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Suppose you borrow $53938.15M when financing a gym with a cost of $86024.40M. You expect to generate a cash flow of $83618.25M at the end of the year if demand is weak, $92150.14M if demand is as expected and $108635.81M if demand is strong. Each scenario is equally likely. The current risk-free interest rate is 5.20% (risk of debt) and there's a 9.64% risk premium for the risk of the assets. What would be the realized return of equity if the demand is strong? (HINT: If you need it, to compute the WACC of the firm, add the risk free plus the risk premium)

User Caty
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Final answer:

The realized return of equity if the demand is strong is calculated by determining the cash flow from the strong demand scenario, calculating the amount owed with interest on the borrowed funds, and subtracting the owed amount from the cash flow to find the equity return. The result is a return of $51892.876M.

Step-by-step explanation:

To calculate the realized return of equity if the demand is strong, we first need to calculate the total cash flows generated and the amount owed on the borrowed funds assuming the risk-free interest rate, since this is the cost of debt. The total cash flow from the strong demand scenario is $108635.81M. The borrowed amount is $53938.15M, and since this is a simple yearly calculation and we're assuming a one-year period, the amount owed would be the initial loan plus the interest at the risk-free rate of 5.20%. Therefore:

Amount owed = Initial loan + (Initial loan × Risk-free interest rate)
= $53938.15M + ($53938.15M × 5.20%)

Next, we calculate the equity by subtracting the amount owed from the total cash flow in the strong demand scenario, which then gives us the return on equity:

Return on equity = Cash flow (strong demand) - Amount owed

Now we apply these calculations:

  1. Calculate amount owed
  2. $53938.15M + ($53938.15M × 0.052) = $53938.15M + $2804.784M = $56742.934M owed after one year.
  3. Calculate the return on equity:
  4. $108635.81M - $56742.934M = $51892.876M.

The realized return of equity would therefore be $51892.876M if the demand is strong.

User Fatu
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