Let’s say we have a company that will cease operations 1 year from now. The total cash flows produced in 1 year (from profits, sales of assets etc.) have an 80% chance of being 250 and a 20% chance of being 0. Furthermore, assume that the risk-free rate is 0% and that the uncertain cash flow of the company has a beta of 0.
The company has just taken out 100 of debt financing to fund the operations for the final year and has no other debt. Since the beta is 0 and the risk-free rate is 0%, the fair interest charged by the bank is 25% (this way the expected value of the repaid amount is 100). One can now see that the equity holders and debt holders have the exact same claim (125 with an 80% chance).
Now to the actual question and what confuses me: If we now calculate the cost of equity with the CAPM we get a cost of equity of 0. If we calculate the cost of debt using the interest rate, we get a cost of debt of 25%. How does it make sense for these “costs” to be different for the exact same cashflows? I can see that the issue lies in what we are discounting (the expected value of 100 or the repayment rate of 125) but I am still quite confused.