Salmon inc. has debt with both a face and a market value of $3,000. this debt has a coupon rate of 7% and pays interest annually. the expected earnings before interest and taxes is $1,200, the tax rate is 34%, and the unlevered cost of capital is 12%. what is the firm's cost of equity?

14.143%

Explanation:

Data provided in the question:

market value of debt = $3,000

Coupon rate, r = 7% = 0.07

Expected earnings before interest and taxes = $1,200

Tax rate = 34% = 0.34

The unlevered cost of capital, Ra = 12% = 0.12

Now,

Value of firm = VU + Tax

Here

VU = [expected earnings before interest and taxes( 1 - t )] ÷ [ Ra ]

= [$1,200 ( 1 - 0.34)] ÷ 0.12

= $6,600

Thus,

Value of firm = $6,600 + ( $3,000 × 0.34 )

= $6,600 + 1,020

= $7,620

Thus,

Equity = Value of firm - Debt

= $7,620 - $3,000

= $4,620

Therefore,

Cost of equity = Ra + [ (Debt ÷ Equity ) × (1 - t ) × (Ra - r ) ]

= 0.12 + [ (3,000 ÷ 4,620) × (1 – 0.34) × (0.12 - 0.07) ]

= 0.14143

or

= 0.14143 × 100%

= 14.143%

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