Gamma is an all-equity, stationary firm with perpetual EBIT €2,000.00, unlevered cost of capital 10%, corporate tax rate 30% and 70 shares. It issues permanent debt of €4,000.00 to repurchase shares. Assume MM with corporate taxes and no distress costs.
Equity = €11,200.00.
At a fair repurchase price, the tax benefit is reflected when the transaction is announced. All original shares participate in that value increase.
Fair price = €217.14.
If instead the shares are explicitly bought back at the old price €200.00, 50.0000 shares remain and their price is €224.00. This alternative matches the source’s convention, but requires sellers to accept the pre-announcement price.
Omega is an all-equity, stationary firm with perpetual EBIT €3,000.00, unlevered cost of capital 10%, corporate tax rate 30% and 70 shares. It issues permanent debt of €6,000.00 to repurchase shares. Assume MM with corporate taxes and no distress costs.
Equity = €16,800.00.
At a fair repurchase price, the tax benefit is reflected when the transaction is announced. All original shares participate in that value increase.
Fair price = €325.71.
If instead the shares are explicitly bought back at the old price €300.00, 50.0000 shares remain and their price is €336.00. This alternative matches the source’s convention, but requires sellers to accept the pre-announcement price.
Theta is an all-equity, stationary firm with perpetual EBIT €4,000.00, unlevered cost of capital 10%, corporate tax rate 30% and 70 shares. It issues permanent debt of €8,000.00 to repurchase shares. Assume MM with corporate taxes and no distress costs.
Equity = €22,400.00.
At a fair repurchase price, the tax benefit is reflected when the transaction is announced. All original shares participate in that value increase.
Fair price = €434.29.
If instead the shares are explicitly bought back at the old price €400.00, 50.0000 shares remain and their price is €448.00. This alternative matches the source’s convention, but requires sellers to accept the pre-announcement price.
Epsilon is an all-equity, stationary firm with perpetual EBIT €1,000.00, unlevered cost of capital 10%, corporate tax rate 30% and 70 shares. It issues permanent debt of €2,000.00 to repurchase shares. Assume MM with corporate taxes and no distress costs.
Equity = €5,600.00.
At a fair repurchase price, the tax benefit is reflected when the transaction is announced. All original shares participate in that value increase.
Fair price = €108.57.
If instead the shares are explicitly bought back at the old price €100.00, 50.0000 shares remain and their price is €112.00. This alternative matches the source’s convention, but requires sellers to accept the pre-announcement price.
Delta is an all-equity, stationary firm with perpetual EBIT €2,500.00, unlevered cost of capital 10%, corporate tax rate 30% and 100 shares. It issues permanent debt of €4,900.00 to repurchase shares. Assume MM with corporate taxes and no distress costs.
Equity = €14,070.00.
At a fair repurchase price, the tax benefit is reflected when the transaction is announced. All original shares participate in that value increase.
Fair price = €189.70.
If instead the shares are explicitly bought back at the old price €175.00, 72.0000 shares remain and their price is €195.42. This alternative matches the source’s convention, but requires sellers to accept the pre-announcement price.
Fama is initially all-equity financed, with 20 shares and equity value 350.00. Its unlevered required return is 14.00%. It issues permanent debt of 40.00 at 5.00% to repurchase shares. Corporate tax is 35.00%. Values and share counts are in millions. Scenario cash flows are 15, 30, 70 and 90 with probabilities 20%, 30%, 40% and 10%, giving expected annual FCF 49 and VU = 49/0.14 = 350. The displayed cash flows are already after tax.
Values and share counts are in millions. Scenario cash flows are 15, 30, 70 and 90 with probabilities 20%, 30%, 40% and 10%, giving expected annual FCF 49 and VU = 49/0.14 = 350. The displayed cash flows are already after tax.
Unlevered required return = 14.00%.
No. MM I keeps firm value and the fair share price of 17.50 unchanged. Equity becomes riskier; cheaper debt alone does not create value.
The main answer assumes repurchase at the fair price after the announcement. If shares are contractually bought at the old price, the remaining share price instead equals 18.290323.
WACC = 13.4615%.
Dynamic has 1,000 shares priced at 250 and 2,000 risk-free bonds with face value 100, priced at 104. Equity beta is 1.6, the market expected return is 6%, the risk-free debt rate is 3.5% and corporate tax is 30%. It issues a further 50,000 of permanent debt at par to repurchase shares.
5.2066%
No. Leverage raises the required equity return. In this idealised model the gain comes from the additional interest tax shield, not simply from substituting a cheaper source of funds.
Equity value = 473,000 − 258,000 = 215,000.
5.0414%
Corot has perpetual revenue 5,800, cash costs 50% of revenue, depreciation 900 and total reinvestment 900. Tax is 30%, debt is 40% of firm value, WACC 14%, debt cost 5%, and there are 100 shares. It issues another 1,500 of permanent debt for a buyback.
Initial share price = 60.
At a fair announced buyback price, remaining shares are also worth 64.50. The extra tax shield creates 450 of shareholder value. If the repurchase is imposed at the old 60 price, 75 shares remain and their price is 66; that alternative redistributes the gain.
BluSky has sales 1,000, cash operating costs 700 and depreciation 80. Total reinvestment equals depreciation, operations are perpetual and stationary, and tax is 30%. It has a short-term loan of 220 valued at par and a four-year bond with face 200 and annual coupon 6.5%. Both debts require 5%. Market equity is 1,200. It plans to borrow another 130 permanently for a share buyback.
9.4442%
1,109.00.
Smart has perpetual EBIT 5,000, permanent debt 10,000 costing 10%, equity cost 15%, 1,000 shares and full earnings payout. Corporate tax is 40%. It then issues 5,000 additional debt to repurchase equity, with the debt rate unchanged.
16.1538%
| Division | Perpetual annual FCF | Asset beta |
|---|---|---|
| A | 4,500 | 0.80 |
| B | 2,500 | 1.20 |
Goldstar has 1,000 shares and initially no debt. The risk-free rate is 4%, the market premium 5%, and corporate tax 30%. It issues permanent risk-free debt to buy 200 shares specifically at the initial price calculated in part A.
Equity = 81,250; share price = 81.25.
Required return = 8.6154%.
87.34375.
This uses the explicitly imposed pre-announcement repurchase price. A buyback at the fair post-announcement price would redistribute the tax-shield benefit differently.
Cost of equity = 9.3667%.
Honeymoon generates perpetual EBIT of 7,500. Corporate tax is 30%, unlevered cost of capital 10%, permanent risk-free debt 35,000 and there are 1,000 shares. It issues 10,000 of new equity to retire debt at par.
Equity = 28,000; price = 28.00.
The loss of 3,000 of tax shields reduces old shareholders’ wealth. If the issue is specifically priced at the old 28, the resulting 357.1429 new shares give a post-issue price of 25.7895; that convention transfers value between old and new holders.
Tax-only MM predicts a decline. A positive response can be explained if reduced expected distress or agency costs outweigh lost tax shields, or if the transaction conveys favourable information.
No. Operating risk and operating free cash flows remain unchanged when investment policy is fixed. Enterprise value falls in the standard model because the debt tax shield shrinks. Equity beta and its required return fall; WACC rises as the tax advantage is lost. Any share-price conclusion must also account for the terms and timing of the equity issue.