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Investment and Risk Management 2020- Tutorial 11 answers – Equity Valuation III
- The effects are as follows:
- The solution is as follows: A. Free cash flow to the firm, found with Equation 7, is FCFF=NI+NCC+Int(1−Taxrate) −FCInv−WCInvFCFF=285+180+130(1−0.40)−349−(39+44−22−23)FCFF=285+180+78−349−38=$ million B. Free cash flow to equity, found with Equation 10, is FCFE=NI+NCC−FCInv−WFCInv+NetborrowingFCFE=285+180−349−(39+44−22−23)+(10+40)FCFE =285+180−349−38+50=$128million C. To find FCFE from FCFF, one uses the relationship in Equation 9: FCFE=FCFF−Int(1−Taxrate) +NetborrowingFCFE=156−130(1−0.40)+(10+40)FCFE=156−78+50=$128million
- The firm value using the FCFF approach is the present value of FCFF discounted at WACC: V (^) F =
FCF F 1
rWACC − g
1.7 × 1.
= $ 45.475 billion The market value of the equity is the firm value less market value of debt: V (^) E = $ 45.475 billion − $ 15.0 billion = $ 30.475 billion The equity value using the FCFE approach is the present value of FCFE discounted at CAPM: V (^) E =
FCF E 1
rCAPM − g
1.3 × 1.
= $ 25.409 billion
- The required rate of return found with the CAPM is r=E(Ri)=RF+βi[E(RM)−RF]=6.4%+2.1(5.0%)=16.9% The following table shows the values of sales, net income, capital expenditures less depreciation, and investments in working capital. FCFE equals net income less the investments financed with equity: FCFE=Netincome−(1−DR)(Capitalexpenditures−Depreciation)−(1−DR) (Investmentinworkingcapital) where DR is the debt ratio (debt financing as a percentage of debt and equity). Because 20 percent of net new investments are financed with debt, 80 percent of the investments are financed with equity, which reduces FCFE by 80 percent of (Capital expenditures – Depreciation) and 80 percent of the investment in working capital. For a $100 increase in: Change in FCFF (in US Dollars) Change in FCFE (in US Dollars) A. Net income +100 + B. Cash operating expenses –60 – C. Depreciation +40 + D. Interest expense 0 – E. EBIT +60 + F. Accounts receivable –100 – G. Accounts payable +100 + H. Property, plant, and equipment –100 – I. Notes payable 0 + J. Cash dividends paid 0 0 K. Proceeds from new shares issued 0 0 L. Share repurchases 0 0
(All Data in Billions of US Dollars) 2018 2019 2020 2021 2022 Sales (growing at 28%) 5.500 7.040 9.011 11.534 14. Net income = 32% of sales 1.760 2.253 2.884 3.691 4. FCInv – Dep = (35% – 9%) × Sales 1.430 1.830 2.343 2.999 3. WCInv = (6% of Sales) 0.330 0.422 0.541 0.692 0. 0.80 × (FCInv – Dep + WCInv) 1.408 1.802 2.307 2.953 3. FCFE = NI – 0.80 × (FCInv – Dep + WCInv)
PV of FCFE discounted at 16.9% 0.301 0.330 0.361 0.395 0. Terminal stock value 85. PV of terminal value discounted at 16.9% 38. Total PV of FCFE 1. Total value of equity 40. The terminal stock value is 18.0 times the earnings in 2013, or 18 × 4.724 = $85.03 billion. The present value of the terminal value ($38.95 billion) plus the present value of the first five years’ FCFE ($1. billion) is $40.77 billion. Because NYL Manufacturing has 17 billion outstanding shares, the value per ordinary share is $2.398.
- The solution is as follows: A. The FCFF is (in euros) FCFF=NI+NCC+Int(1−Taxrate) −FCInv−WCInvFCFF=250+90+150(1−0.30)−170−40FCFF=250+90+105− 0−40=235million The weighted-average cost of capital is WACC = 9%(1 – 0.30)(0.40) + 13%(0.60) = 10.32% The value of the firm (in euros) is V (^) F =
FCF F 1
rWACC − g
235 × 1.
= € 5,766.20 million The total value of equity is the total firm value minus the value of debt, Equity = €5,766.20 million
- €1,800 million = €3,966.20 million. Dividing by the number of shares gives the per share estimate of V 0 = €3,966.20 million/10 million = €396.62 per share. B. The free cash flow to equity is FCFE=NI+NCC−FCInv−WCInv+NetborrowingFCFE=250+90−170−40+0.40( 70−90+40)FCFE=250+90−170−40+48=€178million Because the company is borrowing 40 percent of the increase in net capital expenditures (170 – 90) and working capital (40), net borrowing is €48 million. The total value of equity is the FCFE discounted at the required rate of return of equity, V (^) E =
FCF E 1
rCAPM − g
178 × 1.
= € 3,174.33 million The value per share is V 0 = €3,174.33 million/10 million = €317.43 per share.
- The WACC for PHB Company is WACC = 0.30(7.0%)(1 – 0.35) + 0.15(6.8%) + 0.55(11.0%) = 8.435% The firm value is Firmvalue=FCFF 0 (1+g)/(WACC−g)Firmvalue=28(1.04)/ (0.08435−0.04)=29.12/0.04435=$656.60million The value of equity is the firm value minus the value of debt minus the value of preferred stock: Equity = 656.60 − 145 − 65 = $446.60 million. Dividing this amount by the number of shares gives the estimated value per share of $446.60 million/8 million shares = $55.82. The estimated value for the stock is greater than the market price of $32.50, so the stock appears to be undervalued.
- The solution is as follows: A. The required return on equity is
WCInv=Increaseinaccountsreceivable+Increaseininventory−Increaseinaccountspayable−Increaseinaccru edliabilities=(770−711)+(846−780)−(476−443)−(149−114)=$57million Netborrowing=Increaseinnotespayable+Increaseinlong-termdebt=(465−450)+(1,575−1,515)=$75million FCFE=485+270−523−57+75=$250million An alternative calculation is FCFE = FCFF – Int(1 – Tax rate) + Net borrowing FCFE = 307.6 – 195(1 – 0.32) + (15 +60) = $250 million
- C is correct. Inventory cannot be reduced below zero. Furthermore, sales growth tends to increase inventory.
- A is correct. The FCFF model is often selected when the capital structure is expected to change because FCFF estimation may be easier than FCFE estimation in the presence of changing financial leverage.
- The solution is as follows: A. Vn = Benchmark value of P/E × En = 12 × $3.00 = $36.0. B. In the expression for sustainable growth rate g = b × ROE, you can use (1 − 0.45) = 0.55 = b , and ROE = 0.10 (the industry average), obtaining 0.55 × 0.10 = 0.055. Given the required rate of return of 0.09, you obtain the estimate $3.00(0.45)(1.055)/(0.09 − 0.055) = $40.69. In this case, the estimate of terminal value obtained from the Gordon growth model is higher than the estimate based on multiples. The two estimates may differ for a number of reasons, including the sensitivity of the Gordon growth model to the values of the inputs.
- The solution is as follows: A. The P/Es are: Hoppelli 25.70/1.30 = 19. Telli 11.77/0.40 = 29. Drisket 23.65/1.14 = 20. Whitelin e
The EV/S multiples for each company are: Hoppelli 3,779/4,124 = 0. Telli 4,056/10,751 = 0. Drisket 3,846/17,388 = 0. Whitelin e
B. The data for the problem include measures of profitability, such as operating profit margin, ROE, and net profit margin. Because EV includes the market values of both debt and equity, logically the ranking based on EV/S should be compared with a pre-interest measure of profitability, namely, operating profit margin. The ranking of the stocks by EV/S from highest to lowest and the companies’ operating margins are: Company EV/S Operating Profit Margin (%) Hoppelli 0.916 6. Whitelin e
Telli 0.377 1. Drisket 0.221 1. The differences in EV/S appear to be explained, at least in part, by differences in cost structure as measured by operating profit margin.
- The solution is as follows: A. EBITDA = Net income (from continuing operations) + Interest expense + Taxes + Depreciation + Amortization EBITDA for RGI = €49.5 million + €3 million + €2 million + €8 million = €62.5 million
Per-share EBITDA = (€62.5 million)/(5 million shares) = €12. P/EBITDA for RGI = €150/€12.5 = 12 EBITDA for NCI = €8 million + €5 million + €3 million + €4 million = €20 million Per-share EBITDA = (€20 million)/(2 million shares) = € P/EBITDA for NCI = €100/€10 = 10 B. For RGI: Market value of equity = €150 × 5 million = €750 million Market value of debt = € Total market value = €750 million + €50 = €800 million EV = €800 million − €5 million (cash and investments) = €795 million Now, Zaldys would divide EV by total (as opposed to per-share) EBITDA: EV/EBITDA for RGI = (€795 million)/(€62.5 million) = 12. For NCI: Market value of equity = €100 × 2 million = €200 million Market value of debt = € Total market value = €200 million + €100 = €300 million EV = €300 million − €2 million (cash and investments) = €298 million Now, Zaldys would divide EV by total (as opposed to per-share) EBITDA: EV/EBITDA for NCI = (€298 million)/(€20 million) = 14. C. Zaldys should select RGI as relatively undervalued. First, it is correct that NCI appears to be relatively undervalued based on P/EBITDA, because NCI has a lower P/EBITDA multiple: P/EBITDA = €150/€12.5 = 12 for RGI. P/EBITDA = €100/€10 = 10 for NCI. RGI is relatively undervalued on the basis of EV/EBITDA, however, because RGI has the lower EV/EBITDA multiple: EV/EBITDA = (€795 million)/(€62.5 million) = 12.72 for RGI. EV/EBITDA = (€298 million)/(€20 million) = 14.9 for NCI. EBITDA is a pre-interest flow; therefore, it is a flow to both debt and equity and the EV/EBITDA multiple is more appropriate than the P/EBITDA multiple. Zaldys would rely on EV/EBITDA to reach his decision if the two ratios conflicted. Note that P/EBITDA does not take into account differences in the use of financial leverage. Substantial differences in leverage exist in this case (NCI uses much more debt), so the preference for using EV/EBITDA rather than P/EBITDA is supported.
- A is correct. The forward P/E ratio should be used given the recent significant acquisition of the water bottling company. Since a major change such as an acquisition or divestiture can affect results, the forward P/E, also known as the leading P/E or prospective P/E, is the most appropriate P/E to use for Delite. Earnings estimates for 2011 should incorporate the performance of the water bottling company. The forward P/E is calculated as the current price divided by the projected earnings per share, or $65.50/$3.50 = 18.71.
- C is correct. The price-to-sales ratio is calculated as price per share divided by annual net sales per share. Price per share = $37. Annual net sales per share = $67.44 billion/1.638821 billion shares = $41. Price-to-sales ratio (P/S) = $37.23/$41.15 = 0.
- C is correct. You Fix It is in the cyclical home improvement industry. The use of normalized earnings should address the problem of cyclicality in You Fix It earnings by estimating the level of earnings per share that the company could achieve currently under mid-cyclical conditions.
- C is correct. The price to sales (P/S) ratio fails to consider differences in cost structures. Also, while share price reflects the effect of debt financing on profitability and risk, sales is a pre-financing income measure and does not incorporate the impact of debt in the firm’s capital structure. Earnings reflect operating and financial leverage, and thus the price-to-earnings (P/E) ratio incorporates the impact of debt in the firm’s capital structure.
- A is correct. Free cash flow to equity (FCFE) is defined as cash flow available to shareholders after deducting all operating expenses, interest and debt payments as well as investments in working and fixed
