CFI SAMPLE QUESTION FOR FINAL EXAM QUESTIONS AND
VERIFIED ANSWERS
Capital Structure Q1:
ABC Inc., is an unlevered firm with expected annual earnings before taxes (EBIT)
of $30 million in perpetuity. The required return on the firm’s unlevered equity
is 15%, and the firm distributes all of its earnings as dividends at the end of each
year. ABC has 1 million shares of common stock outstanding.
The firm is planning a recapitalization (levered firm) under which it will issue $50
million of perpetual debt and use the proceeds to buy back shares. The annual cost
of debt is 10%. Assume that there is no issuing cost and that the firm is operating
under perfect capital markets.
→ MMI: no taxes, no cost, perfect capital market → homemade leverage → tự đòn
bẩy tài chính
→ có thể mua/ bán share tuỳ ý
EBIT = 30m Re = Ru =
15% no of share
outstanding = 1m D =
50m rd = 10%
pg. 1
,Part 1: If there is no corporate tax: → t = 0
a. Calculate the value of ABC before the recapitalization plan (VU) is
announced. What is the price per share? (Vunlevered = Vequity)
Before recapitalization plan →V unlevered firm
→ Vu = EBIT(1-t) /Ru = $30m/15% = $200m
Price per share = Ve/no of share
Price per share = 200m/1m =
200$/share
b. Calculate the value of ABC after the recapitalization plan (VL) is announced.
What is the price per share right after the announcement?
After recapitalization plan is announced → levered firm without taxes
→ VL =Vu + t * D = 200m
Price per share = Ve/no of share
Price per share = 200
Ko thuế → giá trị của cty ko thay đổi (Vu = VL = 200m) → debt ko lm thay đổi giá
trị của cty (kiểu như debt vs equity là như nhau) → debt ko ảnh hưởng đến giá của
share → khi tính price of share sẽ ko trừ đi debt →
Share repurchase → ko làm ảnh hưởng đến value of the firm → giảm lượng no of
share ở trên thị trường
c. How many shares will be repurchased (assume shares are perfectly divisible,
i.e. can take fractional shares)?
use proceeds → use 50,000,000 để mua
shares use 10% debt → use 10% *
50,000,000/200
Share repurchased = 50,000,000/200 = 250,000 shares
pg. 2
, lOMoAR cPSD| 22896205
Part 2: Company is subjected to 35% corporate tax.
d. Redo the a, b, c
Có thuế → làm cho giá trị cty tăng từ 130 → 147.5m → thể hiện rằng có nợ sẽ ảnh
hưởng đến value của công ty → debt làm ảnh hưởng đến giá của share → khi tính
price of share phải trừ đi debt
a. Vu = 30m*(1 - 35%)/15% = 130,000,000
→ Price per share = 130,000,000/1,000,000 = 130$/share
b. VL = Vu + t * D = 130,000,000 + 35% * 50,000,000 = 147,500,000
c. Ve = Vfirm - D = 147,500,000 - 50,000,000 = 97,500,000 → Price per
share = (147,500,000 - 50,000,000)/1,000,000 = 97.5$/share share repurchase =
số tiền mua lại share/price per share
Share repurchase = 50,000,000/97.5 = 512,820.5128 shares
Q2: M&M theory. Star, Inc., a prominent consumer products firm, is debating
whether or not to convert its all-equity capital structure to one that is 50 percent debt.
Currently there are 6,000 shares outstanding and the price per share is $58. EBIT
is expected to remain at $33,000 per year forever (perpetuity). The interest rate on
new debt is 8 percent, and there are no taxes.
no of shares = 6,000
Price per share = $58
EBIT = $33,000
Rd = 8%
t=0
a. Ms. Brown, a shareholder of the firm, owns 1,000 shares of stock. What is
her cash flow under the current capital structure, assuming the firm has a
dividend payout rate of 100 percent?
pg. 3
, owns 1,000 shares
dividend payout rate =
100%
EPS (profit per share of equity holders/dividend)
= EBIT/ No of shares = 33,000/6,000 = 5.5$/shares
NI = EBIT - Interest → ko sd nợ → nên ko có lãi vay → NI = EBIT
Ms Brown CF = 5.5 * 1,000 = 5,500
b. What will Ms. Brown’s cash flow be under the proposed capital structure of
the firm?
Assume that she keeps all 1,000 of her shares.
All equity firm + no tax → Vu = VL = 6,000 * 58 = 348,000$
50% debt (under proposed cap structure)
→ D = 348,000 * 50% = 174,000$ → sd debt để mua lại share
→ vay tiền để mua lại share thì Vfirm mới k thay đổi theo MMI theory → phải tính
số share htai đc lưu hành sau khi mua lại share
Share repurchase = 174,000/58 = 3,000 → remaining share = 6,000 - 3,000 = 3,000
shares
NI (Earing for equity holders) = EBIT - Interest payment (lãi vay) = 33,000 -
(174,000 * 8%) = 19,080$
EPS (dividend - dựa trên net income) = 19,080/3,000 = 6.36$/share
Ms Brown CF (total dividend) = 6.36$ * 1,000 = 6,360$
c. Suppose Star does convert (levered), but Ms. Brown prefers the current all-
equity capital structure. Show how she could unlever her shares of stock to
recreate the original capital structure.
pg. 4
VERIFIED ANSWERS
Capital Structure Q1:
ABC Inc., is an unlevered firm with expected annual earnings before taxes (EBIT)
of $30 million in perpetuity. The required return on the firm’s unlevered equity
is 15%, and the firm distributes all of its earnings as dividends at the end of each
year. ABC has 1 million shares of common stock outstanding.
The firm is planning a recapitalization (levered firm) under which it will issue $50
million of perpetual debt and use the proceeds to buy back shares. The annual cost
of debt is 10%. Assume that there is no issuing cost and that the firm is operating
under perfect capital markets.
→ MMI: no taxes, no cost, perfect capital market → homemade leverage → tự đòn
bẩy tài chính
→ có thể mua/ bán share tuỳ ý
EBIT = 30m Re = Ru =
15% no of share
outstanding = 1m D =
50m rd = 10%
pg. 1
,Part 1: If there is no corporate tax: → t = 0
a. Calculate the value of ABC before the recapitalization plan (VU) is
announced. What is the price per share? (Vunlevered = Vequity)
Before recapitalization plan →V unlevered firm
→ Vu = EBIT(1-t) /Ru = $30m/15% = $200m
Price per share = Ve/no of share
Price per share = 200m/1m =
200$/share
b. Calculate the value of ABC after the recapitalization plan (VL) is announced.
What is the price per share right after the announcement?
After recapitalization plan is announced → levered firm without taxes
→ VL =Vu + t * D = 200m
Price per share = Ve/no of share
Price per share = 200
Ko thuế → giá trị của cty ko thay đổi (Vu = VL = 200m) → debt ko lm thay đổi giá
trị của cty (kiểu như debt vs equity là như nhau) → debt ko ảnh hưởng đến giá của
share → khi tính price of share sẽ ko trừ đi debt →
Share repurchase → ko làm ảnh hưởng đến value of the firm → giảm lượng no of
share ở trên thị trường
c. How many shares will be repurchased (assume shares are perfectly divisible,
i.e. can take fractional shares)?
use proceeds → use 50,000,000 để mua
shares use 10% debt → use 10% *
50,000,000/200
Share repurchased = 50,000,000/200 = 250,000 shares
pg. 2
, lOMoAR cPSD| 22896205
Part 2: Company is subjected to 35% corporate tax.
d. Redo the a, b, c
Có thuế → làm cho giá trị cty tăng từ 130 → 147.5m → thể hiện rằng có nợ sẽ ảnh
hưởng đến value của công ty → debt làm ảnh hưởng đến giá của share → khi tính
price of share phải trừ đi debt
a. Vu = 30m*(1 - 35%)/15% = 130,000,000
→ Price per share = 130,000,000/1,000,000 = 130$/share
b. VL = Vu + t * D = 130,000,000 + 35% * 50,000,000 = 147,500,000
c. Ve = Vfirm - D = 147,500,000 - 50,000,000 = 97,500,000 → Price per
share = (147,500,000 - 50,000,000)/1,000,000 = 97.5$/share share repurchase =
số tiền mua lại share/price per share
Share repurchase = 50,000,000/97.5 = 512,820.5128 shares
Q2: M&M theory. Star, Inc., a prominent consumer products firm, is debating
whether or not to convert its all-equity capital structure to one that is 50 percent debt.
Currently there are 6,000 shares outstanding and the price per share is $58. EBIT
is expected to remain at $33,000 per year forever (perpetuity). The interest rate on
new debt is 8 percent, and there are no taxes.
no of shares = 6,000
Price per share = $58
EBIT = $33,000
Rd = 8%
t=0
a. Ms. Brown, a shareholder of the firm, owns 1,000 shares of stock. What is
her cash flow under the current capital structure, assuming the firm has a
dividend payout rate of 100 percent?
pg. 3
, owns 1,000 shares
dividend payout rate =
100%
EPS (profit per share of equity holders/dividend)
= EBIT/ No of shares = 33,000/6,000 = 5.5$/shares
NI = EBIT - Interest → ko sd nợ → nên ko có lãi vay → NI = EBIT
Ms Brown CF = 5.5 * 1,000 = 5,500
b. What will Ms. Brown’s cash flow be under the proposed capital structure of
the firm?
Assume that she keeps all 1,000 of her shares.
All equity firm + no tax → Vu = VL = 6,000 * 58 = 348,000$
50% debt (under proposed cap structure)
→ D = 348,000 * 50% = 174,000$ → sd debt để mua lại share
→ vay tiền để mua lại share thì Vfirm mới k thay đổi theo MMI theory → phải tính
số share htai đc lưu hành sau khi mua lại share
Share repurchase = 174,000/58 = 3,000 → remaining share = 6,000 - 3,000 = 3,000
shares
NI (Earing for equity holders) = EBIT - Interest payment (lãi vay) = 33,000 -
(174,000 * 8%) = 19,080$
EPS (dividend - dựa trên net income) = 19,080/3,000 = 6.36$/share
Ms Brown CF (total dividend) = 6.36$ * 1,000 = 6,360$
c. Suppose Star does convert (levered), but Ms. Brown prefers the current all-
equity capital structure. Show how she could unlever her shares of stock to
recreate the original capital structure.
pg. 4
