EM & Valuation Assignment 1

(a) What is GSB Inc’s ROE for 2015? ROE = Net Income / Beginning Shareholders’ Equity = $25/$100 = 0.25 (25%) An ROE of 25% is exceptionally high, suggesting GSB Inc. has a strong competitive advantage or “moat”. (b) If GSB Inc. continues to earn the same ROE, what would be its Net Income in 2016? To calculate the 2016 Net Income, we first need to find the Beginning Equity for 2016, which is the same as the Ending Equity of 2015. Find 2015 Ending Equity: End Equity = Beg. Equity + Net Income – Dividends = $100 + $25 -$10 = $115 million Calculate 2016 Net Income: Net Income 2016 = Beg. Equity 2016 * ROE = $115 * 0.25 = $28.75 million (c) If GSB Inc. continues the same payout ratio, how much dividends would it pay in 2016? To find the 2016 dividend, we must first determine the Dividend Payout Ratio from 2015. Calculate 2015 Payout Ratio: Payout Ratio = Dividend Paid / Net Income = $10 / $25 = 0.4 (40%) Calculate 2016 Dividend: Dividend 2026 = Net Income 2016 * Payout Ratio = $28.75 * 0.4 = $11.5 million (d) How much has the Shareholders’ Equity, Net Income, and Dividend increased from 2015 to 2016 in terms of percentage growth? We compare the results we calculated for 2016 against the given 2015 data. Growth in Shareholders’ Equity: (Equity 2016 – Equity 2015) / Equity 2015 = (115-100)/100 = 0.15 (15%) Growth in Net Income : (NI 2016 – NI 2015) / NI 2015 = (28.75-25)/25 = 0.15 (15%) Growth in Dividends: (Div 2016 – Div 2015) / Div 2015 = (11.5-10)/10 = 0.15 (15%) (e) Compute the following: retention ratio * ROE. How does it compare to the growth rates you computed in (d)? First, we define the retention ratio (b), which is the portion of earnings kept in the business. Retention Ratio ( b ): 1 – Payout Ratio = 1 – 0.4 = 0.6 (60%) Calculation: b * ROE = 0.6 * 0.25 = 0.15 (15%) Comparison: This matches the 15% growth rate calculated in part (d) exactly. This confirms the Sustainable Growth Rate formula: g = b * ROE (f) If you believe GSB Inc. will perform this way indefinitely, what is your estimate of the value of its equity as of the end of 2015? Assume the required return (r) is the same as the ROE (25%). We use the Gordon Growth Model (GGM) to find the intrinsic value. Formula: V0 = D1 / (r-g) Inputs: D1 (Dividend in 2016) = $11.50 (from part c). r (Required Return) = 25% (given as equal to ROE). g (Growth Rate) = 15% (from part e). Calculation: V0 = 11.5 / (0.25 – 0.15) = $115 million (g) Suppose GSB Inc., starting in 2016, decides to pay NO dividends and reinvest all earnings. Assume ROE remains 25%. What is the 2016 Net Income, Shareholders' Equity, and the Earnings Growth Rate? To solve this, we must recognize that the performance in 2016 is still based on the capital available at the beginning of 2016. 2016 Beginning Shareholders' Equity: As calculated in Part 1, the 2015 ending equity is $115.00 million. 2016 Net Income: Net Income = Beg. Equity * ROE = 115 * 0.25 = $28.75 million 2016 Ending Shareholders' Equity: Under the new policy, Dividends = $0. End Equity = Beg. Equity + Net Income – Dividends 115 + 28.75 – 0 = $143.75 million Earnings Growth Rate (2015 to 2016): (NI 2016 – NI 2015) / NI 2015 = (28.75 – 25)/25 = 15% While the growth from 2015 to 2016 is 15%, the new sustainable growth rate (g) for 2017 and beyond has changed. New Retention Ratio (b) = 1.0 (100%). N ew g = b * ROE = 1 * 0.25 = 25% (h) In the case of (g), how would you estimate the value of the equity for GSB Inc.? If GSB Inc. pays no dividends (D1 = 0), the standard Gordon Growth Model (V0 = D1/(r-g)) appears to result in a value of zero. However, we know the firm has assets and earnings. To value this Zero-Dividend firm, we use the Earnings-Based Valuation (PVGO) Model. The No-Growth Component: If the firm paid out all its expected 2016 earnings (E1 = $28.75M) as dividends Value = E1/r = 28.75/025 = $115 million . The Growth Component (PVGO): As we discussed in Topic 4, PVGO is created only when ROE > r Since the firm is earning exactly its cost of capital, the Net Present Value (NPV) of its future reinvestments is zero. Therefore, PVGO = 0. Total Value: V0 = Value of Assets in Place + PVGO = 115 + 0 = $115 million. Conclusion: The value of the equity remains $115.00 million, exactly the same as in part (f). Final Summary: If ROE > r: Reinvesting (lower dividends) increases firm value If ROE < r: Reinvesting (lower dividends) decrease firm value If ROE = r: Reinvesting has no effect on firm value