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Homework answers / question archive / Consider two firms, With and Without, that have identical assets that generate identical cash flows
Consider two firms, With and Without, that have identical assets that generate identical cash flows. Without is an all-equity firm, with 10 million shares outstanding that trade for a price of $8 per share. With has 5 million shares outstanding and $20 million in debt at an interest rate of 5%.
Assume Miller and Modigliani (MM) perfect capital markets with no taxes and that firms and individuals can borrow and lend at the same 5% rate as With.
Value of With = Value of the levered firm = D + E = 20 + 65 = 85 = Value of the unlevered firm = Value of Without =
P x N = P x 10
Hence, no arbitrage price per share of With = 85 / 10 = $ 8.50
However, the current trading price of Without = $ 8 per share.
Hence, Without is undervalued and hence we should invest in Without.
Part (b)
If you want ownership of 10% of Without, number of shares to be bought = 10 million shares x 10% = 1 million. Cost to buy = P x N = 8 x 1 = $ 8 million
Hence, funds required = F = $ 8 million
Price per share of With = Equity value / Number of shares = 65 / 5 = 13
You therefore need to short = F / Price per share of With = 8 / 13 = 0.615385 million shares of With.
Hence your arbitrage transaction should be:
| Sl. No. | Action | Cash flow | How it has been calculated? |
| 1 | Buy (long) 1 million shares of Without | -8,000,000 | '= 1 million share @ price of $ 8 per share |
| 2 | Short (sell) 615,385 shares of With | 8,000,000 | '= 615,385 shares @ price of $ 13 per share |
| 3 | Borrow an amount = 1 million shares x price differential of Without = 1,000,000 x (8.5 - 8.0) | 500,000 | '= (8.5 - 8) x 1 million |
| Net cash flows | 500,000 | '=Arbitrage profit |
And the amount of profit = 500,000
