Question

Firm C currently has 250,000 shares outstanding with current market value of $47.40 per share and generates an annual EBIT of $1,250,000. Firm C also has $1 million of debt outstanding. The current cost of equity is 8 percent and the current cost of debt is 5 percent. The firm is considering issuing another $2 million of debt and using the proceeds of the debt issue to repurchase shares (a pure capital structure change). It is estimated that the cost of the new debt will be 5.5 percent and that the cost of equity will rise to 9 percent with the additional debt. The marginal tax rate is 21 percent.

1. What is the current market value of the firm?

2. Before the capitalization, what is the firm's weighted average cost of capital? Answer in decimal form.

3. What will the firm’s market value be after the announcement of the new debt issue?

4. What will the estimated new share price be after the capital structure change announcement?

5. What is the firm's net income after the recapitalization?

Note: The total interest costs that must be subtracted from EBIT must be calculated in two parts and then added.

6. How many shares are outstanding after the repurchase?

Answer 1

Given, Firm C

Shares outstanding = 250,000

Current market value = $47.40 per share

EBIT = $1,250,000.

Debt outstanding = $1 million

Cost of equity = Re = 8 percent

Cost of debt = Rd = 5 percent

Marginal tax rate = 21 percent

New Debt issue = $2 million to repurchase the shares at current market price which will increase the debt and reduces the equity which will change the capital structure.

cost of the new debt = 5.5 percent

cost of equity = 9 percent with the additional debt.

Answer 1 ) . What is the current market value of the firm?

Value of the firm is total worth of the company and it is the product of totak shares outstanding and share price.

Hence,

Value of the Firm = Share Price * Total shares outstanding

Value of the Firm = $47.40 * 250,000

Value of the Firm = $11850000

Value of the Firm = $11.85 Millions

Answer 2) . Before the capitalization, what is the firm's weighted average cost of capital

Given,

Cost of equity = Re = 8 percent

Cost of debt = Rd = 5 percent.

Marginal tax rate = 21 percent.

The given Cost of debt pre tax cost of debt hence we need to calculate post tax of debt with the help of below formula,

Post tax cost of debt = Cost of debt * (1-Marginal Tax rate)

Post tax cost of debt =5%*(1-0.21)

Post tax cost of debt =5% * 0.79

Post tax cost of debt = 3.95 %

->Formula to calculate the Weighted average cost of capital(WACC),

WACC = (Weight of debt * Post tax-Cost of Debt) + (Weight of equity * Cost of equity)

Weight of debt in total capital can be calculated using below formula,

Weight of debt = Total Debt/Total Capital

where, Total Debt = $1 Million

and Total Capital = Total Debt + Total Equity = ( $1 + $11.85) Million = $12.85 Million

Hence, Weight of debt = 1/12.85 = 0.07

and Weight of Equity = 1- Weight of debt =

= 1- 0.07

= 0.93

Lets Calculate WACC with the help of above formula,

WACC = (0.07 * 3.95%) + (0.93 * 8%)

WACC = 7.71%

3. What will the firm’s market value be after the announcement of the new debt issue?

Cuurent Value of the Firm = $11.85 Millions and Firm has issue new debt of $2 Millions to repurchase the shares $47.40 per share

Therefore, No of Shares Repurchase = Amount Paid / Share Price

= $2 Million/47.40

= 42,194

New Shares outstanding = Old Shares Oustanding - No of shares repurchase

= 250,000 - 42,194

= 207,806

H|ence, New market value = New Shares Outstanding * Share Price

= 207,806 * $47.40

= 9850004.4

Value of the Firm post announcement = $9.85 Million

4. What will the estimated new share price be after the capital structure change announcement?

Lets Calculate the P/E with the help of below given data and formula,

P/E = Share Price / Earning per share

Where, eps = earning per share = net income / shares outstanding

let us calculate the eps first,

Shares outstanding = 250,000

Current market value = $47.40 per share

EBIT = $1,250,000.

Debt outstanding = $1 million

Cost of equity = Re = 8 percent

Cost of debt = Rd = 5 percent.

Marginal tax rate = 21 percent.

To calculate Net Income, let us calculate PBT

PBT = EBIT - Interest

=1250000 - 62500(Debt*Pre tax cost of debt)

= 1187500

Net Income = PBT - Tax

= 1187500 - 249375(PBT*Tax Rate)

= 938125

Now, EPS = 938125/250000

= 3.75

Now, P/E = 47.40/3.75

= 12.64

Now post change is capital structure, firm is paying additional $110,000 towards interest payments,

hence, PBT = 1250000- 62500-110000

= 1077500

Net Income = PBT * ( 1-tax rate)

= 1077500*(1-0.21)

= 851225

lets divide new net income by new shares outstanding to get new eps which can be used to calculate share price with the help of old P/E

new EPS = 851225/207806

= 4.09

Multilpying above new EPS by P/E will provide the after capital structure share price,

New Share Price = 4.09 * 12.64

New Share Price = $ 51.77