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The Hamada equation is a formula used to calculate the cost of equity capital for a company with debt. It is based on the capital asset pricing model (CAPM), which is a model used to determine the expected return on an investment. The Hamada equation takes into account the company's debt-to-equity ratio and the tax rate to determine the cost of equity capital.

The CAPM equation is:

```
E(r) = Rf + ß(Rm - Rf)
```

where:

* E(r) is the expected return on the investment
* Rf is the risk-free rate of return
* ß is the beta of the investment
* Rm is the expected return on the market

```
Ke = Rf + ß(Rm - Rf) * [1 + (1 - T) * (D/E)]
```

where:

* Ke is the cost of equity capital
* Rf is the risk-free rate of return
* ß is the beta of the investment
* Rm is the expected return on the market
* T is the tax rate
* D/E is the debt-to-equity ratio

The Hamada equation is used to calculate the cost of equity capital for a company with debt because the company's debt-to-equity ratio affects the risk of the investment. A company with a high debt-to-equity ratio is more risky than a company with a low debt-to-equity ratio. This is because a company with a high debt-to-equity ratio is more likely to default on its debt, which would reduce the value of the investment.

The Hamada equation takes into account the company's debt-to-equity ratio and the tax rate to determine the cost of equity capital. The tax rate is used to adjust the cost of debt because interest payments on debt are tax-deductible. This means that the after-tax cost of debt is lower than the before-tax cost of debt.

The Hamada equation is a useful tool for calculating the cost of equity capital for a company with debt. It takes into account the company's debt-to-equity ratio and the tax rate to determine the cost of equity capital. This information can be used to make decisions about the company's capital structure.

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