POTFOOLER--DEBT ISSUED TO REPURCHASE SHARES

Unlevered company

Annual free cash flow (FCF)

$2,000,000

Number of shares

100,000

Price per share

$100

Total equity value

$10,000,000

Question 1: V_U, unlevered value of Potfooler

$10,000,000

Levered company

Debt issued

$3,000,000

Interest rate on debt

8%

T_C, Lower Fantasia corporate tax rate

40%

Question 2: V_L, levered value of Potfooler, V_L = V_U + T_C*D

$11,200,000

Question 3: Equity value after share repurchase, E = V_L - D

$8,200,000

Incremental firm value from exchanging equity by debt = V_L - V_U = T_C*D

$1,200,000

Incremental firm value on a per-share basis

$12

Question 4: New share value, after repurchase

$112

Question 5: Number of shares repurchased = [debt used for repurchase]/[new share value]

26,785.71

Number of shares remaining after repurchase = original number of shares minus number of shares repurchased

73,214.29

Check: Market value of remaining shares = number of remaining shares * new share value

$8,200,000

Question 6: Potfooler's cost of equity when unlevered, r_U=FCF/V_U

20.00%

Annual interest costs, before taxes

$240,000

Annual equity cash flow, after interest = FCF - (1-TC)*interest

$1,856,000

Question 7: Potfooler's cost of equity when levered, r_E(L)=[FCF-(1-T_C)*interest]/[value of equity, E]

22.63%

Question 8: Potfooler's WACC before the debt issuance = r_U

20.00%

Question 9: Potfooler's WACC after the debt issuance = r_E(L)*E/(E+D)+r_D*(1-T_C)*D/(E+D)

Percentage of equity in Potfooler = E/(E+D)

73.21%

Percentage of debt in Potfooler = D/(E+D)

26.79%

WACC = r_E(L)*E/(E+D)+r_D*(1-T_C)*D/(E+D)

17.86%

Debt issued

Cost of equity r_E(L)

WACC

0

1,000,000

2,000,000

3,000,000

4,000,000

5,000,000

6,000,000

7,000,000

8,000,000

9,000,000

POTFOOLER--DEBT ISSUED TO REPURCHASE SHARES

Unlevered company

Annual free cash flow (FCF)

$2,000,000

Number of shares

100,000

Price per share

$100

Total equity value

$10,000,000

Question 1: V_U, unlevered value of Potfooler

$10,000,000

Levered company

Debt issued

$3,000,000

Interest rate on debt

8%

T_C, Lower Fantasia corporate tax rate

40%

Question 2: V_L, levered value of Potfooler, V_L = V_U + T_C*D

$11,200,000

Question 3: Equity value after share repurchase, E = V_L - D

$8,200,000

Incremental firm value from exchanging equity by debt = V_L - V_U = T_C*D

$1,200,000

Incremental firm value on a per-share basis

$12

Question 4: New share value, after repurchase

$112

Question 5: Number of shares repurchased = [debt used for repurchase]/[new share value]

26,785.71

Number of shares remaining after repurchase = original number of shares minus number of shares repurchased

73,214.29

Check: Market value of remaining shares = number of remaining shares * new share value

$8,200,000

Question 6: Potfooler's cost of equity when unlevered, r_U=FCF/V_U

20.00%

Annual interest costs, before taxes

$240,000

Annual equity cash flow, after interest = FCF - (1-TC)*interest

$1,856,000

Question 7: Potfooler's cost of equity when levered, r_E(L)=[FCF-(1-T_C)*interest]/[value of equity, E]

22.63%

Question 8: Potfooler's WACC before the debt issuance = r_U

20.00%

Question 9: Potfooler's WACC after the debt issuance = r_E(L)*E/(E+D)+r_D*(1-T_C)*D/(E+D)

Percentage of equity in Potfooler = E/(E+D)

73.21%

Percentage of debt in Potfooler = D/(E+D)

26.79%

WACC = r_E(L)*E/(E+D)+r_D*(1-T_C)*D/(E+D)

17.86%

Debt issued

Cost of equity r_E(L)

WACC

0

1,000,000

2,000,000

3,000,000

4,000,000

5,000,000

6,000,000

7,000,000

8,000,000

9,000,000

SMOTFOOLER--DEBT ISSUED TO REPURCHASE SHARES Smotfooler is located in Upper Fantasia
Upper Fantasia tax system
TC, Upper Fantasia corporate tax rate	40%
TE, Upper Fantasia personal tax rate on equity income	10%
TD, Upper Fantasia personal tax rate on ordinary income	30%
Annual debt advantage: (1-TD)-(1-TE)*(1-TC)	%
PV of debt advantage: T = [(1-TD)-(1-TE)*(1-TC)]/(1-TD)	22.86%
Unlevered company
Annual free cash flow (FCF)	$2,000,000
Number of shares	100,000
Price per share	$100
Total equity value	$10,000,000
Question 1: VU, unlevered value of Smotfooler	$10,000,000
Levered company
Debt issued	$3,000,000
Interest rate on debt	8%
Question 2: VL, levered value of Smotfooler, VL = VU + T*D	$10,685,714
Question 3: Equity value after share repurchase, E = VL - D	$7,685,714
Incremental firm value from exchanging equity by debt = VL - VU = T*D	$685,714
Incremental firm value on a per-share basis	$7
Question 4: New share value, after repurchase
Question 5: Number of shares repurchased = [debt used for repurchase]/[new share value]	#DIV/0!
Number of shares remaining after repurchase = original number of shares minus number of shares repurchased
Check: Market value of remaining shares = number of remaining shares * new share value
Question 6: Smotfooler's cost of equity when unlevered, rU=FCF/VU
Annual interest costs, before taxes
Annual equity cash flow, after interest = FCF - (1-TC)*interest
Question 7: Smotfooler's cost of equity when levered, rE(L)=[FCF-(1-TC)*interest]/[value of equity, E]
Note: See formula in row 44 below for another way to compute the levered cost of equity
Question 8: Smotfooler's WACC before the debt issuance = rU
Question 9: Smotfooler's WACC after the debt issuance = rE(L)*E/(E+D)+rD*(1-TC)*D/(E+D)
Percentage of equity in Smotfooler = E/(E+D)
Percentage of debt in Smotfooler = D/(E+D)
WACC = rE(L)*E/(E+D)+rD*(1-TC)*D/(E+D)
Additional formula: rE(L)=rU+[rU*(1-T)-rD*(1-TC))*D/E