Vc 5.84917883958384

d1( 0.02020270731751950.0626986301369863

0.2215140924426370.374248593127202

d2 0.152734500684566

N(d1) 0.64589031285574N(d2) 0.560696173828221

a) Net present Value

Shares outstanding 900,000.00 Price per share in cash 27.00 Total cash paid 24,300,000.00

Market price

Shares outstanding 900,000.00 Market price per share 24.00 Total value 21,600,000.00

Shares outstanding 1,500,000.00 Market price per share 34.00 Total value 51,000,000.00

Net present value

Market price 75,300,000.00 Synergistic benefits 3,000,000.00 Present value of the merger 78,300,000.00 Less cash paid 24,300,000.00 Value of Firm B 51,000,000.00 NPV 3,000,000.00

b) Price per share

Firm B+ Firm T 75,300,000.00 Synergistic benefits 3,000,000.00

78,300,000.00

Number of shares 2,400,000.00

Price per share 32.63

c) Premium

Shares outstanding 900,000.00 Premium per share 3

2,700,000.00

d) Price of merged firm

Shares issued to Firm T shareholders 2700000

Value of Firm B (after merger) 72,600,000.00 Synergistic benefits 3,000,000.00

75,600,000.00

Number of shares 4,200,000 Price per share 18

e) NPV

Additional share 2,700,000.00 Total sahres 4,200,000.00 Value

B 51,000,000.00 T 21,600,000.00 Synergy 3,000,000.00

75,600,000.00

cost of takeover 27,000,000.00

Gain in value 3,000,000.00

Loss (24,000,000.00)

Review of the computationThe consultant did not accurately calcualte the value of the company. It should have been calculated as follows:

Year 0 Year 1 Year 2 Year 3cash flow 12,000,000.00 12,360,000.00 12,730,800.00 Discount factor 0.89 0.80 0.71

165,552,113.70 10,714,285.71 9,853,316.33 9,061,531.98

Problem#1 computation

# 2 WACC could not be equal to r.

# 3 PV 12M?

#4 Cash flow in perpetuityCost determined as 0.5m. The Benefit not clearly identified.If 0.5m is assumed to be the net cash flow, this should not be added unless otherwise the benefit is refering to synergitic effect.

#5 WACC 10%

Elliot should have to take the weght of both WACC.

Recommondation

The valuation based on DCF methods revealed 164million while the offer was 144 million. I recommend the management to proceed with the takeover.

Additional information required for the deccison are:

Profit after tax of bothMarket value based on PEShare price of bothEPSNo. of shares WACC of both

1The consultant did not accurately calcualte the value of the company. It should have been calculated as follows:

Terminal value 190,962,000.00 0.71 135,922,979.68

If 0.5m is assumed to be the net cash flow, this should not be added unless otherwise the benefit is refering to synergitic effect.

The valuation based on DCF methods revealed 164million while the offer was 144 million. I recommend the management to proceed with the takeover.

Income Statement for the Year Ending December 31 (Millions of Dollars)2009

Net Sales $ 63,122.0 Costs (except depreciation) $ 56,403.0

Depreciation $ -

Total operating costs $ 56,403.0 Earning before int. & tax $ 6,719.0

Less interest $ - Earning before taxes $ 6,719.0

Taxes (40%) $ 1,307.0 Net income before pref. div. $ 5,412.0 Preferred Comm. Equity

Preferred div. $ 344.0 9.9% 11.5%

Net income avail. for com. div. $ 5,068.0 0.080816 91.9%Common dividends $ 1,861.2 Addition to retained earnings $ 3,206.8

Number of shares (in millions) 423 Dividends per share $ 4.40

Balance Sheets for December 31 (Millions of Dollars)Assets 2009 Liabilities and EquityCash $ 7,867.0 Accounts PayableMarketable Securities 67,243.0 Notes payable

Accounts receivable 450,301.0 Accruals

other assets 8,088.0 Total current liabilities Total current assets $ 533,499.0 Long-term bondsother non current assets $ 32,237.0 other non current liab

Minority interest

Net plant and equipment 4,967.0 Preferred stock

Total Assets $ 570,703.0

Retained earnings

Common equity

Total liabilities and equityProjected ratios and selected information for the current and projected years are shown below.

Inputs Actual Projected Projected Projected2009 2010 2011 2012

Sales Growth Rate 17% 17% 17% 17%Costs / Sales 89% 89% 89% 89%

Common Stock

Depreciation / Net PPE 0% 0% 0% 0%Cash / Sales 12% 12% 12% 12%marketable securities / Sales 107% 107% 107% 107%Acct. Rec. / Sales 713% 713% 713% 713%other current assets 13% 13% 13% 13%Net PPE / Sales 8% 8% 8% 8%Acct. Pay. / Sales 765% 765% 765% 765%Accrual/Sales 18% 18% 18% 18%longterm bond/sales 32% 32% 32% 32%other current liabilities / Sales 18% 18% 18% 18%Minority interest/sales 3% 3% 3% 3%Preferred stock 1% 1% 1% 1%Tax rate 19% 19% 19% 19%Weighted average cost of capital (WACC) 11.4% 11.4% 11.4% 11.4%

a. Forecast the parts of the income statement and balance sheets necessary to calculate free cash flow.

Partial Income Statement for the Year Ending December 31 (Millions of Dollars)

Actual Projected Projected Projected2009 2010 2011 2012

Net Sales $ 63,122.0 $ 74,042.1 $ 86,851.4 $ 101,876.7 Costs (except depreciation) $ 56,403.0 $ 66,160.7 $ 77,606.5 $ 91,032.5

Depreciation $ - $ - $ - $ -

Total operating costs $ 56,403.0 $ 66,160.7 $ 77,606.5 $ 91,032.5 Earning before int. & tax $ 6,719.0 $ 7,881.4 $ 9,244.9 $ 10,844.2

Partial Balance Sheets for December 31 (Millions of Dollars)

Actual Projected Projected ProjectedOperating Assets 2009 2010 2011 2012

Cash $ 7,867.0 $ 9,228.0 $ 10,824.4 $ 12,697.1 Accounts receivable $ 450,301.0 $ 528,203.1 $ 619,582.2 $ 726,769.9 Net plant and equipment $ 4,967.0 $ 5,826.3 $ 6,834.2 $ 8,016.6 Accounts Payable $ 482,937.0 $ 566,485.1 $ 664,487.0 $ 779,443.3 Accruals $ 11,567.0 $ 13,568.1 $ 15,915.4 $ 18,668.7 Long-term bonds $ 20,084.0 $ 23,558.5 $ 27,634.2 $ 32,414.9 Minority interest $ 1,849.0 $ 2,168.9 $ 2,544.1 $ 2,984.2 Preferred stock $ 3,486.0 $ 13,056.7 $ 15,315.5 $ 17,965.0

Actual Projected Projected ProjectedCalculation of FCF 2009 2010 2011 2012

Operating current assets 458,168.0 537,431.1 630,406.6 739,467.0

Operating current liabilities 494,504.0 580,053.2 680,402.4 798,112.0 Net operating working capital (36,336.0) (42,622.1) (49,995.8) (58,645.0)

Net PPE 4,967.0 5,826.3 6,834.2 8,016.6 Net operating capital (31,369.0) (36,795.8) (43,161.5) (50,628.5)

b. Calculate free cash flow for each projected year. Also calculate the growth rates of free cash flow each year to ensure that there is constant growth (i.e., the same as the constant growth rate in sales) by the end of the forecast period.

Investment in operating capital na (5,426.8) (6,365.7) (7,466.9)NOPAT 5,412.0 6,348.3 7,446.5 8,734.8 Free cash flow na 11,775.1 13,812.2 16,201.7 Growth in FCF na na 17.3% 17.3%Growth in sales 17.3% 17.3% 17.3%

Actual Projected Projected Projected2009 2010 2011 2012

8.6% 8.6% 8.6% 8.6%

-49.7% -49.7% -49.7% -49.7%

na -20.2% -20.2% -20.2%Weighted average cost of capital (WACC) na 11.4% 11.4% 11.4%Spread between ROIC and WACC na -31.6% -31.6% -31.6%

Actual Projected Projected Projected2009 2010 2011 2012

Free cash flow 11,775.1 13,812.2 16,201.7 Long-term constant growth in FCFWeighted average cost of capital (WACC) 11.4% 11.4% 11.4% 11.4%Horizon valueFCF in Years 1-7 and FCF8 + horizon value in Year 2016 10,573.1 11,136.3 11,729.5 Value of operations (PV of FCF + HV) 309,549.1

Operating capital (31,369.0)

340,918.1

e. Calculate the price per share of common equity as of 12/31/2010.

Actual2009

Value of Operations 309,549.1

c. Calculate operating profitability (OP=NOPAT/Sales), capital requirements (CR=Operating capital/Sales), and return on invested capital (ROIC=NOPAT/Operating capital at beginning of year). Based on the spread between ROIC and WACC, do you think that the company will have a positive market value added (MVA= Market value of company - book value of company = Value of operations - Operating capital)?

Operating profitability (OP=NOPAT/Sales)

Capital requirement (CR=Operating capital/Sales)

Return on invested capital (ROIC=NOPAT/Operating capital at start of year)

d. Calculate the value of operations and MVA. (Hint: first calculate the horizon value at the end of the forecast period, which is equal to the value of operations at the end of the forecast period. Assume that the annual growth rate beyond the horizon is 6 percent.)

Market value added (MVA=Market value of company - book value of company = Value of operations - Operating capital)

Plus Value of Mkt. Sec. 64,200.0 Total Value of Company 373,749.1 Less Value of Debt 20,084.0

Less Value of Pref. 3,486.0 Value of Common Equity 350,179.1 Divided by number of shares 423 Price per share 827.8

Income Statement for the Year Ending December 31 (Millions of Dollars)

Comm. Equity

11.4%

Balance Sheets for December 31 (Millions of Dollars)2009

$ 482,937.0 -

11,567.0

$ 494,504.0 $ 20,084.0 $ 11,131.0 $ 1,849.0

$ 3,486.0

$ 531,054.0 $ 14,164.0

25,485.0

$ 39,649.0

$ 570,703.0 Projected ratios and selected information for the current and projected years are shown below.

Projected Projected Projected Projected2013 2014 2015 2016

17% 17% 17% 17%89% 89% 89% 89%

0% 0% 0% 0%12% 12% 12% 12%

107% 107% 107% 107%713% 713% 713% 713%13% 13% 13% 13%

8% 8% 8% 8%765% 765% 765% 765%18% 18% 18% 18%32% 32% 32% 32%18% 18% 18% 18%

3% 3% 3% 3%1% 1% 1% 1%

19% 19% 19% 19%11.4% 11.4% 11.4% 11.4%

a. Forecast the parts of the income statement and balance sheets necessary to calculate free cash flow.

Partial Income Statement for the Year Ending December 31 (Millions of Dollars)

Projected Projected Projected Projected2013 2014 2015 2016

$ 119,501.3 $ 140,175.1 $ 164,425.4 $ 192,871.0 $ 106,781.1 $ 125,254.2 $ 146,923.2 $ 172,340.9

$ - $ - $ - $ -

$ 106,781.1 $ 125,254.2 $ 146,923.2 $ 172,340.9 $ 12,720.3 $ 14,920.9 $ 17,502.2 $ 20,530.1

Partial Balance Sheets for December 31 (Millions of Dollars)

Projected Projected Projected Projected2013 2014 2015 2016

$ 14,893.7 $ 17,470.3 $ 20,492.6 $ 24,037.8 $ 852,501.1 $ 999,983.8 $ 1,172,981.0 $ 1,375,906.7 $ 9,403.4 $ 11,030.2 $ 12,938.4 $ 15,176.8 $ 914,287.0 $ 1,072,458.6 $ 1,257,994.0 $ 1,475,626.9 $ 21,898.4 $ 25,686.8 $ 30,130.7 $ 35,343.3 $ 38,022.6 $ 44,600.6 $ 52,316.5 $ 61,367.2 $ 3,500.5 $ 4,106.1 $ 4,816.4 $ 5,649.7 $ 21,073.0 $ 24,718.6 $ 28,994.9 $ 34,011.1

Projected Projected Projected Projected2013 2014 2015 2016

867,394.8 1,017,454.1 1,193,473.6 1,399,944.6

936,185.4 1,098,145.5 1,288,124.6 1,510,970.2 (68,790.6) (80,691.4) (94,651.0) (111,025.6)

9,403.4 11,030.2 12,938.4 15,176.8 (59,387.2) (69,661.2) (81,712.5) (95,848.8)

b. Calculate free cash flow for each projected year. Also calculate the growth rates of free cash flow each year to ensure that there is constant growth (i.e., the same as the constant growth rate in sales) by the end of the forecast period.

(8,758.7) (10,274.0) (12,051.4) (14,136.3) 10,245.9 12,018.4 14,097.6 16,536.5 19,004.6 22,292.4 26,149.0 30,672.8

17.3% 17.3% 17.3% 17.3%17.3% 17.3% 17.3% 17.3%

Projected Projected Projected Projected2013 2014 2015 2016

8.6% 8.6% 8.6% 8.6%

-49.7% -49.7% -49.7% -49.7%

-20.2% -20.2% -20.2% -20.2%11.4% 11.4% 11.4% 11.4%

-31.6% -31.6% -31.6% -31.6%

Projected Projected Projected Projected2013 2014 2015 2016

19,004.6 22,292.4 26,149.0 30,672.8 2.0%

11.4% 11.4% 11.4% 11.4% 333,965.2

12,354.2 13,012.3 13,705.3 237,038.3

e. Calculate the price per share of common equity as of 12/31/2010.

c. Calculate operating profitability (OP=NOPAT/Sales), capital requirements (CR=Operating capital/Sales), and return on invested capital (ROIC=NOPAT/Operating capital at beginning of year). Based on the spread between ROIC and WACC, do you think that the company will have a positive market value added (MVA= Market value of company - book value of company =

d. Calculate the value of operations and MVA. (Hint: first calculate the horizon value at the end of the forecast period, which is equal to the value of operations at the end of the forecast period. Assume that the annual growth rate beyond the horizon is 6

1. Find the price today.

$4.40

17.4%

30% Short-run g; for Years 1-2 only.

6% Long-run g; for Year 3 and all following years.30% 6%

Year 0 1 2 3 4Dividend $4.40 $5.71 $7.40 $9.59 $12.44

PV of dividendsYear Dividend

P0 P1 P2 2009 $4.40 4.86 2010 $5.71 5.37 6.30 2011 $7.40 5.93 6.96 8.17 2012 $9.59 6.55 7.69 9.03 2013 $12.44 7.23 8.49 9.97 2014 $16.13 7.99 9.38 11.01 2015 $20.92 8.83 10.36 12.16 2016 $27.13

2017 $28.76 82.06 96.34 113.11 252.2515 Terminal value

$128.8221 $145.5315 $163.4551

2. Find the expected dividend yield.

Recall that the expected dividend yield is equal to the next expected annual dividend divided by the price at the beginning of the period.

Dividend yield = /Dividend yield = $5.706 / $128.822

Dividend yield = 4.43%

3. Find the expected capital gains yield.

The capital gains yield can be calculated by simply subtracting the dividend yield from the total expected return.

Cap. Gain yield= Expected return – Dividend yieldCap. Gain yield= 17.4% – 4.43%Cap. Gain yield= 12.97%

=+

D0

rs

gs

gL

D1 P0

Alternatively, we can recognize that the capital gains yield measures capital appreciation, hence solve for the price in one year, then divide the change in price from today to one year from now by the current price. To find the price one year from now, we will have to find the present values of the terminal value and second year dividend to time period one.

P1

P2 D2

(1 + rs)

=$163.455 + $7.399

1.17

= $145.53

Cap. Gain yield= /Cap. Gain yield= $16.71 / $128.8221Cap. Gain yield= 12.97%

P1

P1

(P1 – P0) P0

5 6 7 8$16.13 $20.92 $27.13 $28.76

11.4%

Recall that the expected dividend yield is equal to the next expected annual dividend divided by the price at the beginning of the period.

The capital gains yield can be calculated by simply subtracting the dividend yield from the total expected return.

captial gain

= rs – gL

Alternatively, we can recognize that the capital gains yield measures capital appreciation, hence solve for the price in one year, then divide the change in price from today to one year from now by the current price. To find the price one year from now, we will have to

Price per share

2009 2008 2007 2006 2005 2004Closing 12405 9550 13600 13350 10000 7780High 12900 13975 15810 13950 10280 7999Low 6492 7498 12325 9790 6700 5240Average 10599 10341 13911.7 12363.33 8993.333 7006.333

Price per share 105.99Basic earning per share 12current year earning 5068value per share in cents 44763.1Number of shares 423value per share 105.82

26372.81Book value $380,567.07 Number of shares 423Value per share $899.69

Earning in 2009 5412WACC (as above) 0.113681Retained earning (as above) 3206.8Return on equity 0.174Growth in earning (2008-2017) 0.015

Value of the companyCurrent earnings are a perpetuity with 100% payout 47606.85Growth in earnings 17242.6Total value 64849.45Number of shares 423value per share 153.3084

Decision Tree

Time Periods, Earnings, Probabilities, and Decision Points2010 2011 2012 2013 2014

2009 Prob. CFS CFS CFS CFS CFS CFS

8% 10,902.88 11,841.74 12,861.45 13,968.96 15,171.84 16,478.31

11% 11,775.11 13,812.21 16,201.72 19,004.62 22,292.42 26,149.00

10,570.12 11,129.94 11,719.40 12,340.09 12,993.65 13,681.82

15% 10,239.23 12,010.62 14,088.45 16,525.75 19,384.71 22,738.26

Coefficient of Variation (CV) = Std Dev/Expected NPV =

1

Time Periods, Earnings, Probabilities, and Decision Points2015 2016 perpetuity Calculating σ step-by-step

CFS CFS CFS Prob. NPV Deviation Sqrd dev

17,897.27 975,401.39 1,074,523.85 0.40 $429,810 (506,825.57) 256,872,160,950.37

30,672.78 33,433.33

14,406.44 805,172.27 892,013.74 0.40 $356,805 (579,829.62) 336,202,384,285.18

26,671.98 628,441.38 750,100.39 0.20 $150,020 (786,615.03) 618,763,210,421.91

Expected NPV = 936,635.11 Standard Deviation (SD) = 600,818.16 Sum = variance

Coefficient of Variation (CV) = Std Dev/Expected NPV = 0.64 Sq root of Var = σ

Sqrd*prob

102,748,864,380.15

134,480,953,714.07

123,752,642,084.38

360,982,460,178.60

600,818.16

A A-A1 (A-A1)^2 (A-A1 )(M-M1)2009 12405 1,290.83 1,666,250.69 6,153,617.64 2008 9550 (1,564.17) 2,446,617.36 2,098,850.97 2007 13600 2,485.83 6,179,367.36 9,864,200.97 2006 13350 2,235.83 4,998,950.69 9,419,938.47 2005 10000 (1,114.17) 1,241,367.36 2,979,095.97 2004 7780 (3,334.17) 11,116,667.36 29,783,555.14

Total 66685 - 27,649,220.83 60,299,259.17

Average (A1) 11114.1666667Standard deviation 2,351.56

M M-M1 (M-M1)^22009 36675 4,767.17 22,725,878.03 2008 30566 (1,341.83) 1,800,516.69 2007 35876 3,968.17 15,746,346.69 2006 36121 4,213.17 17,750,773.36 2005 29234 (2,673.83) 7,149,384.69 2004 22975 (8,932.83) 79,795,511.36

191447 - 144,968,410.83

Average 31907.8333333Standard deviation 5,384.58

R 0.95243169362Beta 0.41594757658

DIVIDEND P1-P0 P1-P0+D (P1-P0+D)/P0440 2855 3295 0.35 0.176 0.030976 0.01584620 -4050 -3430 -0.25 -0.424 0.179776 0.11024660 250 910 0.07 -0.104 0.010816 0.01248493 3350 3843 0.38 0.206 0.042436 0.02678290 2220 2510 0.32 0.146 0.021316 0.02336120 0.28532 0.1887

Average return 0.174standard deviation 0.267076768

1.0854045083

(P1-P0)/P00.2 0.09 0.0081

-0.15 -0.26 0.0676-0.01 -0.12 0.01440.24 0.13 0.01690.27 0.16 0.0256

Average 0.11 0.1326Standard deviation 0.1820714146

R 0.970139

Beta 2.355469

r

5100000021600000

300000075600000

2700