The valuation of NETWORKS LTD. was done by an investment Analyst. Based on an expected free cash flow of ₹54 million for the following year and an expected growth rate of 9%, the analyst has estimated the book value of t

Given: Expected Free Cash Flow (FCF) = ₹54 million Expected Growth Rate (g) = 9% = 0.09 Estimated Book Value of the firm = ₹1800 million Cost of Equity (Ke) = 20% = 0.20 Post-tax Cost of Debt (Kd) = 10% = 0.10 Market Value of Equity (MVE) = 3 * Book Value of Equity (BVE) Market Value of Debt (MVD) = 0.9 * Book Value of Debt (BVD) First, calculate the discount rate (r) used by the analyst: Firm Value = FCF / (r - g) 1800 = 54 / (r - 0.09) r - 0.09 = 54 / 1800 r - 0.09 = 0.03 r = 0.03 + 0.09 r = 0.12 or 12% This 'r' is the WACC calculated using book value weights. Let X be the book value weight of equity. WACC = (X * Ke) + ((1 - X) * Kd) 0.12 = (X * 0.20) + ((1 - X) * 0.10) 0.12 = 0.20X + 0.10 - 0.10X 0.12 - 0.10 = 0.10X 0.02 = 0.10X X = 0.02 / 0.10 X = 0.20 So, the book value weight of equity (BVE / (BVE + BVD)) is 0.20. This means the book value weight of debt (BVD / (BVE + BVD)) is 1 - 0.20 = 0.80. Ratio of Book Value of Debt to Book Value of Equity (BVD/BVE) = 0.80 / 0.20 = 4. Now, let's find the market value weights: Let BVE = 1 (for simplicity) Then BVD = 4 MVE = 3 * BVE = 3 * 1 = 3 MVD = 0.9 * BVD = 0.9 * 4 = 3.6 Total Market Value (MVE + MVD) = 3 + 3.6 = 6.6 Market Value Weight of Equity (W_e) = MVE / (MVE + MVD) = 3 / 6.6 ≈ 0.4545 Market Value Weight of Debt (W_d) = MVD / (MVE + MVD) = 3.6 / 6.6 ≈ 0.5455 Alternatively, using the provided solution's approach: Book value weight of equity (X) = 0.20 Book value weight of debt (1-X) = 0.80 Ratio of Debt/Equity (Book Value) = 0.8 / 0.2 = 4 Market value of equity is thrice its book value, so if BVE = 1, MVE = 3. Market value of debt is nine-tenths of its book value, so if BVD = 4, MVD = 0.9 * 4 = 3.6. Let's assume the total book value is 1. Then BVE = 0.2 and BVD = 0.8. Market Value of Equity (relative) = 0.2 * 3 = 0.6 Market Value of Debt (relative) = 0.8 * 0.9 = 0.72 Total Market Value (relative) = 0.6 + 0.72 = 1.32 Now, calculate the correct WACC using market value weights: WACC = ( (0.6 / 1.32) * 0.20 ) + ( (0.72 / 1.32) * 0.10 ) WACC = (0.454545 * 0.20) + (0.545455 * 0.10) WACC = 0.090909 + 0.0545455 WACC = 0.1454545 ≈ 0.1454 or 14.54% Finally, calculate the correct value of the firm: Firm Value = FCF / (WACC - g) Firm Value = 54 / (0.1454 - 0.09) Firm Value = 54 / 0.0554 Firm Value = ₹974.73 million (approximately) The solution provided in the document uses 0.1454 for WACC, leading to: Firm Value = 54 / (0.1454 - 0.09) = 54 / 0.0554 = ₹974.7 million.