Serendipity inc. is re-evaluating its debt level. its current capital structure consists of 80% debt and 20% common equity, its beta is 1.60, and its tax rate is 35%. however, the cfo thinks the company has too much debt, and he is considering moving to a capital structure with 40% debt and 60% equity. the risk-free rate is 5.0% and the market risk premium is 6.0%. by how much would the capital structure shift change the firm's cost of equity?

a: -5.2%
b: -5.78%
c: -6.36%
d: -6.99%
e: -7.69%

Using the current capital structure

Ke = Rf + β(Risk premium)

Ke = 5 + 1.60(6)

Ke = 5 + 9.60

Ke = 14.60

Weighted cost of equity

= 14.60(20/100)

= 2.92%

Using the new debt-equity ratio

Ke = 5 + 1.60(6)

Ke = 5 +  9.6

Ke  = 14.60%

Weighted cost of equity

Ke = 14.60(60/100)

Ke = 8.76%

Difference in cost of equity

= 2.92% - 8.76%

= -5.8%

Explanation:

There is need to calculate the cost of equity based on capital asset pricing model where Rf  represents risk-free rate, Rp denotes risk-premium and β refers to beta. Then, we will calculate the weighted cost of equity by multiplying cost of equity by the proportion of equity in the capital structure. We will also calculate the new weighted cost of equity by multiplying the cost of equity the new proportion of equity in the capital structure. Finally, we will deduct the new weighted cost of equity from the old weighted cost of equity.  

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