# Convert Debt to Equity

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Chapter 17
Problems 1-21

Input boxes in tan
Output boxes in yellow
Given data in blue
Calculations in red
Chapter 17
Question 1

Input Area:

Market value         \$   100,000
EBIT                 \$     6,000
Debt issue           \$    40,000
Interest rate                 5%
Shares outstanding         2,500
Expansion-EBIT               30%
Recession-EBIT               60%

Output Area:

No debt
EBIT                 \$      2,400   \$   6,000
Interest             \$        -     \$     -
NI                   \$      2,400   \$   6,000
EPS                  \$       0.96   \$    2.40
Change EPS%               -60.00%       0.00%

With debt
Share price =        \$      40.00
Shares repurchased =     1,000.00

EBIT                 \$      2,400   \$   6,000
Interest             \$      2,000   \$   2,000
NI                   \$        400   \$   4,000
EPS                  \$       0.27   \$    2.67
Change EPS%               -90.00%       0.00%
\$    7,800
\$      -
\$    7,800
\$     3.12
30.00%

\$    7,800
\$    2,000
\$    5,800
\$     3.87
45.00%
Chapter 17
Question 2

Input Area:

Market value         \$   100,000
EBIT                 \$     6,000
Debt issue           \$    40,000
Interest rate                 5%
Shares outstanding         2,500
Expansion-EBIT               30%
Recession-EBIT               60%
Tax rate                     35%

Output Area:

No debt with taxes
EBIT                 \$      2,400   \$   6,000
Interest                        -           -
Taxes                         840       2,100
NI                   \$      1,560   \$   3,900
EPS                  \$      0.624   \$   1.560
Change EPS%               -60.00%       0.00%

With debt and taxes
Share price =        \$      40.00
Shares repurchased =     1,000.00

EBIT                 \$      2,400   \$   6,000
Interest                    2,000       2,000
Taxes                         140       1,400
NI                   \$        260   \$   2,600
EPS                  \$      0.173   \$   1.733
Change EPS%               -90.00%       0.00%
\$    7,800
-
2,730
\$    5,070
\$    2.028
30.00%

\$    7,800
2,000
2,030
\$    3,770
\$    2.513
45.00%
Chapter 17
Question 3

Input Area:

No debt
TE = MV =        \$   100,000

With debt
TE =             \$    60,000

Output Area:

a. ROE                   2.40%   6.00%
Change ROE%         -60.00%   0.00%

b. ROE                   0.67%   6.67%
Change ROE %        -90.00%   0.00%

c. No debt
No debt, ROE          1.56%   3.90%
Change ROE %        -60.00%   0.00%

With debt
With debt, ROE         0.43%   4.33%
Change ROE %         -90.00%   0.00%
7.80%
30.00%

9.67%
45.00%

5.07%
30.00%

6.28%
45.00%
Chapter 17
Question 4

Input Area:

Plan I:
Shares outstanding        100,000

Plan II:
Shares outstanding          50,000
Debt outstanding     \$   1,500,000
Interest rate                  10%

a. EBIT                   \$    200,000
b. EBIT                   \$    700,000

Output Area:

a.                            NI              EPS
Plan I               \$    200,000    \$          2.00
Plan II              \$      50,000   \$          1.00

b. Plan I                 \$    700,000    \$          7.00
Plan II                \$    550,000    \$         11.00

c. Breakeven EBIT =                       \$   300,000.00
Chapter 17
Question 5

Input Area:

Plan I:
Shares outstanding        100,000

Plan II:
Shares outstanding          50,000
Debt outstanding     \$   1,500,000
Interest rate                  10%

a. EBIT                \$    200,000
b. EBIT                \$    700,000

Output Area:

Price                \$       30.00
V (I)                \$   3,000,000
V (II)               \$   3,000,000
Chapter 17
Question 6

Input Area:

Plan I:
Shares outstanding                800
Debt                 \$          9,000
Plan II:
Shares outstanding                 700
Debt outstanding     \$          13,500
Interest rate                      10%

a. EBIT                   \$          8,000
Stock outstanding                 1,000
d. Tax rate                            40%

Output Area:

a.                               I                    II
EBIT                 \$          8,000     \$           8,000
Interest             \$            900     \$           1,350
NI                   \$          7,100     \$           6,650
EPS                  \$           8.88     \$            9.50

b. Plan I vs. all equity
Plan II vs. all equity
The break even levels of EBIT are the same because of M&M Proposition I.

c. Breakeven EBIT: Plan I vs. Plan II
This break-even level of EBIT is the same as in part (b) again, because of M&M
Proposition (I).

d.                               I                    II
EBIT                 \$          8,000     \$           8,000
Interest             \$            900     \$           1,350
Taxes                \$          2,840     \$           2,660
NI                   \$          4,260     \$           3,990
EPS                  \$           5.33     \$            5.70
Breakeven EBIT
Plan I vs. all-equity
Plan II vs. all-equity
PLanI vs. Plan II

The break-even levels of EBIT do not change because of additions of taxes reduces
the income of all three plans by the same percentage; therefore they do not change
relative to one another.
All-Equity
\$          8,000
\$              -
\$          8,000
\$            8.00

EBIT
\$             4,500
\$             4,500
f M&M Proposition I.

\$        4,500
again, because of M&M

All-equity
\$          8,000
\$              -
\$          3,200
\$          4,800
\$            4.80
\$          4,500
\$          4,500
\$          4,500

herefore they do not change
Chapter 17
Question 7

Input Area:

Plan I:
Shares outstanding                         800
Debt                         \$           9,000
Plan II:
Shares outstanding                        700
Debt outstanding             \$         13,500
Interest rate                             10%

Output Area:

Price (I)                      \$              45
Price (II)                     \$              45
This shows that when there are no corporate
taxes, the stockholder does not care about the
capital structure decision of the firm. This is
M&M Proposition I without taxes.
Chapter 17
Question 8

Input Area:

Shares outstanding                              1,000
Debt                                              40%
Price                            \$                 70
Interest rate                                      7%
EBIT                             \$              7,000
Rico:
Shares owned                                     100
Dividend payout rate                            100%

Output Area:

a. EPS                                \$           7.00
Shareholder's cash flow            \$         700.00

b. V                                  \$         70,000
D                                  \$         28,000
Shares bought                                   400
NI                                 \$          5,040
EPS                                \$           8.40
Shareholder's cash flow            \$         840.00

c.                          Sell 40 shares of stock and
lend the proceeds at 7%
Interest cash flow             \$            196
Cash flow from shares held     \$            504
Total cash flow                \$        700.00

d. The capital structure is irrelevant because
shareholders can create their own leverage
or unlever the stock to create the payoff they
desire, regardless of the capital structure the
firm actually chooses.
Chapter 17
Question 9

Input Area:

ABC:
All-equity                  \$       600,000
XYZ:
Stock value                 \$       300,000
Interest rate                           10%

EBIT                        \$        85,000

Stockholder:
Owns XYZ                    \$        45,000

Output Area:

a. EBIT                        \$        55,000
Stockholders CF             \$         8,250
Return                               18.33%

b. Sell all XYZ shares: nets \$         45,000
Borrow \$         45,000
at             10%
Interest cash flow =       \$     (4,500.00)
Use the proceeds from selling shares
and the borrowed funds to buy ABC
shares:
Stock cash flow (ABC)      \$        12,750
Total cash flow            \$         8,250
Rate                                18.33%

c. ABC: RE                              14.17%
XYZ: RE                              18.33%

d. ABC: WACC                               14.17%
XYZ: WACC                               14.17%
When there are no corporate taxes, the cost
of cost of capital for the firm is unaffected
by the capital structure, this is M&M
Proposition I without taxes.
Chapter 17
Question 10

Input Area:

WACC                         14%
Value of equity   \$   40,000,000

Output Area:

EBIT              \$    5,600,000
Chapter 17
Question 11

Input Area:

WACC                            14%
Value of equity     \$    40,000,000
Tax rate                        35%

Output Area:

EBIT                    \$ 8,615,384.62
WACC                            14.00%
Due to taxes, EBIT for an all-equity
firm would have to be higher for the
\$
firm to still be worth \$25M.40,000,000
Chapter 17
Question 12

Input Area:

Debt-equity ratio     2.0
WACC                  11%
Tax rate              35%
Cost of debt          11%
c. Debt-equity ratio    1.50
Debt-equity ratio    1.00
Debt-equity ratio    0.00

Output Area:

a. RE                  18.70%

b. RU                  14.35%

c. RE I                16.78%
RE II               14.85%
RE III = WACC       11.00%
Chapter 17
Question 13

Input Area:

WACC                      15%
Tax rate                  35%
Interest rate              9%
b. Convert to debt           25%
c. Convert to debt           50%

Output Area:

a.   All-equity financed   15.00%
b.   RE                    16.30%
c.   RE                    18.90%
d.   WACC(B)               13.69%
WACC(C)               12.38%
Chapter 17
Question 14

Input Area:

EBIT              \$      80,000
Tax rate                    35%
Interest rate               14%
Cost of equity              25%
Amount borrowed   \$      50,000

Output Area:

VU                \$   208,000.00
V                 \$   225,500.00
Chapter 17
Question 15

Input Area:

EBIT                      \$            80,000
Tax rate                                  35%
Interest rate                             14%
Cost of equity                            25%
Borrows                   \$            50,000
VU                        \$           208,000
V                         \$           225,500

Output Area:

RE                                        27.04%
WACC                                      23.06%
When there are corporate taxes, the
overall cost of capital for the firm declines
the more highly leveraged is the firm's
capital structure. This is M&M Proposition I
with taxes.
Chapter 17
Question 16

Input Area:

EBIT                    \$             26,000
Tax rate                                 35%
Interest rate                          8.00%
WACC                                  12.00%
Outstanding debt        \$             60,000
Debt-equity ratio                       0.60

Output Area:

Value of equity         \$            100,000
RE                                    16.08%
RU                                    13.81%
VL                       \$       140,833.33
VU                       \$        122,348.96
D                        \$          52,812.50
Applying M&M Proposition I with taxes, the firm
has increased its value by issuing debt. As long
as M&M Proposition I holds, that is, there are no
bankruptcy costs and so forth, then the company
should continue to increase its debt/equity ratio
to maximze the value of the firm.
Chapter 17
Question 17

Input Area:

EBIT Perpetuity          \$      6,000
Tax rate                          35%
Interest rate                     10%
Cost of equity                    16%
Convert to debt                   50%
Convert to debt                  100%

Output Area:

No debt: VU              \$   24,375.00
Debt              50%    \$   28,640.63
Debt              100%   \$   32,906.25
Chapter 17
Question 18

Output Area:

RE = RU + (RU - RD)(D/E)(1 - t)
WACC = (E/V)RE + (D/V)RD(1 - t) = (E/V)[RU + (RU - RD)(D/E)(1 - t)] + (D/V)RD(1 - t)
WACC = RU[(E/V) + (E/V)(D/E)(1 - t)] + RD(1 - t)[(D/V) - (E/V)(D/E)]
WACC = RU[(E/V) + (D/V)(1 - t)] = RU[{(E+D)/V} - t(D/V)] = RU[1 - t(D/V)]
/E)(1 - t)] + (D/V)RD(1 - t)

RU[1 - t(D/V)]
Chapter 17
Question 19

Output Area:

RE = (EBIT - RDD)(1 - t)/E = [EBIT(1 - t)/E] - [RD(D/E)(1 - t)]
RE = RUVU/E - [RD(D/E)(1 - t)] = RU(VL - tD)/E - [RD(D/E)(1 - t)]
RE = RU(E + D - tD)/E - [RD(D/E)(1 - t)] = RU + (RU - RD)(D/E)(1 - t)
Chapter 17
Question 20

Output Area:

M&M Proposition II, with RD = RF
β                        β
RE = RA + (RA - RF)(D/E)
β                             β
CAPM: RE = E(RM - RF) + RF ; RA = A(RM - RF) + RF
β   β
RE = E(RM - RF) + RF = [1 + (D/E)][ A(RM - RF) + RF] - RF(D/E)
E   =   A[1   + D/E]
Chapter 17
Question 21
β

Asset                                1.00
Debt-equity ratio                    0.00
Debt-equity ratio                    1.00
Debt-equity ratio                    5.00
Debt-equity ratio                   20.00

Output Area:
β   β

E   =   A(1   + D/E)       β

Debt-equity ratio               E
0.00                  1.00
1.00                  2.00
5.00                  6.00
20.00                 21.00

The equity risk to the shareholder is composed of both
business and financial risk. Even if the assets of the firm are
not very risky, the risk to the shareholder can still be large if
the financial leverage is high. These higher levels of risk will
be reflected in the shareholder's required rate of return Re,
which will increase with higher debt/equity ratios.

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