and small (<$5 billion). We also show the standard default spreads for bonds in each ratings class in July 2021.

Worksheet 1.9 Interest Coverage Ratios and Ratings

Source: Federal Reserve: https://fred.stlouisfed.org

Now, let's look at a private firm with $10 million in earnings before interest and taxes and $3 million in interest expenses; it has an interest coverage ratio of 3.33. Based on this interest coverage ratio, we would assign a synthetic rating of BB for the company and attach a default spread of 3.31 percent to the risk-free rate to come up with a pretax cost of debt. A large market cap firm with the same interest coverage ratio would be assigned a rating of A- and a default spread of .84%.

Calculating the Weights of Debt and Equity Components

Once we have costs for each of the different financing pieces, all we need are weights on each piece to figure out a cost of capital. In this section, we consider the choices for weighting, the reason for using market value weights, and if the weights can adjust over time.

Estimating and Using the Cost of Capital

With the estimates of the costs of the individual pieces-debt, equity and preferred stock (if any)-and the market value weights of each of the pieces, the cost of capital can be calculated. So if E, D, and PS are the market values of equity, debt, and preferred stock in order, the cost of capital can be shown as follows:

Cost of Capital = k_E [E/(D + E + PS)] + k_D [D/(D + E + PS)] + k_PS [PS/(D + E + PS)]

The cost of capital is a gauge of the combined cost of raising money that a company faces. It will usually be less than the cost of equity, which is the cost of just equity funding.

Example 1.3: Estimating Cost of Capital

Completing the analysis in this section, we first determine the costs of capital for Capital Construction. In making this estimate, we use the costs of equity that we figured out in Example 1.2 and Capital Construction's cost of debt from Worksheet 1.10. We also assume that the project is funded with the same mix of debt and equity as the parent company. Worksheet 1.10 provides estimates of the costs of capital for the self-storage project:

Table 1.3 Cost of Capital (Industry Average )

Worksheet 1.10 Cost of Capital for Capital Construction Self-Storage Project

The cost of capital for Capital Construction's self-storage project is 12.90 percent.

Previously, we built a path for estimating costs of equity, debt, and capital and presented an argument that the cost of capital is the minimum acceptable hurdle rate when considering new investments. We also argued that an investment has to earn a return greater than this hurdle rate to create value for the owners of a business. In this section, we turn to the question of how best to measure the return on a project. In doing so, we will attempt to answer the following questions:

• What is a project? In particular, how general is the definition of an investment and what are the different types of investment decisions that firms have to make?
• In measuring the return on a project, should we look at the cash flows generated by the project or at the accounting earnings?
• If the returns on a project are unevenly spread over time, how do we consider (or should we not consider) differences in returns across time?

What Is a Project?

Project analysis looks at which projects a company should accept and which it should reject; accordingly, the question of what makes up a project is central to this. The traditional project reviewed in capital budgeting has three criteria: (1) a large up-front cost, (2) cash flows for a specific time period, and (3) a salvage value at the end, which captures the value of the assets of the project when the project ends. Although such projects unquestionable form a substantial percentage of project decisions, particularly for construction companies, it would be foolish to think that project analysis stops there. If a project is defined more broadly to include any decision that results in using the limited capital of a business, then everything from strategic decisions and acquisitions to decisions about which air conditioning system to install in a building would fit within its reach.

Defined broadly then, any of the following decisions would meet the requirements as projects:

• Key planned decisions to enter new types of construction projects (such as Capital Construction's constructing a self-storage facility).
• Acquisitions of other companies are projects as well, despite efforts to invent separate sets of rules for them.
• Decisions on new undertakings within existing businesses or markets.
• Decisions that may alter the way existing divisions and projects are managed, including new construction projects.

Decisions on the best way to deliver an essential service for the business to function profitable. A perfect example would be Capital Construction's choice of what type of CAD system to buy to allow engineers and construction managers to do their jobs. Given, the CAD system itself generally won't generate revenues and profits, it is an absolute must for other revenue generating projects.

Hurdle Rates for Companies versus Hurdle Rates for Projects

In the previous section we developed a way to calculate the costs of equity and capital for companies. In this section, we will broaden the discussion to hurdle rates in the context of new or individual projects.

Using the Company's Hurdle Rate for Individual Projects

Can we use the costs of equity and capital that we have calculated for the companies for these projects? In some cases we can, but only if all projects made by a company are similar in terms of their risk exposure. As a company's projects become more diverse, the company will no longer be able to use its cost of equity and capital to review these projects. Projects that are riskier have to be reviewed using a higher cost of equity and capital than projects that are safer. In this section, we consider how to estimate project costs of equity and capital.

Cost of Equity for Projects

In estimating the beta for a project, we will look at three possible outcomes. The first outcome is the one where all the projects considered by a company are identical in their exposure to risk; this plain vanilla approach makes risk assessment simple. The second outcome is one where a company is in many businesses with broad exposures to risk, but projects within each business have the same risk exposure. The third outcome is the most challenging where each project considered by a company has different risk exposure.

Single Business; Project Risk Similar within Business

When a company works in only a single type of business and all projects within that business share the same risk profile, the company can use its company cost of equity as the cost of equity for the project. Since we determined the cost of equity using a company beta previously, we can use this same beta to calculate the cost of equity for each project the company is currently reviewing. The benefit of this approach is that it does not require risk estimation prior to every project, providing managers with a fixed target for their project analysis. The approach is limited, though, because it can only be used for companies who work a single line of business and take on the same type of projects repeatedly.

Multiple Businesses with Different Risk Profiles: Project Risk Similar within Each Business

When companies operate in more than one line of business, the risk profiles are likely to be unique across different businesses. Making the assumption that projects taken within each business have the same risk characteristic, we can calculate the cost of equity for each business individually and use that cost of equity for all projects within that business. Riskier businesses will have higher costs of equity than safer businesses, and projects taken by riskier businesses will have to pay these higher costs. Inserting the company's cost of equity on all projects in all businesses will lead to overinvesting in risky businesses (because the cost of equity will be set too low) and under investing in safe businesses (because the cost of equity will be set too high).

How do we determine the cost of equity for individual businesses?

When the evaluation requires using equity betas, we cannot use the traditional regression method (in the CAPM) because these methods require past prices. Instead, we have to use one of the two methods that we described in the last section as substitutes to regression betas-bottom-up betas based on other publicly traded companies in the same business, or accounting betas, calculated based on the accounting earnings for the division.

Projects with Different Risk Profiles

One could contend that each project's risk profile is, in fact, unique and that it is inappropriate to use either the company's cost of equity or divisional costs of equity to evaluate projects. Even though this may have some merit, we have to think of the trade-off. Given that small differences in the cost of equity should not make a meaningful difference in our project estimates, we need to judge if the additional benefits of reviewing each project individually is greater than the costs of doing so.

When does it make sense to examine a project's risk independently? If a project is large in terms of its capital contribution requirements relative to the company's experience, and the project has a number of unusual risk characteristics, it would seem right to calculate the cost of equity for the project independently. The only sensible way of determining betas and costs of equity for individual projects is the bottom-up beta approach.

Cost of Debt for Projects

In the previous section, we stated that the cost of debt for a company should explain its default risk. With individual projects, determining the default risk becomes much more complicated, because projects seldom borrow on their own; most companies borrow money for all the projects that they undertake.

Financing Mix and Cost of Capital for Projects

To get from the costs of debt and equity to the cost of capital, we have to weight each by their relative proportions in financing. Again, the task is much easier at the company level, where we use the current market values of debt and equity to arrive at these weights. We may borrow money to fund a project, but it is often not clear whether we are using the debt capacity of the project or the company's debt capacity. The answer to this problem will again change depending on the conditions we face.

• When we are establishing the financing weights for small projects that do not involve a company's debt capacity, the financing weights should be those of the company before the project.
• When determining the financing weights of large projects, with risk characteristics uncommon from that of the company, we have to be more careful. Employing the company's financing mix to determine the cost of capital for these projects can be wrong, because the project being reviewed could be riskier than the company as a whole and thus unable of carrying the company's debt ratio. In this case, we would press for the use of the average debt ratio of the other companies in the business in calculating the cost of capital of the project.
• The financing weights for stand-alone projects that are large enough to issue their own debt should be based on the actual amounts borrowed by the projects. For companies with such projects, the financing weights can change from project to projects, as will the cost of debt.

In summary, the cost of debt and debt ratio for a project will show the size of the project relative to the company, and its risk profile, again relative to the company. Worksheet 1.11 summarizes our analyses.

Worksheet 1.11 Cost of Debt and Debt Ratio: Project Analyses

Example 1.4: Estimating Hurdle Rates for Individual Projects

Using the estimation approach that we just laid out, we can calculate the hurdles rates for the projects that we are reviewing in this section.

Capital Construction: construction of a self-storage facility : Because the beta and cost of equity that we calculated for Capital Construction as a company explain its status as a construction company, we will re-calculate the beta for this project by looking at publicly traded Construction Material retailers. The unlevered total beta for construction material retailers is 2.769, and we imagine that this project will be funded with the same mix of debt and equity (D/E = 25.00%, Debt/Capital = 25.00%) that Capital Construction uses in the rest of the business. We will imagine that Capital Construction's tax rate (25%) and pretax cost of debt (6.99%) apply to this project.

Levered Beta _{Engineering/Construction/Materials/Products Service} = 2.769 x [1 + (1 - 0.25) x (0.25)] = 3.29

Cost of Equity _{Engineering/Construction/Materials/Products} = 1.29% + 3.29 x 4.31% = 15.45%

Cost of Capital_{Engineering/Construction/Materials/Products}= 15.45% x (0.75) + 6.99%*(1 - 0.25)*.25 = 12.90%

This is much higher than the indusry average cost of capital we computed previously, but it shows the higher risk of small privately owned construction business.

From Accounting Earnings to Cash Flows

The three factors outlined can cause accounting earnings to deviate significantly from the cash flows. To get from after-tax operating earnings, which measures the earnings to the company, to cash flows to all investors in the company, we have to:

Add back all noncash charges , such as depreciation and amortization, to the operating earnings.

Subtract out all cash outflows that represent capital expenditures. Net out the effect of changes in noncash working capital , that is, changes in accounts receivable, inventory, and accounts payable. If noncash working capital increased, the cash flows will be reduced by the change, whereas if it decreased, there is a cash inflow.

The first two adjustments change operating earnings to account for the distinction drawn by accountants between operating, financing and capital expenditures, whereas the last adjustment converts accrual revenues and expenses into cash revenues and expenses.

Cash Flow to Company = Earnings before interest and taxes (1 - t) + Depreciation & Amortization - Change in Noncash Working Capital - Capital Expenditures

The cash flow to the company is a pre-debt, after-tax cash flow that measures the cash generated by a project for all claim holders in the company after reinvestment needs have been met.

To get from net income, which measures the earnings of equity investors in the company, to cash flows to equity investors requires the added step of looking at the net cash flow created by repaying old debt and taking on new debt. The difference between new debt issues and debt repayments is called the net debt, and it must be added back to arrive at cash flows to equity. Also, other cash flows to nonequity claim holders in the company, such as preferred dividends, have to be netted from cash flows.

Cash Flow to Equity = Net Income + Depreciation & Amortization - Change in Noncash Working Capital - Capital Expenditures + (New Debt Issues - Debt Repayments) - Preferred Dividends

The cash flow to equity measures the cash flows generated by a project for equity investors in the company, after taxes, debt payments, and reinvestment needs.

Example 1.5: Estimating Cash Flows: Capital Construction

As described earlier, Capital Construction is considering constructing a small self-storage facility.

• The typical owner equity requirement to complete the one year project, including all labor and materials is 75% of cost, the remaining 25% is from debt. For simplicity there is no depreciation, no capital expenditures , no working capital and no salvage value.
• The Owner will pay Capital Construction three times based on the approved project completions: 25% at the end of month 5, 25% at the end of month 9 and 50% at the end of month 12.
• The total cost of the project is 94.69% of the $3.5 million contract with an operating margin of 5.31% (US Construction industry average).
• The tax rate on income is expected to be 25%, which is also the marginal tax rate for Capital Construction.

Based on this information, we calculate the operating income for Capital Construction in Worksheet 1.12:

Worksheet 1.12 Expected Operating Income on Capital Construction: construction of a self-storage facility

To get from operating income to cash flows, we normally add back the depreciation charges and subtract out the working capital requirements (which are the changes in working capital from month to month) in Worksheet 1.13. We are ignoring that here, instead we include the construction cost over the 12 month period, including interest (cash outflows) and cash inflows (from the owner) along with the payback of contractor equity (subtracted from total project capital) and increases in short-term debt.

Worksheet 1.13 From Operating Income to After-Tax Cash Flows

Return on Capital

The return on capital on a project measures the returns earned by the company based on it is total capital contribution in the project. Consequently, it is a return to all claimholders in the company on their collective contribution in a project. Defined generally,

Return on Capital (Pretax) =Earnings before interest and taxes/Average Book Value of Capital Invested in Project

Return on Capital (After-tax) = Earnings before interest and taxes (1- tax rate)/Average Book Value of Capital Invested in Project

To illustrate, consider a one-year project, with an initial capital contribution of $1 million, and earnings before interest and taxes (EBIT) of $300,000. Imagine that the project has a salvage value at the end of the year of $800,000, and that the tax rate is 25%. In terms of a time line, the project has the following inputs:

Earnings before interest & taxes (EBIT)= $ 300,000

Book Value (BV)= $ 1,000,000
Salvage Value = $ 800,000

Average Book Value of Capital = $(1,000,000+$800,000)/2 = $ 900,000

The pretax and after-tax returns on capital can be calculated as follows:

Return on Capital (Pre-tax) = $ 300,000/$900,000 = 33.33%

Return on Capital (After-tax) = $300,000 * (1-0.25)/$900,000 = 25%

Even though this calculation is rather straightforward for a one-year project, it becomes more complicated for multiyear projects, where both the operating income and the book value of the project change over time. In these cases, the return on capital can either be calculated each year and then averaged over time or the average operating income over the life of the project can be used in conjunction with the average capital contribution during the period to determine the average return on capital.

The after-tax return on capital on a project has to be compared to a hurdle rate that is defined consistently. The return on capital is calculated using the earnings before debt payments and the total capital invested in a project. Thus, it can be viewed as return to the company, rather than just to equity investors. Therefore, the cost of capital should be used as the hurdle rate.

If the after-tax return on capital > Cost of Capital → Accept the project

If the after-tax return on capital < Cost of Capital → Reject the project

For example, if the company considering this project had a cost of capital of 10%, it would view the investment in the new project as a good one.

Example 1.6: Estimating and Using Return on Capital in Decision Making: Capital Construction: self-storage project

In Example 1.5 we computed the operating income on constructing a self-storage facility by Capital Construction Company. We will calculate the return on capital on this project using our earlier estimates of operating income. Worksheet 1.14 summarizes the estimates of operating income and the book value of capital at Capital Construction.

Worksheet 1.14 Return on Capital on Capital Construction: Self-Storage Facility

The book value of capital each year includes the capital contribution in fixed assets and the noncash working capital. If we average the year-specific returns on capital, the average return on capital is 13.96%, but this number is pushed up by the extremely high return in month twelve. A better estimate of the return on capital is computed by dividing the average after-tax operating income ($109,176) over the twelve months by the average capital invested ($1,467,337) over this time, which yields a return on capital of 7.44%. Because this number is well below the cost of capital of 12.90% that we calculated in Example 1.4 for this project, the return on capital approach would suggest that this is a bad project.

Return on Equity

The return on equity looks at the return to equity investors, using the accounting net income as a measure of this return. Again, defined generally,

Return on Equity = Net Income /Average Book Value of Equity in Project

To illustrate, consider a four-year project with an initial equity contribution of $800, and the following estimates of net income in each of the four years:

Net Income $ 140/($800 + $700)/2 = 18.67%
Net Income $ 170/($700 + $600)/2 = 26.15%
Net Income $ 210/($600 + $500)/2 = 38.18%
Net Income $ 250/($500 + $400)/2 = 55.56%

Like the return on capital, the return on equity tends to increase over the life of the project, as the book value of equity in the project is depreciated.

Just as the correct comparison for the return on capital is the cost of capital, the correct comparison for the return on equity is the cost of equity, which is the rate of return equity investors demand.

The cost of equity should explain the riskiness of the project being considered and the financial debt taken on by the company. When choosing between mutually exclusive projects of similar risk, the project with the higher return on equity will be viewed as the better project.

Net Present Value (NPV): The sum of the present values of the expected cash flows on the project, net of the initial funding.

The full estimate of cash flows, described earlier in the section, requires subtracting out capital expenditures and changes in non-cash working capital but it is far too volatile on a year-to-year basis to yield reliable measures of returns on equity or capital.

Discounted Cash Flow Measures

Project decision rules based on discounted cash flows not only replace accounting income with cash flows but explicitly factor in the time value of money. The two most widely used discounted cash flows rules are net present value and the internal rate of return.

Net Present Value (NPV)

The net present value of a project is the sum of the present values of each of the cash flows-positive as well as negative-that occurs over the life of the project. The general formulation of the NPV rule is as follows:

NPV of Project =∑ CF_t/(1 + r)^t - Initial Funding

where

CF_t = Cash flow in period t
r = Discount rate
N = Life of the project.

Consider a simple project, with an initial funding of $ 1 billion and expected cash flows of $300 million in year 1, $400 million in year 2, $500 million in year 3 and $600 million in year 4. Assuming a discount rate of 12%, the NPV of a project is shown in Image 1.4:

Image 1.4: NPV of a Project

Once the NPV is computed, the decision rule is extremely simple because the hurdle rate is already factored in the present value.

Decision Rule for NPV for Independent Projects

If the NPV > 0 → Accept the project
If the NPV < 0 → Reject the project

Note that an NPV that is greater than zero means that the project makes a return greater than the hurdle rate.

Example 1.7: NPV from the Company's Point of View: Capital Construction: Self-Storage Facility

Worksheet 1.15 we calculated the present value of the cash flows to Capital Construction as a company from the proposed construction of a self-storage facility the cost of capital of 12.90% as the discount rate on the cash flows. (The cash flows are shown in Example 1.5 and the cost of capital is shown in Example 1.4.)

Worksheet 1.15 NPV of Capital Construction

This project has a net present value of -$33,113, suggesting that it is a project that should not be accepted based on the projected cash flows and the cost of capital of 12.90%.

Properties of the NPV Rule

The NPV has several important properties that make it an attractive decision rule and the preferred rule, at least if corporate finance practitioner were doing the picking.

NPVs Are Additive

The NPVs of individual projects can be aggregated to arrive at a cumulative NPV for a business or a division. No other project decision rule has this property. The property itself has a number of implications.

The value of a company can be written in terms of the present values of the cash flows of the projects it has already taken on as well as the expected NPVs of prospective future projects:

Value of company = ∑Present Value of Projects in Place +∑NPV of Future Projects

The first term in this equation captures the value ofassets in place, whereas the second term measures the value of expected future growth. Note that the present value of projects in place is based on anticipated future cash flows on these projects.

• When a company terminates an existing project that has a positive present value based on anticipated future cash flows, the value of the company will increase by that amount. Similarly, with an investments in a new project, with an expected negative NPV, the value of the company will decrease by that amount.
• When a company divests itself of an existing asset, the price received for that asset will impact the value of the company. If the price received exceeds the present value of the anticipated cash flows on that project to the company, the value of the company will increase with the divestiture; otherwise, it will decrease.
• When a company invests in a new project with a positive NPV, the value of the company will be impacted depending on if the NPV meets expectations. For example, a company like Apple is expected to take on high positive NPV projects, and this expectation is built into value. Even if the new projects taken on by Apple have positive NPV, there may be a drop in value if the NPV does not meet the high expectations of financial markets.

When a company makes an acquisition and pays a price that exceeds the present value of the expected cash flows from the company being acquired, it is the equivalent of taking on a negative NPV project and will lead to a drop in value.

Intermediate Cash Flows Are Invested at the Hurdle Rate

Hurdle Rate: The minimum acceptable rate of return that a company will accept for taking a given project.

Implicit in all present value calculations are assumptions about the rate at which intermediate cash flows get reinvested. The NPV rule assumes that intermediate cash flows on a projects-that is, cash flows that occur between the initiation and the end of the project-get reinvested at the hurdle rate, which is the cost of capital if the cash flows are to the company and the cost of equity if the cash flows are to equity investors. Given that both the cost of equity and capital are based on the returns that can be made on alternative projects of equivalent risk, this assumption should be reasonable.

NPV Calculations Allow for Expected Term Structure and Interest Rate Shifts

In all the examples throughout in this section, we have imagined that the discount rate remains unchanged over time. This is not always the case, however; the NPV can be computed using time-varying discount rates. The general formulation for the NPV rule is as follows:

NPV of Project = ∑ CF_t/∏(1 + r_t ) - Initial Funding

where

CF_t = Cash flow in period t

r_t = One-period discount rate that applies to period t

N = Life of the project.

The discount rates may change for three reasons:

• The level of interest rates may change over time, and the term structure may provide some insight on expected rates in the future.
• The risk characteristics of the project may be expected to change in a predictable way over time, resulting in changes in the discount rate.
• The financing mix on the project may change over time, resulting in changes in both the cost of equity and the cost of capital.

Example 1.8: NPV Calculation with Time-Varying Discount Rates

Imagine that you are analyzing a four-year project investing in artificial intelligence software development. Furthermore, imagine that the technological uncertainty associated with the software industry leads to higher discount rates in future years.

The present value of each of the cash flows can be computed as follows.

PV of Cash Flow in year 1 = $400/1.12 = $357.14
PV of Cash Flow in year 2 = $500/(1.12 * 1.13) = $395.06
PV of Cash Flow in year 3 = $600/(1.12 * 1.13 * 1.14) =$415.86
PV of Cash Flow in year 4 = $700/(1.11 * 1.12 * 1.13 * 1.15) =$421.88
NPV of Project = $357.14 + $395.06 + $415.86 + $421.27 - $1000.00 = $589.94

Internal Rate of Return

Internal Rate of Return (IRR): The rate of return earned by the project based on cash flows, allowing for the time value of money.

The internal rate of return (IRR) is based on discounted cash flows. Unlike the NPV rule, however, it takes into account the project's scale. It is the discounted cash flow analog to the accounting rates of return. Again, in general terms, the IRR is that discount rate that makes the NPV of a project equal to zero. To illustrate, consider again the project described at the beginning of the NPV discussion.

Cash Flow = -$1,000 + $400 + $500 + $600 + $700
Internal Rate of Return = 30.35%

At the internal rate of return, the NPV of this project is zero. The linkage between the NPV and the IRR is most obvious when the NPV is graphed as a function of the discount rate in a net present value profile. An NPV profile for the project described is illustrated in Image 1.5.

Image 1.5: NPV Profile

NPV Profile: This measures the sensitivity of the NPV to changes in the discount rate.

The NPV profile provides several insights on the project's viability. First, the internal rate of return is clear from the graph-it is the point at which the profile crosses the x- axis. Second, it provides a measure of how sensitive the NPV-and, by extension, the project decision-is to changes in the discount rate. The slope of the NPV profile is a measure of the discount rate sensitivity of the project. Third, when mutually exclusive projects are being reviewed, graphing both NPV profiles together provides a measure of the break-even discount rate-the rate at which the decision maker will be indifferent between the two projects.

Using the IRR

One advantage of the IRR is that it can be used even in cases where the discount rate is unknown. While this is true for the calculation of the IRR, it is not true when the decision maker has to use the IRR to decide whether to take a project. At that stage in the process, the IRR has to be compared to the discount rate-f the IRR is greater than the discount rate, the project is a good one; alternatively, the project should be rejected.

Like the NPV, the IRR can be computed in one of two ways:

• The IRR can be calculated based on the free cash flows to the company and the total capital contribution in the project. In doing so, the IRR has to be compared to the cost of capital.
• The IRR can be calculated based on the free cash flows to equity and the equity contribution in the project. If it is calculated with these cash flows, it has to be compared to the cost of equity, which should explain the riskiness of the project.

Decision Rule for IRR for Independent Projects

A. IRR is computed on cash flows to the company

When choosing between projects of equivalent risk, the project with the higher IRR is viewed as the better project.

Example 1.9: Estimating the IRR Based on FCFF: Capital Construction

The cash flows to the company from Capital Construction, are used to arrive at a NPV profile for the project in Image 1.6.

Image 1.6: Capital Construction NPV

The IRR in dollar terms on this project is 10.35%, which is lower than the cost of capital of 12.90%. These results are consistent with the findings from the NPV rule, which also recommended not to construct the self-storage facility.

Biases, Limitations, and Caveats

The IRR is the most widely used discounted cash flow rule in project analysis, but it does have some serious limitations.

• Because the IRR is a scaled measure, it tends to bias decision makers toward smaller projects, which are much more likely to yield higher returns, and away from larger ones.
• There are a number of scenarios in which the IRR cannot be computed or is not meaningful as a decision tool. The first is when there is no or only a very small initial capital contribution and the cashflows are spread over time. In such cases, the IRR cannot be computed or, if computed, is likely to be meaningless. The second is when there is more than one internal rate of return for a project, and it is not clear which one the decision maker should use.

Example 1.10: Multiple IRR Projects

Consider a project to manufacture and sell a consumer product, with a hurdle rate of 12%, that has a four-year life and the following cash flows over those four years. The project, which requires the licensing of a trademark, requires a large payment at the end of the fourth year. Image 1.7 shows the cash flows.

Image 1.7 Cash Flows on Project

The NPV profile for this project, shown in Image 1.8, explains the problems that arise with the IRR measure.

Image 1.8: NPV Profile for Multiple IRR Project