FIN 350 Business Finance Homework 7 Fall 2014 Solutions 1. Home Builder Supply, a retailer in the home improvement industry, currently operates seven retail outlets in Georgia and South Carolina. Management is contemplating building an eighth retail store across town from its most successful retail outlet. The company already owns the land for this store, which currently has an abandoned warehouse located on it. Last month, the marketing department spent $10,000 on market research to determine the extent of customer demand for the new store. Now, Home Builder Supply must decide whether to build and open the new store. Which of the following costs should be included in Home Builder Supply s analysis? (a) The cost of the land where the store will be located. No, this is a sunk cost since the company already owns the land. (b) The value of the land if sold. Yes, this is the opportunity cost of not selling the land. (c) The cost of demolishing the abandoned warehouse and clearing the lot. Yes, this is a cost that is incurred if the project is undertaken. (d) The loss of sales in the existing retail outlet if customers switch stores. Yes, this is a side effect (erosion). (e) The $10,000 in market research spent to evaluate customer demand. No, this is a sunk cost that was incurred last month. (f) Construction costs for the new store. Yes, this is a capital expenditure. (g) Interest expense on the debt borrowed to pay the construction costs. No, this is a financing cost. 2. The Jones Company has just completed the third year of a five-year MACRS recovery period for a piece of equipment that it originally purchased for $300,000. (a) What is the book value of the equipment? Using a five-year MACRS recovery period, the depreciation charge and remaining book value is detailed in the table below: Year 1 2 3 4 5 6 MACRS schedule: 20.00% 32.00% 19.20% 11.52% 11.52% 5.76% Deprecation expense: $60,000 $96,000 $57,600 $34,560 $34,560 $17,280 Remaining book value: $240,000 $144,000 $86,400 $51,840 $17,280 $0
The depreciation expense is calculated by multiplying the cost of the equipment by the MACRS schedule for the current year. The remaining book value is the previous year s book value minus the current year s depreciation. In year 1, the remaining book value is $300, 000 $60, 000 = $240, 000. (b) If Jones sells the equipment today for $180,000 and its tax rate is 35%, what is the after-tax cash flow from selling it? The after-tax cash flow from selling the equipment is: after-tax cash flow = selling price tax rate (selling price book value) = $180, 000 0.35 ($180, 000 $86, 400) = $147, 240 3. Over the past two years, your company designed a smartphone at a cost of $2 million. Now, you are deciding whether to produce the smartphone that you developed. You estimate that you will sell 100,000 units per year for $200 per phone for three years and then shut down production. The variable costs of producing each phone will be $150 per unit. You will use existing equipment for production, which has a book value of $1,000,000 and a market value of $2,500,000. The existing equipment would be depreciated completely in year 1. You will also need to purchase additional equipment for $3,000,000. The new equipment would be depreciated on a 3-year straight line basis to zero. Your company s current level of capital is $200,000. The new product will require the working capital to increase to a level of $300,000 today. Working capital will increase to $350,000 in year 1, then decrease to $300,000 in year 2, and finally to $200,000 in year 3. Your discount rate is 9% and your tax rate is 35%. Compute the incremental free cash flows and compute the NPV of producing the smartphone. The cost for designing the smartphone is a sunk cost and not included in the incremental cash flow below. Revenue for this project is $20,000,000 per year (100,000 units * $200 revenue per phone) and the costs are $15,000,000 per year (100,000 units * $150 costs per phone). The existing equipment has a book value of $1,000,000, which is included in the depreciation for year 1. The cash flow from potentially selling the existing equipment is: selling price (selling price book value)(tax rate) = $2, 500, 000 ($2, 500, 000 $1, 000, 000)(0.35) = $1, 975, 000 This is the after-tax opportunity cost of using the existing equipment. New equipment costs $3,000,000 in year 0. Depreciation for the new equipment is $1,000,000 per year, based on 3-year straight-line depreciation. The cash flow from the change in net working capital is given in the last row: Time Without Project 0 1 2 3 Levels $200,000 $300,000 $350,000 $300,000 $200,000 Change +$100,000 +$50,000 $50,000 $100,000 Cash Flow $100,000 $50,000 +$50,000 +$100,000 2
Using the details above, the free cash flow (FCF) can be calculated, as in the table below: Time 0 1 2 3 Revenue 0 $20,000,000 $20,000,000 $20,000,000 Costs 0 $15,000,000 $15,000,000 $15,000,000 Depreciation 0 $2,000,000 $1,000,000 $1,000,000 = Taxable Income 0 $3,000,000 $4,000,000 $4,000,000 Taxes 0 $1,050,000 $1,400,000 $1,400,000 + Depreciation 0 $2,000,000 $1,000,000 $1,000,000 Cap. Ex. $3,000,000 0 0 0 Opportunity Cost $1,975,000 0 0 0 Changes in NWC $100,000 $50,000 $50,000 $100,000 Free Cash Flow $5,075,000 $3,900,000 $3,650,000 $3,700,000 Using the free cash flows from above, let s calculate the NPV of the project: NPV = $5, 075, 000 + = $4, 432, 192.50 $3, 900, 000 1.09 + $3, 650, 000 $3, 700, 000 (1.09) 2 + (1.09) 3 Since the NPV is positive, your company should take the project. 4. Tablet Computers (TC), a private company, has 500,000 outstanding bonds with a $1,000 face value. The coupon rate for its bonds is 5% and coupons are paid annually. The bonds mature in 4 years and have a YTM spread of 340 basis points above the 4-year Treasury note. The yield on the 4-year Treasury note is 2%. The value of TC s equity is $1.24 billion and its tax rate is 34%. Three comparable firms to TC are provided in the table below. What is the equity (levered) beta for TC? First, let s fill in the last three rows of the table below, using the formulas provided. Apple Microsoft Cisco Enterprise value (EV) $2.3B $4B $1.2B Equity value $1.7B $2.5B $0.9B Equity beta 0.93 0.89 1.33 Debt = EV equity value $0.6B $1.5B $0.3B D/E = debt / equity 0.353 0.600 0.333 β Assets = β Equity / (1 + (1 - t)*d/e)) 0.754 0.638 1.090 The average asset beta across the three comparable firms is: 0.754 + 0.638 + 1.090 β Assets,mean = 3 = 0.827 Now, let s find the market value of TC s debt. The yield-to-maturity is 2% + 3.4% = 5.4% and the annual coupon payments are $50 (5% $1, 000). Then, the price of a bond is: $50 1.054 + $50 (1.054) 2 + $50 $1, 050 + (1.054) 3 (1.054) 4 = $985.95 3
Then, the market value of TC s debt is the number of outstanding bonds multiplied by the price of a bond: 500, 000 $985.95 = $492.9M. Next, the debt-to-equity ratio for TC is: = 0.398. Lastly, the equity (levered) beta for TC is: D E = $492.9M $1,240M β Equity = β Assets,mean (1 + (1 t) D/E) = 0.827 (1 + (1 0.34) 0.398) = 1.044 5. Paccar Inc. is currently comprised of 75% equity and 25% debt. Its bond rating is A, the yield-to-maturity for its bonds is 5.5%, and its equity (levered) beta is 1.1. Assume that the risk-free rate is 3%, the expected return on the market portfolio is 10%, and the corporate tax rate is 34%. Find the WACC of Paccar if the firm raises its debt to 35% and if the firm lowers its debt to 15%. The yield-to-maturity of its bonds is 5% if it lowers its debt to 15% and the yield-to-maturity of its bonds is 6% if it raises its debt to 35%. How does its current WACC compare to its WACC with more or less debt? First, let s find the asset beta for Paccar: β Assets = β Equity /(1 + (1 t) D/E) = 1.1/(1 + (1 0.34) (0.25/0.75)) = 0.902 Now, let s find the equity beta for the decrease and increase in debt: β Equity,15% = β Assets (1 + (1 t) D/E) = 0.902 (1 + (1 0.34) (0.15/0.85)) = 1.007 β Equity,35% = β Assets (1 + (1 t) D/E) = 0.902 (1 + (1 0.34) (0.35/0.65)) = 1.222 Next, let s find the cost of equity for debt at 15%, 25% and 35%: r E,15% = r f + β Equity,15% (E[r M ] r f ) = 0.03 + 1.007 (0.10 0.03) = 0.100 r E,25% = r f + β Equity,25% (E[r M ] r f ) = 0.03 + 1.1 (0.10 0.03) = 0.107 r E,35% = r f + β Equity,35% (E[r M ] r f ) = 0.03 + 1.222 (0.10 0.03) = 0.116 4
Lastly, let s compute the WACC for debt at 15%, 25% and 35%: r W ACC,15% = r E,15% E% + r D,15% (1 T C )D% = 0.100 0.85 + 0.05 (1 0.34) 0.15 = 0.090 r W ACC,25% = r E,25% E% + r D,25% (1 T C )D% = 0.107 0.75 + 0.055 (1 0.34) 0.25 = 0.089 r W ACC,35% = r E,35% E% + r D,35% (1 T C )D% = 0.116 0.65 + 0.06 (1 0.34) 0.35 = 0.08896 The current WACC of 8.9% decreases to 8.896% when debt increases from 25% to 35%. 6. You are recently hired as an analyst for Foster Research. The first project that you are given is to value the stock of Seattle Technologies (ST). ST has both equity and debt in its capital structure. The company has 20 million common shares outstanding and its debt has a market value of $500 million with a yield-to-maturity of 7%. ST s target capital structure has 25% debt and 75% equity. ST s cash flow data for the past 12 months is summarized below: Financials Value, $mil EBITDA 200 EBIT 150 Capital expenditures 14 Changes in net working capital 7 The forecast of free cash flows is detailed below: Years 0 1 2 3 4 Steady State FCF growth rate N/A 10% 8% 7% 5% 2% growth forever Portland Electronics is the only comparable peer company. This company has an enterprise value of $350 million, its market value of equity is $200 million and a levered beta of 1.7. Assume that the tax rate for all companies is 35%, the risk-free rate is 3% and the market risk premium is 8%. Using the discounted cash flow method, what is the price per share of ST? First, let s calculate Seattle Technologies (ST) free cash flow over the past 12 months: Financials Value, $mil EBITDA 200 EBIT 150 Taxes on EBIT of 35% 52.5 + Depreciation/Amortization +50 Capital expenditures 14 Increase in NWC 7 Free cash flow 126.5 5
Next, let s find ST s weighted average cost of capital, which we will use to discount its future cash flows. Unlevering Portland Electronics beta, we find that: β lev β unlev = 1 + (1 t) D/E 1.7 = 1 + (1 0.35) (350 200)/200 = 1.143 Levering based on ST s target capital structure, we find that: β lev = (peer β unlev ) (1 + (1 t) D/E) = 1.143 (1 + (1 0.35) 0.25/0.75) = 1.390 Using the CAPM, we can find ST s cost of equity: E[r ST ] = r f + β ST (E[r m ] r f ) = 0.03 + 1.390 0.08 = 0.141 The cost of debt for ST is 7%. Then, using the WACC, we find that: W ACC ST = w E r E + w D r D (1 t) = 0.75 0.141 + 0.25 0.07 (1 0.35) = 0.117 Next, using the free cash flow calculated above and the FCF growth rate, let s find future FCFs: Years 0 1 2 3 4 FCF growth rate N/A 10% 8% 7% 5% Nominal FCF, $mil 126.50 139.15 150.28 160.80 168.84 The terminal value (TV) in year 4 is: ( ) 1 + g T V 4 = F CF 4 r g ( ) 1 + 0.02 = 168.84 0.117 0.02 Then, the enterprise value (EV) of ST is: = $1, 769.91 mil EV = P V (F CF s) + P V (T V ) = 139.15 1.117 + 150.28 (1.117) 2 + 160.80 (1.117) 3 + 168.84 1, 769.91 + (1.117) 4 (1.117) 4 = $1, 604.26 mil 6
Then, the value of ST s equity is: Lastly, the price per share of ST is: Value of equity = EV market value of debt = 1, 604.26 500 = $1, 104.26 mil market value of equity Price per share = shares outstanding 1, 104.26 mil = 20 mil = $55.21 7. Bob s Diner has 1 million shares. Its estimated free cash flows per share are: 2015 2016 2017 $5.00 $5.50 $6.00 5% growth forever (a) If your discount rate for Bob s Diner s stock is 10%, what is your estimate of its price per share? (You expect to receive the first dividend one year from today.) The estimate of its price per share using discounted cash flow valuation is: P 0 = $5.00 (1 + 0.10) + $5.50 (1 + 0.10) 2 + $6.00 0.10 0.05 = $108.26 ( ) 1 (1 + 0.10) 2 (b) Bob s Diner has an EBITDA of $8 million in 2015. You notice that Bob s Diner s competitor, Pat s Cafe, has an EBITDA of $50 million in 2015 and an enterprise value of $300 million. Assume that Bob s Diner and Pat s Cafe have no debt. Based on the information above, what would you expect Bob s Diner s price per share to be? Using multiple-based valuation, EBITDA is the selected value driver for Bob s Diner. The peer group is Pat s Cafe. The valuation multiple for Pat s Cafe is: EV = $300 } EBIT {{ DA} $50 Pat s Cafe = 6 Then, the enterprise value of Bob s Diner is: EV Bob s Diner = EBIT DA Bob s Diner 6 = $8 6 = $48 This shows that the enterprise value of Bob s Diner is $48 million. Since there are 1 million shares, then Bob s Diner s price is: $48 million / 1 million = $48. 7
(c) What might explain the difference between your two estimates of Bob s Diner s price per share? Multiple-based valuation assumes that both companies are exactly alike in their growth prospects, risk, customers, etc. and it only provides an estimate for Bob s Diner s stock price. It appears that the market expects more growth from Bob s Diner than from Pat s Cafe. 8