Finance Tutorial 4
Question 1
Homemade leverage: under Modigliani-Miller assumptions, recall the example in the lecture
The interest rate on both personal and corporate loans is the same, 10%. Analyse and compare the
following strategies:
Strategy A: Buy 100 shares of levered equity, at price $20 a share.
Strategy B: Borrow $2,000 from a bank. Use the loan plus your own investment of $2,000 to
purchase 200 shares of the current unlevered equity at $20 per share.
Discuss a key assumption of MM that leads to your results. Now suppose that the value of the levered
firm is higher than the value of the unlevered firm. What would be a rational investment strategy?
Strategy A:
Own 50% of the company, so earnings attributable to your equity holdings (that can be given
out as dividends) in the 3 states of the world is {0, 800, 1600}/2 = {0, 400, 800}
Divide by initial investment to calculate the strategy's returns: {0, 400, 800}/2000 = {0, 0.2, 0.4}
Strategy B:
Own 50% of the company, so earnings attributable to your equity holdings (that can be given
out as dividends) in the 3 states of the world is {400, 1200, 2000}/2 = {200, 600, 1000}
Regardless of the state of the world, interest payment: $2000*10% = $200
Hence, the strategy's net cashflows: {200-200, 600-200, 1000-200} = {0, 400, 800}
Divide by initial investment to calculate the strategy's returns: {0, 400, 800}/2000 = {0, 0.2, 0.4}
Hence, returns of strategy A and B are identical in all states of the world.
Correct.
This result assumes that the cost of homemade leverage is equal to that of corporate debt, which is
unlikely, as firms often can borrow at a lower rate.
Correct.
Assumption: VL > VU.
Rational investment strategy 2: buy fraction α of the unlevered firm's equity (αEU = αVU) using funds
from shorting equity of the levered firm. Obtain riskless arbitrage profit
Question 1
Homemade leverage: under Modigliani-Miller assumptions, recall the example in the lecture
The interest rate on both personal and corporate loans is the same, 10%. Analyse and compare the
following strategies:
Strategy A: Buy 100 shares of levered equity, at price $20 a share.
Strategy B: Borrow $2,000 from a bank. Use the loan plus your own investment of $2,000 to
purchase 200 shares of the current unlevered equity at $20 per share.
Discuss a key assumption of MM that leads to your results. Now suppose that the value of the levered
firm is higher than the value of the unlevered firm. What would be a rational investment strategy?
Strategy A:
Own 50% of the company, so earnings attributable to your equity holdings (that can be given
out as dividends) in the 3 states of the world is {0, 800, 1600}/2 = {0, 400, 800}
Divide by initial investment to calculate the strategy's returns: {0, 400, 800}/2000 = {0, 0.2, 0.4}
Strategy B:
Own 50% of the company, so earnings attributable to your equity holdings (that can be given
out as dividends) in the 3 states of the world is {400, 1200, 2000}/2 = {200, 600, 1000}
Regardless of the state of the world, interest payment: $2000*10% = $200
Hence, the strategy's net cashflows: {200-200, 600-200, 1000-200} = {0, 400, 800}
Divide by initial investment to calculate the strategy's returns: {0, 400, 800}/2000 = {0, 0.2, 0.4}
Hence, returns of strategy A and B are identical in all states of the world.
Correct.
This result assumes that the cost of homemade leverage is equal to that of corporate debt, which is
unlikely, as firms often can borrow at a lower rate.
Correct.
Assumption: VL > VU.
Rational investment strategy 2: buy fraction α of the unlevered firm's equity (αEU = αVU) using funds
from shorting equity of the levered firm. Obtain riskless arbitrage profit
