Question

Suppose you borrow $57951.25M when financing a gym with a cost of $90570.98M. You expect to generate a cash flow of $77816.02M at the end of the year if demand is weak, $88233.82M if demand is as expected and $101247.04M if demand is strong. Each scenario is equally likely. The current risk-free interest rate is 5.44% (risk of debt) and there's a 10.39% risk premium for the risk of the assets. What should the value of the equity be?

Answer 1

Calculate the expected cash flow using the probabilities of the demand scenarios, discount it by the total cost of capital, and subtract the borrowed amount to find the equity value.

Step-by-step explanation:

The student is asking how to calculate the value of equity in a gym financing scenario given different cash flow outcomes based on demand and known interest rates for risk-free debt and a risk premium for the assets. To solve this, we need to calculate the expected cash flow by finding the weighted average of the cash flows based on the probabilities of the demand scenarios, then discount it by the total cost of capital, which includes both the risk-free rate and the risk premium. Finally, we subtract the borrowed amount to get the equity value.