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Homework answers / question archive / Consider firm A and B with identical assets
Consider firm A and B with identical assets. A is an all-equity firm with 1 million shares outstanding trading for $24 per stock. B is a levered firm with 2 million shares outstanding and $12 million in debt paying an annual interest rate of 5%, which is the same as the risk-free rate. Assume that MM's perfect capital market conditions are met, and that you can borrow and lend at the same 5% rate as B.
1. Estimate B?s share price by using MM Proposition I
2. You have $1.2 mil of your own money to invest and you plan on buying A?s stock. Using leverage (i.e. borrowing), how much do you need to borrow in your margin account so that the payoff of your margined purchase of A?s stock will be the same as a $1.2 mil investment in B?s stock?
3. You have $5000 of your own money to invest and you plan on buying A?s stock. Using leverage, you borrow enough in your margin account so that the payoff of your margined purchase of A?s stock will be the same as a $5000 investment in B?s stock. What will be the number of shares of A you will purchase?
4. You have $5000 in cash to invest in B?s stock. You aim to replicate the payoff of a $5000 investment in A. Using homemade unleverage (i.e. putting unused money in risk-free assets), how much do you need to invest at the risk-free rate so that the payoff of your account will be the same as a $5000 investment in A?s stock? What is the number of shares of B?s stock you will purchase?
Part (1)
Value of firm A = P x N = 24 x 1 million = 24 million
Using MM porporsition I, in the absence of taxes, the value of the firm is independent of capital structure. Hence value of firm B = Value of firm A = 24 million
Hence, D + E = 24
12 + E = 24
Hence, E = 24 - 12 = 12
Share price of B = E/N* = 12/2 = $ 6 per share
Part (2)
By using 1.2 million of your money, you can own 1.2/E = 1.2/12 = 10% in B
In order to own 10% in A, you need 10% x Value of firm A = 10% x 24 = 2.4 million.
You already have 1.2 million.
Hence, amount you need to borrow in your margin account so that the payoff of your margined purchase of A?s stock will be the same as a $1.2 mil investment in B?s stock = 2.4 million - 1.2 million = $ 1.20 million
Part (3)
By using $ 5,000 you can own 5,000/E* = 5,000 / 12,000,000 = 0.041667% of B
In order to own 0.041667% of A, you need to buy 0.041667% x N = 0.041667% x 1,000,000 = 416.67 shares of A.
Part (4)
$ 5,000 investment in A can help you get, an ownership of 5,000 / 24,000,000 = 0.0208%
In order to own 0.0208% of B, you need an amount = 0.0208% x E* = 0.0208% x 12,000,000 = 2,500.00
Hence, you need to invest at the risk-free rate so that the payoff of your account will be the same as a $5000 investment in A?s stock = 5,000 - 2,500 = $ 2,500
