ContentsProblemsProblem 9-18Problem 9-20Problem 9-21Problem 9-23Problem 9-24Problem 9-25Problem 9-26Table 9-1

Problem 9-18Problem 9-20Problem 9-21Table 9-1Problem 9-23Problem 9-24Problem 9-25Problem 9-26

9-18Problem 9-18Heavy Metal Corporation is expected to generate the following free cash flows over the next five years:Year12345FCF ($ million)5368787582After then, the free cash flows are expected to grow at the industry average of 4% per year. Using the discounted free cash flow model and a weighted average cost of capital of 14%:a.Estimate the enterprise value of Heavy Metal.b.If Heavy Metal has no excess cash, debt of $300 million, and 40 million shares outstanding, estimate its share price.Cost of capital14.00%Long-run growth rate4.00%Year12345FCF (millions)53.0068.0078.0075.0082.00Terminal Value820.00Total cash flow53.0068.0078.00895.00a.Enterprise Value681.37b.Debt300.00Equity value381.37Number of shares outstanding40Stock price9.53

9-20Problem 9-20Sora Industries has 60 million outstanding shares, $120 million in debt, $40 million in cash, and the following projected free cash flow for the next four years:Year01234Earnings and FCF Forecast ($ million)1Sales433.0468.0516.0547.0574.32Growth versus Prior Year8.1%10.3%6.0%5.0%3Cost of Goods Sold(313.6)(345.7)(366.5)(384.8)4Gross Profit154.4170.3180.5189.55Selling, General, and Administrative(93.6)(103.2)(109.4)(114.9)6Depreciation(7.0)(7.5)(9.0)(9.5)7EBIT53.859.662.165.28Less: Income Tax at 40%(21.5)(23.8)(24.8)(26.1)9Plus: Depreciation7.07.59.09.510Less: Capital Expenditures(7.7)(10.0)(9.9)(10.4)11Less: Increase in NWC(6.3)(8.6)(5.6)(4.9)12Free Cash Flow25.324.630.833.3a.Suppose Soras revenue and free cash flow are expected to grow at a 5% rate beyond year 4. If Soras weighted average cost of capital is 10%, what is the value of Soras stock based on this information?b.Soras cost of goods sold was assumed to be 67% of sales. If its cost of goods sold is actually 70% of sales, how would the estimate of the stocks value change?c.Lets return to the assumptions of part (a) and suppose Sora can maintain its cost of goods sold at 67% of sales. However, now suppose Sora reduces its selling, general, and administrative expenses from 20% of sales to 16% of sales. What stock price would you estimate now? (Assume no other expenses, except taxes, are affected.)d.Soras net working capital needs were estimated to be 18% of sales (which is their current level in year 0). If Sora can reduce this requirement to 12% of sales starting in year 1, but all other assumptions remain as in part (a), what stock price do you estimate for Sora? (Hint: This change will have the largest impact on Soras free cash flow in year 1.)Cost of Capital10.00%Long-run growth rate5.00%Cost of goods sold as a percent of sales67.00%Selling, General, and Administrative as a percent of sales20.00%Net working capital as a percent of sales18.00%Initial Value for Net Working Capital77.94Shares outstanding60Debt120.00Cash40.00Year01234Earnings and FCF Forecast ($ million)1Sales433.00468.00516.00547.00574.302Growth vs. Prior Year8.1%10.3%6.0%5.0%3Cost of Goods Sold(313.6)(345.7)(366.5)(384.8)4Gross Profit154.4170.3180.5189.55Selling, General, and Administrative(93.6)(103.2)(109.4)(114.9)6Depreciation(7.0)(7.5)(9.0)(9.5)7EBIT53.859.662.165.28Less: Income Tax at 40%(21.5)(23.8)(24.8)(26.1)9Plus: Depreciation7.07.59.09.510Less: Capital Expenditures(7.7)(10.0)(9.9)(10.4)11Less: Increase in NWC(6.3)(8.6)(5.6)(4.9)12Free Cash Flow25.324.630.833.3Terminal Value665.63Total Cash Flow25.3024.61696.41a.Enterprise value566.57Cash40.00Debt120.00Number of shares60.00Stock price8.11b.Cost of goods sold as a percent of salesStock PriceBase case of 67%8.1170.00%5.14c.Selling, general and administrative as a percent of salesStock PriceBase case of 20%8.1116.00%12.07d.Net working capital as a percent of salesStock PriceBase case of 18%8.1112.00%9.01Extension: Both COGS and Selling, general and administrative change8.1116.00%70.00%9.10Extension: Both COGS and Net working capital change8.1112.00%70.00%6.04Extension: Both Selling, general and administrative and net working capital change8.1116.00%12.00%12.97

Excel note: Parts b, c, and d can also be done in two dimensional tables to see the effects of simultaneous changes in two inputs. See below. To change more than two, you should use a software add-in.

9-21Problem 9-21Consider the valuation of Kenneth Cole Productions in Example 9.7.a.Suppose you believe KCPs initial revenue growth rate will be between 7% and 11% (with growth slowing in equal steps to 4% by year 2011.) What range of share prices for KCP is consistent with these forecasts?b.Suppose you believe KCPs EBIT margin will be between 7% and 10% of sales. What range of share prices for KCP is consistent with these forecasts (keeping KCP's initial revenue growth at 9%)?c.Suppose you believe KCPs weighted average cost of capital is between 10% and 12%. What range of share prices for KCP is consistent with these forecasts (keeping KCP's initial revenue growth and EBIT margin at 9%)?d.What range of share prices is consistent if you vary the estimates as in parts (a), (b), and (c) simultaneously?Kenneth Cole ProductionsCost of Capital11.00%Year2005200620072008200920102011FCF Forecast ($millions)1Sales518.00564.62609.79652.47691.62726.20755.252growth vs. prior year9.00%8.00%7.00%6.00%5.00%4.00%3EBIT9.00%of sales50.854.958.762.265.468.04Less: Income Tax37.00%of EBIT(18.8)(20.3)(21.7)(23.0)(24.2)(25.1)5Less: Net Investment8.00%of sales(3.7)(3.6)(3.4)(3.1)(2.8)(2.3)6Less: Increase in NWC10.00%of sales(4.7)(4.5)(4.3)(3.9)(3.5)(2.9)7Free Cash Flow23.6226.4429.3132.1734.9537.598Terminal Value558.549PV of Free Cash Flows424.8310Value of Cash100.0011Value of Debt3.0012Number of Shares2113Share price24.85a.If Initial Revenue Growth Rate can vary between 4% and 11%, the stock price can vary between22.86and25.70b.If EBIT Margin can vary between 7% and 10%, the stock price can vary between19.59and27.48c.If Weighted Average Cost of Capital can vary between 10% and 12%, stock price can vary between22.24and28.34d.If all three of the above can vary, the stock price can vary between16.54and32.62Initial Revenue Growth RateEBIT MarginWeighted Average Cost of CapitalBase Case Stock Price24.85Base Case24.85Base Case24.854.00%22.867.00%19.5910.00%28.344.18%22.937.15%19.9810.10%27.944.35%22.997.30%20.3810.20%27.554.53%23.067.45%20.7710.30%27.174.70%23.137.60%21.1710.40%26.814.88%23.197.75%21.5610.50%26.465.05%23.267.90%21.9510.60%26.125.23%23.338.05%22.3510.70%25.795.40%23.408.20%22.7410.80%25.465.58%23.478.35%23.1410.90%25.155.75%23.538.50%23.5311.00%24.855.93%23.608.65%23.9311.10%24.556.10%23.678.80%24.3211.20%24.276.28%23.748.95%24.7211.30%23.996.45%23.819.10%25.1111.40%23.726.63%23.889.25%25.5111.50%23.466.80%23.959.40%25.9011.60%23.206.98%24.029.55%26.3011.70%22.957.15%24.099.70%26.6911.80%22.707.33%24.169.85%27.0911.90%22.477.50%24.2310.00%27.4812.00%22.247.68%24.307.85%24.378.03%24.458.20%24.528.38%24.598.55%24.668.73%24.738.90%24.819.08%24.889.25%24.959.43%25.039.60%25.109.78%25.189.95%25.2510.13%25.3210.30%25.4010.48%25.4710.65%25.5510.83%25.6311.00%25.70Worst case scenario:Initial Revenue Growth is 4%, initial EBIT margin is 7%, and initial WACC is 12%:Cost of Capital12.00%Kenneth Cole ProductionsYear2005200620072008200920102011FCF Forecast ($millions)1Sales518.00538.72560.27582.68605.99630.23655.442growth vs. prior year4.00%4.00%4.00%4.00%4.00%4.00%3EBIT7.00%of sales37.739.240.842.444.145.94Less: Income Tax37.00%of EBIT(14.0)(14.5)(15.1)(15.7)(16.3)(17.0)5Less: Net Investment8.00%of sales(1.7)(1.7)(1.8)(1.9)(1.9)(2.0)6Less: Increase in NWC10.00%of sales(2.1)(2.2)(2.2)(2.3)(2.4)(2.5)7Free Cash Flow20.0320.8321.6622.5323.4324.378Terminal Value316.779PV of Free Cash Flows250.3510Value of Cash100.0011Value of Debt3.0012Number of Shares2113Share price16.54Best Case Scenario:Initial Revenue Growth is 11%, initial EBIT margin is 10%, and iniitial WACC is 10%:Cost of Capital10.00%Kenneth Cole ProductionsYear2005200620072008200920102011FCF Forecast ($millions)1Sales518.00574.98630.18681.85728.22767.54798.242growth vs. prior year11.00%9.60%8.20%6.80%5.40%4.00%3EBIT10.00%of sales57.563.068.272.876.879.84Less: Income Tax37.00%of EBIT(21.3)(23.3)(25.2)(26.9)(28.4)(29.5)5Less: Net Investment8.00%of sales(4.6)(4.4)(4.1)(3.7)(3.1)(2.5)6Less: Increase in NWC10.00%of sales(5.7)(5.5)(5.2)(4.6)(3.9)(3.1)8Free Cash Flow25.9729.7733.6637.5341.2844.769Terminal Value775.8910PV of Free Cash Flows588.0011Value of Cash100.0012Value of Debt3.0013Number of Shares2114Share price32.62

Notice that the cells that calculate the future growth rates must be a function of the initial growth rate. Otherwise, only the initial growth rate will be varied in the Data Table.

9-23Problem 9-23Suppose that in January 2006, Kenneth Cole Productions had EPS of $1.65 and a book value of equity of $12.05 per share.EPS1.65Book value of equity12.05a.Using the average P/E multiple in Table 9.1, estimate KCPs share price.Price per share24.77b.What range of share prices do you estimate based on the highest and lowest P/E multiples in Table 9.1?Range based on highest to lowestHigh37.32Low14.29c.Using the average price to book value multiple in Table 9.1, estimate KCPs share price.Price per share34.22d.What range of share prices do you estimate based on the highest and lowest price to book value multiples in Table 9.1?Range based on highest to lowestHigh97.73Low13.50

9-24Problem 9-24Suppose that in January 2006, Kenneth Cole Productions had sales of $518 million, EBITDA of $55.6 million, excess cash of $100 million, $3 million of debt, and 21 million shares outstanding.Sales518.00EBITDA55.60Cash100.00Debt3.00Shares outstanding21a.Using the average enterprise value to sales multiple in Table 9.1, estimate KCPs share price.Price per share30.77b.What range of share prices do you estimate based on the highest and lowest enterprise value to sales multiples in Table 9.1?Range based on highest to lowestHigh58.64Low16.21c.Using the average enterprise value to EBITDA multiple in Table 9.1, estimate KCPs share price.Price per share27.10d.What range of share prices do you estimate based on the highest and lowest enterprise value to EBITDA multiples in Table 9.1?Range based on highest to lowestHigh33.08Low22.25

9-25Problem 9-25In addition to footwear, Kenneth Cole Productions designs and sells handbags, apparel, and other accessories. You decide, therefore, to consider comparables for KCP outside the footwear industry.Kenneth Cole informationEPS1.65EBITDA55.60Cash100.00Debt3.00Shares outstanding21a.Suppose that Fossil, Inc., has an enterprise value to EBITDA multiple of 9.73 and a P/E multiple of 18.4. What share price would you estimate for KCP using each of these multiples, based on the data for KCP in Problems 23 and 24?FossilmultiplepriceEBITDA9.7330.38P/E18.4030.36Thus, KCP is trading at a discount relative to Fossil.b.Suppose that Tommy Hilfiger Corporation has an enterprise value to EBITDA multiple of 7.19 and a P/E multiple of 17.2. What share price would you estimate for KCP using each of these multiples, based on the data for KCP in Problems 23 and 24?Tommy HilfigermultiplepriceEBITDA7.1923.66P/E17.2028.38Thus, KCP is trading at a premium relative to Tommy Hilfiger using EV/EBITDA, but a slight discount using P/E.

9-26Problem 9-26Consider the following data for the airline industry in early 2009 (EV = enterprise value, BV = book value,NM = not meaningful because divisor is negative). Discuss the usefulness of using multiples to value an airline.Company NameMarket CapEVEV/SalesEV/EBITDAEV/EBITP/EP/BookDelta Air Lines4,799.6016,887.600.715.0NMNMNMAMR Corp.1,296.508,743.500.417.5NMNMNMJetBlue Airways1,246.903,834.901.110.425.7NM1.0xContinental Airlines1,216.804,506.800.314.7NMNMNMUAL Corp.7016,192.000.3NMNMNMNMAir Tran Holdings651.31,354.700.521.7NMNM2.3SkyWest588.71,699.700.53.87.56.50.5Hawaiian257.1262.10.21.72.73.6NMPinnacle Airlines44699.70.86.610.13.41.0Average0.5311.4311.504.501.27Median0.5012.558.803.601.00Max Value1.1021.7025.706.502.30Min Value0.201.702.703.400.50Standard Deviation0.297.009.951.730.93Many of the cases are not meaningful, because the earnings are negative or even (in several cases) the book value of equity is negative.There is a wide variation between low and high values.There must be more to valuation than what is revealed by the multiples.

Table 9-1Table 9-1Stock Prices and Multiples for the Footwear Industry, January 2006TickerNameStock Price ($)Market Capitalization ($ millions)Enterprise Value ($ millions)P/EPrice/BookEnterprise Value/SalesEnterprise value/EBITDANKENike84.221,83020,51816.643.591.438.75PMMAYPuma AG312.055,0884,59314.995.022.199.02RBKReebok58.723,5143,45114.912.410.98.58WWWWolverine World Wide22.11,2571,25317.422.711.29.53BWSBrown Shoe43.368001,01922.621.910.479.09SKXSketchers17.0968361417.632.020.626.88SRRStride Rite13.749752420.721.870.899.28DECKDeckers Outdoor30.0537336713.322.291.487.44WEYSWeco Group19.923022611.971.751.066.66RCKYTocky Shoes & Boots19.961062328.661.120.927.55DFZR.G. Barry Corp.6.8368929.28.110.8710.75BOOTLaCross Footwear10.4627512.091.280.768.3Average15.012.841.068.49Maximum51%186%106%27%Minimum-42%-61%-56%-22%