Valuation, Cost of Capital and Capital Budgeting
a. Valuation Concepts
The valuation of a financial asset is based on determining the present value of
future cash flows. Thus we need to know the value of future cash flows and the discount
rate to be applied to the future cash flows to determine the current value.
The market-determined required rate of return, which is the discount rate, depends
on the market’s perceived level of risk associated with the individual security. Also
important is the idea that required rates of return are competitively determined among the
many companies seeking financial capital. For example, Microsoft, due to its low
financial risk, relatively high return, and strong market position, is likely to raise debt
capital at a significantly lower cost than can United Airlines, a firm with high financial
risk. This implies that investors are willing to accept low return for low risk, and vice
versa. The market allocates capital to companies based on risk, efficiency, and expected
returns—which are based to a large degree on past performance. The reward to the
financial manager for efficient use of capital in the past is a lower required return for
investors than that of competing companies that did not manage their financial resources
as well.
Throughout the balance of this , we apply concepts of valuation to corporate
bonds, preferred stock, and common stock. Although we describe the basic characteristics
of each form of security as part of the valuation process, extended discussion of each
security is deferred until later.
b. Valuation of Bonds
As previously stated, the value of a financial asset is based on the concept of the
present value of future cash flows. Let’s apply this approach to bond valuation. A bond
provides an annuity stream of interest payments and a $1,000 principal payment at
maturity.1 These cash flows are discounted at Y, the yield to maturity. The value of Y is
determined in the bond market and represents the required rate of return for bonds of a
given risk and maturity. More will be said about the concept of yield to maturity in the
next section.
The first term in the equation says to take the sum of the present values of the
interest payments (It); the second term directs you to take the present value of the
principal payment at maturity (Pn). The discount rate used throughout the analysis is the
yield to maturity (Y). The answer derived is referred to as Pb (the price of the bond). The
analysis is carried out for n periods.
The price of the bond in this case is essentially the same as its par, or stated, value
to be received at maturity of $1,000. This is because the annual interest rate is 10 percent
(the annual interest payment of $100 divided by $1,000) and the yield to maturity, or
discount rate, is also 10 percent. When the interest rate on the bond and the yield to
maturity are equal, the bond will trade at par value. Later we will examine the
mathematical effects of varying the yield to maturity above or below the interest rate on
the bond.
Bond values can be found using the PV function on a financial calculator. The
first calculator solution box in the margin shows the present value of the twenty $100
coupon payments. The calculator keystrokes are identical to those used to find the present
value of an annuity. Notice that the PMT value is entered as a negative number. As we
found earlier, the present value of the coupon payment annuity stream is $851.36.
The second calculator solution shows the present value of the $1,000 principal
payment that will be received at the end of 20 years. The calculator keystrokes are
identical to those used to find the present value of a single amount. If the value is entered
as a negative number, the present value of the principal will be $148.64. This is the value
found using the present value equation earlier. Of course, the value of the bond ($1,000)
is the sum of the present values in panel A and panel B.
Finally, the third calculator solution demonstrates how we calculate the bond
value when entering the principal and coupon payments simultaneously. Again, the
coupon amounts are entered as a negative value using the PMT key, and the principal is
entered as a negative value using the FV key. The value of the bond is $1,000.
Excel’s PV function can calculate the price of a bond. In order to produce a
positive bond price, the coupon payment annuity amount is input as a negative value for
the pmt argument. The principal payment (−1000) is entered as the fv argument. The
function in cell D1 references the arguments in cells B1 to B4. The function in cell D5
uses hard-coded numerical values. In both cases, the bond values produced by the PV
function are identical to the calculator solution.
The required real rate of return—This is the rate of return the investor demands
for giving up the current use of the funds on a noninflation-adjusted basis. It is the
financial “rent” the investor charges for using his or her funds for one year, five years, or
any given period. Although it varies from time to time, historically the real rate of return
demanded by investors has been about 2 to 3 percent.
Inflation premium—In addition to the real rate of return discussed above, the
investor requires a premium to compensate for the eroding effect of inflation on the value
of the dollar. It would hardly satisfy an investor to have a 3 percent total rate of return in
a 5 percent inflationary economy. Under such circumstances, the lender (investor) would
be paying the borrower 2 percent for use of the funds, or in other words, losing 2 percent
in purchasing power. This would represent an irrational action. No one wishes to pay
another party to use his or her fund. The inflation premium added to the real rate of return
ensures that this will not happen. The size of the inflation premium will be based on the
investor’s expectations about future inflation. In the last two decades, the inflation
premium has been 1 to 4 percent. In the late 1970s, it was in excess of 10 percent.
If one combines the real rate of return (part 1) and the inflation premium (part 2),
the risk-free rate of return is determined. This is the rate that compensates the investor for
the current use of his or her funds and for the loss in purchasing power due to inflation,
but not for taking risks. As an example, if the real rate of return were 3 percent and the
inflation premium were 4 percent, we would say the risk-free rate of return is 7 percent.
Risk premium—We must now add the risk premium to the risk-free rate of return.
This is a premium associated with the special risks of a given investment. Of primary
interest to us are two types of risk: business risk and financial risk. Business risk relates
to the inability of the firm to hold its competitive position and maintain stability and
growth in its earnings. Financial risk relates to the inability of the firm to meet its debt
obligations as they come due. In addition to the two forms of risk mentioned above, the
risk premium will be greater or less for different types of investments. For example,
because bonds possess a contractual obligation for the firm to pay interest to bondholders,
they are considered less risky than common stock where no such obligation exists.
The risk premium of an investment may range from as low as zero on a very-
shortterm U.S. government–backed security to 10 to 15 percent on a gold mining
expedition. The typical risk premium is 2 to 6 percent. Just as the required real rate of
return and the inflation premium change over time, so does the risk premium. For
example, high-risk corporate bonds (sometimes referred to as junk bonds) normally
require a risk premium of about 5 percentage points over the risk-free rate. However, in
September 1989 the bottom fell out of the junk bond market as Campeau Corp.,
International Resources, and Resorts International began facing difficulties in making
their payments. Risk premiums almost doubled. The same phenomenon took place in the
fall of 2008 in reaction to the U.S. financial crisis and in the spring of 2010 in reaction to
the debt crisis in Greece, Portugal, Ireland, Italy, and Spain. As is emphasized in many
parts of the text, there is a strong correlation between the risk the investor is taking and
the return the investor demands. Supposedly, in finance as in other parts of business,
“There is no such thing as a free lunch.” As you take more risk hoping for higher returns,
you also expose yourself to the possibility of lower or negative returns on the other end of
the probability curve.
In this instance, we assume we are evaluating the required return on a bond issued
by a firm. If the security had been the common stock of the same firm, the risk premium
might be 5 to 6 percent and the required rate of return 12 to 13 percent. Finally, in
concluding this section, you should recall that the required rate of return on a bond is
effectively the same concept as required yield to maturity.
In the earlier bond value calculation, we assumed the interest rate was 10 percent
($100 annual interest on a $1,000 par value bond) and the yield to maturity was also 10
percent. Under those circumstances, the price of the bond was basically equal to par
value. Now let’s assume conditions in the market cause the yield to maturity to change.
For example, assume the inflation premium goes up from 4 to 6 percent. All else
remains constant. The required rate of return would now be 12 percent. With the required
rate of return, or yield to maturity, now at 12 percent, the price of the bond will change.5
A bond that pays only 10 percent interest when the required rate of return (yield to
maturity) is 12 percent will fall below its current value of approximately $1,000. The new
price of the bond is $850.61.
In this example, we assumed increasing inflation caused the required rate of
return (yield to maturity) to go up and the bond price to fall by approximately $150. The
same effect would occur if the business risk increased or the demanded level for the real
rate of return became higher.
The bond is now trading at $196.36 over par value. This is certainly the expected
result because the bond is paying 10 percent interest when the yield required in the
market is only 8 percent. The 2 percentage point differential on a $1,000 par value bond
represents $20 per year. The investor will receive this differential for the next 20 years.
The present value of $20 for the next 20 years at the current market rate of interest of 8
percent is approximately $196.36. This explains why the bond is trading at $196.36 over
its stated, or par, value.
The impact of a change in yield to maturity on valuation is also affected by the
remaining time to maturity. The effect of a bond paying 2 percentage points more or less
than the going rate of interest is quite different for a 20-year bond than it is for a 1-year
bond. In the latter case, the investor will be gaining or giving up only $20 for one year.
That is certainly not the same as having this $20 differential for an extended period. Let’s
once again return to the 10 percent interest rate bond and show the impact of a 2
percentage point decrease or increase in yield to maturity for varying times to maturity.
The values are. The lower part of the figure shows how the amount (discount) below par
value is reduced with progressively fewer years to maturity. Clearly, the longer the
maturity, the greater the impact of changes in yield.
Until now we have used yield to maturity as well as other factors, such as the
interest rate on the bond and number of years to maturity, to compute the price of the
bond. We shall now assume we know the price of the bond, the interest rate on the bond,
and the years to maturity, and we wish to determine the yield to maturity. Once we have
computed this value, we have determined the rate of return that investors are demanding
in the marketplace to provide for inflation, risk, and other factors.
We wish to compute the yield to maturity, or discount rate, that equates future
flows with the current price. It turns out that there is no algebraic formula that allows us
to solve for the yield to maturity directly. Once upon a time, this presented a difficult
puzzle that required tedious trial-and-error estimations to be checked before a solution
could be found. Fortunately, our tools have improved. Both Excel and financial
calculators are able to do these calculations so rapidly that the user is frequently left
unaware that they are using the same trial-and-error process that was once done by hand.
The Excel function RATE(n,pmt,pv,fv) shown at the bottom of the spreadsheet
can also be used to find the yield to maturity, but the full spreadsheet has the advantage
of making all the steps transparent to the reader. The spreadsheet also introduces Excel’s
very flexible Goal Seek feature, which has many uses in addition to finding yields to
maturity.
In the spreadsheet, the time (n) of each payment is shown in column B, and each
payment amount is shown in column C. The last two payments are at time n = 15 when
both the last coupon payment and the principal are paid. In column D, we see a “PV
factor” that is used to find the present value of each payment. The general equation for
each factor is shown in the first comment box that points to cell D2. The comment box
pointing to cell D4 shows the actual Excel equation and syntax for that cell. Each of the
PV factor cells references the discount rate in cell D$1, which is also the yield to
maturity. The dollar sign in the cell ensures that each row in the D column is referencing
cell D1. Column E shows the present value of each payment, and the sum of the present
value of all these payments is shown in cell E20. This is the bond price. Once you have
created the spreadsheet and entered the data and appropriate equations, you are ready to
use Goal Seek.
The yield to maturity of Y = 12.00% is shown in red in cell D1. This cell was
calculated using the Goal Seek function in Excel. Goal Seek is used when you know the
result that you want for a formula, but you are not sure what input value the formula
needs to get the result. In the case of the yield to maturity, we know the bond price should
be $931.89, but we do not know the discount rate that produces that price. The Goal Seek
function can be found in the most recent version of Excel on the Data tab, in the Data
Tools group, under What-If Analysis. Excel Ribbon location. Earlier versions of Excel
also include Goal Seek, but the feature may be in a menu or toolbar instead of on the
Excel Ribbon. The financial calculator keystrokes function much like Excel’s
RATE(nper,pmt,pv,(fv)) function.
The answer of $849.54 is slightly below what we found previously for the same
bond, assuming an annual interest rate ($850.61). This value was initially shown on page
309. In terms of accuracy, the semiannual analysis is a more acceptable method and is the
method used in bond tables. As is true in many finance texts, we present the annual
interest rate approach first for ease of presentation, and then the semiannual basis is
given. In the problems at the back of, you will be asked to do problems on both an annual
and semiannual interest payment basis.
c. Valuation of Common Stock
The value of a share of common stock may be interpreted by the shareholder as
the present value of an expected stream of future dividends. Although in the short run
stockholders may be influenced by a change in earnings or other variables, the ultimate
value of any holding rests with the distribution of earnings in the form of dividend
payments. Though the stockholder may benefit from the retention and reinvestment of
earnings by the corporation, at some point the earnings must be translated into cash flow
for the stockholder.
Under the no-growth circumstance, common stock is very similar to preferred
stock. The common stock pays a constant dividend each year. For that reason, we merely
translate the terms in Formula 10-3, which applies to preferred stock, to apply to common
stock. A no-growth policy for common stock dividends does not hold much appeal for
investors and so is seen infrequently in the real world.
The discussion of stock valuation to this point has related to the concept of the
present value of future dividends. This is a valid concept, but suppose we wish to
approach the issue from a slightly different viewpoint. Assume we are going to buy a
stock and hold it for three years and then sell it. We wish to know the present value of our
investment. This is somewhat like the bond valuation analysis. We will receive a
dividend for three years (D1, D2, D3) and then a price (payment) for the stock at the end
of three years (P3). What is the present value of the benefits? To solve this, we add the
present value of three years of dividends and the present value of the stock price after
three years. Assuming a constant growth dividend analysis, the stock price after three
years is simply the present value of all future dividends after the third year (from the
fourth year on). Thus the current price of the stock in this case is nothing other than the
present value of the first three dividends, plus the present value of all future dividends
(which is equivalent to the stock price after the third year). Saying the price of the stock
is the present value of all future dividends is also the equivalent of saying it is the present
value of a dividend stream for a number of years, plus the present value of the price of
the stock after that time period. The appropriate formula would be Formula 10-7, where
the fourth term would be replaced by P3 = D4/(Ke − g).
In our analysis of common stock, we have used the first year’s dividend (D1), the
required rate of return (Ke), and the growth rate (g) to solve for the stock price (P0) based
on Formula 10-8. We could change the analysis to solve for the required rate of return
(Ke) as the unknown, given that we know the first year’s dividend (D1), the stock price
(P0), and the growth rate (g). We take the preceding formula and algebraically change it
to provide Formula 10-9.
The first term represents the dividend yield the stockholder will receive, and the
second term represents the anticipated growth in dividends, earnings, and stock price.
While we have been describing the growth rate primarily in terms of dividends, it is
assumed the earnings and stock price will also grow at that same rate over the long term
if all else holds constant. You should also observe that the preceding formula represents a
total-return concept. The stockholder is receiving a current dividend plus anticipated
growth in the future. If the dividend yield is low, the growth rate must be high to provide
the necessary return. Conversely, if the growth rate is low, a high dividend yield will be
expected. The concepts of dividend yield and growth are clearly interrelated.
The price-earnings (P/E) ratio represents a multiplier applied to current earnings
to determine the value of a share of stock in the market. It is considered a pragmatic,
everyday approach to valuation. If a stock has earnings per share of $3 and a P/E ratio of
15 times, it will carry a market value of $45. Another company with the same earnings
but a P/E ratio of 20 times will enjoy a market price of $60.
The price-earnings ratio is influenced by the earnings and sales growth of the
firm, the risk (or volatility in performance), the debt-equity structure of the firm, the
dividend policy, the quality of management, and a number of other factors. Firms that
have bright expectations for the future tend to trade at high P/E ratios while the opposite
is true for low P/E firms. For example, the average P/E for the S&P 500 Index firms was
26 in early 2018, but Amazon.com traded at a P/E of 351 because its earnings were
expected to grow dramatically, and Ford traded at a P/E of just above 10 because auto
sales were expected to decline after several good years.
P/E ratios can be looked up in Barron’s, at finance.yahoo.com, and a number of
other publications and Internet sites. Quotations from Barron’s are presented. The first
column after the company’s name shows the ticker symbol and is followed by the yield
(dividends per share divided by stock price). The third column is the item of primary
interest and it indicates the current price-earnings (P/E) ratio. The remaining columns
cover the stock price (last), the weekly price change, and dividend data. For IBM, which
is highlighted in, the P/E ratio is 14, indicating that the company’s stock price of $162.37
represents 14 times earnings (of approximately $11.60) for the past 12 months. Firms that
are operating at a loss (deficit) have the symbol dd in the P/E ratio column.
The dividend valuation approach (based on the present value of dividends) that
we have been using throughout the is more theoretically sound than P/E ratios and more
likely to be used by sophisticated financial analysts. To some extent, the two concepts of
P/E ratios and dividend valuation models can be brought together. A stock that has a high
required rate of return (Ke) because it’s risky will generally have a low P/E ratio.
Similarly, a stock with a low required rate of return (Ke) because of the predictability of
positive future performance will normally have a high P/E ratio. These are generalized
relationships. There are, of course, exceptions to every rule of thumb.
In the discussion of common stock valuation, we have considered procedures for
firms that had no growth in dividends and for firms that had a constant growth. Most of
the discussion and literature in finance assumes a constant growth dividend model.
However, there is also a third case, and that is one of variable growth in dividends. The
most common variable growth model is one in which the firm experiences supernormal
(very rapid) growth for a number of years and then levels off to more normal, constant
growth. The supernormal growth pattern is often experienced by firms in emerging
industries, such as in the early days of electronics or microcomputers.
In evaluating a firm with an initial pattern of supernormal growth, we first take
the present value of dividends during the exceptional growth period. We then determine
the price of the stock at the end of the supernormal growth period by taking the present
value of the normal, constant dividends that follow the supernormal growth period. We
discount this price to the present and add it to the present value of the supernormal
dividends. This gives us the current price of the stock.
Finally, in the discussion of common stock valuation models, readers may ask
about the valuation of companies that currently pay no dividends. Since virtually all our
discussion has been based on values associated with dividends, how can this “no
dividend” circumstance be handled? One approach is to assume that even for the firm that
pays no current dividends, at some point in the future, stockholders will be rewarded with
cash dividends. We then take the present value of their deferred dividends. A second
approach to valuing a firm that pays no cash dividends is to take the present value of
earnings per share for a number of periods and add that to the present value of a future
anticipated stock price. The discount rate applied to future earnings is generally higher
than the discount rate applied to future dividends.
d. Cost of Debt
The cost of debt is measured by the interest rate at which a company can raise
new capital. For companies that do not issue bonds but simply borrow from a bank, this
rate will be the rate at which they can borrow from the bank. The more interesting case
arises when the cost of debt is measured by the interest rate, or yield, paid to
bondholders. The simplest case would be a $1,000 bond paying $100 annual interest, thus
providing a 10 percent yield. The computation may be more difficult if the bond is priced
at a discount or premium from par value.
Assume the firm is preparing to issue new debt. To determine the likely cost of
the new debt in the marketplace, the firm will compute the yield on its currently
outstanding debt. This is not the rate at which the old debt was issued, but the rate that
investors are demanding today. Assume the debt issue pays $90 per year in interest, has a
15-year life (at which time the principal amount of $1,000 will be paid), and is currently
selling for $968.50. The yield to maturity is the interest rate that the market uses to price
the bond. In saw how the yield to maturity can be obtained using Excel’s Goal Seek
function or Excel’s RATE function. Using the RATE functio, we find that the yield to
maturity for this bond is 9.40 percent. Calculator keystrokes shown in the margin produce
the same result.
In many cases, you will not have to compute the yield to maturity. It will simply
be given to you. The practicing corporate financial manager also can normally consult a
source such as S&P Capital IQ Net Advantage to determine the yield to maturity on the
firm’s outstanding debt. An excerpt from this bond guide is presented. If the firm
involved is Keyspan Corp., for example, the financial manager could observe that debt
maturing in 2030 would have a yield to maturity of 4.71 percent as highlighted.
Once the bond yield is determined through the formula, a calculator, or the tables
(or is given to you), you must adjust the yield for tax considerations. Yield to maturity
indicates how much the corporation has to pay on a before-tax basis. But keep in mind
the interest payment on debt is a tax-deductible expense. Since interest is tax-deductible,
its true cost is less than its stated cost because the government is picking up part of the
tab by allowing the firm to pay less tax. The aftertax cost of debt is actually the yield to
maturity times 1 minus the tax rate.1 This is presented as Formula 11-1.
The term Y (yield) in the formula is interchangeable with yield to maturity.
Earlier in this section, we determined that the existing yield on the debt was 9.40 percent.
We shall assume new debt can be issued at the same going market rate,2 and that the firm
is paying a 25 percent tax (a nice, easy rate with which to work). Applying the tax
adjustment factor, the aftertax cost of debt would be 7.05 percent.
Please refer back and observe in column 1 that the aftertax cost of debt is the 7.05
percent that we have just computed. The 2017 Tax Cuts and Jobs Act introduced
complexity in calculating the cost of debt for companies with high interest expense.
Beginning in 2022, a company can only deduct interest of up to 30 percent of its earnings
before interest and taxes (EBIT). Until then a more generous limitation applies; the
company can deduct interest up to 30 percent of earnings before interest, taxes,
depreciation, and amortization (EBITDA). EBITDA is higher than EBIT as long as the
company has depreciation or amortization expenses. For companies with very high
interest expense, or very low EBIT, the interest expense limitation will remove the tax
advantage to issuing debt, and Equation 11-1 would need to be adjusted to reflect the fact
that the pretax and aftertax costs are the same for these firms.
e. Cost of Preferred Stock
The cost of preferred stock is similar to the cost of debt in that a constant annual
payment is made, but dissimilar in that there is no maturity date on which a principal
payment must be made. Determining the yield on preferred stock is simpler than
determining the yield on debt. All you have to do is divide the annual dividend by the
current price. This represents the rate of return to preferred stockholders as well as the
annual cost to the corporation for the preferred stock issue.
We need to make one slight alteration to this process by dividing the dividend
payment by the net price or proceeds received by the firm. Since a new share of preferred
stock has a selling cost (flotation cost), the proceeds to the firm are equal to the selling
price in the market minus the flotation cost. The cost of preferred stock is presented as
Formula 11-2.
In the case of the Baker Corporation, we shall assume the annual dividend is
$10.50, the preferred stock price is $100, and the flotation, or selling cost, is $4. Because
a preferred stock dividend is not a tax-deductible expense, there is no downward tax
adjustment. Please refer back to and observe in column 1 that 10.94 percent is the value
we used for the cost of preferred stock.
f. Cost of Common Equity
Determining the cost of common stock in the capital structure is a more involved
task. The out-of-pocket cost is the cash dividend, but is it prudent to assume the
percentage cost of common stock is simply the current year’s dividend divided by the
market price? If such an approach were followed, the common stock costs for selected
U.S. corporations in February 2018 would be as follows: Target (3.25 percent), Microsoft
(1.82 percent), Walmart (1.91 percent), and PepsiCo (2.66 percent). Ridiculous, you say!
If new common stock costs were assumed to be so low, the firms would have no need to
issue other securities and could profitably finance projects that earned only 2 or 3
percent. How then do we find the correct theoretical cost of common stock to the firm?
In determining the cost of common stock, the firm must be sensitive to the pricing
and performance demands of current and future stockholders. An appropriate approach is
to develop a model for valuing common stock and to extract from this model a formula
for the required return on common stock.
The required return on common stock can also be calculated by an alternate
approach called the capital asset pricing model. This topic is covered in Appendix 11A,
so only brief mention will be made at this point. Some accept the capital asset pricing
model as an important approach to common stock valuation, while others suggest it is not
a valid description of how the real world operates.
In this calculation, we have assumed that Kj (the required return under the capital
asset pricing model) would equal Ke (the required return under the dividend valuation
model). They are both computed to equal 12 percent. Under this equilibrium
circumstance, the dividend valuation model and the capital asset pricing model would
produce the same answer. For now we shall use the dividend valuation model
exclusively; that is, we shall use Ke = (D1/P0) + g in preference to Kj = Rf (11-5) page
348 (11-6) + β(Km − Rf). Those who wish to study the capital asset pricing model further
are referred to Appendix 11A.
Up to this point, we have discussed the cost (required return) of common stock in
a general sense. We have not really specified who is supplying the funds. One obvious
supplier of common stock equity capital is the purchaser of new shares of common stock.
But this is not the only source. For many corporations the most important source of
ownership or equity capital is in the form of retained earnings, an internal source of
funds.
Accumulated retained earnings represent the past and present earnings of the firm
minus previously distributed dividends. Retained earnings, by law, belong to the current
stockholders. They can be either paid out to the current stockholders in the form of
dividends or reinvested in the firm. As current funds are retained in the firm for
reinvestment, they represent a source of equity capital that is being supplied by the
current stockholders. However, they should not be considered free. An opportunity cost is
involved. As previously indicated, the funds could be paid out to the current stockholders
in the form of dividends, and then redeployed by the stockholders in other stocks, bonds,
real estate, and so on. What is the expected rate of return on these alternative
investments? That is, what is the opportunity cost? We assume stockholders could at least
earn an equivalent return to that provided by their present investment in the firm (on an
equal risk basis). This represents D1/P0 + g. In the security markets, there are thousands
of investments from which to choose, so it is not implausible to assume the stockholder
could take dividend payments and reinvest them for a comparable yield. Thus when we
compute the cost of retained earnings, this takes us back to the point at which we began
our discussion of the cost of common stock. The cost of retained earnings is equivalent to
the rate of return on the firm’s common stock. This is the opportunity cost.
Thus Ke represents not only the required return on common stock as previously
defined but also the cost of equity in the form of retained earnings. It is a symbol that has
double significance. For ease of reference, the terms in Formula 11-5 are reproduced in
the box that follows. They are based on prior values presented in this section on the cost
of common equity.
Let’s now consider the other source of equity capital, new common stock. If we
are issuing new common stock, we must earn a slightly higher return than Ke, which
represents the required rate of return of present stockholders. The higher return is needed
to cover the distribution costs of the new securities. Assume the required return for
present stockholders is 12 percent and shares are quoted to the public at $40. A new
distribution of securities must earn slightly more than 12 percent to compensate the
corporation for not receiving the full $40 because of sales commissions and other
expenses. The formula for Ke is restated as Kn (the cost of new common stock) to reflect
this requirement.
g. Optimum Capital Structure—Weighting Costs
Having established the techniques for computing the cost of the various elements
in the capital structure, we must now discuss methods of assigning weights to these costs.
We will attempt to weight capital components in accordance with our desire to achieve a
minimum overall cost of capital. This represents an optimum capital structure. For the
purpose of this discussion.
How does the firm decide on the appropriate weights for debt, preferred stock,
and common stock financing? Though debt is the cheapest form of financing, it should be
used only within reasonable limits. In the Baker Corporation example, debt carried an
aftertax cost of 7.05 percent, while other sources of financing cost at least 10.94 percent.
Why not use more debt? The answer is that the use of debt beyond a reasonable point
may greatly increase the firm’s financial risk and thereby drive up the costs of all sources
of financing.
The firm is able to initially reduce the weighted average cost of capital with debt
financing, but beyond Plan B the continued use of debt becomes unattractive and greatly
increases the costs of the sources of financing. Traditional financial theory maintains that
there is a U-shaped cost-of-capital curve relative to debt utilization by the firm, as
illustrated. In this example, the optimum capital structure occurs at a 40 percent debt-to-
assets ratio. The weighted average cost of capital is such a fundamental concept that
finance professionals often referred to it simply as “the WACC.”
The weights that are used to calculate the WACC should be market-value
weights. This is consistent with our use of marketbased costs of capital for the WACC’s
component costs. The optimal level of corporate debt depends on the business risks faced
by the firm and the nature of the assets that the firm employs. “Operating and Financial
Leverage,” a growth firm in a reasonably stable industry can afford to absorb more debt
than its counterparts in cyclical industries. In determining the appropriate capital mix, the
firm generally begins with its present capital structure and ascertains whether its current
position is optimal. If not, subsequent financing should carry the firm toward a mix that is
deemed more desirable. Only the costs of new or incremental financing should be
considered.
Examples of debt levels by companies in various industries are presented. Despite
the fact that low interest rates have encouraged firms to issue more debt, for most of these
firms the 2018 percent debt is less than the 2015 percentage. This happened because
equity market values rose dramatically from late 2016 to early 2018, and firms usually
move gradually toward their optimal debt-equity mix.
h. Capital Acquisition and Investment Decision Making
So far the various costs of financial capital and the optimum capital structure have
been discussed. Financial capital, as you may have figured out, consists of bonds,
preferred stock, and common equity. These forms of financial capital appear on the
corporate balance sheet under liabilities and equity. The money raised by selling these
securities and retaining earnings is invested in the real capital of the firm, the long-term
productive assets of plant and equipment.
Long-term funds are usually invested in long-term assets, with several asset-
financing mixes possible over the business cycle. Obviously a firm wants to provide all
of the necessary financing at the lowest possible cost. This means selling common stock
when prices are relatively high to minimize the cost of equity. The financial manager also
wants to sell debt at low interest rates. Since there is short-term and long-term debt, the
manager needs to know how interest rates move over the business cycle and when to use
short-term versus long-term debt.
A firm has to find a balance between debt and equity to achieve its minimum cost
of capital. Although we discussed minimizing the overall cost of capital (Ka) at a single
debt-to-equity ratio, in reality a firm operates within a relevant range of debt to equity
before it becomes penalized with a higher overall cost because of increased risk. As we
move from time period t to time period t + 2, falling interest rates and rising stock prices
cause a downward shift in Ka. This graph illuminates two basic points: (1) The firm
wants to keep its debt-to-assets ratio between x and y along the bottom axis at all times
because this is the lowest area on each of the three curves; and (2) the firm would like to
finance its long-term needs at time period t + 2 rather than the other two time periods
because overall costs are lowest during this time frame.
Corporations are allowed some leeway in the money and capital markets, and it is
not uncommon for the debt-to-equity ratio to fluctuate between x and y over a business
cycle. The firm that is at point y has lost the flexibility of increasing its debt-to-assets
ratio without incurring the penalty of higher capital costs.
The current cost of capital for each source of funds is important when making a
capital budgeting decision. Historical costs for past fundings may have very little to do
with current costs against which present returns must be measured. When raising new
financial capital, a company will tap the various sources of financing over a reasonable
time. Regardless of the particular source of funds the company is using for the purchase
of an asset, the required rate of return, or discount rate, will be the weighted average cost
of capital. As long as the company earns its cost of capital, the common stock value of
the firm will be maintained or will increase, since stockholder expectations are being met.
Baker Corporation is considering $95 million in potential projects, but given the
weighted average cost of capital of 10.41 percent, it will choose only projects A through
E, or $50 million in new investments. Selecting assets F, G, and H would probably
reduce the market value of the common stock because these projects do not provide a
return equal to the overall costs of raising funds. The use of the weighted average cost of
capital assumes the Baker Corporation is in its optimum capital structure range.
i. The Marginal Cost of Capital
Nothing guarantees the Baker Corporation that its cost of capital will stay
constant for as much money as it wants to raise even if a given capital structure is
maintained. If a large amount of financing is desired, the market may demand a higher
cost of capital for each amount of funds desired. The point is analogous to the fact that
you may be able to go to your relatives and best friends and raise funds for an investment
at 10 percent. After you have exhausted the lending or investing power of those closest to
you, you will have to look to other sources and the marginal cost of your capital will go
up.
We need to review the nature of the firm’s capital structure to explain the concept
of marginal cost of capital as it applies to the firm. Note the firm has 60 percent of the
capital structure in the form of equity capital. The equity (ownership) capital is
represented by retained earnings. It is assumed that 60 percent is the amount of equity
capital the firm must maintain to keep a balance between fixed income securities and
ownership interest. But equity capital in the form of retained earnings cannot grow
indefinitely as the firm’s capital needs expand. Retained earnings are limited to the
amount of past and present earnings that can be redeployed into the investment projects
of the firm. Let’s assume the Baker Corporation has $23.40 million of retained earnings
available for investment. Since retained earnings are to represent 60 percent of the capital
structure, there are adequate retained earnings to support a capital structure of up to $39
million.
After the first $39 million of capital is raised, retained earnings will no longer be
available to provide the 60 percent equity position in the capital structure. Nevertheless,
lenders and investors will still require that 60 percent of the capital structure be in the
form of common equity (ownership) capital. Because of this, new common stock will
replace retained earnings to provide the 60 percent common equity component for the
firm. That is, after $39 million, common equity capital will be in the form of new
common stock rather than retained earnings. In the left portion of on the next page, we
see the original cost of capital that we have been discussing throughout. This applies up
to $39 million. After $39 million, the concept of marginal cost of capital becomes
important.
Kmc in the bottom right portion of the table represents the marginal cost of
capital, and it is 10.77 percent after $39 million. The meaning of Kmc is basically the
same as Ka ; they both represent the cost of capital, but the mc subscript after K indicates
the (marginal) cost of capital is going up. The marginal cost of capital has increased after
$39 million because common equity is now in the form of new common stock rather than
retained earnings. The aftertax (A/T) cost of new common stock is slightly more
expensive than retained earnings because of flotation costs (F).
The flotation cost (F) is $4 and the cost of new common stock is 12.60 percent.
This is higher than the 12 percent cost of retained earnings that we have been using and
causes the increase in the marginal cost of capital. To carry the example a bit further, we
will assume the cost of debt of 7.05 percent applies to the first $15 million of debt the
firm raises. After that the aftertax cost of debt will rise to 8.60 percent. Since debt
represents 30 percent of the capital structure for the Baker Corporation, the cheaper form
of debt can be used to support the capital structure up to $50 million. We derive the $50
million by using Formula 11-8.
After the first $50 million of capital is raised, lower-cost debt will no longer be
available to provide 30 percent of the capital structure. After $50 million in total
financing, the aftertax cost of debt will go up to the previously specified 8.60 percent.
The marginal cost of capital for over $50 million in financing. The change in the cost of
debt gives way to a new marginal cost of capital (Kmc) of 11.23 percent after $50 million
of financing. You should observe that the capital structure with over $50 million of
financing reflects not only the change in the cost of debt, but also the continued exclusive
use of new common stock to represent common equity capital. This change occurred at
$39 million, but must be carried on indefinitely as the capital structure expands.
We could continue this process by next indicating a change in the cost of
preferred stock, or by continually increasing the cost of debt or new common stock as
more capital is used. For now it is sufficient that you merely observe the basic process.
To summarize, we have said the Baker Corporation has a basic weighted average cost of
capital of 10.41 percent. This value was developed throughout and was originally.
However, as the firm began to substantially expand its capital structure, the weighted
average cost of capital increased. This gave way to the term marginal cost of capital. The
first increase or break point was at $39 million in which the marginal cost of capital went
up to 10.77 percent as a result of replacing retained earnings with new common stock.
The second increase or break point was at $50 million in which the marginal cost of
capital increased to 11.23 percent as a result of the utilization of more expensive debt.
The changes are summarized.
The cost of capital for the firm is determined by computing the costs of various
sources of financing and weighting them in proportion to their representation in the
capital structure. The cost of each component in the capital structure is closely associated
with the valuation of that source, which we studied in the prior. For debt and preferred
stock, the cost is directly related to the current yield, with debt adjusted downward to
reflect the tax-deductible nature of interest. For common stock, the cost of retained
earnings (Ke) is the current dividend yield on the security plus an anticipated rate of
growth for the future. Minor adjustments are made to the formula to determine the cost of
new common stock. A summary of Baker Corporation’s capital costs. We weight the
elements in the capital structure in accordance with our desire to achieve a minimum
overall cost. While debt is usually the “cheapest” form of financing, excessive debt use
may increase the financial risk of the firm and drive up the costs of all sources of
financing. The wise financial manager attempts to ascertain what debt component will
result in the lowest overall cost of capital. Once this has been determined, the weighted
average cost of capital is the discount rate we use in present-valuing future flows to
ensure we are earning at least the cost of financing.
j. Accounting Flows versus Cash Flows
In most capital budgeting decisions the emphasis is on cash flow, rather than
reported income. Let us consider the logic of using cash flow in the capital budgeting
process. Because depreciation does not represent an actual expenditure of funds in
arriving at profit, it is added back to profit to determine the amount of cash flow
generated.1 Assume the Alston Corporation has $50,000 of new equipment to be
depreciated at $5,000 per year. The firm has $20,000 in earnings before depreciation and
taxes and pays 25 percent in taxes. The information is presented in illustrate the key
points involved.
The firm shows $11,250 in earnings after taxes, but it adds back the noncash
deduction of $5,000 in depreciation to arrive at a cash flow figure of $16,250. The logic
of adding back depreciation becomes even greater if we consider the impact of $20,000
in depreciation for the Alston Corp. Net earnings before and after taxes are zero, but the
company has $20,000 cash in the bank.
To the capital budgeting specialist, the use of cash flow figures is well accepted.
However, top management does not always take a similar viewpoint. Assume you are the
president of a firm listed on the New York Stock Exchange and must select between two
alternatives. Proposal A will provide zero in aftertax earnings and $100,000 in cash flow,
while Proposal B, calling for no depreciation, will provide $50,000 in aftertax earnings
and cash flow. As president of a publicly traded firm, you have security analysts
constantly penciling in their projections of your earnings for the next quarter, and you
fear your stock may drop dramatically if earnings are too low by even a small amount.
Although Proposal A is superior, you may be more sensitive to aftertax earnings than to
cash flow and you may therefore select Proposal B. Perhaps you are overly concerned
about the shortterm impact of a decision rather than the long-term economic benefits that
might accrue. You must be sensitive to executives’ concessions to short-term pressures.
Nevertheless in the material that follows, the emphasis is on the use of proper evaluation
techniques to make the best economic choices and ensure long-term wealth
maximization.
k. Methods of Ranking Investment Proposals
The payback period for Investment A is 2 years, while Investment B requires 3.8
years. In the latter case, we recover $6,000 in the first 3 years, leaving us with the need
for another $4,000 to recoup the full $10,000 investment. Since the fourth year has a total
inflow of $5,000, $4,000 represents 0.8 of that value. Thus the payback period for
Investment B is 3.8 years. In using the payback method to select Investment A, we ignore
two important considerations. First there is no consideration of inflows after the cutoff
period. The $2,000 in year 3 for Investment, as is the $5,000 in year 5 for Investment B.
Even if the $5,000 were $50,000, it would have no impact on the decision under the
payback method. Second, the method fails to consider the concept of the time value of
money. If we had two $10,000 investments with the following inflow patterns, the
payback method would rank them equally.
Although both investments have a payback period of two years, the first
alternative is clearly superior because the $9,000 comes in the first year rather than the
second. The payback method does have some features that help to explain its use by U.S.
corporations. It is easy to understand, and it emphasizes liquidity. An investment must
recoup the initial investment quickly or it will not qualify (most corporations use a
maximum time horizon of three to five years). A rapid payback may be particularly
important to firms in industries characterized by rapid technological developments.
Nevertheless the payback method, concentrating as it does on only the initial years of
investment, fails to discern the optimum or most economic solution to a capital budgeting
problem. The analyst is therefore required to consider more theoretically correct methods.
Net present value (NPV) is often the preferred investment selection method for
two important reasons. First, it is a theoretically valid method. Second, it is well
understood and used by real-world finance professionals. In other words, not only is NPV
a theoretically correct method, it is also often the preferred method in practice. The net
present value is the sum of the present values of all outflows and inflows related to a
project. The present value of each inflow and outflow is usually discounted using the
weighted average cost of capital, Ka, for the firm. Thus inflows that arrive in later years
must provide a return that at least equals the cost of the invested capital.
For Investment A, the timing of each cash flow is shown in column A with the
amount of each cash flow shown in column B. Together these columns produce a vertical
time-line of cash flows. The discount rate of 10 percent is shown in cell C2, and each of
the values in cells C4 to C7 is the present value factor needed to convert the values in
column B into the present values in column D. The net present value is simply the sum of
all the individual present values in column D. The NPV of $180.32 is highlighted in cell
D8.
Excel also provides an NPV function, which is shown in cell C13. Unfortunately,
when the initial cash flow occurs at time zero (as the $10,000 investment outflow does in
our example), the NPV function does not provide an accurate calculation unless the user
conducts a slight manipulation. Excel’s NPV function behaves badly because it assumes
that the first cash flow comes at the page 387 end of the first year. To treat the initial
outlay properly, we must leave the initial outlay out of the NPV function. Then we must
subtract the initial outlay separately. Also note that because the initial outlay is entered as
a negative number in cell B4, we must actually add the outlay to the NPV calculation. For
Investment A, the cash flows in cells B5 through B7 are entered inside the NPV function,
and the initial outlay in cell B4 must be added to the NPV function value. Unless you
look carefully at cell C13, you may overlook this subtle but important point.
The NPV for Investment B is calculated in an identical manner. The cash flow
timeline is inserted in columns F and G. Present value factors are computed in column H
using the 10 percent discount rate from cell H2, and the present value of each cash flow is
shown in column I. The sum of the present values is the NPV of $1,414.49 value
highlighted in cell I10. Using the Excel NPV function yields the same result in cell H13.
The internal rate of return (IRR) is another important metric used to make capital
budgeting decisions. While NPV measures the attractiveness of a project in dollar (i.e.,
currency) terms, the IRR measures the profitability of investments as a return percentage
—much like finding the interest rate (i) in a time value of money problem. The key to
fully understanding the meaning of the internal rate of return is to understand how IRR
relates to NPV: The internal rate of return on an investment or project is the “rate of
return” that makes the net present value of the project equal to zero.
Let us return to our analysis of Investment A and Investment B. At the top of, the
cash flows for Investment A are set up exactly as before when we calculated the NPV of
the investment. However, you will notice that instead of using a discount rate of 10
percent, the discount rate is 11.16 percent. This is the discount rate that forces the NPV
value shown in cell D8 to be exactly zero! Because the NPV is zero when the discount
rate is 11.16 percent, we have found the IRR. The internal rate of return is 11.16 percent.
An inquisitive student like you may not be satisfied with simply understanding this
definition of the IRR (the rate that makes NPV = 0). Instead, you would probably like to
know how the IRR was found. Unfortunately, there is usually no simple equation to find
the IRR. However, once again we can make use of the Goal Seek function that was
introduced. Recall that Goal Seek was used to find the yield to maturity of a bond
(YTM). In fact, the concept behind IRR is almost identical to the YTM concept.
Excel’s Goal Seek feature doesn’t use an equation. It operates by using an
iterative method to find a solution. Specifically, it tries an initial input value to see
whether that value produces the result you want. If it doesn’t, Goal Seek tries other input
values until it converges on a solution.
Now that we have determined the IRR of each investment, we will need to assess
whether these returns are high enough to justify investing in the firm. The final selection
of any project under the internal rate of return method will depend on whether the yield
exceeds some minimum threshold, such as the firm’s cost of capital. You will recall that
we assumed that the firm has a 10 percent weighted average cost of capital (WACC) in
the preceding NPV analysis. Given this threshold, both projects are expected to produce
returns in excess of the WACC.
Under most circumstances, both the net present value and the internal rate of
return methods give theoretically correct answers. Payback is simple, and it may produce
useful insights, but it is not theoretically sound. Payback’s usefulness depends on rules of
thumb that differ from firm to firm, and it has serious shortcomings when applied to
complicated cash flow patterns. Therefore, subsequent discussion will be restricted to
further examination of the NPV and the IRR methods.
l. Selection Strategy
In both the internal rate of return and net present value methods, the profitability
must equal or exceed the cost of capital for the project to be potentially acceptable.
However, other distinctions are necessary—namely, whether the projects are mutually
exclusive or not. If investments are mutually exclusive, the selection of one alternative
will preclude the selection of any other alternative. Assume we are going to build a
specialized assembly plant, and four major international cities are under consideration,
only one of which will be picked. In this situation, we select the alternative with the
highest acceptable yield or the highest net present value and disregard all others. Even if
certain other locations provide a marginal return in excess of the cost of capital, assumed
to be 10 percent, they will be rejected. In the table below, the possible alternatives are
presented.
Among the mutually exclusive alternatives, only Bangkok would be selected. If
the alternatives were not mutually exclusive (for example, much-needed multiple retail
outlets), we would accept all of the alternatives that provide a return in excess of our cost
of capital, and only Singapore would be rejected. Applying this logic to Investments A
and B in the prior discussion and assuming a cost of capital of 10 percent, only
Investment B would be accepted if the alternatives were mutually exclusive, while both
would clearly qualify if they were not mutually exclusive.
It is only under this second state of events that a preference for one method over
the other must be established. A prime characteristic of the internal rate of return is the
reinvestment assumption that all inflows can be reinvested at the yield from a given
investment. For example, in the case of the aforementioned Investment A yielding 11.17
percent, the assumption is made that the dollar amounts coming in each year can be
reinvested at that rate. For Investment B, with a 14.33 percent internal rate of return, the
new funds are assumed to be reinvested at this high rate.
You should also be aware of an alternative methodology that combines the
reinvestment assumption of the net present value method (cost of capital) with the
internal rate of return. This process is termed the modified internal rate of return (MIRR).
The analyst searches for the discount rate that will equate the future value of the inflows,
each growing at the cost of capital, with the investment.
As can be seen in this equation, the MIRR is the discount rate that equates the
future value of inflows with the value of the original investment. As an example, we will
return to the cash flow stream from our NPV valuation of Investment B. Notice in the
MIRR spreadsheet that for each of the cash inflows, we have calculated a future value in
column E. As an example, in line 6 we calculate the future value of the $1,500 inflow by
assuming it is reinvested for four years at the 10 percent cost of capital. Specifically,
$1,500 × 1.464 = $2,196.15, the value in cell E6. The sum of these future values
($18,383.15) in cell E11 represents the numerator in Formula 12-1. Since we now know
both the future value of the cash inflows and the present value of the outflows (the
investment), we can use Excel’s RATE function to find the MIRR. Being careful to enter
a zero for the pmt argument in the RATE function, we find that the MIRR is 12.95
percent.
The list of value arguments in the MIRR function are the same as those used in
Excel’s IRR function, but a finance rate and reinvestment rate must be entered also. In
most instances, including our example, these rates are the same. Recall that the
conventional internal rate of return for Investment B was 14.33 percent. The modified
internal rate of return, using the more realistic assumption of reinvestment at the cost of
capital, gives a more conservative, and more theoretically correct, answer. For that reason
you should be familiar with it. However, both NPV and IRR are used more often by
financial analysts than is the MIRR. Therefore, we will end our discussion of MIRR here
and continue the analyses in this using IRR where an internal return measure is needed.
The MIRR indicates that when you have an IRR higher than the cost of capital, the MIRR
will be smaller than the IRR. In the case of Investment A, the difference between the
11.17 percent IRR and the 10 percent cost of capital is small, and while the MIRR would
fall below the cost of capital, it would not decline as much as Investment B.
