Question20 Orion Health Corp. has a share price of $18.60 and 24.5 million shares outstanding. The corporate tax rate is 28%. The firm issues $120 million of perpetual debt at 4.5% and uses the proceeds to repurchase shares. Note: Enter answers in millions of dollars, rounded to two decimal places. Example: Enter 1.25 instead of $1,250,000. a) Calculate the annual before tax interest payment. $[input] million b) Calculate the present value of the interest tax shield. $[input] million c) Calculate the value of the firm after the recapitalisation (ignoring financial distress costs). $[input] million After the announcement, the share price increases to $19.10. d) Calculate the present value of expected financial distress costs. $[input] million ResetMaximum marks: 4 Flag question undefined

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Question20 Orion Health Corp. has a share price of $18.60 and 24.5 million shares outstanding. The corporate tax rate is 28%. The firm issues $120 million of perpetual debt at 4.5% and uses the proceeds to repurchase shares. Note: Enter answers in millions of dollars, rounded to two decimal places. Example: Enter 1.25 instead of $1,250,000. a) Calculate the annual before tax interest payment. $[input] million b) Calculate the present value of the interest tax shield. $[input] million c) Calculate the value of the firm after the recapitalisation (ignoring financial distress costs). $[input] million After the announcement, the share price increases to $19.10. d) Calculate the present value of expected financial distress costs. $[input] million ResetMaximum marks: 4 Flag question undefined [input]简答题

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BlackTom AI · Accepted Answer

Interest payment = debt × interest rate, so the annual before-tax interest is 120 × 0.045 = 5.40 million.

1) Relevant concepts
- Annual interest = face value of perpetual debt × coupon rate.
- PV of a perpetual interest tax shield (when debt is perpetual and discount rate for the tax shield equals the debt rate) = tax rate × debt.
- Firm value after recapitalisation (ignoring distress) can be computed by adding the value of debt and the PV of tax shields to the pre‑recapitalisation equity value (or equivalently V_L = V_U + PV(tax shield)).
- Expected financial distress costs = theoretical levered firm value (ignoring distress) − observed market value after the recapitalisation.

2) Step-by-step calculations
a) Annual before-tax interest:
- Debt = 120 million; rate = 4.5%
- Interest = 120 × 0.045 = 5.40 million.

b) PV of interest tax shield:
- Corporate tax rate τ = 28%
- PV(tax shield) = τ × Debt = 0.28 × 120 = 33.60 million.
(Equivalently τ × interest / r_d = 0.28 × (120×0.045)/0.045 = 0.28×120.)

c) Value of the firm after recapitalisation (ignoring distress):
- Initial equity value = share price × shares = 18.60 × 24.5 = 455.70 million.
- Add the new debt (120) and the PV tax shield (33.60):
- V_after = 455.70 + 120.00 + 33.60 = 609.30 million.
(Interpretation: starting market equity reflects the unlevered firm; issuing debt brings in 120 of financing and the tax shield adds value.)

d) PV of expected financial distress costs:
- Number of shares repurchased = proceeds / repurchase price = 120 / 18.60 = 6.4516129 million.
- Remaining shares = 24.5 − 6.4516129 = 18.0483871 million.
- After announcement the new share price = 19.10, so observed remaining equity value = 18.0483871 × 19.10 = 344.72 million (rounded).
- Observed firm market value after recapitalisation = equity remaining + debt = 344.72 + 120.00 = 464.72 million.
- Expected PV of financial distress costs = theoretical V_after (ignoring distress) − observed market value = 609.30 − 464.72 = 144.58 million.

3) Why the answers are correct
- Each step applies standard formulas for interest, the perpetual tax shield (τD), and firm valuation after leverage. The observed post‑repurchase market value uses the reduced share count multiplied by the announced new price; the shortfall versus the theoretical no‑distress value is the market’s valuation of expected distress.

4) Common mistakes (why other approaches are incorrect)
- Forgetting to reduce shares when computing post‑repurchase equity value leads to wrong observed firm value.
- Using V_L = V_U + τD (without adding the new debt when comparing to observed equity+debt) can cause mismatches when computing the distress gap; consistent definitions of firm value must be used.

Final confirmation: a) 5.40 million; b) 33.60 million; c) 609.30 million; d) 144.58 million — these match the provided answers.

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