# Constant growth of FCFE

John Hopkins is the Senior Portfolio Manager for the Far East Fund. He has asked Shirley Reynolds to meet with him to discuss the valuation of several stocks that he has been tracking over the last few weeks. Earlier that week, Shirley met with the CFO of ToyCo to discuss his company. The CFO provided Shirley with the following information about his firm: Estimated Earnings 2003 2004 2005 EPS 1.00 1.12 1.25 Depreciation (000’s) 200 224 251 Capital Expenditures (000’s) 300 336 376 Number of shares Outstanding 2 million Debt outstanding 0 The CFO also informed Shirley that the cost of equity capital is 14% and that they expect earnings, depreciation, and capital expenditures for 2006 and beyond to average 4%. Question: Shirley calculates the constant growth of FCFE. The average constant growth rate in FCFE is closest to: a) 12.0% b) 11.0% c) 12.8% d) 11.8%

Answer: Shirley calculates the constant growth of FCFE. The average constant growth rate in FCFE is closest to: incorrect You chose: 11.0% Correct answer: 11.8% Rationale: We will need to calculate the FCFE for 2004 and 2005 and then calculate the trend for 2003 to 2004 and 2004 to 2005. We will then average the two rates. Free Cash Flow to Equity 2003, from prior question = 1,900 Free Cash Flow to Equity 2004: FCFE = Number of Shares × Net income - (Capital Expenditures - Depreciation) × (1 - % of debt) FCFE = 2 million shares x 1.12 EPS - (336 - 224) x 1 = 2,240 - 112 = 2,128 Free Cash flow to Equity 2005: FCFE = Net income - (Capital Expenditures - Depreciation) × (1 - % of debt) FCFE = 2 million shares x 1.25 EPS - (376 - 251) x 1 = 2,240 - 112 = 2,375 These next few steps are really for illustrative purposes as you can see that 12% and 11.61% roughly equal 11.8% in your head… The 2003 to 2004 trend: FCFE growth = (2,128 - 1,900) / 1,900 = 12% The 2004 to 2005 trend: FCFE growth = (2,375 - 2,128) / 2,128 = 11.61% Average FCFE growth: Average FFE = (12% + 11.61%)/2 Average FCFE = 11.8% Question ID: 37653

My question: Why the [edited for profanity] do they use the arithmetic average rather than the geometric average. A geometric average gets you to 11.803%

1900 2128 2375 0.12 0.116071429 This is the geometric average. 0.125 This is the arithmetic average. 2375/1900 all /2 The average of the two years is 11.803. The average they are asking for is the average of two “numbers”, or the average of the geometric growth rates. There is only 1 way to take the average of two numbers…I had to look at it for a second, but I think you read into it too much. Hope this helps.

I agree w/ malnoll. Q asks for the avg growth rate OVER a 3 yr period (i.e. avg of yr 1 to yr 2 and yr 2 to yr 3)) not the growth from yr 1 to yr 3. Hope this helps.

^^ditto But either way… Year 2003 2004 2005 FCFE 1900 2128 2375 ((2375/1900)^0.5) - 1 = 11.8% D