Posted: June 9th, 2015

finance campus deli

finance campus deli

14-18    assume that you have just been hired as business manager of campus deli (cd), which is located adjacent to the campus.  sales were $1,100,000 last year; variable costs were 60 percent of sales; and fixed costs were $40,000.  therefore, ebit totaled $400,000.  because the university’s enrollment is capped, ebit is expected to be constant over time.  since no expansion capital is required, cd pays out all earnings as dividends.  assets are $2 million, and 80,000 shares are outstanding.  the management group owns about 50 percent of the stock, which is traded in the over-the-counter market.
cd currently has no debt–it is an all-equity firm–and its 80,000 shares outstanding sell at a price of $25 per share, which is also the book value.  the firm’s federal-plus-state tax rate is 40 percent.  on the basis of statements made in your finance text, you believe that cd’s shareholders would be better off if some debt financing were used. when you suggested this to your new boss, she encouraged you to pursue the idea, but to provide support for the suggestion.
in today’s market, the risk-free rate, krf, is 6 percent and the market risk premium, km – krf, is 6 percent.  cd’s unlevered beta, bu, is 1.0.  since cd currently has no debt, its cost of equity (and wacc) is 12 percent.
if the firm were recapitalized, debt would be issued, and the borrowed funds would be used to repurchase stock.  stockholders, in turn, would use funds provided by the repurchase to buy equities in other fast-food companies similar to cd.  you plan to complete your report by asking and then answering the following questions.

a.    1.    what is business risk?  what factors influence a firm’s business risk?

a.    2.    what is operating leverage, and how does it affect a firm’s business risk?

b.    1.    what is meant by the terms “financial leverage” and “financial risk”?

b.    2.    how does financial risk differ from business risk?

c.        now, to develop an example which can be presented to cd’s management as an illustration, consider two hypothetical firms, firm u, with zero debt financing, and firm l, with $10,000 of 12 percent debt.  both firms have $20,000 in total assets and a 40 percent federal-plus-state tax rate, and they have the following ebit probability distribution for next year:

probability ebit
0.25          $2,000
0.50           3,000
0.25           4,000

1.    complete the partial income statements and the firms’ ratios in table ic14-1.

table ic14-1.  income statements and ratios

firm u                   firm l
assets         $20,000  $20,000  $20,000   $20,000  $20,000  $20,000
equity         $20,000  $20,000  $20,000   $10,000  $10,000  $10,000
probability       0.25     0.50     0.25      0.25     0.50     0.25
sales          $ 6,000  $ 9,000  $12,000   $ 6,000  $ 9,000  $12,000
oper. costs      4,000  6,000  8,000  4,000  6,000  8,000
ebit           $ 2,000  $ 3,000  $ 4,000   $ 2,000  $ 3,000  $ 4,000
int. (12%)           0      0      0  1,200  1,200
ebt            $ 2,000  $ 3,000  $ 4,000   $   800  $        $ 2,800
taxes (40%)        800  1,200  1,600    320  1,120
net income     $ 1,200$ 1,800$ 2,400$   480$      $ 1,680

bep              10.0%    15.0%    20.0%     10.0%        %    20.0%
roe               6.0%     9.0%    12.0%      4.8%        %    16.8%
tie                ???        1.7??    3.3?

e(bep)                    15.0%                           %
e(roe)                     9.0%                       10.8%
e(tie)                      ?                          2.5?

sd(bep)                    3.5%                           %
sd(roe)                    2.1%                        4.2%
sd(tie)                      0                         0.6?

answer:    [show s14-9 through s14-14 here.]  here are the fully completed statements:

firm u                   firm l
assets         $20,000  $20,000  $20,000   $20,000  $20,000  $20,000
equity         $20,000  $20,000  $20,000   $10,000  $10,000  $10,000
ebit           $ 2,000  $ 3,000  $ 4,000   $ 2,000  $ 3,000  $ 4,000
i (12%)              0      0      0  1,200  1,200  1,200
ebt            $ 2,000  $ 3,000  $ 4,000   $   800  $ 1,800  $ 2,800
taxes (40%)        800  1,200  1,600    320    720  1,120
ni             $ 1,200$ 1,800$ 2,400$   480$ 1,080$ 1,680
bep              10.0%    15.0%    20.0%     10.0%    15.0%    20.0%
roe               6.0%     9.0%    12.0%      4.8%    10.8%    16.8%
tie                ???        1.7?     2.5?     3.3?
e(bep)                    15.0%                       15.0%
e(roe)                     9.0%                       10.8%
e(tie)                      ?                          2.5?
sd(bep)                    3.5%                        3.5%
sd(roe)                    2.1%                        4.2%
sd(tie)                      0                         0.6?

c.    2.    be prepared to discuss each entry in the table and to explain how this example illustrates the impact of financial leverage on expected rate of return and risk.

answer:    [show s14-15 and s14-16 here.]  conclusions from the analysis:

1.    the firm’s basic earning power, bep = ebit/total assets, is unaffected by financial leverage.

2.    firm l has the higher expected roe:

e(roeu) = 0.25(6.0%) + 0.50(9.0%) + 0.25(12.0%) = 9.0%.

e(roel) = 0.25(4.8%) + 0.50(10.8%) + 0.25(16.8%) = 10.8%.

therefore, the use of financial leverage has increased the expected profitability to shareholders.  tax savings cause the higher expected roel.  (if the firm uses debt, the stock is riskier, which then causes kd and ks to increase.  with a higher kd, interest increases, so the interest tax savings increases.)

3.    firm l has a wider range of roes, and a higher standard deviation of roe, indicating that its higher expected return is accompanied by higher risk. to be precise:

?roe (unlevered) = 2.12%, and cv = 0.24.

?roe (levered) = 4.24%, and cv = 0.39.

thus, in a stand-alone risk sense, firm l is twice as risky as
firm u–its business risk is 2.12 percent, but its stand-alone risk is 4.24 percent, so its financial risk is 4.24% – 2.12% = 2.12%.

4.    when ebit = $2,000, roeu> roel, and leverage has a negative impact on profitability.  however, at the expected level of ebit, roel> roeu.

5.    leverage will always boost expected roe if the expected unlevered roa exceeds the after-tax cost of debt.  here e(roa) = e(unlevered roe) = 9.0% >kd(1 – t) = 12%(0.6) = 7.2%, so the use of debt raises expected roe.

6.    finally, note that the tie ratio is huge (undefined, or infinitely large) if no debt is used, but it is relatively low if 50 percent debt is used. the expected tie would be larger than 2.5? if less debt were used, but smaller if leverage were increased.

d.    after speaking with a local investment banker, you obtain the following estimates of the cost of debt at different debt levels (in thousands of dollars):

amount         debt/assets       debt/equity       bond
borrowed          ratio             ratio          rating        kd
$    0           0.000             0.0000           —          —
250           0.125             0.1429           aa          8.0%
500           0.250             0.3333           a           9.0
750           0.375             0.6000           bbb        11.5
1,000           0.500             1.0000           bb         14.0

now consider the optimal capital structure for cd.

1.    to begin, define the terms “optimal capital structure” and “target capital structure.”

answer:    [show s14-17 through s14-19 here.]  the optimal capital structure is the capital structure at which the tax-related benefits of leverage are exactly offset by debt’s risk-related costs.  at the optimal capital structure, (1) the total value of the firm is maximized, (2) the wacc is minimized, and the price per share is maximized.  the target capital structure is the mix of debt, preferred stock, and common equity with which the firm plans to raise capital.

d.    2.    why does cd’s bond rating and cost of debt depend on the amount of money borrowed?

answer:    [show s14-20 here.]  financial risk is the additional risk placed on the common stockholders as a result of the decision to finance with debt. conceptually, stockholders face a certain amount of risk that is inherent in a firm’s operations.  if a firm uses debt (financial leverage), this concentrates the business risk on common stockholders.
financing with debt increases the expected rate of return for an investment, but leverage also increases the probability of a large loss, thus increasing the risk borne by stockholders.  as the amount of money borrowed increases, the firm increases its risk so the firm’s bond rating decreases and its cost of debt increases.

d.    3.    assume that shares could be repurchased at the current market price of $25 per share.  calculate cd’s expected eps and tie at debt levels of $0, $250,000, $500,000, $750,000, and $1,000,000. how many shares would remain after recapitalization under each scenario?

answer:    [show s14-21 through s14-25 here.]  the analysis for the debt levels being considered (in thousands of dollars and shares) is shown below:

at d = $0:

eps =   =   = $3.00.
tie =  = ?.

at d = $250,000:

shares repurchased = $250,000/$25 = 10,000.

remaining shares outstanding = 80,000 – 10,000 = 70,000.

(note:  eps and tie calculations are in thousands of dollars.)

eps =   = $3.26.

tie =   = 20?.

at d = $500,000:

shares repurchased = $500,000/$25 = 20,000.

remaining shares outstanding = 80,000 – 20,000 = 60,000.

(note:  eps and tie calculations are in thousands of dollars.)

eps =   = $3.55.

tie =   = 8.9?.

at d = $750,000:

shares repurchased = $750,000/$25 = 30,000.

remaining shares outstanding = 80,000 – 30,000 = 50,000.

(note:  eps and tie calculations are in thousands of dollars.)

eps =   = $3.77.

tie =   = 4.6?.

at d = $1,000,000:

shares repurchased = $1,000,000/$25 = 40,000.

remaining shares outstanding = 80,000 – 40,000 = 40,000.

(note:  eps and tie calculations are in thousands of dollars.)

eps =   = $3.90.

tie =   = 2.9?.

d.    4.    using the hamada equation, what is the cost of equity if cd recapitalizes with $250,000 of debt?  $500,000?$750,000?$1,000,000?

answer:    [show s14-26 through s14-31 here.]

krf = 6.0%    km – krf = 6.0%
bu = 1.0    total assets = $2,000
tax rate = 40.0%

amount        debt/assets       debt/equity     leveraged
borrowedaratiobratiocbetadkse
$    0           0.00%              0.00%         1.00        12.00%
250          12.50              14.29          1.09        12.51
500          25.00              33.33          1.20        13.20
750          37.50              60.00          1.36        14.16
1,000          50.00             100.00          1.60        15.60

notes:
a data given in problem.
b calculated as amount borrowed divided by total assets.
c calculated as amount borrowed divided by equity (total assets less amount borrowed).
d calculated using the hamada equation, b = bu[1 + (1 – t)(d/e)].
e calculated using the capm, ks = krf + (km – krf)b, given the risk-free rate, the market risk premium, and using the levered beta as calculated with the hamada equation.

d.    5.    considering only the levels of debt discussed, what is the capital structure that minimizes cd’s wacc?
answer:    [show s14-32 here.]

krf = 6.0%    km – krf = 6.0%
bu = 1.0    total assets = $2,000
tax rate = 40.0%

amount    debt/assets  equity/assets  debt/equity  leveraged
borrowedaratiobratiocratiodbetaeksfkdakd(1 – t)  waccg
$    0        0.00%       100.00%         0.00%       1.00    12.00%  0.0%    0.0%    12.00%
250       12.50         87.50         14.29        1.09    12.51   8.0     4.8     11.55
500       25.00         75.00         33.33        1.20    13.20   9.0     5.4     11.25
750       37.50         62.50         60.00        1.36    14.16  11.5     6.9     11.44
1,000       50.00         50.00        100.00        1.60    15.60  14.0     8.4     12.00

notes:
a data given in problem.
b calculated as amount borrowed divided by total assets.
c calculated as 1 – d/a.
d calculated as amount borrowed divided by equity (total assets less amount borrowed).
e calculated using the hamada equation, b = bu[1 + (1 – t)(d/e)].
f calculated using the capm, ks = krf + (km – krf)b, given the risk-free rate, the market risk premium, and using the levered beta as calculated with the hamada equation.
g calculated using the wacc equation, wacc = wdkd(1 – t) + wcks.

cd’s wacc is minimized at a capital structure that consists of 25 percent debt and 75 percent equity, or a wacc of 11.25 percent.

d.    6.    what would be the new stock price if cd recapitalizes with $250,000 of debt?  $500,000?$750,000?$1,000,000?  recall that the payout ratio is 100 percent, so g = 0.

answer:    [show s14-33 here.]  we can calculate the price of a constant growth stock as dps divided by ks minus g, where g is the expected growth rate in dividends:  p0 = d1/(ks – g).  since in this case all earnings are paid out to the stockholders, dps = eps.  further, because no earnings are plowed back, the firm’s ebit is not expected to grow, so g = 0.

here are the results:

debt level      dps      ks     stock price
$      0     $3.00   12.00%     $25.00
250,000      3.26   12.51       26.03
500,000      3.55   13.20       26.89*
750,000      3.77   14.16       26.59
1,000,000      3.90   15.60       25.00

*maximum

d.    7.    is eps maximized at the debt level which maximizes share price?  why or why not?

answer:    [show s14-34 here.]  we have seen that eps continues to increase beyond the $500,000 optimal level of debt. therefore, focusing on eps when making capital structure decisions is not correct–while the eps does take account of the differential cost of debt, it does not account for the increasing risk that must be borne by the equity holders.

d.    8.    considering only the levels of debt discussed, what is cd’s optimal capital structure?

answer:    [show s14-35 and s14-36 here.]  a capital structure with $500,000 of debt produces the highest stock price, $26.89; hence, it is the best of those considered.

d.    9.    what is the wacc at the optimal capital structure?

answer:    [show s14-37 here.]  debt/total assets = 0%, so total assets = initial equity = $25 ? 80,000 shares = $2,000,000.

wacc = ($500,000/$2,000,000)(9%)(0.60) + ($1,500,000/$2,000,000)(13.2%)
= 1.35% + 9.90% = 11.25%.

note:  if we had (1) used the equilibrium price for repurchasing shares and (2) used market value weights to calculate wacc, then we could be sure that the wacc at the price-maximizing capital structure would be the minimum.  using a constant $25 purchase price, and book value weights, inconsistencies may creep in.
e.        suppose you discovered that cd had more business risk than you originally estimated. describe how this would affect the analysis. what if the firm had less business risk than originally estimated?

answer:    [show s14-38 here.]  if the firm had higher business risk, then, at any debt level, its probability of financial distress would be higher.  investors would recognize this, and both kd and ks would be higher than originally estimated.  it is not shown in this analysis, but the end result would be an optimal capital structure with less debt.  conversely, lower business risk would lead to an optimal capital structure that included more debt.

f.    what are some factors a manager should consider when establishing his or her firm’s target capital structure?

answer:    [show s14-39 through s14-41 here.]  since it is difficult to quantify the capital structure decision, managers consider the following judgmental factors when making capital structure decisions:

1.    the average debt ratio for firms in their industry.

2.    pro forma tie ratios at different capital structures under different scenarios.

3.    lender/rating agency attitudes.

4.    reserve borrowing capacity.

5.    effects of financing on control.

6.    asset structure.

7.    expected tax rate.

figure ic14-1.
relationship between capital structure and stock price

g.    put labels on figure ic14-1 above, and then discuss the graph as you might use it to explain to your boss why cd might want to use some debt.

answer:    [show s14-42 through s14-44 here.]  the use of debt permits a firm to obtain tax savings from the deductibility of interest.  so the use of some debt is good; however, the possibility of bankruptcy increases the cost of using debt.  at higher and higher levels of debt, the risk of bankruptcy increases, bringing with it costs associated with potential financial distress.  customers reduce purchases, key employees leave, and so on.  there is some point, generally well below a debt ratio of 100 percent, at which problems associated with potential bankruptcy more than offset the tax savings from debt.
theoretically, the optimal capital structure is found at the point where the marginal tax savings just equal the marginal bankruptcy-related costs.  however, analysts cannot identify this point with precision for any given firm, or for firms in general.  analysts can help managers determine an optimal range for their firm’s debt ratios, but the capital structure decision is still more judgmental than based on precise calculations.

h.    how does the existence of asymmetric information and signaling affect capital structure?

answer:    [show s14-45 through s14-47 here.]  the asymmetric information concept is based on the premise that management’s choice of financing gives signals to investors.  firms with good investment opportunities will not want to share the benefits with new stockholders, so they will tend to finance with debt.  firms with poor prospects, on the other hand, will want to finance with stock.  investors know this, so when a large, mature firm announces a stock offering, investors take this as a signal of bad news, and the stock price declines.  firms know this, so they try to avoid having to sell new common stock.  this means maintaining a reserve of borrowing capacity so that when good investments come along, they can be financed with debt.

optional question

you might expect the price of a mature firm’s stock to decline if it announces a stock offering. would you expect the same reaction if the issuing firm were a young, rapidly growing company?

answer:    if a mature firm sells stock, the price of its stock would probably decline.  a mature firm should have other financing alternatives, so a stock issue would signal that its earnings potential is not good.  a young, rapidly growing firm, however, may have so many good investment opportunities that it simply cannot raise all the equity it needs as retained earnings, and investors know this.  therefore, the stock price of a young, rapidly growing firm would probably not fall because of a new stock issue, especially if the firm’s managers announce that they are not selling any of their own shares in the offering.