FIN 508 Assignment Week 6
Culbert
fin508solutionweek6.pdf
FIN 508 Assignment Week 6 _____________________________________________________________________________
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6.1. Kerry Corporation needs $30 million in new capital, which it may acquire by selling bonds at par with 6% coupon or by selling stock at $40 (net) per share. The current
capital structure of Kerry consists of $250 million (face value) of 3% coupon bonds
selling at 80, and 12 million shares of stock selling at $42 apiece. After the new financing,
the EBIT of Kerry is expected to be $50 million with a standard deviation of $20 million.
The income tax rate of Kerry is 33%. Which method of financing do you recommend?
What is the probability that you are right? [Use bonds, 72.41% ♥]
First, determine the critical EBIT, where the debt financing and equity financing provide
equal EPS, by using
E* = I + r(NP + F) (10.7)
In this equation, I = interest on existing debt = .03(250) = $7.5 million
r = coupon rate on new debt = .06
N = number of shares of stock at present = 12 million
P = price per share of new equity = $40
F = amount of new financing needed = $30 million
E* = 7.5 + .06*(12*40 + 30) = $38.1 million
Since the company expects to make $50 million in EBIT, which is more than E*, it is
better to sell bonds. ♥
To find the probability that you have made the right decision, find z as
z = (38.1 – 50)/20 = −0.595
Draw the normal probability distribution curve, with z = 0 in the middle. The required z =
−.595 is to the left of center. The area on the right of z = −.595 represents the probability
of making the right decision. From the tables, we get the probability of being right
P(being right) = .5 + .2224 + .5(.2257 − .2224) = 72.41% ♥
To check the answer at Excel, copy and paste the following in any cell.
EXCEL =1-NORMDIST(38.1,50,20,TRUE)
6.2. Clinton Company is expecting to have EBIT next year of $15 million, with a standard deviation of $10 million. Clinton has $60 million in bonds with 5% coupon,
selling at par. Clinton is retiring $6 million (face amount) of bonds annually. Clinton also
has 100,000 shares of preferred stock, which pays annual dividend of $3.50 per share.
The tax rate of Clinton is 32%. Calculate the probability that Clinton will not be able to
pay interest, sinking fund, and preferred dividends, out of its current income, next year.
[39.51% ♥]
Suppose Clinton’s EBIT next year is just sufficient to pay its interest, taxes, sinking fund
and preferred dividends. To do so, minimum EBIT must be
FIN 508 Assignment Week 6 _____________________________________________________________________________
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(EBIT – I)(1 – t) – SF – PD = 0
In this equation, interest due, I = .05*60 = $3 million, income tax rate, t = .32, sinking
fund = $6 million, preferred dividends = 3.5*100,000 = $350,000 = $0.35 million. This
gives
(EBIT – 3)(1 – .32) – 6 – .35 = 0
Solving for EBIT, we get EBIT = $12.33823529 million.
Since the company expects to have EBIT of $15 million, it should be able to make it. The
probability of not being able to pay the interest is less than 50%. To find this probability,
calculate z = (12.33823529 − 15)/10 = −.266176471 −.2661
Draw a probability diagram with z = 0 in the center, and z = −.2661 to the left of center.
The area to the left of z = −.2661, the area under the tail of the curve, gives the required
probability. Using tables, we get
Prob(unable to pay) = .5 – [.1026 + .61(.1064 – .1026)] = .4244
The probability of default is thus 39.51% ♥
To verify the result, use the following expression in Excel:
EXCEL =NORMDIST(12.33823529,15,10,TRUE)
6.3. Rice Corporation has the following information for the current year.
Cost of debt 6%
Debt-to-equity ratio 30%
Dividend payout ratio 40%
Dividend per share $1.50
Income tax rate 32%
Long-term debt $30 million
Number of common shares 10 million
Find the EBIT and the price per share for Rice. [$56.947 million, $10.00 ♥]
Combine EPS = (EBIT − I) (1 − t) − SF − PD
N (10.3)
and DPS = EPS * DPR
to get DPS = (EBIT − I) (1 − t) − SF − PD
N * DPR
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Put DPS = $1.50, I = .06*30 = $1.8 billion, t = .32, SF = PD = 0, N = 10 million, DPR
= .4,
to get 1.5 = (EBIT − 1.8) (1 − .32) − 0 − 0
10 * .4
which gives EBIT = 1.5(10)
.4(1 − .32) + 1.8 = $56.947 million ♥
Since debt to equity ratio is .3, therefore, B/S = .3
With B = $30 million, it gives 30/S = .3. Or, S = 30/.3 = $100 million
Because N = 10 million, the price per share = $10 ♥
6.4. Powell Corporation has 5 million shares of common stock selling at $21 each. It has $25 million in bonds with 5% coupon, selling at par. Powell Corporation needs $20
million in new capital, which it can raise by selling stock at $20 per share, or bonds at 6%
interest. The expected EBIT after the new capitalization is $6 million, with a standard
deviation of $5 million. The income tax rate of Powell is 35%. What is the preferred
method of raising new capital? What is the probability that you are right? [Answer not
given ♥]
Since SF = PD = 0, E* = I + r (N P + F) (10.7)
Put I = .05*25 = $1.25 million, r = .06, N = 5 million, P = $20, and F = $20 million. This
gives the critical EBIT as
E* = 1.25 + .06 (5*20 + 20) = 7.85 = $8.45 million
Since the expected EBIT, $6 million is less than the critical EBIT, $8.45 million, it is
better to sell stock to get new financing. ♥
To find the probability of being right, calculate z = (8.45 – 6)/5 = .49
Draw a normal probability distribution diagram with z = 0 in the center and z = .49 to the
right of center. The critical EBIT will be about one-third standard deviation on the right
of the center. The area to the left of z = .49 point will represent the probability that the
FIN 508 Assignment Week 6 _____________________________________________________________________________
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company will make less than the critical EBIT. This represents the probability of being
right in this decision. From the tables, get
P(EBIT < $8.45 million) = .5 + .1879 = 68.79%. ♥
To verify the result on Excel, use this expression
EXCEL =NORMDIST(8.45,6,5,TRUE)
6.5. Albright Company is an all-equity firm with a total value of $51 million. It requires additional capital of $6 million, which may be either equity, or debt at the interest rate of
5%. After the new capitalization, the expected EBIT is $2 million, with standard
deviation of $1 million. The company pays income tax at 30% rate, and it has 1.7 million
shares outstanding. What is the expected earnings per share for (A) bond financing and
(B) stock financing? What is the preferred method of raising new capital, if the objective
is to maximize the EPS? What is the probability that you are right in your decision?
[EPS(bonds) = $0.7000, EPS(stock) = $0.7368, Use stock, 80.23% ♥]
The company is an all-equity firm, meaning it has no debt. The total value of the
company is $51 million, which is due to 1.7 million shares of stock. The price per share
of stock is thus, 51/1.7 = $30. Further, we know EBIT = $2 million, I = 0, r = .05. F = $6
million, N = 1.7 million, t = .3, and SF = PD = 0. To find the earnings per share for bond
and stock financing, use
EPS(bonds) = (EBIT − I − r F) (1 − t) − SF − PD
N (10.4)
Find the EPS(bonds) = (2 − 0 − .05*6) (1 − .3) − 0 − 0
1.7 = $0.70 ♥
Use EPS(stock) = (EBIT − I) (1 − t) − SF − PD
N + F/P (10.5)
Find the EPS(stock) = (2 − 0) (1 − .3) − 0 − 0
1.7 + 6/30 = $0.7368 ♥
Comparing $0.70 with $0.7368, obviously stock financing is better. ♥
Next, find the critical EBIT. It comes as
Since SF = PD = 0, E* = I + r (N P + F) (10.7)
This gives E* = 0 + .05 (1.7*30 + 6) = $2.85 million
This confirms that stock financing is better because the expected EBIT, $2 2illion, is
much less than the critical EBIT, $2.85 million.
To find the probability of being right, calculate z = (2.85 – 2)/1 = .85
FIN 508 Assignment Week 6 _____________________________________________________________________________
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Draw a probability distribution curve, with z = 0 in the center. The critical EBIT, E*, will
be .85 standard deviations on the right of center. The area under the hump of the curve, to
the left of E*, will give the desired answer. From the tables, find
P(Being right) = .5 + .3023 = .80.23 = 80.23% ♥
You may verify the above result by using the following expression at Excel:
EXCEL =NORMDIST(2.85,2,1,TRUE)
6.6. Baker Company has debt-to-assets ratio of 40%, tax rate of 33%, and total value of $300 million. James Baker, the CFO, would like to increase the leverage ratio to 42%,
and he believes that there will be no change in the bankruptcy cost of the company. How
many dollars’ worth of 4% coupon bonds should the company sell, and buy back its own
stock, to accomplish the financial restructuring? [$6.965 million ♥]
Before: B1/V1 = .4, total value, V1 = $300 million, total debt, B1 = .4*300 = $120 million.
After: B2/V2 = .42
Suppose the company issues x million dollars (face amount) of bonds and buys back its
own stock from the proceeds. This adds value by tax shield = tB, and increases the debt
by x. Thus
V2 = 300 + .33x
B2 = 120 + x
Thus B2 V2
= 120 + x
300 + .33x = .42
To solve this equation at Wolfram|Alpha, type the following instruction
solve((120+x)/(300+.33*x)=.42)
Solving for x, we get x = $6.9654 million ♥
FIN 508 Assignment Week 6 _____________________________________________________________________________
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6.7. Schultz Company plans to buy back 1.5 million shares of its own stock from its cash reserves at $20 a share. This will increase the bankruptcy costs by $5 million, and the
debt/assets ratio from 20% to 22%. Using careful reasoning, do the following:
(A) Write two equations representing debt/assets ratio of the company, before and after
the capital restructuring. Solve them to find the debt and total value of the company
before and after the share buyback.
(B) The total equity and the number of shares of stock before and after the buyback.
(C) The price per share before and after the buyback. Did the company make a wise
move? [No, because the price of the stock fell from $20 to $19.64 per share. ♥]
(A) The company buys 1.5 million shares at $20 per share and pays out 1.5(20) = $30
million from its cash reserves. Thus, the value of company will go down by $30 million.
The value of the company will further decrease by $5 million because of the increase in
bankruptcy costs. The net total loss in value will be $35 million. If the initial value of
company is V1, its final value is V2 = V1 – 35. There is no change in the initial debt, B1, of
the company.
Thus, Before: B1/V1 = .2, and After: B1/(V1 – 35) = .22
To solve these equations at Wolfram|Alpha, type in
solve(B1/V1=.2,B1/(V1-35)=.22)
Solving these equations, we find B1 = $77 million and V1 = $385 million. These are the
values before share buyback.
After the share repurchase, the value of debt remains the same, $77 million, but the value
of the company is down by $35 million. Thus it is 385 − 35 = $350 million. The values of
debt and total value are B2 = $77 million and V2 = $350 million. ♥
(B) Initially, the company had $385 million in total value, of which $77 million was debt.
The value of stock was S1 = 385 − 77 = $308 million. Since the stock was selling at $20 a
share, it had 308/20 = 15.4 million shares. This means N1 = 15.4 million
Finally, the company had $350 million in total value, of which $77 million was debt. The
value of stock was S2 = 350 − 77 = $273 million. Since the company bought back 1.5
million shares, the remaining shares were 15.4 − 1.5 = 13.9 million shares, or N2 = 13.9
million. ♥
(C) The price per share before buyback is S1/N1 = 308/15.4 = $20. After buyback, S2/N2 =
273/13.9 = $19.64. Thus P1 = $20, P2 = $19.64 ♥
FIN 508 Assignment Week 6 _____________________________________________________________________________
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The company has made a mistake. First, it lost $30 million from its cash reserves for no
good reason. Second, by eroding the equity base, it has increased the possibility of
bankruptcy. The mistake is reflected in the lower value of the stock. ♥
6.8. Kissinger Company has debt/assets ratio 30%, which is too high and it should be at 25% to be optimal. This debt reduction should also reduce the bankruptcy costs by $25
million. At present, Kissinger has 20 million shares of common stock selling at $40 each.
The tax rate of Kissinger is 32%. How many shares of stock should the company sell, and
buy back bonds from the proceeds, to attain its optimal capital structure? [1,382,958 ♥]
The debt/assets ratio is 30% at present, which means that equity is 70% of the value of
the company. Find the value of equity as 20*40 = $800 million. If the total value of the
company is V1, then .7V1 = 800. This gives V1 = 800/.7 = $ 1,142.857 million. The value
of stock is $800 million. The value of debt is 1,142.857 – 800 = $342.857 million. Using
symbols, we write the results as
Before: B1 = $342.857 million, S1 = $800 million, V1 = $1,142.857 million
Suppose the number of shares that Kissinger should sell is x million, at $40 each. This
will give it $40x million in new cash. The company will use this money to pay off its debt.
The debt will decrease by $40x million.
After: B2 = 342.857 – 40x (1)
There are two changes in the total value of the company: it will decrease due to lower tax
shield, but it will increase due to lower bankruptcy costs.
Since the debt has decreased by $40x million, there is a corresponding decrease in tax
shield by $.32(40x) million, where .32 or 32% is the income tax rate of the company.
This will decrease the overall value of the company by .32(40x) = 12.8x million.
Since the bankruptcy costs have gone down by $25 million, the overall value of the
company will increase by $25 million. Therefore, final value will become,
After V2 = 1,142.857 – 12.8x + 25 (2)
We know that the new debt/assets ratio of the company is .25. Combining (1) and (2),
B2 V2
= 342.857 – 40x
1142.857 – 12.8x + 25 = .25
To solve the equation at Wolfram|Alpha, type as follows.
(342.857-40*x)/(1142.857-12.8*x+25)=.25
Solving this equation for x, we get
x = 1.38296 million 1,382,960 shares. ♥
