Hi!!
1) WACC.
A firm with all-equity financing, its equity beta is .80. The Treasury
bill rate is 4 percent and the market risk premium is expected to be
10 percent. What is the firmīs asset beta? What is the firms
weighted-average cost of capital? The firm is exempt from paying
taxes.
If the firm is an all-equity firm then firm's asset beta is equal to
the equity beta. Then:
Assets Beta = 0.80
Now we need to know the cost of equity (Re):
According to CAPM:
Re = Riskless Return + Beta * (Market Risk Premium) =
= 0.04 + 0.80 * 0.10 =
= 0.12
Re = 12%
Now we can calculate WACC:
WACC = Rd*D/(D+E) + Re*E/(D+E) =
= Re*E/(E) = (all-equity firm)
= 0.12*1 =
= 0.12
WACC = 12% ; that is for an all-equity firm the WACC is equal to the
cost of equity.
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2)
A firm makes a rights issue at a subscription price of $5 a share. One
new share can be purchased for every four shares held. Before the
issue there were 10 million shares outstanding and the share price was
$6.
1. What is the total amount of new money raised?
One new share can be purchased for every set of four shares held, so
the first question we must answer here is how many sets of four shares
are there in 10 million shares, the answer to this one is easy:
10,000,000 / 4 = 2,500,000 sets of four shares
Then 2,500,000 new shares are issued at a subscription price of $5 per
share, so the total amount of money raised is:
2,500,000 * $5 = $12,500,000
2. What is the expected stock price after the rights are issued?
You can see this problem in two different ways:
- For every set of four existing shares:
Four existing shares at $6 per share ---------> $24
One new share issued at $5 per share ---------> $5
------
Value of the five shares you hold now --------> $29
New value per share ($29/5) -----------------> $5.8
- Consider the market capitalization.
Before the right issue the firm's capitalization was $60 million
($6*10 million shares). After the right issue the company raised its
capitalization by $12.5 million, but now there are 2.5 million of new
shares. Then the new price for the stocks will be:
Market capitalization / N°of shares = $72.5 million/12.5 million =
= $5.8 per share
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3)Earnings and Leverage.
A firm currently is all-equity financed. It has 10,000 shares of
equity outstanding, selling at $100 a share. The firm is considering a
capital restructuring. The low-debt plan calls for a debt issue of
$200,000 with the proceeds used to buy back stock. The high-debt plan
would exchange $400,000 of debt for equity. The debt will pay an
interest rate of 10 percent. The firm pays no taxes.
1 What will be the debt-to-equity ratio after each possible restructuring?
- Low Debt Plan:
Debt Issue = $200,000
With this money the firm will buy back $200,000 / $100 = 2,000 shares,
then:
Equity =(10,000-2,000) * $100 =
= 8,000 * $100 =
= $800,000
Debt/Equity Ratio = $200,000 / $800,000 = 0.25
- High Debt Plan:
ssue Debt: $400,000
With this money the firm will buy back $400,000 / $100 = 4,000 shares,
then:
Equity =(10,000-4,000) * $100 =
= 6,000 * $100 =
= $600,000
Debt/Equity Ratio = $400,000 / $600,000 = 0.67
2 If earnings before interest and tax (EBIT) will be either $90,000 or
$130,000, what will be earnings per share for each financing mix for
both possible values of EBIT?
- EBIT of $90,000:
_Low Debt Plan:
Interest = 0.10 * $200,000 = $20,000
Net Income = $90,000 ? $20,000 = $70,000
EPS = $70,000 / 8,000 = $8.75
_High Debt Plan:
Interest = 0.10 x $400,000 = $40,000
Net Income = $90,000 ? $40,000 = $50,000
EPS = $50,000 / 6,000 = $8.33
-EBIT of $130,000:
_Low Debt Plan:
Interest = 0.10 * $200,000 = $20,000
Net Income = $130,000 ? $20,000 = $110,000
EPS = $110,000 / 8,000 = $13.75
_High Debt Plan:
Interest = 0.10 * $400,000 = $40,000
Net Income = $130,000 ? $40,000 = $90,000
EPS = $90,000 / 6,000 = $15
- If both scenarios are equally likely, what is expected (i.e.,
average) EPS under each financing mix?
Since both scenarios are equally likely the expected EPS for each
financing mix is just the average of the two EPS:
_Low Debt Plan:
Expected EPS = ($8.75 + $13.75)/2 = $11.25
_High Debt Plan:
Expected EPS = ($8.33 + $15)/2 = $11.67
- Is the high-debt mix preferable?
The high debt plan has a higher EPS, considering that the goal of a
company is to maximize shareholder?s wealth, the high debt plan is the
preferable one.
NOTE:
The increase in debt will increase the risk of financial distress. The
company's total assets are $1,000,000 ; so you must ask yourself if a
40% of debt is the best for the company. Before take a high debt plan
you must be sure that the company is strong enough (stable cash flows
and cushion in case of low sales).
3 Suppose that EBIT is $100,000.
What is EPS under each financing mix?
_Low Debt Plan:
Interest = 0.10 * $200,000 = $20,000
Net Income = $100,000 ? $20,000 = $80,000
EPS = $80,000 / 8,000 = $10
_High Debt Plan:
Interest = 0.10 * $400,000 = $40,000
Net Income = $100,000 ? $40,000 = $60,000
EPS = $60,000 / 6,000 = $10
Why are they the same in this particular case?
Recall that company's total assets are $1,000,000; then EBIT is 10% of
assets, this is the same that the interest rate on debt.
When ROA (= EBIT/Total Assets) is equal to the interest rate on debt,
EPS is unaffected by leverage, just see the following:
EPS = (EBIT - I) / N = ; N = number of shares and I = interest paid.
= (EBIT - Debt*i) / N = ; i is the interest rate on debt
= (EBIT - (Assets-Equity)*i) / N = ; since Asset=Debt+Equity
= (EBIT - (Assets-N*S)*i) / N = ; S is price per share
= (EBIT - (Assets-N*S)*ROA) / N = ; ROA = i (in this case)
= (EBIT - (Assets-N*S)*(EBIT/Assets))/ N = ; ROA = EBIT/Total Assets
= (EBIT - (Assets*(EBIT/Assets) + N*S*ROA/ N =
= (EBIT - EBIT + N*S*ROA)/ N =
= N*S*ROA / N =
= S*ROA =
= S*i ==> independent of the number of shares!!!
So in the case that ROA = cost of debt, like this case, EPS is equal
to cost of debt times share price:
EPS = $100 * 0.10 = $10
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I hope this helps you. Feel free to request for a clarification if you
need it before rate this answer. I will be glad to give you further
assistance on this question if you need it.
Best regards,
livioflores-ga |
