Fyre, Inc., has a target debtequity ratio of 1.20. Its WACC is 8.6 percent, and

Question

Fyre, Inc., has a target debtequity ratio of 1.20. Its WACC is 8.6 percent, and the tax rate is 35 percent.

If the company’s cost of equity is 16 percent, what is its pretax cost of debt? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

If instead you know that the aftertax cost of debt is 3.5 percent, what is the cost of equity? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Fyre, Inc., has a target debtequity ratio of 1.20. Its WACC is 8.6 percent, and the tax rate is 35 percent.

Explanation / Answer

Debt to Equity ratio is a metric to identify how leveraged a company is and is calculated by deriving the ratio between total liabilities to shareholders' equity. However, for the sake of this particular question, let the following variables represent the elements

Debt: D
Equity: E
Total Financial Structure of the company: V = D+E

The proportion of debt in the company's financial structure is D/V
The proportion of equity in the company's financial structure is E/V

Return on Equity (Also known as cost of equity): Re
Interest Rate on Debt (also known as cost of debt): Rd
Tc: Corporate Tax (given to be 35%)

WACC is the weighted Average Cost of Capital is the cost at which a firm borrows capital calculated by averaging the proportion of debt and equity of a company and is given to be 8.60% (i.e. 0.086). It uses the following formula:

WACC = E/V*Re + D/V*Rd*(1-Tc)
This is the post tax WACC

Fyre Inc's Debt-Equity Ratio is: 1.20
Thus D/E = 1.20 = 1.20/1

Basic Algebra allows us to perform the following operation for equal ratios:

(D+E)/E = (1.20+1)/1 = 2.20
A reciprocal of the equation will yield: E/(D+E) = 1/2.20

Thus E/V = 0.454545

D/E = 1.20. Therefore E/D = 1/1.20 = 0.8333
Using similar algebraic functions, we can derive (E+D)/D

Thus (E+D)/D = (0.8333+1)/1 = 1.8333

Taking a reciprocal; D/(D+E) = 1/1.8333

Thus D/V = 0.5454

Part a.

The cost of Equity of Fyre Inc (i.e. Re) = 16%

Re*E/V = 16%*0.4545 = 0.07272

Substituting these values in the formula of WACC:

0.086 = 0.7272 + 0.5454*Rd*(1-Tc)

Rd*(1-Tc) = 0.02433

Rd = 0.02433/(1-Tc) = 0.02433/(1-0.35)

Therefore Rd = 0.037436 = 3.7436%

The pre tax cost of debt for Fyre Inc. is 3.74%

Part b.

The after tax cost of debt is given to be 3.5%
Thus Rd*(1-Tc) = 3.5%

Again, WACC is given by the following formula
WACC = E/V*Re + D/V*Rd*(1-Tc)

D/V*[Rd*(1-Tc)] = 0.5454*3.5% = 0.019091

E/V*Re = WACC - [D/V*Rd*(1-Tc)] = 0.086 - 0.019091
Thus E/V*Re = 0.0669 (where E/V = 0.4545)

Re = 0.0669/0.4545 = 0.1472

Thus the cost of Equity is 14.72%

/*Important Tips*/
/*Higher Risk yields higher return

Debt is a safer financial instrument. Equity is riskier. The cost of debt therefore is always lower than the cost of equity*/

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