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Unformatted text preview: WEB APPENDIX 10A
The Cost of New Common Stock and WACC
Recall that Allied’s target capital structure calls for 45% debt, 2% preferred stock,
and 53% common equity. In Chapter 10, we saw that Allied’s before-tax cost of
debt is 10%, its after-tax cost of debt is rd(1 À T) ¼ 10%(0.6) ¼ 6.0%, its cost of
preferred stock is 10.3%, its cost of common equity from retained earnings is
13.5%, and its marginal tax rate is 40%. We also noted that if all of its new equity
comes from retained earnings, its WACC, designated WACC1, would be 10.1%:
WACC1 ¼ wd rd ð1 À TÞ þ wP rP þ wC rS
¼ 0:45ð10%Þð0:6Þ þ 0:02ð10:3%Þ þ 0:53ð13:5%Þ
¼ 10:1% Under these conditions, every dollar of new capital that Allied raises would
consist of 45 cents of debt with an after-tax cost of 6%, 2 cents of preferred stock
with a cost of 10.3%, and 53 cents of common equity (all from additions to retained
earnings) with a cost of 13.5%. The average cost of each whole dollar, or the WACC,
would be 10.1%.1 This WACC is good for a variety of analyses (for example, capital
budgeting and managerial performance) as long as the equity requirement in the
optimal capital budget can be fully funded by retained earnings. But what if new
equity is required? When will we know when new common stock must be issued?
What WACC must be used then?
In Chapter 10, we also calculated Allied’s retained earnings breakpoint and
the cost of issuing new common stock. Recall that the retained earnings breakpoint
can be calculated as follows:
breakpoint = Addition to retained earnings
Common equity fraction Allied’s addition to retained earnings in 2009 is expected to be $66 million and its
target capital structure consists of 45% debt, 2% preferred, and 53% equity.
Therefore, its retained earnings breakpoint is as follows:
Retained earnings breakpoint ¼ $66=0:53 ¼ $124:5 million Recall that in Chapter 10, when we calculated Allied’s cost of new common stock,
we modified the DCF approach to account for flotation costs using the following
Cost of equity
¼ re ¼
P0 ð1 À FÞ
from new stock issues Here F is the percentage flotation cost required to sell the new stock, so
P0(1 À F) is the net price per share received by the company. 1
The WACC is the cost of investor-supplied capital used to finance new projects. The debt component of the
target capital structure includes only interest-bearing, investor-supplied debt—long-term bonds and bank notes
payable. It does not include accounts payable and accruals because those items are not provided by investors. 10A-1 10A-2 Web Appendix 10A We assumed that Allied has a flotation cost of 10%; so its cost of new common
equity, re, is calculated as follows:
$23:06ð1 À 0:10Þ
¼ 6:0% þ 8:3% ¼ 14:3% re ¼ Remember that Allied’s DCF cost of equity without flotation costs is 13.7%:
þ 8:3% ¼ 13:7%
$23:06 rs ¼ Consequently, the difference between these two cost-of-equity equations represents the added cost of equity due to flotation: 14.3% À 13.7% ¼ 0.6%. Therefore,
we should add 0.6% to Allied’s rs (determined from all three estimates as shown
in Chapter 10, 13.5%) and use that adjusted number in the WACC with the flotation equation.
Suppose Allied has so many attractive new projects (that is, projects whose
expected returns exceed the company’s cost of capital) that its capital requirements
exceed the $124.5 million breakpoint calculated earlier. In that situation, each
dollar up to $124.5 million will still cost 10.1%, but each dollar beyond
$124.5 million will include higher cost equity (14.1% versus 13.5%) raised by
selling new common stock. This will cause the WACC to increase from 10.1% to
WACC2 ¼ 10.4%:
WACC2 ¼ wd rd ð1 À TÞ þ wP rP þ wc re
¼ 0:45ð10%Þð0:6Þ þ 0:02ð10:3%Þ þ 0:53ð14:1%Þ
¼ 10:4% Figure 10A-1 shows a graph of this situation. The WACC is constant at WACC1
¼ 10.1% out to $124.5 million of total capital; then it increases to WACC2 ¼ 10.4%
and remains at that level going on out. We also show two Investment Opportunity FIGURE 10A-1 Relationship between WACC and the Amount of Funds Raised Cost of
IOS2 IOS1 WACC2 = 10.4
WACC1 = 10.1 0 124.5 Funds Raised in Millions ($) Web Appendix 10A Schedules, or IOS curves, on the graph. If IOS1 was Allied’s actual IOS curve, this
would indicate that the firm has relatively few good investment opportunities;
hence, its capital budget is small enough so that all the necessary equity can come
from retained earnings. In this case, the WACC is 10.1%. If IOS2 is a graph of the
firm’s investment opportunities, Allied will have to supplement its retained
earnings with funds from the sale of new common stock; and in that situation, its
WACC will increase to WACC2 ¼ 10.4%.
While Figure 10A-1 illustrates that the WACC would increase if the firm
raised a relatively large amount of capital during a given year, WACC would
probably not take the sharp jump that is shown here. Rather, the firm would make
adjustments to its capital structure and/or its dividend payments, and these
adjustments would cause the WACC curve to increase slowly and smoothly
beyond the breakpoint. We will return to this point in the dividend chapter,
where we discuss changes in dividend policy to reflect changes in investment
10A-1 10A-2 10A-3 A firm is analyzing its portfolio of investment opportunities and has calculated its WACC
and determined flotation costs if new equity is required. The WACC using only retained
earnings is 11.5%, while the WACC with new common stock (WACC2) is 12.0%. At
the point where the firm has exhausted retained earnings, there are still projects with
returns greater than 11.5%; however, the remaining projects’ returns are less than 12.0%.
Should the firm issue new common stock and accept these projects? Explain.
A firm’s managers know that the firm’s investment opportunities are relatively modest
and can be satisfied with retained earnings. However, the managers want to issue new
common stock, as they hope to buy most of the new common stock and gain more control
over the company. A manager has suggested just pushing the firm’s IOS curve out to
the right (creating more favorable opportunities). What is wrong with this argument?
It has been demonstrated that a firm can have more than one corporate WACC (WACC1
and WACC2) because it may have to issue new common stock at some point. Is it possible
for a firm to have even more potential WACCs? What are the circumstances in which
this might happen? PROBLEMS
10A-1 WACC WITH NEW COMMON STOCK Anthony Auto Parts wants to calculate its WACC.
The company’s CFO has collected the following information:
The company’s long-term bonds currently offer a yield to maturity of 8%.
l The company recently paid a dividend of $2 a share (D0 ¼ $2). l The dividend is expected to grow at an annual 6% constant rate. l The company’s stock price is $32 a share (P0 ¼ $32). l The company pays a 10% flotation cost whenever it issues new common stock (F ¼ 10%). l The company’s target capital structure is 75% equity and 25% debt. l The company’s tax rate is 40%. l The firm’s net income for the coming year is expected to be $96 million. l The firm’s dividend payout ratio is 40%. a.
c. What is the company’s WACC if the equity portion of the capital budget is completely
satisfied by retained earnings?
What is Anthony’s retained earnings breakpoint?
If the firm’s optimal capital budget is $144 million, what marginal WACC should be
used to evaluate projects? 10A-3 10A-4 Web Appendix 10A 10A-2 COST OF EXTERNAL EQUITY Fisher Electric has a capital structure that consists of 70%
equity and 30% debt. The company’s long-term bonds have a before-tax YTM of 8.4%.
The company uses the DCF approach to determine the cost of equity. Fisher’s common
stock currently trades at $45 per share. The year-end dividend (D1) is expected to be
$2.50 per share, and the dividend is expected to grow forever at an annual 7% constant rate.
The company estimates that it will have to issue new common stock to help fund this year’s
projects, and the flotation cost associated with issuing new common stock is 10%.
The company’s tax rate is 40%.
a. If the firm did not have to issue new equity, what would be the firm’s WACC? b. If new equity is issued, what is the firm’s WACC? c. Assume that new equity is issued. Over what range of returns would projects not be
acceptable but would appear to be okay if the firm mistakenly used the WACC in
which no new equity is issued? ...
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