Question

Suppose you borrow $52001.46M when financing a gym with a cost of $87431.36M. You expect to generate a cash flow of $59074.45M at the end of the year if demand is weak, $97856.28M if demand is as expected and $124613.63M if demand is strong. Each scenario is equally likely. The current risk-free interest rate is 5.28% (risk of debt) and there's a 9.34% risk premium for the risk of the assets. What would be the realized return of equity if

Answer 1

The realized return of equity would be -32.6% in the weak demand scenario, 11.9% in the expected demand scenario, and 42.3% in the strong demand scenario.

Step-by-step explanation:

The realized return of equity can be calculated as the difference between the cash flow generated and the cost of financing, divided by the initial investment. To calculate the realized return of equity, we need to consider the cash flow in each scenario.

In the weak demand scenario, the cash flow is $59,074.45 million.

In the expected demand scenario, the cash flow is $97,856.28 million.

In the strong demand scenario, the cash flow is $124,613.63 million.

The cost of financing can be calculated using the risk-free interest rate and the risk premium. In this case, the risk-free interest rate is 5.28% and the risk premium is 9.34%. So, the cost of financing is 5.28% + 9.34% = 14.62%.

The initial investment is $87,431.36 million.

Now, we can calculate the realized return of equity for each scenario:

In the weak demand scenario: ($59,074.45 million - $87,431.36 million) / $87,431.36 million = -0.326 (or -32.6%).

In the expected demand scenario: ($97,856.28 million - $87,431.36 million) / $87,431.36 million = 0.119 (or 11.9%).

In the strong demand scenario: ($124,613.63 million - $87,431.36 million) / $87,431.36 million = 0.423 (or 42.3%).