So i have this question on leverage and cost of capital:
Leverage and the cost of capital Gamma Airlines has an asset beta of 1.5. The risk-free interest rate is 6%, and the market risk premium is 8%. Assume the capital asset pricing model is correct. Gamma pays taxes at a marginal rate of 35%. Draw a graph plotting Gam- ma’s cost of equity and after-tax WACC as a function of its debt-to-equity ratio D/E, from no debt to D/E = 1.0. Assume that Gamma’s debt is risk-free up to D/E = .25. Then the interest rate increases to 6.5% at D/E = .5, 7% at D/E = .8, and 8% at D/E = 1.0. As in Problem 21, you can assume that the firm’s overall beta (βA) is not affected by its capital structure or the taxes saved because debt interest is tax-deductible.
The answer sheet is this ( only a part of the table is shown)
I understand how they got to the RA and how it doesn't change according to the capital structure.
I also know how to calculate D/V from D/E.
The problem is that i dont seem to understand which formula I should use to calculate RE.
If , for example, i use this formula
RE=RA+(RA-RD)D/E for D/E equal to 0.10 i get
RE=0.180+(0.180-0.06) · 0.10 = 0.192 which is not 0.1941.
Then which formula should i use ?
Why do i need to calculate DV?
Somebody please explain how i can get accurate results of RE using which formula? Thanks i greatly appreciate it.