Magician please weigh in: cost of equity clarification from corporate finance reading.

[NeverQuit]

Question 10, reading 23 capital structure (2015 curriculum)
the question asks for the current cost of equity. I arrive at the correct answer of 10.80% using MM proposition 2 and related formula with taxes; re= r0 + (ro-rd)(1-T)D/E. However, I am not clear on when to use this formula versus information in exhibit 2 that suggests the cost of equity is between 12.5% and 13%. relevant part of exhibit 2 data is below. Note, in subsequent WACC question, exhibit 2 cost of equity information was used.
Exhibit 2. Estimates of MBG’s before Tax Costs of Debt and Equity
Debt-to-Total Capital Ratio (%) Cost of Debt (%) Cost of Equity (%)
20 7.7 12.5
30 8.4 13.0

 

[Harrogath]

I had the same problem. Indeed, I answered 12.75%, then saw I was wrong and unfortunately the solution answer simply uses the formula with no extra explanation of why 12.75% would not be correct, despite one option was 12.75%…
If the correct answer is 10.8% cost of equity with 25% debt and 75% equity, then table does not give accurate numbers of cost of equity at each leverage level: 20% debt = 12.5% cost of equity and 30% = 13.0%, even the 20% debt level is way above the 10.8% cost of equity at 25% debt.
As I see this, always use the formula… and other data of cost of equity is leading info. The rest is just useful for cost of debt calculation (like question 9 for example)
Aaaand, if they don’t give us the r0, then we cannot apply the formula, so maybe use the table’s… who knows.

 

[NeverQuit]

Harrogath,
thank you for the response, however, there has to be a better solution than just use the forumula if they provide r0.
Magician, where are you? your insight to this question is needed.

 

[Harrogath]

Yeah Magician, we need ya!
We’ll Never Quit