Question

1. We are in an MM world with no taxes. The Casbah firm is an unlevered firm with a cost of equity capital of 10%. The firm is worth 10 million USD, and has two future states of the world in one years’ time. There is a 50% chance of the firm being worth 9 million USD and a 50% chance of the firm being worth 13 million USD. Anna would like to invest in a levered version of the Casbah firm in which the Casbah firm has a 25% D/V (1/4 ratio Debt to value). Assume that Anna can borrow and lend at 5%. How would she synthetically create the leveraged equity and what would her upside and downside be?

Answer 1

For every amount invested 25% would constitute debt borrowed by Anna. Accordingly for every 100 USD invested 1.25 USD will be borrowing costs i.e. 5%*100*25%

If Casbah net worth goes down to 9 million USD it will be 10% loss from the current value. Accordingly, Anna will incurr 10% + 1.25% i.e. 11.25% of loss.

If Casbah net worth goes up to 13 million USD it will be 30% gain. Accordingly Anna will gain 30% - 1.25% i.e. 28.75% net gain.