Book Reviews, Valuation

Book Review: Valuation for Mergers, Buyouts and Restructuring

Book: Valuation for Mergers, Buyouts and Restructuring, by Enrique R. Arzac (Columbia University)

Review: Excellent book on valuation theory! Highly recommended!

Key Points:

  • Unlevered net income = net income + (1 – tax rate)*(interest expense – interest income)
  • Unlevered net income  + change in deferred taxes = net operating profit after tax (NOPAT)
  • NOPAT + depreciation – capex – increase in net working capital =Free cash flow
  • Net interest expense = interest expense – interest income
  • Since Net Income = (1 – tax rate)*(EBIT – net interest expense), unlevered net income = (1 – tax rate)*EBIT
  • Adjusting multiples for leverage
    • Definitions
      • delta = depreciation / sales
      • m = EBITDA / sales
      • d = Net debt / Enterprise Value
      • r = cost of Net Debt
      • t = corporate tax rate
      • M(ebitda) = Enterprise Value / EBITDA
      • M(p/e) = Value of Equity / Net income = [(1-d)*EV] / Net income
      • M(d) = Net Debt / EBITDA = d*M(ebitda)
      • Interest expense = r * Net Debt
      • Net Income = (1 – t)*(EBIT – r * Net Debt)
      • Net Debt = d*(M(p/e) * Net Income) / (1-d)
      • rho = cost of equity
    • Expressing one multiple in terms of the other
      • M(ebitda) = [(1 – delta/m)*M(p/e)] /[(1-d)/(1-t) + r*d*M(p/e)]
      • M(p/e) = [(1-d)*M(ebitda)]/[(1-t)*(1 – delta/m – r*d*M(ebitda))]
    • Value of Levered Firm = Net Debt + Equity = Equity(0) + t*(Net Debt) where Equity(0) is the value of equity of a firm with no leverage, and is equals to (1-t)*EBIT / rho = (1-t)*(1 – delta/m)*EBITDA / rho
    • Expressing multiples as a function of leverage (i.e. net debt multiple M(d))
      • M(ebitda) = (D+E)/EBITDA =[(1-t)(1-delta/m)EBITDA/rho + tD] / EBITDA = (1-t)(1-delta/m)/rho + t*M(d)
      • M(p/e) = Equity / Net Income = [Equity(0) – (1-t)D] / {(1-t)[(1-delta/m)EBITDA – rD]} = [rho^(-1) – M(d) * (1-delta/m)^(-1)] / [1 – rM(d) * (1-delta/m)^(-1)]
    • To use the multiple of firm A for firm B, first solve for the rho^(-1) for firm A, substitute that rho into the M(ebitda) and M(p/e) equations to use for firm B.
    • Normalising P/E ratios by growth rate
      • Forward P/E ratio: P/E1 = p/(k-g) where p is the dividend payout ratio, k is cost of equity, g is growth rate
      • For g = 0, (P/E1) = p/k, and p = k(P/E1)
      • Hence P/E1 = k(P/E1 when g = 0) / (k-g)
      • Finally we get P/E1 when g = 0, = P/E1 * (1 – g/k). This equation can remove growth from P/E ratios.
  • to- be-continued
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