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Suppose you borrow $120000 when financing a coffee shop which is valued at $175000. Assume that the unlevered cost of capital for the coffee shop is 7.5% and that the cost of debt is valued at 9%. What should be the cost of equity of your firm? Note: Express your answers in strictly numerical terms. For example, if the answer is 5%, write 0.05"

Question

Suppose you borrow 120000whenfinancingacoffeeshopwhichisvaluedat120000 when financing a coffee shop which is valued at 175000. Assume that the unlevered cost of capital for the coffee shop is 7.5% and that the cost of debt is valued at 9%. What should be the cost of equity of your firm? Note: Express your answers in strictly numerical terms. For example, if the answer is 5%, write 0.05"

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Solution

To find the cost of equity, we can use the Modigliani-Miller theorem, which states that the cost of equity is equal to the unlevered cost of capital plus the cost of debt times the debt-to-equity ratio.

First, we need to find the debt-to-equity ratio. The debt is 120,000andtheequityisthevalueofthecoffeeshopminusthedebt,whichis120,000 and the equity is the value of the coffee shop minus the debt, which is 175,000 - 120,000=120,000 = 55,000. So, the debt-to-equity ratio is 120,000/120,000 / 55,000 = 2.18.

Next, we can calculate the cost of equity. The unlevered cost of capital is 7.5% or 0.075, the cost of debt is 9% or 0.09, and the debt-to-equity ratio is 2.18. So, the cost of equity is 0.075 + 0.09 * 2.18 = 0.2712 or 27.12%.

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