Hartford Mining has 90 million shares that are currently trading for $2 per share and $160 million worth of debt. The debt is risk free and has an interest rate of 4%, and the expected return of Hartford stock is 11%. Suppose a mining strike causes the price of Hartford stock to fall 25% to $1.50 per share. The value of the risk-free debt is unchanged. Assuming there are no taxes and the risk (unlevered beta) of Hartfords assets is unchanged, what happens to Hartfords equity cost of capital?Hubbard Industries is an all-equity firm whose shares have an expected return of 10.9%. Hubbard does a leveraged recapitalization by issuing debt and repurchasing stock until its debt-equity ratio is 0.66. Due to the increased risk, shareholders now expect a return of 17.1%. Assuming there are no taxes and Hubbards debt is risk-free, what is the interest rate on the debt?Global Pistons (GP) has common stock with a market value of $470 million and debt with a value of $299 million. Investors expect a 13% return on the stock and a 5% return on the debt. Assume perfect capital markets.Suppose GP issues $299 million of new stock to buy back the debt. What is the expected return of the stock after this transaction?Suppose instead GP issues $71 million of new debt to repurchase stock.Suppose Alpha Industries and Omega Technology have identical assets that generate identical cash flows. Alpha Industries is an all-equity firm, with 14 million shares outstanding that trade for a price of $24 per share. Omega Technology has 22 million shares outstanding as well as debt of $100 million.According to MM Proposition I, what is the stock price for Omega Technology?Suppose Omega Technology stock currently trades for $15 per share. What arbitrage opportunity is available? What assumptions are necessary to exploit this opportunity?Wolfrum Technology (WT) has no debt. Its assets will be worth $444 million in one year if the economy is strong, but only $226 million in one year if the economy is weak. Both events are equally likely. The market value today of its assets is $257 million.What is the expected return of WT stock without leverage?Suppose the risk-free interest rate is 5%. If WT borrows $52 million today at this rate and uses the proceeds to buy back its equity, what will be the market value of its equity just after this transaction, according to MM?What is the expected return of WT stock after the transaction in part (b)? If the risk of the debt does not change, what is the expected return of the stock after this transaction?ii. If the risk of the debt increases, would the expected return of the stock be higher or lower than in part (i)? Share on Facebook Tweet Follow us Sample Answer Here’s a structured analysis of the financial scenarios you’ve presented, broken down into each company’s situation along with calculations and assumptions needed to arrive at the answers. 1. Hartford Mining: Change in Equity Cost of Capital Given Data: – Shares: 90 million – Initial Price: $2 per share – Debt: $160 million (risk-free) – Interest Rate on Debt: 4% – Expected Return on Equity: 11% – New Price after Strike: $1.50 per share Steps to Calculate New Equity Cost of Capital: 1. Market Value of Equity Before Strike: [ text{Market Value of Equity} = text{Shares} times text{Price} = 90,000,000 times 2 = 180,000,000 ] 2. Market Value of Equity After Strike: [ text{New Market Value of Equity} = 90,000,000 times 1.50 = 135,000,000 ] 3. Total Value of the Firm (V): [ V = text{Debt} + text{Equity} = 160,000,000 + 135,000,000 = 295,000,000 ] 4. Equity Beta Using Formula: Since the risk (unlevered beta) is unchanged, we can apply the formula: [ r_E = r_0 + (r_0 – r_D) times frac{D}{E} ] Where: – ( r_E ) = new cost of equity – ( r_0 ) = return on assets (unlevered), which is still the same as pre-strike expected return of equity (11%) – ( r_D ) = return on debt (4%) – ( D ) = Debt – ( E ) = New Equity From previous calculations: – ( D = 160,000,000 ) – ( E = 135,000,000 ) 5. Calculate New Cost of Equity: Using the formula above, [ r_E = 11% + (11% – 4%) times frac{160,000,000}{135,000,000} ] [ = 11% + 7% times 1.1852 ] [ = 11% + 8.3072% = 19.3072% approx 19.31% ] Conclusion: Hartford Mining’s equity cost of capital increases to approximately 19.31% after the mining strike. 2. Hubbard Industries: Interest Rate on Debt Given Data: – Expected Return on Equity before recapitalization: 10.9% – Debt-Equity Ratio after recapitalization: 0.66 – Expected Return on Equity after recapitalization: 17.1% Steps to Calculate Interest Rate on Debt: 1. Let E be the equity value and D be the debt value. 2. From the debt-equity ratio: [ frac{D}{E} = 0.66 implies D = 0.66E ] 3. Using weighted average cost of capital (WACC) since the firm is now levered: [ WACC = frac{E}{E+D}r_E + frac{D}{E+D}r_D ] 4. Substituting Values: Let ( r_D ) be the interest rate on debt. Given ( r_E = 17.1% ), we can express WACC using the equity value ( E ) and debt value ( D = 0.66E ): [ WACC = frac{E}{E + 0.66E}(17.1%) + frac{0.66E}{E + 0.66E}(r_D) ] Simplifying gives: [ WACC = frac{1}{1.66}(17.1%) + frac{0.66}{1.66}(r_D) ] 5. Set WACC Equal to Pre-leverage Return: Since Hubbard was an all-equity firm with a return of (10.9%), we set: [ 10.9% = WACC ] 6. Solving for (r_D): Substitute WACC into the equation and solve for (r_D): [ 10.9 = frac{1}{1.66}(17.1) + frac{0.66}{1.66}(r_D) ] Rearranging gives us: Multiply through by (1.66): [ 10.9(1.66) = 17.1 + 0.66r_D ] Solving for (r_D): – Calculate (10.9(1.66) = 18.094) – Thus, [ 18.094 – 17.1 = 0.66r_D ] So,- (0.994 = 0.66r_D) – Therefore, – (r_D ≈ 1.5057 ≈ 1.51%) Conclusion: The interest rate on Hubbard Industries’ debt is approximately 1.51%. 3. Global Pistons (GP): Expected Return After Stock Repurchase Given Data: – Market Value of Stock: $470 million – Market Value of Debt: $299 million – Expected Return on Stock: 13% – Expected Return on Debt: 5% Steps for Stock Buyback Scenario: If GP issues $299 million of new stock to buy back the debt: 1. Total Value Before Transaction: Total value remains constant due to perfect capital markets. – Total Value ( V = E + D = 470 + 299 = 769 million) 2. After Transaction: After issuing $299 million in stock to repurchase debt, – New Market Value of Debt becomes $0. – The new market value of equity becomes $769 million since debt is removed entirely. 3. Expected Return After Transaction: Using the formula for expected return for an all-equity firm as it becomes all-equity after buying back debt: [ r_E’ = r_{equity} = r_{debt} + (r_{equity} – r_{debt})cdotfrac{D}{E} ] But since now there’s no debt left, [ Expected Return on Stock after transaction = Expected Return of all-equity firm = r_{equity} original. = 13% ] Conclusion for Stock Buyback Scenario: The expected return of the stock after this transaction will remain at 13%. Stock Repurchase with New Debt If instead GP issues $71 million of new debt to repurchase stock: Steps for This Scenario: 1. New Debt Issued: $71 million 2. Debt After Transaction: Total Debt will now be $299 million (old) + $71 million (new) = $370 million. 3. New Market Value of Equity After Repurchase: Since GP is repurchasing stock with new debt, – New market value of equity reduces by amount spent on repurchase. 4. New Market Value of Stock: Letting ( x ) be the new value of equity after the buyback, [ x + D_{new} = Total Value ] 5. Expected Return on Equity after leverage: Using the weighted average return formula: [ Expected Return (Leveraged) = r_{equity} + (r_{equity} – r_{debt})D/E ] Calculating the new return will require knowing how much equity remains after repurchasing. Conclusion for This Scenario: This calculation will need exact values from how much was repurchased against how much debt was issued thus far. 4. Omega Technology: Stock Price According to MM Proposition I Given Data for MM Proposition I – Alpha Industries Price per Share: $24 – Shares Outstanding: 14 million – Omega Technology Shares Outstanding: 22 million – Omega Technology Debt: $100 million Steps to Calculate Stock Price for Omega Technology: According to Modigliani and Miller Proposition I (MM Proposition I), in a world without taxes, the value of a leveraged firm equals the value of an unleveraged firm: 1. Value of Alpha Industries: [ Value_{Alpha} = Price_{Per Share} * Shares Outstanding = 24 * 14,000,000 = $336,000,000 ] 2. The total value of Omega Technology should equal that, since they generate identical cash flows. Thus, the total value for Omega Technology before any leverage adjustment should also be equal to this value. 3. Total Value Calculation for Omega with Debt: Let ( E_O ) represent the equity value. So, [ E_O + D_O = V_text{Alpha} ] Where ( D_O = $100 million): 4. [ E_O + 100,000,000 = 336,000,000 => E_O = $236,000,000 ] 5. Now price per share for Omega Technology becomes: [ Price_{Omega} = E_O / Shares Outstanding = $236,000,000 / 22,000,000 = $10.73 ] Conclusion for Omega Technology Stock Price: The stock price for Omega Technology according to MM Proposition I is approximately $10.73 per share. Arbitrage Opportunity in Omega Technology Current Price Data – Current Trading Price: $15 per share Identifying Arbitrage Opportunity: If Omega Technology trades at $15 per share but MM indicates it should trade at $10.73 per share: 1. Arbitrage Position: Buy shares at $10.73 and sell them at $15 to lock in profit. Profit per share would be (15 – 10.73 = $4.27). Assumptions Necessary to Exploit Opportunity: To exploit this arbitrage opportunity effectively, we must assume: – No transaction costs in buying/selling shares. – Perfect information among investors regarding values and pricing. – Ability to execute trades instantly without impact on market prices. Wolfrum Technology (WT): Expected Returns and Equity Value After Transaction Given Data: – Future Asset Values: $444 million (strong economy), $226 million (weak economy) – Current Market Value: $257 million – Risk-Free Rate: 5% Steps to Calculate Expected Return Without Leverage: 1. Expected Asset Value Calculation: [ E(Assets) = P_{strong}cdot V_{strong} + P_{weak}cdot V_{weak} = (0.5)(444) + (0.5)(226) = 222 + 113 = $335 million ] 2. Expected Return Calculation: Using expected future values from current market values, [ Expected Return_{WT} = (frac{335}{257})^{(1/t)} -1 ] Assuming t=1 year, [ = (frac{335}{257}) -1 = approximately .3035 or about a 30% expected return without leverage. ] After Borrowing for Buyback: 1. If WT borrows $52 million at a risk-free rate of 5%, its total assets would be leveraged but remain unchanged in risk profile. 2. Market Value Post-Borrowing: [ Value_{Assets Post Transaction} = V_{Assets} + Debt = $257M + $52M = $309M ] 3. After paying off debt with buyback, [ Equity Post Transaction ≈ V_{Assets Post Transaction} – Debt_issued = $$309M – $52M = $257M = No change in overall market value but now leveraged. Expected Return After Transaction with Unchanged Risk Profile: If risk remains unchanged, Expected Return stays similar to above levels without leverage. If Risk of Debt Increases: If debt risk increases due to borrowing, the expected return may increase further due to heightened risks associated with leveraging up. In summary, the detailed analysis covers multiple scenarios involving leveraged and unleveraged firms along with their respective expected returns and possible arbitrage opportunities in perfect capital markets versus non-perfect scenarios in finance theory contexts like MM Proposition I and other concepts relevant in corporate finance decision-making. This question has been answered. Get Answer