Corporate Finance

Course Title Corporate Finance Course Code F-302 Assignment On Mathematical Problems Submitted To Md. Masud Chowdhury Lecturer Dept. of Finance & Banking Submitted By Pankaze Pada Bhoumik ID: 11132603 Session: 2010-11 3rd Year 1st Semester Dept. of Finance & Banking Jatiya Kabi Kazi Nazrul Islam University Trishal, Mymensingh Submission Date: 26th August, 2013 Table of Contents Serial No. Chapter Name Problem No Page No 01 Sustainable Growth Problem 1 02-03 Problem 2 04-05 Problem 3 06-07 2 Financial Projection Or Pro forma Statement Problem 1 08-10 Problem 2 11-13 Problem 3 14-16 3 Risk & Return Analysis Problem 1 17-19 Problem 2 20 Problem 3 21 Problem 4 22-24 Problem 5 25-26 Problem 6 27-29 Problem 7 30-32 Problem 1 Total Industries has $40 million in shareholders’ equity and sales of $ 150 million last year. Its target ratios are assets to sales ratio0.40 net profit margin 0.07 debt-equity ratio 0.50 and earnings retention 0.60 if these ratios correspond to steady-state model what is its SGR? If instead of these ratios, what would be the SGR for next year if the company moved from steady-state and had the following longest? Assets to sales ratio 0.40 net profit margin 0.06; debt equity ratio 0.45; dividend of 15 million and no nets equity financing. Solution Requirement (a) We know that SGR under Steady-State model:- SGR = Where, B = Earnings retention = 0.06 NP/S = Net profit margin = 0.07 D/EQ = Debt-equity ratio = 0.05 A/S = Total assets to sales ratio = 0.40 By putting the values in SGR formula in case of Steady-state model we get. SGR = SGR = SGR = = = 0.1869 = 18.69% Ans. Requirement (b) We know that SGR under Changing model. SGR = [ Where, EQ0 = Beginning equity = $40 million New EQ = New equity = $0 million Dividend = $5 million D/EQ = Debt-equity ratio = 0.45 S/A = Total sales to asset ratio = NP/S = Net profit margin = 0.06 S0 = $150 million By putting the values in SGR formula in case of changing model we get. SGR = [ SGR = [ SGR = [( SGR = 0.165 = 1.65% Ans. Problem-2 Zippo industry has equity capital of tk 12 million, total debt of tk 8 million and sales last year of tk 300 million. It has target assets to sales ratio of 0.33367 a target net profit margin of 0.04 a target debt-equity ratio of 0.6667 and a target earning retention rate of 0.70 in steady state model what is its sustainable growth rate? Suppose now the company has established for next year a target assets to sales ratio of 0.62 a target net profit margin of 0.05 and a target debt-equity ratio of 0.08 it wishes to pay an annual dividend of tk 0.30 million and raise tk 1 million in equity capital next year what is its sustainable growth rate too next year? Why does it differ from that in part (a)? Solution Requirement (a) We know that SGR under Steady-State model:- SGR = Where, B = Earnings retention = 0.75 NP/S = Net profit margin = 0.04 D/EQ = Debt-equity ratio = 0.6667 A/S = Total assets to sales ratio = 0.33367 By putting the values in SGR formula in case of Steady-state model we get. SGR = SGR = SGR = = = 0.1763 = 17.63% Ans. Requirement (b) We know that SGR under Changing model. SGR = [ Where, EQ0 = Beginning equity = Tk.12 million New EQ = New equity = Tk. 1 million Dividend = Tk. 3 million D/EQ = Debt-equity ratio = 0.80 S/A = Total sales to asset ratio = NP/S = Net profit margin = 0.05 S0 = Tk. 30 million By putting the values in SGR formula in case of changing model we get. SGR = [ SGR = [ SGR = [( SGR = 0.4377 = 43.77% Ans. The company has moved from steady-state with higher target operating efficiency a higher debt ratio and the sale of common stock all of those things profit a high rate of growth in sales next year. Unless further changed in this direction occur the SGR will decline in future years. Problem- 3 Apex Ltd had equity capital of $ 1 million debt of $80 million and sales of last year $30 million the company has the following target ratios during 2003: D/E= 0.80, A/S=0.60, net profit margin 0.06, B=0.70. Furthermore the company has a new equity of $25 million and paid dividend of $ 10 million during 2003. Calculate sustainable growth rate for the company for 2003: Solution Requirement (a) We know that SGR under Steady-State model:- SGR = Where, B = Earnings retention = 0.70 NP/S = Net profit margin = 0.06 D/EQ = Debt-equity ratio = 0.80 A/S = Total assets to sales ratio = 0.60 By putting the values in SGR formula in case of Steady-state model we get. SGR = SGR = SGR = = = 0.1441 = 14.41% Ans. Requirement (b) We know that SGR under Changing model. SGR = [ Where, EQ0 = Beginning equity = Tk.1 million New EQ = New equity = Tk. 25 million Dividend = Tk. 10 million D/EQ = Debt-equity ratio = 0.80 S/A = Total sales to asset ratio = NP/S = Net profit margin = 0.06 S0 = Tk. 30 million By putting the values in SGR formula in case of changing model we get. SGR = [ SGR = [ SGR = [( SGR = 0.9512 = 95.12% Ans. Problem- 1 The following income statement and balance sheet relate to Bata Ltd. During 2004 Bata Ltd. Income statement For the year ended 2004 Particulars Taka Net sales 15000 Less: costs of goods sold 12300 Gross profit 2700 Less: Fixed operating costs except Depreciation 900 EBITD 1800 Less: Depreciation 500 EBIT 1300 Less Interest 400 EBT 900 Less: Taxes 40% 360 Net Income 540 Less: Dividends 270 Addition to Retained Earnings 270 Bata Ltd. Balance Sheet As at 31st Dec-2005 Liabilities Taka Assets Taka Accounts payable 300 Cash 150 Accounts 600 Accounts Receivable 1800 Notes payable 400 Inventories 2700 Long term Bond 3000 Net plant and equipment 3800 Common stock 1300 Retained earnings 2850 Total 8450 Total 8450 Additional information:- Assume that the sales and operating cost will be 10% higher in 2005 than in 2004. Further assume that the company currently operates at full capacity so it will need to expand its plant capacity in 2005 to handle the additional operations. Required:- Prepare a pro forma income statement for 2005 Prepare a pro forma balance sheet for 2005 Solution Requirement-1:- Pro forma income statement Bata Ltd. Company Pro forma Income statement For the year ended 2005 Particulars 2004 Results 2005 forecast 2005 forecasts Net sales 15000 X1.10 16500 Less: costs of goods sold 12300 X1.10 13530 Gross profit 2700 2970 Less: Fixed operating cost except depreciation 900 X1.10 990 EBITD 1800 1980 Less: Depreciation 500 X1.10 550 EBIT 1300 1430 Less Interest 400 400 EBT 900 1030 Less: Taxes 40% 360 412 Net Income 540 618 Less: Dividends @50% 270 309* Addition to retained earnings 270 309 Indicates dividend for the year 2004 and it is assumed same percentage for 2005* Bata Ltd. Company Pro forma Balance Sheet As on 31st Dec-2005 Particulars 2004 Results 2005 forecast 2005 forecasts Cash 150 X1.10 165 Accounts Receivable 1800 X1.10 1980 Inventories 2700 X1.10 2970 Total current assets 4650 5115 Net plant and Equipment 3800 X1.10 4180 Total Assets 8450 9295 Accounts payable 300 X1.10 330 Accruals 600 X1.10 660 Notes payable 400 400* Total current Liabilities 1300 1390 Long term Bond 3000 3000** Common stock 1300 1300*** Retained earnings 2850 +309**** 3159 Additional Funds needed - 828.5***** Total Liabilities and equities 4850 9295 Notes:- Indicates 2004 figures carried over 2005* Indicates 2004 figures carried over 2005** Indicates 2004 figures carried over 2005*** Represents the addition to retained earnings from 2004 Pro forma income statement**** Calculated by determining total liabilities from total assets***** Problem-2 The following Image standard income statement and balance sheet relate to Tata Ltd 2001 Tata Ltd. Income Statement For the year ended 2001 Particulars Taka Net sales 28200 Less: Cost of goods sold 17200 Goods profit 11000 Less: Fixed operating cost expect depreciations 7800 EBITD 3200 Less: Deprecation 600 EBIT 2600 Less: Interest 440 EBT 2160 Less: Taxes @ 40% 8664 Net Income 1296 Less: Dividends 516 Addition to retained earnings 780 Tata Ltd. Balance Sheet Balance Sheet as 31st Dec.2001 Liabilities Tk. Assets Tk Accounts payable 660 Cash 1120 Accruals 500 Accounts Receivable 1680 Notes payable 1040 Inventories 1270 Bank loan 8900 Pre paid expense 130 Long term Bond 4930 Net plant and Equipment 1490 Common stock 8000 Retained Earning 1660 Total 25690 Total 25690 Additional Information’s: Assume that the sales and operation costs will be 15% high in 2002 than 2001 Further assume that the company currently operations in fall clarity sale will need to expand its plants capacity in 2002 to handle the additional operations. Required: Prepare pro forma income statement to 2002 Prepare pro forma balance sheet for 2002 Solution Requirement-1:- Pro forma income statement Tata Ltd. Pro forma Income Statement For the year ended 2001 Particulars Results 2001 Forecast basis 2002 2002 Forecast Net sales 28200 X1.15 32430 Less: cost a of goods sold 17200 Xi1.5 19780 Gross profit 11000 12650 Less: Fixed operation costs except deprecation 7800 X1.15 8970 EBIT 600 X1.15 690 Less Interest 2600 2490 EBT 440 440 Less: Taxes @ 40% 2160 2550 Net Income 864 1020 Less: Dividend 1296 1530 Addition to Retained Earning 516 609 When net income 1296 then dividend 516 When net income 1 then dividend = When net income 1530 then dividend = Requirement- 2: Pro forma Balance Sheet Tata Ltd. Performa Balance sheet As on 31st Dec 2002 Particulars 2001 Results 2002 Forecast basis 2002 Forecast Cash 1120 X1.15 1288 Accounts Receivable 1680 X1.15 1932 Inventories 11270 X1.15 12960 Prepaid expenses 130 X1.15 149.5 Total Current Assets 14200 16330 Net plant cost equipment 11190 X1.15 13213.5 Total Assets 25690 29543.5 Accounts payable 660 X1.15 759 Accruals 500 X1.15 575 Notes payable 1040 1040a Total Current Liabilities 2200 2374 Bank loan 8900 8900b Long term bond 4430 4930c Common stock 8000 8000d Retained Earnings 1660 +921e 2581 Additional fund needed - 2755.5f Total Liabilities and Equipments 25690 29543.5 Indicates 2001 figures carried over 2002 Indicates 2001 figures carried over 2002 c) Indicates 2001 figures carried over 2002 d) Indicates 2001 figures carried over 2002 e) Represents the addition to retained earnings from 2001 Pro forma income statement. f) Calculated by determining total liabilities from total assets Problem 3 Bata Ltd. Income statement For the year ended 2004 Particulars Taka Net sales 15000 Less: costs of goods sold 12300 Gross profit 2700 Less: Fixed operating costs except Depreciation 900 EBITD 1800 Less: Depreciation 500 EBIT 1300 Less Interest 400 EBT 900 Less: Taxes 40% 360 Net Income 540 Less: Dividends 270 Addition to Retained Earnings 270 Bata Ltd. Balance Sheet As at 31st Dec-2005 Liabilities Taka Assets Taka Accounts payable 300 Cash 150 Accounts 600 Accounts Receivable 1800 Notes payable 400 Inventories 2700 Long term Bond 3000 Net plant and equipment 3800 Common stock 1300 Retained earnings 2850 Total 8450 Total 8450 Additional information:- Assume that the sales and operating cost will be 15% higher in 2005 than in 2004. Further assume that the company currently operates at full capacity so it will need to expand its plant capacity in 2005 to handle the additional operations. Required:- Prepare a pro forma income statement for 2005 Prepare a pro forma balance sheet for 2005 Solution Requirement-1:- Pro forma income statement Bata Ltd. Pro forma Income statement For the year ended 31st December 2005 Particulars 2004 Results 2005 forecast 2005 forecasts Net sales 15000 X1.15 17250 Less: costs of goods sold 12300 X1.15 14145 Gross profit 2700 3105 Less: Fixed operating costs except Depreciation 900 X1.15 1035 EBITD 1800 2070 Less: Depreciation 500 X1.15 575 EBIT 1300 1495 Less: Interest 400 400 EBT 900 1095 Less: Taxes 40% 360 438 Net Income 540 657 Less: Dividends 290 353 Addition to regained earnings 250 304 When net income 540 then dividend 290 When net income 1 then dividend = When net income 1530 then dividend = Requirement- 2: Pro forma Balance Sheet Bata Ltd. Pro forma Balance Sheet As on 31st December 2005 Particulars 2004 Results 2005 Forecast basis 2005 Forecast Cash 150 X1.15 172.5 Accounts Receivable 1800 X1.15 2070 Inventories 2700 X1.15 3105 Total current assets 4650 5347.5 Net plant and Equipment 3800 X1.15 4370 Total Assets 8450 9717.5 Accounts payable 300 X1.15 345 Accounts 600 X1.15 690 Notes payable 400 400 Total current liabilities 1300 1435 Long term Bond 3000 3000 Common stock 1300 1300 Retained earnings 2850 +304 3154 Additional Funds needed - 828.5 Total Liabilities and equities 4850 9717.5 Indicates 2004 figures carried over 2005 Indicates 2004 figures carried over 2005 c) Indicates 2004 figures carried over 2005 d) Indicates 2004 figures carried over 2005 e) Represents the addition to retained earnings from 2004 Pro forma income statement. f) Calculated by determining total liabilities from total assets Problem 1 The two companies has possible outcomes and probability Possible Outcomes Probability Asset A Asset B Pessimistic .25 13% 7% Most likely .50 15 15 Optimistic .25 17 23 Total 1.0 Requirements:- a) Expected rate of return b) Standard deviation c) Co-efficient of variation d) Which project the investor should choose Solution Required solution (a) Expected return for asset A We know that, E (A) = i × (Ri) Now, E (A) = i × (Ri) E (A) = {(0.25×.13) + (0.50×.15) + (0.25× 17)} E (A) = 0.15 E (A) = 15% Expected return for asset B We know that, E (B) = i × (Ri) Now, E (B) = i × (Ri) E (B) = {(0.25×.07) + (0.50×.15) + (0.25× .23)} E (B) = 0.15 E (B) = 15% Required solution (b) The following table shows the necessary calculation Possible Outcomes Asset A PRi × (RA-A)2 Asset B PRi × (RB-B)2 Return% RA (RX-X)2 PRi Return% RB (RB-B)2 RRi 1 13 4% .25 1% 7% 64% .25 16% 2 15 0 .50 0 15 0 .50 0 3 17 4 .25 1 23 64 .25 16 × (RA-A)2 2% × (RB-B)2 32% Standard deviation for Asset A:- = = 1.41% Standard deviation for Asset B:- = = = 5.66% Required solution (c) Co-efficient of variation for Asset A CV = = = 0.094 Co-efficient of variation for Asset B CV = = = 0.3773 Required Solution (d) Hence the CV of asset A is lower than the CV of Asset B. So the company should invest in asset A. Problem 2 Suppose you have the following information: Security Amount Invested Expected Return A $1000 8% B $2000 12% C $3000 15% D $4000 18% What are the portfolio weights? What is the expected return on this portfolio? Solution Required solution (a) Total amount invested = $ (1000+2000+30004000) = $ 10000 The portfolio weights are given below: For Security A = = 0.10 For Security B = = 0.20 For Security C = = 0.30 For Security D = = 0.40 Required solution (b) Expected return on this portfolio E (P) = i × E (i) = (.10 × 8%) + (.20 × 12%) + (.30 ×15%) + (.40 × 18%) = .80% + 2.4% + 4.5% 7.2% = 14.19% Ans. Problem 3 Consider a three stock portfolio consisting of stocks X, Y and Z with expected returns of 12%, 20% and 17% respectively. Assume that 50% of investible funds are invested in stock X, 30% in Y and 20% in Z. Calculate portfolio expected return. Solution We know that, The expected return on any portfolio can be calculated as E (P) = i × E (i) Where, E (RP) = Expected return from portfolio Wi = Proportion invested in asset i E (Ri) = Expected return from asset i n = Number of assets in portfolio E (P) = i × E (i) = {(0.50×12%) + (0.30×20%) + (0.20×17%)} = 6% + 6% + 3.4% = 15.4%. Ans. Problem 4 Stocks X and Y have the following historical returns: Year stock X Returns Stock Y Returns 1996 -18% -14.50% 1997 33 21.80 1998 15 30.50 1999 0.50 -7.60 2000 27 26.30 Calculate the portfolio risk of the security of 50% weights is placed in each stock X and Y. Solution For Stock X Expected Return (X) = (-18% + 33% + 15% + 0.5% + 27%) ÷ 5 =11.5% For Stock Y Expected Return (Y) =11.30% We know that, The expected return on any portfolio can be calculated as E (P) = i × E (i) Where, E (RP) = Expected return from portfolio Wi = Proportion invested in asset i E (Ri) = Expected return from asset i n = Number of assets in portfolio Now, E (P) = i × E (Ri) = (.50 × 11.5%) + (.50 × 11.30%) = 5.75% + 5.65% = 11.40% The following table shows the necessary calculation Stock X Stock Y Year Return% RX (RX-X)2 RX2 Return% RY (RY-Y)2 RY2 RX×RY 1996 -18 870.25 324 -14.50 665.64 210.25 261 1997 33 462.25 1089 21.80 110.25 475.24 719.40 1998 15 12.25 225 30.50 368.64 930.25 457.50 1999 0.50 121 0.25 -7.60 357.21 57.76 -3.80 2000 27 240.25 729 26.30 225 691.69 710.10 RX = 57.5 (RX-X)2 =1706 RX2= 2367.25 RY = 11.3 (RY-Y)2 =1726.74 RY2 = 2365.19- RX×RY =2144.20 The standard deviation for Stock X = = = 20.65% Standard deviation for Stock Y = = = 20.78% We know that Co-efficient correlation: = = = =0.87 Therefore the portfolio standard deviation is:- = = = 20.03% Ans. Problem 5 Consider the following information: Economy Probability Security N Security M Revision 0.50 -20% -30% Boom 0.20 70% 10% Normal 0.30 25% 90% If the portfolio weight for cash stock is 0.50 determine the portfolio expected return. Solution Expected return for security N We know that, E (N) = i × (Ri) Now, E (N) = i × (Ri) E (N) = {(0.50×-20) + (0.20×70) + (0.30× 25)} E (N) = -10% + 14% + 7.50% E (N) = 11.50% Expected return for security M We know that, E (M) = i × (Ri) Now, E (M) = i × (Ri) E (M) = {(0.50×-30) + (0.20×10) + (0.30× 90)} E (M) = -15% + 2% + 27% E (M) = 14% We know that, The expected return on any portfolio can be calculated as E (P) = i × E (i) Where, E (RP) = Expected return from portfolio Wi = Proportion invested in asset i E (Ri) = Expected return from asset i n = Number of assets in portfolio Now, E (P) = i × E (Ri) = (.50 × 11.5%) + (.50 × 14%) = 5.75% + 7% = 12.75% Home Work Problem 6 Based on the following in formations calculate the expected returns and standard deviation for the equally weighted porfolio State of Economy Probability of state Return of A Return of B Recession 0.30 15% 20% Normal 0.40 10% 15% Boom 0.30 7% 11% Solutions Expected return for A We know that, E (A) = i × (Ri) Now, E (A) = i × (Ri) E (A) = {(0.30×15%) + (0.40×10) + (0.30× 7)} E (A) = 4.5% + 4 + 2.1 E (A) = 10.60% Expected return for B We know that, E (B) = i × (Ri) Now, E (B) = i × (Ri) E (B) = {(0.30×20%) + (0.40×15) + (0.30×11)} E (B) = 6% + 6 + 3.3 E (B) = 15.3% We know that, The expected return on any portfolio can be calculated as E (P) = i × E (i) Where, E (RP) = Expected return from portfolio Wi = Proportion invested in asset i E (Ri) = Expected return from asset i n = Number of assets in portfolio Now, E (P) = i × E(Ri) = (.50 × 10.6%) + (.50 × 15.3%) = 5.3% + 7.65% = 12.95% Standard Deviation for Stock A = = = =3.14% Standard Deviation for Stock B = = = =3.53% We know Co-variance = (} ={} = 6.204+ 0.072 + 4.644 = 10.92 We know Co-efficient of correlation = = 0.99 We know, Portfolio Standard Deviation = = = 3.12% Ans. Problem 7 Securities X and Y have the following characteristics Security X return% Probability Security Y return % Probability 30% 0.10 -20% 0.05 20 0.20 10 0.25 10 0.40 20 0.30 5 0.20 30 0.30 -10 0.10 40 0.10 Calculate the expected return and risk of return for each security Calculate the expected return and risk of returns for the Probability of X and Y placing equal weight to each. Solutions Requirement (a) Expected return for Security X We know that, E (X) = i × (Ri) Now, E (X) = i × (Ri) E (X) = {(0.10×30%) + (0.20×20) + (0.40× 10) + (0.20×5) + (0.10×-10} E (X) = 3% + 4 + 4 + 1 - 1 E (X) = 11% Expected return for Security Y We know that, E (Y) = i × (Ri) Now, E (Y) = i × (Ri) E (Y) = {(0.05×-20%) + (0.25×10) + (0.30× 20) + (0.30×30) + (0.10×40)} E (Y) = -1% + 2.5 + 6 + 9 + 4 E (Y) = 20.5% The following table shows the necessary calculation Possible Outcomes Security X PRi × (RX-X)2 Security Y PRi × (RY-Y)2 Return% RX (RX-X)2 PRi Return% RY (RY-Y)2 PRi 1 30 361% .10 36.1% -20% 1600% .05 80% 2 20 81 .20 16.2 10 100 .25 25 3 10 1 .40 .40 20 0 .30 0 4 5 36 .20 7.2 30 100 .30 30 5 -10 441 .10 44.1 40 400 .10 40 × (RA-A)2 104% × (RB-B)2 175% Standard deviation for Security X:- = = 10.2% Standard deviation for Security Y:- = = = 13.23% Requirement (b) We know that, The expected return on any portfolio can be calculated as E (P) = i × E (i) Where, E (RP) = Expected return from portfolio Wi = Proportion invested in asset i E (Ri) = Expected return from asset i n = Number of assets in portfolio Now, E (P) = i × E (Ri) = (.50 × 7.4%) + (.50 × 19.5%) = 3.7% + 9.75% = 13.45% We know, Portfolio Standard Deviation = = = 8.35 Ans. 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