Myoptic Optical is a levered no-growth firm with $1,400,000 debt outstanding. Fi
ID: 2733924 • Letter: M
Question
Myoptic Optical is a levered no-growth firm with $1,400,000 debt outstanding. Firm value is $2,277,500. The firm’s owner is currently contemplating whether to reduce its debt ratio to a more reasonable 40%. The firm will do so by issuing stock and retiring an equal amount of debt. The unlevered cost of equity is 16% and the cost of debt is 6%. The firm currently has 35,100 shares outstanding and the firm’s tax rate is 35%.
Required:
(a) What are Myoptic Optical’s current stock price and cost of levered (with debt)
equity?
(b) What is Myoptic Optical’s EBIT?
(c) What will be the new value of the firm after the recapitalization to a 40% debt ratio (Debt/Value) is announced?
(d) What is the firm’s stock price after it announces the change in capital structure?
(e) How many shares of stock must Myoptic Optical issue?
(f) What will be Myoptic Optical’s new cost of levered (with debt) equity after the recapitalization?
(g) What will Myoptic Optical’s new WACC be?
Explanation / Answer
a) Value of Levered Firm VL $2,277,500 Less: Market Value of Debt B $1,400,000 Equity $877,500 Shares Outstanding 35100 Current stock price = Equity/Shares outstanding = $877,500/35100 $25.00 Cost of levered Equity rS Cost of unlevered Equity r0 16.00% Pre-tax cost of debt for a levered firm rB 6.00% Equity(S) $877,500 Debt(B) $1,400,000 Tax Rate 35.00% Cost of levered Equity rs = r0 + (B/S)(r0 – rB)(1-tax) By MMII with taxes, rS =16%+(16% - 6%)(1 - .35)(1,400,000/877,500) 26.37% b) Modigliani-Miller Proposition I states that in a world with corporate taxes: VU = VL - TC*B VL = the value of a levered firm $2,277,500 VU = the value of an unlevered firm TC = the corporate tax rate 35.00% B = the value of debt in a firm’s capital structure $1,400,000 VU =VL – TC* B =2,277,500 – (.35)*1,400,000 $1,787,500 Value of Unlevered (VU) = EBIT x (1- tax)/Cost of unlevered equity VU =1,787,500=EBIT (1 - .35)/(.16) Solving For EBIT EBIT $440,000 c. value of debt B =40% * VL By MMI with taxes, VL =VU +.35B VL = $1,787,500 + 0.40*B*0.35 B=.4V L VL =1,787,500 + .35(.4)VL Value of levered VL $2,078,488.37
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