ch 6 vid calc

xlsx

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Texas Tech University *

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5320

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Finance

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Apr 3, 2024

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xlsx

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42

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Example 1: Suppose D_0= $5, g = 4%, r = 12%. Find PV_0. D_0 $5 r 12% g 4% Div 1 $5.20 PV $65.00 Example 2: Suppose Div2 = $2.50, g=2%, r=7.5%. Find PV_0 Div 2 $2.50 D1 $2.45 g 2% r 7.50% PV_0 $44.56
Example 5 (Gordon) : Suppose PV_0 = $40.75, g=6%, r=13%. Find D_0 PV_0 $40.75 D1 $2.85 g 6% D0 r 13% Example 6 (Gordon) : Suppose D0=$1.75, PV0=$55, r=10%, find g D0 $1.75 g? 0.06607929515 P0 $55 r 10% P0 $55.00 Example 7 (Gordon) : Suppose D0=$0.95, g=3%, PV0=$22.95, find r D0 $0.95 r 7.26% g 3% D1 $0.98 PV0 $22.95 r 7.26% P0 $22.95 Example 1 (Differential Growth) D0 $6 Time DIV(exp. Fut.) TV Combined g1 12% for 4 years 0 $6 g2 3% y5 to forever 1 $6.72 $6.72 r 9% 2 $7.53 $7.53 3 $8.43 $8.43 P0? $140.51 4 $9.44 $162.07 $171.51 5 $9.72 Example 2 (Differential Growth) D0 $2 Time DIV(exp. Fut.) TV Combined g1 20% for 6 years 0 $2 g2 5% y7 to forever 1 $2.40 $2.40 r 13% 2 $2.88 $2.88 3 $3.46 $3.46 P0? $52.54 4 $4.15 $4.15 5 $4.98 $4.98 6 $5.97 $78.38 $84.35 7 $6.27
Question 1 Company j paid div of $2.57. Div expected to grow at contant g forever a D0 $2.57 D1 $2.67 g 4% r 11% P0? $38.18 Question 2 Next div pmt by company will be $2.14. Divs will grow at 4.4% forever. D1 $2.14 D0 $2.04584 g 4.40% P0 $32 P0 $32.000000 r? 11.0875% Question 3 For company in prior problem, what is dividend yield and expected capit Capital Gains Yield 4.40% g Dividend Yield 6.69% (r-g) 6.69% Total Return 11.0875% Question 4 Cuban corp will pay div of $3.08. increase dividends by 4.6% forever, di D1 $3.08 g 4.60% P0 = D1/(r-g) r 11% P0? $48.13 Question 5 Corp expects to maintain constant 4.1% growth rate in divs indefinitely. g 4.10% Dividend Yield 4.50% (r-g) r? 8.60% Question 6 Stock currently sells for $63/share. Required rate of return is 10.4%. Tota P0 $63 dividend yield 5.20% r 10.40% capital gains 5.20% g g 5.20%
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P0 $63.00 D0? $3.11 Question 7 Corp pays constant div of $10.25. company will maintain div for next 8 y Dividend $10.25 Time Dividend r 9.70% 1 $10.25 2 $10.25 P0? $55.29 3 $10.25 P0? $55.29 4 $10.25 5 $10.25 6 $10.25 7 $10.25 8 $10.25 Question 8 Valuing preferred stock (no growth model). Corp has an issue of preferre DIV $3.85 P0=DIV/r P0 108 r? 3.56% Question 14 Corp. just paid div of $2.73. g in divs will be 4% indefinitely. Investors r find div7 bc that’s where 10% (forever discount rate) will kick in, then fi D0 $2.73 g 4% Time Dividend TV r1 15% y1-3 1 $2.84 r2 13% y4-6 2 $2.95 r3 10% y7-forever 3 $3.07 4 $3.19 P0? $39.15 5 $3.32 6 $3.45 $59.87 7 $3.59 Question 15 Startup company: no divs will be paid on stock over next 11 years. Comp D12 $17 PV_11 $226.67 g 5.50% r 13% P0? $59.09
Question 16 Company has j paid div of $13/share and will increase div $3.50/share fo D0 $13 Time Dividend r 11% 1 $16.50 2 $20.00 P0? $84.17 3 $23.50 4 $27.00 5 $30.50 Question 17 Corp. pays divs: $12, 8, 7, 2.85. after, constant 5% g, r 10%, current pric differential growth g 5% Time Dividends TV r 10% 1 $12 2 $8 P0? $65.60 3 $7 4 $2.85 $59.85 5 $2.99 Question 22 Bank issued new preferred stock. Issue will pay annual div of $6 in perpe D10 $6 Time Dividends r 4.60% PV_9 $130.43 PV_0 $87.02 Question 26 Corp pays equal dividends at end of each of the next 2 years, after, div gr g 4% Time Dividends TV r 9.80% 1 $4 Price $61 2 $4 $65.84 3 $3.82 D1 $3.67 <<first plugged in $3 as a guess, which gave a price of 49. P0 $61.00 Question 35 Company just paid div of $3.35/share. Company will increase divs by 16 D0 $3.35 Time Growth rate Dividends r 10.50% 1 16% $3.89 g 4% 2 12% $4.35 3 8% $4.70
4 4% $4.89 P0? $66.31
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at 4%. If investor require rate of return of 11%, what is current price of stock? What will price be D4 $3.01 P3 $42.95 P3 $42.95 . If stock sells for $32/share, what is required rate of return? tal gains yield? iscount rate 11%. Price of stock today? If company has div yield of 5.4%, what is required rate of return? al return on stock is evenly divided btwn capital gain yield and dividend yield. If constant div gro
years, then cease to pay divs forever. If required rate of return is 9.7%, what is current price per s ed stock outstanding that pays div of $3.85/year in perpetuity. require rate of return on the stock at 15% for the first 3, 13% for next 3 years, then 10% thereafte ind TV at time Combined Combined $2.84 $2.84 $2.95 $2.95 $3.07 $49.32 $52.39 $3.19 $3.32 $63.33 pany will pay $17/share dividend 12 years from today, will increase 5.5% per year. If required ra
or next 5 years. Then will never pay div after that. If 11% r, how much will u pay for share today. ce of share? Combined $12 $8 $7 $63 etuity, beg 10 years from now. If mkt requires 4.6% r, how much will we pay for stock today? rows at constant rate of 4% forever, current stock price is $61, what is next div pmt if r=9.8% Combined $4 $70 .84. 4 gave 66.45. did goal seek by setting set goal to B119 at 61, by changing cell B117 6% next year, then reduce div growth rate by 4% per year until reaches industry avg of 4% div gr TV Combined $3.89 $4.35 $75.21 $79.91
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e in 3 years? owth rate, what is current dividends per share?
share? er. Current share price of the stock? ate of return is 13%, what is current share price?
. rowth rate, then company will maintain this growth rate. R is 10.5%, what is stock selling for toda
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ay?
Question 9 Newspaper reported last week tish enterprise earned $38.6 mil this year, ROE 14%, fi Earnings_t $38.60 million ROE 14% Retention Ratio 75% RE $28.95 million g? 10.50% ROE * RR Earnings_t+1? $42.65 million Question 27 Corp earned $24.5 million for fiscal year ending yesterday. Firm paid out 30% of earn find g, then find expected Div1 by finding earnings_t+1 w the g found. Earnings_t $24.50 million Payout ratio 30% (div/NI) g = retention ratio * ROE Retention Ratio 70% (1-payout rati(Add. RE/NI) g Shares Outst. 2.5 million Price $104 Earnings_t+1 ROE 13% Dividends Div_1 r? 12.1842% Dividend Yield
irm retains 75% of earnings. What is Firms earnings growth rate and what will earnings be next y r = (D1/P0) + g r = Div Yield + g nings as annual end of year divs. 70% will be retained. 2.5 mil shares of CS outstanding. Current NI = Divs paid + Add. RE 9.100% $26.73 million $8.02 million <<amt in divs will be paid next year $3.21 million <<div/share expected to be paid next year 3.08%
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year? t stock price is $104/share. Historical ROE 13%. What is required rate of return on stock?
Question 13 Company has earnings of $2.14 per share. Benchmark P/E is 18. Wh EPS $2.14 EPS $2.14 P/E benchmark 18 P/E benchmar 21 Price $38.52 <<comparable P/E * EPS Price $44.94 Question 29 Company A and B reported earnings of $1.1 million. Both will gener Compnay A will generate additional $220,000 each year in perpetuity MKT Value $9.17 million MKT Value $11.00 Earnings $1.10 million Earnings $1.10 P/E 8.333333333 P/E 10 Question 30 Corp has EPS $3.83. Benchmark P/E is 19. Earnings expected to gro Assume company pays no div, what is implied rate of return on stock EPS_0 $3.83 EPS_1 $4.08 P/E Benchmark 19 g 6.50% Price $72.77 Price_1 $77.50 %change in P 6.50% g Question 31 Corp has yearly sales of $31.5 million. Costs are $17.3 million. BS sh Sales $31.50 million Debt $59 Cost $17.30 million Cash $21 Gross Profit (EBITDA) $14.20 million Shares outst. 0.975 million EV $106.50 EV/EBITDA 7.5 MV Equity $68.50 Price $70.26
hat stock price would u consider appropriate? What if benchmark P/E 21? rate $1.1 million in earnings in perpetutity. All earnings are paid as Divs, both firms require 12% y, recalculate P/E Ratio. What if increase by 440,000 million MKT Value $12.83 million million Earnings $1.10 million P/E 11.66666667 ow at 6.5% per year, estimate current price per share? Target stock price 1 year from now? k over next year, what does this tell u ab implicit stock return using P/E Valuation? hows debt of $59 million. Cash $21 million. 975,000 shares outstanding. EV/EBITDA is 7.5. Co million million (aka value) EV = MV_eq + BV_debt - Cash
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% rate of return. Current P/E for both companies? ompany's enterprise value and stock price per share?
Pro Formas Company has revenues forecasted to be $500 million in 1 year. Sales expected to grow at 10% per y Y1 Y2 Y3 Y4 Y5 10% 10% 8% 8% Sales $500 $550 $605 $653.40 $705.67 Expenses $300.00 $330.00 $363.00 $392.04 $423.40 EBT $200.00 $220.00 $242.00 $261.36 $282.27 Taxes (40%) $80.00 $88.00 $96.80 $104.54 $112.91 Net Income (OCF) $120.00 $132.00 $145.20 $156.82 $169.36 Net investment $50.00 $55.00 $60.50 $65.34 $70.57 FCF (OCF - Net Investment) $70.00 $77.00 $84.70 $91.48 $98.79 Terminal Value $1,047.22 $1,047.22 FCF (combined) $70.00 $77.00 $84.70 $91.48 $1,146.01 MV_Equity $767.98 Shares outstanding (given) 12 million Stock is trading for Price $64.00 $50 and price base if stock is trading for $65, it Benchmark P/E (given) 7 FCF $70.00 $77.00 $84.70 $91.48 $98.79 Terminal Value (P/E) $1,185.53 FCF (combined) $70.00 $77.00 $84.70 $91.48 $1,284.32 MV Equity $833.84 Shares Outst 12 million Price $69.49 Q32 Firm projected sales $153 million next year. Costs $82 million. Net i 14% 12% 10% 8% 1 2 3 4 5 Sales $153 $174.42 $195.35 $214.89 $232.08 Cost $82 $93.48 $104.70 $115.17 $124.38 EBT $71.00 $80.94 $90.65 $99.72 $107.70 Tax (40%) $28.40 $32.38 $36.26 $39.89 $43.08 Earnings after tax $42.60 $48.56 $54.39 $59.83 $64.62 Net Investment $15 $17.10 $19.15 $21.07 $22.75
FCF $27.60 $31.46 $35.24 $38.76 $41.86 Terminal Value $739.61 Combine $27.60 $31.46 $35.24 $38.76 $781.48 MV_Equity $542.87 shares outs 6.2 million price $87.56 If P/E multiple is 12, what is price of stock? FCF $27.60 $31.46 $35.24 $38.76 $41.86 Terminal Value (P/E) $775.41 Combine $27.60 $31.46 $35.24 $38.76 $817.27 MV_Equity $563.19 shares outs 6.2 million price $90.84
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year for 2 years. 8% for next 2 years. Last year will be 6%. Expenses are 60% of revenue. Net inv Y6 6% $748.01 FCF = OCF-NCS-dNWC $448.81 $299.20 OCF=EBIT+DEPR-Tax $119.68 $179.52 $74.80 NCS = MONEY invested in fixed asstes $104.72 PV_5 = FCF_6/(r-g) ed on model is $64, then u would want to buy. t is fairly valued. 10% threshold from current stock price. investment $15 million. Each of the values exp. to grow 14% the following year, growth rate will TERMINAL RATE 6% $246.00 $131.84 $114.16 $45.66 $68.49 $24.12
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$44.38 <<USE earnings from year before terminal rate kicks in
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vestment (including nwc and capital spending less depreciation) is 10% of revenues. net investme gordon model comparables model l decline 2% per year until terminal value of 6%. 6.2 mil shares out, r = 12%
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ent is equal to investment in fixed assets and NWC. Taxes 40%. Discount rate is 16%, perpetual g
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growth 6%
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Constant Growth IBM $145.90 DIV_2022 Price DIV_2017 $6.64 5 year g Div_1 6.7877% ROE R, expect rate 9.0650% Payout Retention Ratio $155.89 Financial g Price Target 11.398% Total Return (%) What I be willing to pay for IBM stock if required rate of return is 10%, g = 3% 10% r 3% g $94.86 <<SO since this is the modeled PV_0 No Growth Preferred shares trading at $89/share w div yield of 8% and par value of 100. PV_0 = DIV / Rate Q8 Par 100 Div DY 8% PV P0 $89 r? DIV $8.00 Non Constant Growth LUV (Southwest) Div_2019 (given) Price $23.42 Div_2014 (given) Div_1 $0.72 5 year g PV_0 $18.77 ROR g1 g2 Textbook Question 5 (end of chapter) g 3.40%
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DY 5.30% <<Div1/Price r? 8.70% <<DY+g Comparable Valuation Benchmark Price Est. Recommendation P/S 2.22 HOLD P/E 19.88 $151.01 HOLD P/B 3.48 $88.47 SELL DCF Price $145.90 FCF_0 $11.515 billion <<ocf-ncs-dnwc growth rate 7% (0 to 5) terminal growth 2.50% (6 to forever) WACC (wt. avg. cost capital) 6% <<discount rate from gurufocus EV $412.66 +cash 8.738 billion -int. bearing liabs 54.013 billion mkt cap $367.38 billion shares outs 0.91101 Price per share $0.0024797 TVM 550,000,000 Time 266,000,000 option 1 0 1 rate 10% 2
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g 5% 3 PMT $18,333,333.33 4 PV $303,434,013.07 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Loan Amortization you will buy mustang for $45,000. u put down 10,000. Price $45,000 Down $10,000 Loan $35,000 Year 3 Rate 2.90% PMT $1,016.30 Total $ paid to bank $36,586.82 Total interest $1,586.82 Retirement Planning
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Assume nominal cash flows Current Salary 70000 % need per year in retirement 110% Withdrawal in retirement? 77000 assuming beg. period Retirement years 20 Working years 40 ROR (working) 9% ROR (retirement) 6% Nest Egg $15,000 Bequest $500,000 Calculate amt needed at rtrmt $1,039,086.30 <<UNSURE Calculate amt needed to deposit $1,680.90
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$6.59 $5.90 2.24% 30.96% 85.42% 14.58% 4.51% d price and observed price is 145.90, u don’t wanna buy PV = Div/Rate $3.80 Rate = Div/PV $93 4.09% $0.70 Time Divs TV Combined $0.22 1 $0.72 $0.72 26.05% 2 $0.91 $0.91 3 $1.14 $1.14 10% 4 $1.44 $1.44 26.05% (1 to 5) 5 $1.82 $23.17 $24.99 2% (6 to forever) 6 $1.85 Q2
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Div1 $1.87 Div_5 $2.21 g 4.30% Div_5 $2.21 r 10% PV? $32.81 n IBM $145.90 $/share Step 1: Find Sales/share, EP Shares Outst. 0.91101 billion Step 2: take per share value Sales 61.17 billion Net Income $6.92 billion Book Equity $23.16 billion Sales per shar $67.15 Earnings per $7.60 BV per share $25.42 Time CF TV Combined 0 $11.515 EV = mkt cap + int. bearing 1 $12.32 $12.321 mkt cap = EV + cash - int. b 2 $13.18 $13.184 3 $14.11 $14.106 4 $15.09 $15.094 5 $16.15 $472.98 $489.126 6 $16.55 $18,333,333.33 $19,250,000.00 $20,212,500.00
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$21,223,125.00 $22,284,281.25 $23,398,495.31 $24,568,420.07 $25,796,841.08 $27,086,683.13 $28,441,017.29 $29,863,068.15 $31,356,221.56 $32,924,032.64 $34,570,234.27 $36,298,745.98 $38,113,683.28 $40,019,367.45 $42,020,335.82 $44,121,352.61 $46,327,420.24 $48,643,791.25 $51,075,980.81 $53,629,779.86 $56,311,268.85 $59,126,832.29 $62,083,173.91 $65,187,332.60 $68,446,699.23 $71,869,034.19 $75,462,485.90
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Step 1: find first withdrawal PV 50000 APR 8% Years 25 EAR 0.0832775718 FV $369,371.85 Total Int. $319,371.85 Simple Int. 100000 simple int always years * rate * pv Int-on-int $219,371.85
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Q32 0.14 0.12 0.1 Forecast Div 1 2 3 4 Find TV Sales 113 128.82 144.2784 158.70624 Costs 64.3 73.302 82.09824 90.308064 Taxes 10.227 11.65878 13.0578336 14.36361696 Net Income ( 38.473 43.85922 49.1223264 54.03455904 Net Investmen 9 10.26 11.4912 12.64032 FCF 29.473 33.59922 37.6311264 41.39423904 29.473 33.59922 37.6311264 41.39423904
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Market cap $579.71 Shares outs 7.5 price per shar $77.30 PS, BV/share es, multiply by benchmark, giving u intrinsic value (est. price) g liabs - cash bearing liabs
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Terminal Growth 0.08 0.06 Q32 0.14 5 6 1 2 171.4027392 181.6869036 Sales 113 128.82 97.53270912 103.3846717 Costs 64.3 73.302 15.51270632 16.4434687 12% given disTaxes 10.227 11.65878 58.35732376 61.85876319 Net Income ( 38.473 43.85922 13.6515456 14.47063834 Net Investmen 9 10.26 44.70577816 47.38812485 FCF 29.473 33.59922 789.8020809 834.507859 29.473 33.59922
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Market cap $594.32 Shares outs 7.5 price per shar $79.24
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0.12 0.1 0.08 0.06 Q16 3.75 div paid 3 4 5 6 144.2784 158.70624 171.4027392 181.6869036 Time Divs 82.09824 90.308064 97.53270912 103.3846717 0 $3.75 13.0578336 14.36361696 15.51270632 16.4434687 1 $8.75 49.1223264 54.03455904 58.35732376 61.85876319 <<earnings 2 $13.75 11.4912 12.64032 13.6515456 14.47063834 3 $18.75 37.6311264 41.39423904 44.70577816 47.38812485 4 $23.75 866.0226846 <<assuming 1 5 $28.75 37.6311264 41.39423904 44.70577816 913.4108095
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now, 5$ more every year in Divs for 5 years. Then no d Q17 PV $65.46 Time Divs TV 1 $15 2 $11 3 $9 4 2.95 48.6984127 5 3.068
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r 10% Combined PV $64.24 $15 $11 $9 $52
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Question 11 Straight Voting Shares Out 415,000 Price $37 Cost? $7,677,537 Straight Votes 207501 Question 12 same info, 4 directors up for election, cumulative voting n 4 1/(n+1) cumulative votes 83001 <<number of shares outstanding price $3,071,037 <<cost
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