<p>Your formula is wrong. The derivation for the cost of equity <span class="math-container">$r_E$</span> is actually:</p>

<p><span class="math-container">$r_A = r_D(1-t)\frac{D}{V}+r_E \frac{E}{V}\\
r_E \frac{E}{V} = r_A -  r_D(1-t)\frac{D}{V}\\
r_E = r_A \frac{V}{E} -  r_D(1-t)\frac{D}{V} \times\frac{V}{E}\\
\mathbf{r_E = r_A \frac{V}{E} -  r_D(1-t)\frac{D}{E}}$</span></p>

<p>Since <span class="math-container">$\frac{D}{V}=\frac{D}{D+E}=0.09091$</span> when <span class="math-container">$r_A=0.1941$</span>, then <span class="math-container">$E=10$</span> which means <span class="math-container">$D=0.10E=1$</span>, making <span class="math-container">$V=D+E=11$</span> for use in the above.</p>

<p><span class="math-container">$r_E = 0.180 \times\frac{11}{10}-0.06(1-0.35)\times 0.10 = 0.1941$</span></p>

CC BY-SA 4.0
2019-06-15T23:27:37.603Z
2019-06-15T23:34:52.527Z
2019-06-15T23:34:52.527Z
develarist
<p>So i have this question on leverage and cost of capital:</p>

<p>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.</p>

<p>The answer sheet is this ( only a part of the table is shown)</p>

<p>..<a href="https://i.sstatic.net/v1A0o.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/v1A0o.png" alt="enter image description here"></a></p>

<p>I understand how they got to the RA and how it doesn't change according to the capital structure.</p>

<p>I also know how to calculate D/V from D/E.</p>

<p>The problem is that i dont seem to understand which formula I should use to calculate RE.</p>

<p>If , for example, i use this formula</p>

<p>RE=RA+(RA-RD)D/E for D/E equal to 0.10 i get </p>

<p>RE=0.180+(0.180-0.06) · 0.10 = 0.192 which is not 0.1941.</p>

<p>Then which formula should i use ?</p>

<p>R=rf+B(rm-rf)?</p>

<p>Why do i need to calculate DV?</p>

<p>Somebody please explain how i can get accurate results of RE using which formula? Thanks i greatly appreciate it.</p>

<finance><stock-market><financial-economics><capital-returns>
How to calculate cost of equity?
Sara Salvante
# How to calculate cost of equity?

(Asked by: username_0 on 2019-06-14)

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)

..[![enter image description here](https://i.sstatic.net/v1A0o.png)](https://i.sstatic.net/v1A0o.png)

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 ?

R=rf+B(rm-rf)?

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.

**Tags:** finance, stock-market, financial-economics, capital-returns

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## 1 answers

### Answer by username_1 on 2019-06-15. Score: 1 | Accepted answer

Your formula is wrong. The derivation for the cost of equity $r\_E$ is actually:

$r\_A = r\_D(1-t)\frac{D}{V}+r\_E \frac{E}{V}\\
r\_E \frac{E}{V} = r\_A - r\_D(1-t)\frac{D}{V}\\
r\_E = r\_A \frac{V}{E} - r\_D(1-t)\frac{D}{V} \times\frac{V}{E}\\
\mathbf{r\_E = r\_A \frac{V}{E} - r\_D(1-t)\frac{D}{E}}$

Since $\frac{D}{V}=\frac{D}{D+E}=0.09091$ when $r\_A=0.1941$, then $E=10$ which means $D=0.10E=1$, making $V=D+E=11$ for use in the above.

$r\_E = 0.180 \times\frac{11}{10}-0.06(1-0.35)\times 0.10 = 0.1941$


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