Solved problem Rs.in million

Profit & Loss Account for year ending 31st March 20X1 20X0Net sales 1065 950Cost of goods sold 805 720Stocks 600 520Wages and salaries 120 110Other manufacturing expenses85 85 90Gross profit 260 230Operating expenses 90 75Depreciation 50 40Selling and general administration 40 35Profit before interest and tax 170 155Interest 35 30Profit before tax 135 125Tax 50 45Profit after tax 85 80Dividends 35 30Retained earnings 50 50Balance sheet as at 31st March 20X1 20X0Sources of Funds Shareholders' funds 505 455 (a) Share capital 125 125 (b) Reserve and surplus 380 330 Loan funds 280 260 (a) Secured loans 180 160 (i) Due after 1 year 130 135 (ii) Due within 1 year 50 25 (b) Unsecured loans 100 100 (i) Due after 1 year 60 70 (ii) Due within 1 year 40 30Total 785 715Application of FundsNet fixed assets 550 495Investments 30 25 (a) Long - term investments 20 20 (b) Current investments 10 5Current assets, loans and advances 355 333 (a) Inventories 160 138 (b) Sundry debtors 120 115 ( c) Cash and bank balances 25 20 (d) Loans and advances 50 60Less: Current liabilities and provisions 150 138Net Current assets 205 195Total 785 715

A. Cash Flow from Operating Activities Net profit before tax and extraordinary items 135 Adjustments for Interest paid 35 Depreciation 50 Operating profit before working capital changes 220 Adjustments for

Classified Cash flow statement for period 1-4-20X0 to 31-3-20X1

Debtors (5) Inventores (22) Loans and advances 10 Current liabilities and provisions 12 Cash generated from operations 215 Tax paid (50) Net cash flow from operating activities 165 B. Cash Flow from Investing Activities Purchases of fixed assets (105) Net investment in marketable securities (5) Net cash flow from investing activities (110)C. Cash Flow from Financing Activities Proceeds from loans 20 Interest paid (35) Dividend paid (35) Net cash flow from financing activities (50)D. Net Increase in cash and cash Equivalents 5 Cash and cash equivalents as on 1-4-20X1 25 Cash and cash equivalents as on 1-4-20X0 20

Solved problem 4.1Current assets 1,600Current liabilities 1,000Minimum current ratio 1.25Maximum borrowing 1400

Solved problem 4.2Current ratio 1.4Acid-test ratio 1.2Current liabilities 1,600Inventory turnover ratio 8Current assets 2,240 Inventories 320Sales 2,560

Solved problem 4.3Net profit margin ratio 4%Current ratio 1.25Return on net worth 15.23%Total debt to total assets ratio 0.4Inventory turnover ratio 25Solution are the figures in italics in the following statementsProfit and Loss accountSales 2535.8Cost of goods sold 1587.9Operating expenses 700Profit before interest and tax 247.9Interest 45Profit before tax 202.9Tax provision at 101.4

50%Profit after tax 101.4Balance sheetNet worth 666 Fixed assets 930Long-term debt: interest at Current assets 180

15% 300 Cash 18.6Accounts payable 144 Receivables 60

Inventory 101.4Total 1110 Total 1110

Solved problem 4.4Rs.in million

Profit & Loss Account for year ending 20X1 20X0Net sales 1065 950Cost of goods sold 805 720Stocks 600 520Wages and salaries 120 110Other manufacturing expenses85 85 90Gross profit 260 230Operating expenses 90 75Depreciation 50 40Selling and general administration 40 35Profit before interest and tax 170 155Interest 35 30Profit before tax 135 125Tax 50 45

Profit after tax 85 80Dividends 35 30Retained earnings 50 50Balance sheet as at 31st March 20X1 20X0Sources of Funds Shareholders' funds 505 455 (a) Share capital 125 125 (b) Reserve and surplus 380 330 Loan funds 280 260 (a) Secured loans 180 160 (i) Due after 1 year 130 135 (ii) Due within 1 year 50 25 (b) Unsecured loans 100 100 (i) Due after 1 year 60 70 (ii) Due within 1 year 40 30Total 785 715Application of FundsNet fixed assets 550 495Investments 30 25 (a) Long - term investments 20 20 (b) Current investments 10 5Current assets, loans and advances 355 333 (a) Inventories 160 138 (b) Sundry debtors 120 115 ( c) Cash and bank balances 25 20 (d) Loans and advances 50 60Less: Current liabilities and provisions 150 138Net Current assets 205 195Total 785 715Current ratio 1.52Acid-test ratio 0.85Cash ratio 0.15Debt-equity ratio 0.55Interest coverage ratio 4.86Fixed charges coverage ratio 1.24Inventory turnover 5.40Debtors turnover 9.06Average collection period in days 40.27Fixed assets turnover 2.04Total assets turnover 1.42Gross profit margin 24.4%Net profit margin 7.98%Return on assets 11.3%Earning power 22.7%Return on equity 17.7%

Solved Problem 5.1

Year 1 Year 2

Net sales 600 720 100.0 Budgeted 850.0

Cost of goods sold 450 500 72.0 611.7

Gross profit 150 220 @ 238.3

Selling expenses 50 60 8.3 70.8

General and administration expen 36 40 5.8 48.9

Depreciation 30 40 Budgeted 45.0

Operating profit 34 80 @ 73.5Non-operating surplus deficit 10 -8 Budgeted 11.9

Profit before interest and tax 44 72 @ 85.4Interest 10 12 1.7 14.2

Profit before tax 34 60 @ 71.2

Tax 14 26 35.6

Profit after tax 20 34 @ 35.6Dividends(given) 12 15 Budgeted 21.0

Retained earnings 8 19 @ 14.6Balance Sheets Year 1 Year2

Fixed assets (net 240 270 Budgeted 300.0

Investments 10 10 No change 10.0

5 6 0.8 7.1

80 90 12.9 109.5

125 144 20.4 173.2

. Loans and advances 25 30 4.2 35.4

15 10 Budgeted 5.0

Total 500 560 640.2

Liabilities Share capital

Equity 100 100 Nochange 100.0

Preference 20 20 No change 20.0

Reserves and surplus 150 169 183.6

Secured loansBank borrowings 60 80 10.6 90.2

Average percent of sales

Proforma profit and

loss account

for year 3

Budgeted @50% of PBT

Current assets, loans and advances· Cash and bank· Receivables · Inventories

Miscellaneous expenditures & losses

Proforma P&L

account

Unsecured loansPublic deposits 11 No change 11.0

Current liabilities andprovisionTrade creditors 125 130 19.3 164.2

Provisions 45 50 7.2 61.2

External funds requirement 10.1

Total 500 560 640.2

Solved Problem 5.2A/S 0.8S(in Rs. Million) 80L/S 0.4m 0.06

100d 0.4EFR(in Rs. Million) 4.4

Solved Problem 5.3m 0.05d 0.3A/E 2.4

1g 9.17%

Balancing item

Note: The slight differences in figures between the above & the text is due to rounding off

S1 (in Rs. Million)

A/S0

Solved problem 6.1Investment today 5,000Interest rate 9%No. of years of investment 75Future value 3,205,954.47

Solved problem 6.2Interest rate in percentage 12Doubling period as per rule of

72 669 6.1

Solved problem 6.3Nominal rate of interest 16%No. of compoundings in a year 4Effective rate of interest 17%

Solved problem 6.4No. of annual deposits 15Amount of each deposit 5,000Rate of interest per annum 14%Total period of deposit in years 15Future value of the annuity 219,212

Solved problem 6.5Period of deposit in years 5Amount of annual deposit 6,000Lumpsum payment at the end 44,650Implicit interest rate 20%

Solved problem 6.6Future value 1,000,000Period 60Discount rate 10%Present value 3,284

Solved problem 6.7No. of annuity payments 12Amount of annuity payment 10,000

8Discount rate 14%

7 56,603 Present value of the annuity 22,621

Solved problem 6.8Discount rate 14%Year 0 1 2 3 4Cash flow 5,000 6,000 8,000 9,000 8,000Present value 27,230

Solved problem 6.9Amount of deposit 200,000Interest rate 10%

No. of years at the end of which the first annuity payment occurs

Value of the annuity at the end of the year

No.of annual withdrawals 15Amount of each withdrawal 26,295

Solved problem 6.10Cost of the tour 1,000,000Amount of annual savings 80,000

14%No. of years of waiting 7.72

Solved problem 6.11Amount of borrowal 80,000Monthly interest rate 1.25%No. of monthly instalments 12Monthly instalment amount 7,221 Loan amortisation schedule

Month Interest1 80,000 7,221 1000 6,221 73,7792 73,779 7,221 922.2 6,298 67,4813 67,481 7,221 843.5 6,377 61,1044 61,104 7,221 763.8 6,457 54,6475 54,647 7,221 683.1 6,538 48,1096 48,109 7,221 601.4 6,619 41,4907 41,490 7,221 518.6 6,702 34,7888 34,788 7,221 434.8 6,786 28,0029 28,002 7,221 350.0 6,871 21,132

10 21,132 7,221 264.1 6,957 14,17511 14,175 7,221 177.2 7,043 7,13212 7,132 7,221 89.1 7,132 0

Rate of interest per annum on savings

Beginning amount

Monthly instalment

Principal repayment

Remaining balance

Solved problem 7.1Par value of the bond 100Coupon rate 12%Maturity period in years 5Discount rate 15%Settlement date(say) 1/1/2007Maturity date 12/31/2011Value of the bond(Price) 89.95

Solved problem 7.2Par value of the bond 1,000Market price of the bond 1,050Coupon rate 14%Maturity period in years 5Settlement date(say) 1/1/2007Maturity date 12/31/2011Yield to maturity 12.59%Reinvestment rate 12%Future value of investment 1,889.40 Realised yield to maturity 12.47%

Solved problem 7.3Par value of the bond 100Coupon rate 14%Maturity period in years 5No.of interest payments in a year 2Required rate of return 16%Settlement date(say) 1/1/2007Maturity date 12/31/2011Value of the bond 93.35

Solved problem 7.4Current selling price per share 30Dividend expected next year 2Required rate of return 15%Expected growth rate 8.3%

Solved problem 7.5Growth rate in dividends 18%Period of 18% growth rate in years 4Subsequent growth rate 12%Period of 12% growth rate in years 4Growth rate after 8 years, forever 6%Last dividend per share 2Required rate of return on equity 15%

Year Dividend PV of dividend1 2.36 2.052 2.78 2.113 3.29 2.164 3.88 2.225 4.34 2.166 4.86 2.107 5.45 2.058 6.10 1.99

Price of the share at the end of 8 years 71.86

23.49Present value of the price of the share at the end of 8 years

Intrinsic value per share 40.33

Solved problem 7.6Current dividend 3Initial Supergrowth rate 40%Period in years for the supergrowth rate 5Consequent stable growth rate 12%Required return 15%Intrinsic value of the share 327.60

Solved problem 7.7Current dividend 5Present growth rate 50%Linearly declining period in years 8Stable rate after 8 years 10%Required rate of return 18%Intrinsic value per share 168.75

Solved problem 8.1

ProbabilityHigh growth 0.3 100 150 125Low growth 0.4 110 130 120Stagnation 0.2 120 90 105Recession 0.1 140 60 100

100

Box Limited Cox LimitedAmount invested 1,000 1,000 1,000

10 10 10Expected return 1120 1210 1165Standard deviation 116.62 291.38 89.58

Solved problem 8.2Risk-free rate of return 9%

13%

7%

2Beta of the stock 1.20(a)

13.80%

31.47(b)(i)

2%

24.32(b)(ii)

3%

57.89(b)(iii)

1.3

29.72

Solved problem 8.3

Return on Box's stock

Return on Cox's stock

Return on a portfolio of half share each of Box and Cox

Current selling price of both the shares

Portfolio where a unit consists of half share each of Box and Cox

No.of shares/units that can be purchased

Expected rate of return on the market

Expected dividend growth rate

Dividend per share last paid

Required rate of return on the stock

Equilibrium price of the stock

Increase in inflation premium

New equilibrium price of the stock

increase in expected dividend growth rate

New equilibrium price of the stock

Increased beta of the stock

New equilibrium price of the stock

Period1 10 122 15 143 18 134 14 105 16 96 16 137 18 148 4 79 (9) 1

10 14 1211 15 (11)12 14 1613 6 814 7 715 (8) 10

Beta 0.354Alpha 6.81

The characteristic line is

Return on stock A (%)

Return on market portfolio(%)

RA = 6.81+0.354RM

Solved Problem 9.1

State of nature Probability Return on asset 1(%)1 0.1 5 0 64 196

2 0.3 10 8 9 36

3 0.5 15 18 4 16

4 0.1 20 26 49 144

Expected value of the return on asset 1 = 13Expected value of the return on asset 2 = 14

(a)Standard deviation of the return on asset 1 = 4.00Standard deviation of the return on asset 2 = 7.27

(b )Covariance between the returns on assets 1 and 2 = 29.00

1.00

Solved Problem 9.2Security no. 1 2 3

0.3 0.5 0.2

6.0 9.0 10.0

1 and 2 1 and 3 2 and 3

0.4 0.6 0.7

7.13

Solved Problem 9.3Stock A Stock B

Expected return (%) 16 12Standard deviation 15 8

0.6

72

14.40

Return on asset 2(%)

Square of the deviation of the return on asset 1 from its expected value

Square of the deviation of the return on asset 2 from its expected value.

( c) Coefficient of correlation between the returns on assets 1 and 2 =

Proportion of the security in the portfolio

Standard deviation of the securityCorrelation coefficient between securities

Correlation coefficient

Standard deviation of portfolio return

Coefficient of correlation between the two stocks

(a) Covariance between the two stocks

(b) Expected return of a portfolio in which A & B have weights of 0.6

& 0.4 (%)

15.34

Solved Problem 9.4

Market return(%) Defensive Stock(%)6 2 8

20 30 16(a) Beta of the aggressive stock 2 Beta of the defensive stock 0.571(b)

Probability Aggressive Stock(%)0.5 6 2 80.5 20 30 16

Expected return on the aggressive stock(%) 16Expected return on the defensive stock(%) 12

( c)Expected return on the market portfolio(%) 13

Market risk premium (5) 6

The SML is(d)

Required return of the aggressive stock (%) 19Alpha of the aggressive stock(%) -3

Required return of the defensive stock (%) 10.429Alpha of fhe defensive stock (%) 1.571

(b) Risk of a portfolio in which A & B have weights of 0.6 & 0.4 (%)

Aggressive Stock(%)

Market return(%)

Defensive Stock(%)

= 7%+βix 6%

112188

84

Product of the deviation of the return on asset 1 from its mean and the deviation of the return on asset 2 from its mean

Chapter 10Solved problem 10.1

S E u r d R60 50 1.4 0.12 0.8 1.12

34 ∆ 0.94

0 B 40.48C 16.19

Solved problem 10.2

E σ t(in years)120 110 0.12 0.4 0.5

0.6612 0.3783 0.7458 0.6474

22.42233

Cu

Cd

S0 rf

d1 d2 N(d1) N(d2)

C0

Chapter 11Solved problem 11.1

Year 0 1 2 3 4 5

Cash flow (100,000.00) 20,000.00 30,000.00 40,000.00 50,000.00 30,000.00 Cost of capital 0.12 NPV 19,042.88 BCR 1.19 IRR 18.69% MIRR 15.97%Calculation of payback periodYear 0 1 2 3 4 5

100,000.00 80,000.00 50,000.00 10,000.00 (40,000.00)

3.20 Calculation of discounted payback periodYear 0 1 2 3 4 5 PV of cash flows (100,000.00) 17,857.14 23,915.82 28,471.21 31,775.90 17,022.81

100,000.00 82,142.86 58,227.04 29,755.83 (2,020.07)

3.94

Unrecovered investment balance

Payback period in years

Unrecovered balance

Discounted payback period in years

Solved problem 12.1Economic life of computer(years) 5Depreciation rate(WDV) 33.33%Tax rate 50.00%

Cash flow for the computer installationYear 0 1 2 3 4 5Cost of computer (1,500,000)Savings in clerical cost 600,000 600,000 600,000 600,000 600,000Savings in space cost 100,000 100,000 100,000 100,000 100,000Operation and maintenance cost 250,000 250,000 250,000 250,000 250,000Depreciation 500,000 333,333 222,222 148,148 98,765 Profit before tax (50,000) 116,667 227,778 301,852 351,235 Tax (25,000) 58,333 113,889 150,926 175,617 Profit after tax (25,000) 58,333 113,889 150,926 175,617 Net salvage value 197,531 Initial flow (1,500,000)Operating flow 475,000 391,667 336,111 299,074 274,383 Terminal flow 197,531 Net cash flow (1,500,000) 475,000 391,667 336,111 299,074 471,914

Solved problem 12.2Old hammer New hammer

Original cost 1,000,000 1,600,000 No. of years ago bought 2 0 Depreciation rate 33.33% 33.33%Remaining life in years 5 5 Tax rate 50% 50%Present book value 444,444

Cash flow of the replacement projectYear 0 1 2 3 4 5Net investment in new hammer (1,155,556)Increase in revenues 200,000 200,000 200,000 200,000 200,000Saving in operating cost 150,000 150,000 150,000 150,000 150,000Depreciation on new hammer 533,333 355,556 237,037 158,025 105,350 Depreciation on old hammer 148,148 98,765 65,844 43,896 29,264

385,185 256,790 171,193 114,129 76,086 Incremental taxable profit (35,185) 93,210 178,807 235,871 273,914 Incremental tax (17,593) 46,605 89,403 117,936 136,957 Incremental profit after tax (17,593) 46,605 89,403 117,936 136,957 Net incremental salvage value 152,172 Initial flow (1,155,556)Operating flow 367,593 303,395 260,597 232,064 213,043 Terminal flow 152,172 Net cash flow (1,155,556) 367,593 303,395 260,597 232,064 365,215

Incremental depreciation on new hammer

Solved problem 13.1Discount rate 10% Investment(Rs. million) 50

(Amts in Rs.million)

Year Probability Cash flow Expected NPV1 0.4 15

0.3 200.3 30 21 39

2 0.4 200.4 250.2 30 24 14

3 0.3 250.5 300.2 40 30.5 11.84 27.25

The standardised difference between the specified point(NPV=0) and NPV =The probability that the NPV will be less than 0 =

Solved problem 13.2

FactorsInitial investment 30,000 Investment 30,000 Cost of capital 10% Sales quantity 1,400

1,400 Price per unit 30

Price per unit 30 Sales 42,000

Variable cost per unit 20 20 Fixed costs 3,000 Variable costs 28,000 Depreciation 2,000 Fixed costs 3,000 Tax rate 50% Depreciation 2,000 Life of the project in years 5 Pre-tax profit 9,000 Net salvage value 0 Taxes 4,500

4,500

6,500 Salvage value 0

Expected cash flow

Variance of the cash

flows

Expected valuesCalculation of expected net

present value

Quantity manufactured and sold annually

Variable cost per unit

For sensitivity analysis proceed as follows.In cell B34 copy the formula for NPV from cell E32. .Leave the adjcacent

cell to the left(A34) blank and then fill the various values of quantity manufactured, one below the other from cell A35 onwards( in this case 800 and 1800). Highlight(select) A34

to B36 and then from the drop-down menu for Data, select table. In the dialogue box that appears, type against column input cell ,thecell reference E32 and click OK. The NPV values corresponding to the various quantity figures will be automatically filled in. Next give headings Quantity and NPV in cells A34 and B34 respectively as separately

shown.To change the numerical value into text in cell B34 go to Format>Cells>Custom and against Type, type out "

Net present value"

Profit after taxes

Cash flow from operations

(5,360)

(5,360) Quantity Net present value800 (16,732) 800 (16,732)

1,800 2,222 1,800 2,222 The following analysis is done using the above technique

Price per unit Net present value Net present value20 (31,895) 15 7,908 50 47,711 40 (58,431)

Solved problem 13.3('000)

Year 0 1 to 10Investment (30,000)

66.67%Tax rate 50.00%Sales per year 42,000 Variable costs per year 28,001 Fixed costs per year 3,000 Depreciation per year 2,000 Pre-tax profit per year 8,999 Taxes per year 4,499 Profit after taxes per year 4,499 Cash flow from operation per year 6,499 Accounting break-even level of sales 15,002 Calculation of the financial break-even level of salesDiscount rate 10%Project life in years 5 Total of the present values of the cash inflows 24,637 Initial investment (30,000)Financial break-even level of sales (51,142)

Solved problem 13.4

Year Expected cash flow0 (100,000) (100,000) (100,000)

For sensitivity analysis proceed as follows.In cell B34 copy the formula for NPV from cell E32. .Leave the adjcacent

cell to the left(A34) blank and then fill the various values of quantity manufactured, one below the other from cell A35 onwards( in this case 800 and 1800). Highlight(select) A34

to B36 and then from the drop-down menu for Data, select table. In the dialogue box that appears, type against column input cell ,thecell reference E32 and click OK. The NPV values corresponding to the various quantity figures will be automatically filled in. Next give headings Quantity and NPV in cells A34 and B34 respectively as separately

shown.To change the numerical value into text in cell B34 go to Format>Cells>Custom and against Type, type out "

Net present value"Net present value

Variable cost per unit

Variable costs as a percentage of sales

Certainty equivalent

value

PV of certainty equivalent

value

1 40,000 38,000 34,545 2 38,000 34,200 28,264 3 36,000 30,600 22,990 4 34,000 27,200 18,578 5 32,000 24,000 14,902 6 30,000 21,000 11,854

Net present value 31,134

(Amts in Rs.million)

7.56-1.5665.87%

Standard deviation

of the NPV

Pessimistic

Page 23

80020

40

Expected

Page 24

140030

20

Optimistic

Page 25

180050

15

Solved problem 14.1Project cost 20,000,000Period in years 10

4,000,000Tax rate 35%

1 : 1Cost of equity 16.90%

14%

12%

2%WACC 13%

7%

199,598

Solved problem 14.2Tax rate 35%

10%

Debt equity ratio 0.6 : 1Risk-free rate 8%

7%

0.81WACC 0.11 Formula used =B71/(B71+D71)*B70*(1-B69)+D71/(B71+D71)*(B72+B74*B73)

The above is obtained using the following steps1. Enter the various given values leaving the value for beta blank. In the WACC value cell type the formula for that as shown2.On the Tools menu, click Goal Seek.3.In the Set cell box, enter the reference for the cell that contains the formula Here, this is cell B75.4.In the To value box, type the result you want. Here it is 11%.5 In the By changing cell box, enter the reference for the cell that contains the value you want to adjust viz. cell B74.6 Click OK.

After-tax annual cash flow

Target debt-equity ratio

Pre-tax cost of debt

Floatation cost of equity

Floaion cost of debt

Average floatation cost

NPV of the expansion project

Pre-tax cost of debt

Market risk premium

Beta of the equity

Formula used =B71/(B71+D71)*B70*(1-B69)+D71/(B71+D71)*(B72+B74*B73)

The above is obtained using the following steps1. Enter the various given values leaving the value for beta blank. In the WACC value cell type the formula for that as shown2.On the Tools menu, click Goal Seek.3.In the Set cell box, enter the reference for the cell that contains the formula Here, this is cell B75.4.In the To value box, type the result you want. Here it is 11%.5 In the By changing cell box, enter the reference for the cell that contains the value you want to adjust viz. cell B74.

Chapter 15Solved problem 15.1

(Amounts in Rs.million)Discount rate 13%System A BInitial outlay 4 3Annual operating costs 1.2 1Life in years 6 4Present value of costs 8.7971 5.9745 UAE 2.2006 2.0086 As the present value of costs associated withSystem B is less than that for A, the firm is advised to choose system B

Solved problem 15.2 ( Amounts in rupees)Initial outlay 15,000,000 Project life in years 6 Net annual cash inflow 3,750,000 Opportunity cost of capital 18%Term loan that can be raised for the project 10,000,000 Interest rate for the term loan 16%

5 YearThe first insalment falling due at the end of year 2 1 10,000,000 Amount that can be raised by issuing equity 5,000,000 2 10,000,000 Issue cost of equity 8% 3 8,000,000 Tax rate for the company 50% 4 6,000,000 Base case NPV (1,883,990) 5 4,000,000 The adjusted NPV after adjustment for issue cost (2,318,773) 6 2,000,000 Present value of tax shield associated with debt 2,177,333 Adjusted NPV (141,440)

No. of annual instalments in which the term loan is repayable

Debt outstanding at the beginiing

689,655 594,530 410,021 265,100 152,356 65,671

Present value of interest tax

shield

Chapter 18Solved problem

( Amount in rupees)

Present stock price Rs. 120 No.of shares required to subscribe to one rights share 2 Subscription price Rs. 80 a) Theoretical value per share of the ex-rights stock Rs. 106.67 b) Theoretical value of a right Rs. 26.67

Chapter 19Solved problem 19.1(a) (Rs.in million) Solved problem 19.2Net operating income 40 Cost of debt 9%Interest on debt 10 Cost of capital 12%Cost of debt 12% Debt equity ratio 0.8 : 1Cost of equity 18% Cost of equity 14.40%Market value of debt 83.33 Market value of equity 166.67 Average cost of capital 16%(b)Debt employed to finance a project 100 Operating income earned by the project 20Net operating income 60Interest on debt 22Equity earnings 38Marketn value of equity 211.11Market value of debt 183.33Market value of the firm 394.44Average cost of capital 15.21%

Solved problem 19.4

30%

10%

15%Tax advantage of a rupee of debt( in rupees) 0.26

tc

tpe

tpd

Solved Problem 20.1

Tax rate for the company

A B

5,000,000 3,000,000

20 20

4,000,000

11%

Amount of dividend to be paid 440000Amount of interest to be paid

PBIT 9166666.66666667 PBIT

=(B14-B13)*(1-D4)/(D2+B6) =((C14-C13)*(1-D4)-C12)/(D2+C6)

0

Solved Problem 20.2

Debt equity ratio 1.2 NotePre-tax cost of debt 12%Tax 30%ROI 19.53%Target ROE 0.2

Formula used =(B22+(B22-B20)*B19)*(1-B21)

Solved Problem 20.3(a) ( Amounts in Rs.million)Amount of debt finance 500Interest rate on debt 14%Annual interest on debt 70

No. of equity shares of the company at present

Amount of external financing required (Rs.)

Alternatives for external financing

No.of equity shares to be issued of face value Rs.10

Issue price of an equity share(Rs.)

No.of preference shares to be issued of Rs.10 par

Dividend to be paid on preference shares @

Amount to be raised through debentures(Rs.)

Interest to be paid on debentures @

To obtain the EPS-PBIT indifferent point for alternatives A and B, first have the formula(see comments)

To start with, keep the cell B22 blank. Then use the Goal Seek feature in Tools and equate the formula to the given value of 20 percent, and show the changing cell to be B22. The correct ROI

value that satisfies the target ROE value will appear in B22

160

90

90

0

-1

Probability of cash inadequecy 15.87%(b)

z value -1.15

Probability of cash inadequecy 0.125

56.5z value -1.15

Expected value of the net cash flows, without taking the interest on debt into account

Expected value of the net cash flows, taking the interest on debt into account(A)

Stanard deviation of the above net cash flows

Specified value of the net cash flow(which signifies cash inadequecy) (B)

Standardised difference between B and A(the z value)

We can use Goal Seek feature in Tools to get the z value ( in cell B39 )corresponding to a cumulative porbabiliy of 12.5 percent as shown below.

Again, use the Goal Seek feature as shown below to get the cash flow ( in cell B42 below) corresponding to a z value of -1.15

Cash flow that would give a z value of -1.15

20,000,000 N OTE

100,000,00040%

C

1,000,000

20

80,000,000

14%

11200000

PBIT

=(D14-D13)*(1-D4)/(D2+D6)

This value would be obtained at the end only. You may leave this cell B14 blank while filling up the

values

In the cell B16 type out the formula (B14-B13)*(1-D4)/(D2+B6)-((B14-C13)*(1-D4)-C12)/(D2+C6). You may use the Goal Seek feature in Tools and equate this formula to 0 to get the PBIT value in cell B14, which would then be the indifferent point

Solved problem 20.4Corporate tax rate 50%Alternative i ii iiiNo. of equity shares to be issued 50,000 25,000 25,000Issue price of an equity share 10 10 10No.of debentures to be issued 0 2,500 0Issue price of a debenture 0 100 0Interest rate on debenture 0 8% 0No.of preference shares to be issued 0 0 2,500Issue price of a preferece share 0 0 100Interest rate on preference share 0 0 8%EBIT EPS for (i) EPS for (ii) EPS for (iii)

10,000 0.1 -0.2 -0.620,000 0.2 0 -0.440,000 0.4 0.4 060,000 0.6 0.8 0.4

100,000 1 1.6 1.2

Solved problem 20.5(Amounts in Rupees)

Profit (earnings before interest and taxes) 300,000 Interest rate on debentures 12%Less: Interest on debentures 60,000 Income tax rate 50%

240,000 No.of equity shares 40,000Income tax 120000 Face value of equity shares 10Profit after tax 120,000 Ruling price of share in market 30EPS 3 Undistributed reserves 600,000PE ratio 10 Additional funds to be raised 200,000

Existing debt 500000 8

Existing equity 1000000 14%Funds currently employed 1500000

0.41

0.29Rate of return earned 20.00%

Alternative-1 Debt issue Debt issueAlternative -2 Equity issueEarnings before interest and taxes 340000 340000Interest on existing debentures 60000 60000Interest on additional debt 28000Profit before tax 252000 280000Income tax 126000 140000Profit after tax 126000 140000

40,000 46667Earning per share 3.15 3PE ratio 8Price of share 25.2 30

P/E ratio if debt-equity ratio is >35%

Interest rate on additional amount borrowed, if debt-equity ratio is >35%

Debt-equity ratio under Plan 1-issuing additional debt

Debt-equity ratio under Plan 2-issuing additional equity

No.of equity shares(assuming that additional share can be issued at the prevailing marke price of Rs.30)

-0.2

Solved problem 21.1Earning per share 4Rate of return on investments 18%Rate of return required by investors 15%

Payout ratio40% 29.8750% 29.3360% 28.80

For the data in 21.1 what would be the price per share as per Gorden model?

Payout ratio40% 38.1050% 33.3360% 30.77

Solved problem 21.2Earning per share 5Rate of return on investments 0.16Dividend payout ratio 0.4Market price as per Gordon model 50Rate of return on investment 20%

Solved problem 21.3Firm X Firm Y

Next year's price(Rs) 180 165Dividend )Rs) 15Total pre-tax payoff 180 180

Current price 154.28 152.86Capital gain 26 12Dividend tax rate 20%Tax rate on capital gains 10% 10%Post-tax dividend 12Post-tax capital gains 23.15 10.93Total post-tax return 23.15 22.93

1/Post-tax rate of return 6.67 6.67The Steps1. On the Tools menu, click Goal Seek.2. In the Set cell box, enter the reference for the cell that contains the formula Here, this is cell B35.3. In the To value box, type the result you want. Here it is 6.66667( i.e.1/0.15-see the Note above)4 In the By changing cell box, enter the reference for the cell that contains the value you want to adjust viz. cell B28 for Firm X and C28 for Firm Y5 Click OK.

Price per share as per Walter model

Price per share as per Gorden model

Note: As we wish to use the Goal Seek set up in Tools, keep B28 and C28 blank to start with. The required values would get filled up automatically at the end.

Note: As we have not filled in the current price value, post-tax return formula will have a zero in the denominator and thus causing. a problem. So we will consider the reciprocal of the post-tax return and equate it to 1/0.15, i.e. 6.666667 in the Goal Seek feature in Tools, to get the corresponding share price in B28 and C28 respectively

1. On the Tools menu, click Goal Seek.2. In the Set cell box, enter the reference for the cell that contains the formula Here, this is cell B35.3. In the To value box, type the result you want. Here it is 6.66667( i.e.1/0.15-see the Note above)4 In the By changing cell box, enter the reference for the cell that contains the value you want to adjust viz. cell B28 for Firm X and C28 for Firm Y5 Click OK.

Note: As we wish to use the Goal Seek set up in Tools, keep B28 and C28 blank to start with. The required values would get filled up automatically at the end.

Note: As we have not filled in the current price value, post-tax return formula will have a zero in the denominator and thus causing. a problem. So we will consider the reciprocal of the post-tax return and equate it to 1/0.15, i.e. 6.666667 in the Goal Seek feature in Tools, to get the corresponding share price in B28 and C28 respectively

Solved problem 22.1

3

1.2Target payout ratio( r) 0.6Adjustment rate( c) 0.7

1.62

EPS for 20X1(EPSt)

DPS for 20X0(Dt-1)

DPS for 20X1 according to the Lintner model(Dt)

Solved problem 23.1

Sales 3,600,000 2

Materials consumed 900,000 2

Wages paid 720,000 1

80,000 1

Total administrative expenses 240,000 1

Sales promotion expenses 120,000 3Gross profit 25%

1Cash balance maintained 100,000

20%Total manufacturing cost 2700000Manufacturing expenses 1,080,000Cash manufacturing expenses 960000Depreciation 120,000Cash manufacturing cost 2,580,000Total cash cost 2,940,000Current assets Current LiabilitiesDebtors 490000 Sundry creditors 150000

Raw material stock 75000 80,000Finished goods stock 215000 Wages outstanding 60,000

Pre-paid sales promotional expenses 30000 20000Cash balance 100,000Total current assets 910000 Total current liabilities 310000Working capital 600000Safety margin on working capital 120000Working capital required 720000

Solved problem 26.2(Rs. million)

Profit and Loss account data Balance sheet data

Sales 80 Inventory 9 12Cost of goods sold 56 Accounts receivable 12 16

Accounts payable 7 10Inventory period in days 68.4Accounts receivable period in days 63.9Accounts payable period in days 55.4Operating cycle in days 132.3Cash operating cycle in days 76.9

Credit period granted on sales(months)

Credit period extended by suppliers(months)

Period of arrear in payment of wages(months)

Manufacturing expenses outstanding at the end of the year

Period of arrear in payment of cash expenses(months)Period of arrear in payment of total administraive expenses(months)

Period of advance payment of sales promotion expenses(months)

Stocking period of raw materials and finished goods(months)

Safety margin on working capital requirement

Manufacturing expeses outstanding

Total administrative expenses outstanding

Beginning of 20X1

End of 20X1

Solved problem 24.1Given:Sales estimated : From January 20X1 through March 20X1 150,000 From April 20X1 to June 20X1 200,000Sales for each of the months of November and December 20X0 120,000Percentage of cash sales 0.30Percentage of credit sales 0.70Credit collection in percentage after one month 0.40Credit collection in percentage after two months 0.60Bad debt losses 0.00Cash receipt in April 2011 from sale of a machine 70,000Cash receipt in June 2011 by way of interest on securities 3,000

Estimated purchases of material per month from January to March 60,000 from April to June 80,000

1

60,000

3,000Wage payments per month from January through June 25,000Manufacturing expenses per month from January through June 32,000General administration and selling expenses per month 15,000Dividend payment scheduled in June 20X1 30,000tax payment scheduled in June 20X1 35,000

Payment in cash planned for purchase of machine in March 20X1 80,000Cash balance as on 1st January 20X1 is 28,000Minimum cash balance required by the firm 30,000Solution:Forecast of Cash Receipts

Forecast of Cash Receipts (Rs. in 000’s)

Sales 120,000 120,000 150,000Credit sales 84,000 84,000 105,000Cash sales 36,000 36,000 45,000Collection of receivables

33,600 33,60050,400

Sale of machineInterest on securitiesTotal receipts 129,000

Forecast of Cash Payments (Rs. in 000’s)

December January FebruaryPurchases 60,000 60,000 60,000Payment of accounts payable 60,000 60,000Cash purchases 3,000 3,000Wage payments 25,000 25,000Manufacturing expenses 32,000 32,000General, administrative and selling expenses 15,000 15,000

Approximate time taken to make payment for the purchases, after the date of purchase- in months

The purchases for the month of December 20X0, for which payment is due in January 20X1 is

Miscellaneous cash purchases per month planned from January through June

November 20X0

December20X0

January 20X1

(a)     Previous month(b)     Two months earlier

DividendsTaxesAcquisition of machinery

Total payments (2to9) 135,000 135,000

Summary of Cash Payments (Rs. in 000’s)

January February MarchOpening balance 28,000Receipts 129,000 137,400 150,000Payments 135,000 135,000 215,000Net cash flow (2-3) -6,000 2,400 -65,000Cumulative net cash flow -6,000 -3,600 -68,600Opening balance + cumulative net cash flow 22,000 24,400 -40,600Minimum cash balance required 30,000 30,000 30,000Surplus / (Deficit) -8,000 -5,600 -70,600Solved problem 24.2Annual yield on marketable securities( Ix360) 0.10Fixed cost of effecting a marketable securities transaction(b) 2,500.00Standard deviation of the change in daily cash balance(σ) 10,000.00Minimum cash balance to be maintained 200,000.00Return point(RP) 287,720.53Upper control limit(UL) 463,161.60

Forecast of Cash Receipts (Rs. in 000’s)

February March April May June

150,000 150,000 200,000 200,000 200,000105,000 105,000 140,000 140,000 140,00045,000 45,000 60,000 60,000 60,000

42,000 42,000 42,000 56,000 56,00050,400 63,000 63,000 63,000 84,000

70,0003,000

137,400 150,000 235,000 179,000 203,000

Forecast of Cash Payments (Rs. in 000’s)

March April May June60,000 80,000 80,000 80,00060,000 60,000 80,000 80,0003,000 3,000 3,000 3,00025,000 25,000 25,000 25,00032,000 32,000 32,000 32,00015,000 15,000 15,000 15,000

30,00035,000

80,000215,000 135,000 155,000 220,000

Summary of Cash Payments (Rs. in 000’s)

April May June

235,000 179,000 203,000135,000 155,000 220,000100,000 24,000 -17,00031,400 55,400 38,40059,400 83,400 66,40030,000 30,000 30,00029,400 53,400 36,400

Solved problem 25.1Expected increase in sales(ΔS) 9,000,000

10%Contribution margin ratio(1-V) 20%Average collection period in days(ACP)) 50Post tax cost of funds(k) 12%Tax rate(t) 40%Increase in residual income 420,000

Solved problem 25.245

80,000,000Cost of capital(k) 13%Variable costs to sales ratio(V) 0.75

60Increase in sales expected(ΔS) 20,000,000

10%Tax rate 35%Increase in residual income 1,191,667Solved problem 25.3

At present ProposedCredit terms discount period in days 15 15Discount allowed during the discount period 2% 3%Credit period allowed- in days 45 45

200,000,000 210,000,00030 27

Variable costs to sales ratio(V) 0.8 0.8Cost of capital(k) 12% 12%

0.5 0.6Tax rate 40% 40%Increase in sales expected(ΔS) 10,000,000Δ DIS 1,780,000Δ I 1,066,667Increase in residual income 260,000

Solved problem 25.4

100,000,000

30Ratio of variable costs to sales(V) 0.75Cost of capital(k) 14%

0.04Tax rate(t) 30%Expected increase in sales(ΔS) 10,000,000

40

0.05Increase in residual income 194,444

Solved problem 25.6(a)

Month Sales(Rs.in million)January 40 3February 50 20March 60 40April 60 5May 50 18

Expected bad debt losses on increental in sales(bn)

Average credit period in days currently allowed(ACP0)

Present sales(S0)

Extended credit period in days considered(ACPN)

Bad debt proportion on the additional sales(bn)

Present sales(S)Average credit period in days currently allowed(ACP)

Proportion of sales on which discount is taken(p)

Present sales(S0)

Average collection period(ACP0) in days

Bad debt ratio(b0)

New average collection period(ACPN) in days

New bad debt ratio(bn)

End of quarter receivables

June 40 25July 50 4August 50 20September 50 30 (Amounts in Rs.million) End of quarter 1 End of quarter Receivables 63 48Daily sales( 30 days averaging) 2 1.333DSO((30 days averaging) 31.5 36Daily sales(60 days averaging) 1.833 1.500DSO( 60 days averaging) 34.4 32.0

Solved problem 25.6 (b)Age bracket Quarter I Quarter II0-30 63.5% 52.1%31-60 31.7% 37.5%61-90 4.8% 10.4%

End of quarter 354

1.66732.4

1.66732.4

Quarter III55.6%37.0%

7.4%

Solved problem 26.1Carrying cost per unit of inventory 10Fixed costs per order(F) 20No. of units required per year(U) 30,000Variable costs per unit ordered 2Purchase cost price per unit 30Price per unit(P) 32Percent carrying cost( C) 0.3125EOQ in no. of units 346

87Time gap between two orders(in days) 4

Solved problem 26.2Annual requirement of the item 90,000Cost of the item per unit(Rs.) 3Cost per purchase order (Rs.) 300Inventory carrying cost per year 20%(a)EOQ if there is no quantity discount 9,487(b)

(Amts in Rs.)Order quantity 3,000 4,500 6,000Discount allowed 0 2% 3%Price per unit 3 2.94 2.91Annual quantity requirement 90,000 90,000 90,000Purchase cost 270,000 264,600 261,900Carrying cost 900 1,323 1,746No.of orders 30 20 15Total ordering cost 9,000 6,000 4,500Total cost 279,900 271,923 268,146

Solved problem 26.3No. of units required per year(U) 2,000Purchase price per unit(P) 30Percent carrying cost( C) 25%Fixed costs per order(F) 1,000EOQ 730No. of orders placed 4.0 No. of units for each order(Q) 500.0

5,875.0 Solved problem 26.4

Daily usage rate in tonnes Probability Probability2 0.2 25 0.2 3 0.6 35 0.5 4 0.2 45 0.3

Stockout cost estimated per ton (Rs.) 8,000 Carrying cost per ton (Rs.) 2,000 (a) 2,000

Since the total cost is minimised when the order quantity is 6000, Modern Enterprises is advised to order 6000 units and avail of 3 percent discount.

Total cost of carrying and ordering inventories when 4 orders of equal size are placed

Lead time in days

Normal usage in tons 108 =SUMPRODUCT(A43:A45,B43:B45)*SUMPRODUCT(C43:C45,D43:D45)

Daily usage rate Safety stock2 25 50 2 35 70 2 45 90 3 25 75 3 35 105 3 45 135 27 4 25 100 4 35 140 32 4 45 180 72

Safety stock (tonnes) Stockout Probability Total cost72 0 0 0.00 0 144,000 144,000 32 40 320,000 0.06 19,200 64,000 83,200 27 45 360,000 0.06 21,600 54,000 79,600

5.0 40,000 0.10 4,000 25,600

0 72.0 576,000 0.06 34,560 32.0 256,000 0.10 25,600 27.0 216,000 0.18 38,880 0 99,040

99,040 The optimal level of safety stock is 27 tons because at that level the cost is minimised.

Lead time in days

Possible levels of usage

Stockout cost(Rs.)

Expected stockout

costCarrying

cost

(a)      The probability of stockout when the safety stock is 27 tons is: (0.06 + 0.10) = 0.16

Solved problem 27.1Credit period(days) 50 40 30 30Discount period(days) 20 15 15 10Discount allowed 2% 2% 1% 1%Interest cost 24.5% 29.4% 24.2% 18.2%

Solved problem 27.2Rs.in million

Current assetsInventories 70Debtors 60Cash 15Total current assets 145Current liabilitiesTrade creditors 40Provisions 20Total current liabilities 60

48.75Maximum permissible bank finance( MPBF) under the second method of Tandon Committee

Solved problem 28.1

Number1 0.8 18 0.000 25.000 0.0002 1 15 0.040 4.000 0.4003 1.2 20 0.160 49.000 2.8004 0.75 12 0.003 1.000 0.050

5 0.65 16 0.023 9.000 -0.4506 1.1 9 0.090 16.000 -1.2007 0.85 22 0.002 81.000 0.4508 0.65 19 0.023 36.000 -0.9009 0.95 15 0.022 4.000 0.300

10 1.05 24 0.063 121.000 2.75011 0.6 8 0.040 25.000 1.00012 0.75 11 0.003 4.000 0.10013 0.7 19 0.010 36.000 -0.60014 0.65 10 0.023 9.000 0.45015 0.8 12 0.000 1.000 0.00016 0.7 4 0.010 81.000 0.90017 0.55 9 0.063 16.000 1.00018 0.65 -9 0.023 484.000 3.300

Mean 0.80 13.00

0.595 10.35

1002

0.9 17

0.675 8

0.035 58.941

0.609 dx 0.225 dy 9a 4.599 b 0.105

The discriminant function is =

Xi Yi (Xi - X) 2 (Yi - Y)2 (Xi - X)*(Yi -Y)

Σ(Xi - X) 2 Σ(Xi - X)*(Yi -Y)

Σ(Yi - Y) 2

X1 Y1

X2 Y2

σx2 σy

2

σxy

4.599 Xi + 0.105Yi

Solved problem 29.1Old bonds New bonds

Amount 300,000,000 300,000,000Balance maturity in years 5 5Coupon rate 16% 14%Call premium on old bonds 5%Issue cost on new bonds 6,000,000

5,000,000Marginal tax rate 35%Cost of calling the old bonds 315,000,000Net proceeds of the new issue 294,000,000Tax savings on tax-deductible expenses 7,000,000Initial outlay 14,000,000Annual interest outflow on old bonds 48,000,000

17,150,000Annual interest ouflow on new bonds 42,000,000

15,120,000Annual net cash savings 3,970,000After-tax cost on new bonds 0.091Present value of the annual cash savings 15,401,932 Net present value of refunding the bond 1,401,932

Solved problem 29.2Face value of the bond 1000Coupon payable annually 16%Years to maturity 6Redemption value 1,000Current market price 964.5Settlement date(Date of purchase,say) 1/1/2007Redemption date 12/30/2012a) Yield to maturiry 17%b) Duration 4.24c) Volatility 3.63

Solved problem 29.3Face value Interest rate Maturity( years) Current price

100,000 0 1 91,000100,000 10.50% 2 99,000100,000 11.00% 3 99,500100,000 11.50% 4 99,900

Forward rate for year1 0.099For the two year government securityPV of interest for the first year 9,555Second year cash flow 110,500

1.2354

0.124For the three year government securityPV of interest for the first two years 18914.027Third year cash flow 111000

1.37741

0.115For the four year government securityPV of the interest for the first three years 28122.753

Unamortised portion of the issue cost on old bonds

Tax savings on interest expenses and amortisation of issue costs of old bonds

Tax savings on interest expenses and amortisation of issue costs of new bonds

(1+0.009)*(1+r2)=

r2=

(1+0.009)*(1+0.124)*(1+r3)=

r3=

Fourth year cash flow 111500

1.553

0.128

(1+0.009)*(1+0.124)*(1+0.115)*(1+r4) =

r4 =

Solved problem 30.1Cost of capital 10%Marginal tax rate 35%Depreciation rate (WDV) 40%Calculation of post-tax cash flows Rs.in millionYear 0 1 2 3 4 5 6Initial cost -1.5Operating and other costs -0.250 -0.265 -0.281 -0.298 -0.316 -0.335Depreciation 0.6 0.36 0.216 0.1296 0.07776 0.0467

0.2975 0.21875 0.1739 0.14957 0.13768 0.1334Net salvage value 0.6Post-tax cash flow -1.5 0.0475 -0.046 -0.107 -0.1482 -0.178 0.3989

-1.562Post-tax EAC 0.359 Lease rental 0.552

Solved problem 30.2Post-tax cost of debt 8%Depreciation rate(WDV) 25%Marginal rate of tax 35%Lease contract cash flows

Rs. In millionYear 0 1 2 3 4 5

Cost of the plant 50Depreciation 12.5 9.375 7.03125 5.27344 3.95508Loss of depreciation tax shield -4.375 -3.28125 -2.4609 -1.8457 -1.384Lease payment -14 -14 -14 -14 -14Tax shield on lease payment 4.900 4.900 4.900 4.900 4.900Loss of salvage value -10Cash flow of lease 50 -13.475 -12.3813 -11.561 -10.946 -20.484NAL of lease -4.256

Tax shield on operating costs and depreciation

Present value of post-tax cash flow

Solved ProblemNo. of shares outstanding 80,000,000

80Ratio of the warrants issued to the no. of outstanding shares 0.05Exercise price(E) 84Standard deviation of continuosly compounded annual returns(σ) 0.3Time to expiration of warrants in years (t) 0.25Risk-free interest rate per year 8%

-0.1169

-0.2669

0.4535

0.3948

3.77

Current stock price(So)

d1 =

d2 =

N(d1) =

N(d2) =

Value of a warrant(C0)

Case Study : BHARAT HOTELS COMPANY

For year 0: Operating Revenues Rs.in millionRoom rent 1043 Assets and Liabilities at the end of year 0Food and beverages 678

73 AssetsOperating Expenses Net worth 1126 Net fixed assets

Materials 258 Debt 900 Gross Block:Personnel 258Upkeep and services 350 Net current assetsSales and general administration 350 2026

2190Year 1 2 3 4 5 6

90 130 80 130 186 355Investment (in million rupees) 200 300 240 500 800 1400Assumptions:

Occupancy rate for year 1 Addition to occupancy rate per year for the next 6 yearsAverage room rent(for both owned & managed) per day for year 1 Rate of increase per year in the average room rent per day till the year 7 .Food and beverage revenues as a percentage of room rentManagement fees for the managed properties as a percentage of room rentDepreciation as a percentage of the net fixed assetsEffective tax rate

Other information relevant for valuationMarket value of equity at the end of year 0 Rs.

The imputed market value of debt at the end of year 0 Rs.Beta of BHC's stockRisk -free rate of returnMarket risk premiumPost-tax cost of debtRate of growth per annum in free cash flow after 7 years

Solution:Financial Projections

PANEL IYear 1 2 3 4 5 6

A. Rooms 2280 2410 2490 2620 2806 3161B. Occupancy rate 0.60 0.61 0.62 0.63 0.64 0.65C. Average room rent ( in Rs.) 2,500 2875 3306 3802 4373 5028

PANEL II*D. Room rent from owned properties 1248 1543 1863 2291 2866 3771E. Food & beverage revenues 811 1003 1211 1489 1863 2451F. Revenue from owned properties(D+E 2060 2545 3074 3780 4729 6222

Management fees for managed properties

Owner's equity & liabilities

depreciation

No.of rooms owned at the beginning of year 1

Additions to rooms planned during the year (all at the beginning )

87 108 130 160 201 264H.Total revenues ( F+G) 2147 2653 3204 3940 4930 6486

PANEL III*Year 1 2 3 4 5 6

I. Material expenses 309 382 461 567 709 933J. Personnel expenses 309 382 461 567 709 933K. Upkeep & services expenses 371 458 553 680 851 1120L. Sales & general admn. Expenses 371 458 553 680 851 1120M. Total operating expenses 1359 1680 2029 2495 3121 4107

788 973 1176 1445 1809 2380O. Depreciation 120 132 140 165 210 293P. EBIT 668 841 1036 1280 1599 2087Q. NOPLAT 534 673 829 1024 1279 1669R. Gross Cash flow 654 805 968 1189 1489 1962

302 446 399 712 1085 1848T. Free cash flow from operations (R_S) 352 359 570 478 404 114* All figures in million rupees

Year 1 2 3 4 5 6A. Net current assets*B. Net current assets addition* C. Gross block*D. Capital expenses*E. Accrued depreciation*F. Net block (C+D_E)G. Depreciation* At the beginning of the year

Cost of capital=Rs. 17.0% =K28/(K28+K29)*(K31+K30*K32)+K29/(K28+K29)*K33Continuing value =Rs. 10,748 million =I63*(1+K34)/(C76-K34)

Present value of continuing value = Rs 3,580 million =C77/(1+C76)^I51Value of non-operating assets = Rs. 0Market value of debt claims = Rs. 900 million =F8Value of equity = Rs. 4,311 million =NPV(C76,C63:I63)+C78+C79+C80

G. Management fees from managed properties

N. EBDIT( H- M)

S. Gross investment( Fixed assets + Current assets)

Case Study : BHARAT HOTELS COMPANY

Assets and Liabilities at the end of year 0(Rs.in million)

AssetsNet fixed assets 1510Gross Block: 2110

600Net current assets 516

2026

7

1501300

60%1% Material expenses 15%

2,500 Personnel expenses 15%15% 18%65% 18%7% 30%7%

20%

Market value of equity at the end of year 0 Rs. 3,050 millionThe imputed market value of debt at the end of year 0 Rs. 900 million

Beta of BHC's stock 0.921Risk -free rate of return 12%Market risk premium 8%Post-tax cost of debt 9%Rate of growth per annum in free cash flow after 7 years 10%

Financial ProjectionsPANEL I

733110.665783

PANEL II*461229987610

depreciation

As a percentage of the total revenues

expensesexpensesassets) investment

3237933

PANEL III*7

114211421370137050232910363

254720382401

1716685

7

=K28/(K28+K29)*(K31+K30*K32)+K29/(K28+K29)*K33=I63*(1+K34)/(C76-K34)=C77/(1+C76)^I51

=F8=NPV(C76,C63:I63)+C78+C79+C80

Solved Problem 32.2Profit and Loss Account( Rs. In million)

Year 1 2

Net sales 5600 6440Income from marketable securities 140 210Non-operating income 70 140Total income 5810 6790Cost of goods sold 3220 3780Selling and administrative expenses 700 770Depreciation 350 420Interest expenses 336 392Total costs and expenses 4606 5362PBT 1204 1428Tax provision 364 448PAT 840 980Dividend 420 560

Retained earnings 420 420Balance Sheet

Equity capital 2100 2100Reserves and surplus 1680 2100Debt 2520 2940

Total 6300 7140Fixed assets 4200 4550Investments 1260 1400Net current assets 840 1190

Total 6300 7140

Tax rate 0.4EBIT for year 2= 1470

Tax on EBIT for year 2= 464.8NOPLAT for year 2 = 1005.2FCFF for year 2 = 389.2

Solved Problem 32.3

( Amounts in rupees million) Base YearNo of years 4

Revenues 3,000 20% 10%

EBIT 500 20% 10%

Capital expenditure 350 20%

Depreciation 250 20%

25% 25% 25%

Corporate tax rate ( for all time) 30%

High growth phase

Growth rate

during high

growth phase

Stable growth period

Growth rate

during stable growth period

Working capital as a percentage of revenues

Paid-up equity capital (Rs.10 par) 400

Market value of debt 1,200

Pre-tax cost of debt 13% 12.14%

Debt - equity ratio 1 is to 1 2 is to 3

Risk-free rate 11% 10%

Market risk premium 7% 6%

Equity beta 1.129 1

WACC 14.00% 13.00%

Calculation of forecasted FCF

Year 0 1 2 3 4

Revenues 3000 3600 4320 5184 6220.8 6842.88

EBIT(1-t) 350 420 504 604.8 725.76 798.34

Capital expenditure - depreciation 100 120 144 172.8 207.36

Δworking capital 150 180 216 259.2 155.52

FCFF 150 180 216 259.2 642.82

569.32

Terminal value of the cash flow 21,432.92

PV of the terminal cash flow 12,689.34

Value of the firm 13,258.66

Terminal year

PV of FCF during the explicit forecast period

Solved problem 33.1Gross margin 20%

10%Discount rate 15%Tax rate 30%

20%

3

10%Current values Income statement projections

Year 0 1 2 3 4Sales 10000 12000 14400 17280 17280Gross margin 2000 2400 2880 3456 3456

1000 1200 1440 1728 1728Profit before tax 1000 1200 1440 1728 1728Tax 300 360 432 518.4 518.4Profit after tax 700 840.00 1008.00 1209.60 1209.60

Balance sheet projectionsFixed assets 4000 4800 5760 6912 6912Net current assets 2000 2400 2880 3456 3456Total assets 6000 7200 8640 10368 10368Equity 6000 7200 8640 10368 10368

Cash Flow projectionsProfit after tax 840.00 1008.00 1209.60 1209.60Depreciation 400 480 576 691.2Capital expenditure 1200.00 1440.00 1728.00 691.20Increase in net current assets 400.00 480.00 576.00 0.00Operating cash flow (360.00) (432.00) (518.40) 1209.60

(980.55)Residual value 8064

5302.21Total shareholder value 4321.66Pre-strategy value 4666.67Value of the strategy -345.01

Solved problem 33.2

Investment outlay5,000 4 0 6,000 4,000

Depreciation Tax rateStraight line 40% 4/5 18% 9%Cost of capital 14.00%Calculation of EVA over the project life

Ratio of selling , general and administrative expenses to sales

Growth rate in sales if new strategy adopted

Period of growth in years under new strategy

Ratio of depreciation to net fixed assets at the beginning of the year under the new strategy

Selling and general administration

Present value of the operating cash flow stream

Present value of the residual value

Project life in years

Salvage value

Annual revenues

Annual costs(excluding depn. Interest and taxes)

Debt-equity

ratioCost of equity

Post-tax cost of debt

Year 1 2 3 4Revenues 6,000 6,000 6,000 6,000Costs 4,000 4,000 4,000 4,000PBDIT 2,000 2,000 2,000 2,000Depreciation 1250 1250 1250 1250PBIT 750 750 750 750NOPAT 450 450 450 450Cash flow 1700 1700 1700 1700Capital at charge 5000 3750 2500 1250EVA -250 -75 100 275NPV( using EVA) (46.7)NPV(using cash flow) (46.7)

Solved problem 33.3Cost of the equipment 2,000,000Economic life in years 4Expected salvage value 600,000Cost of capital 12%PV of salvage value 381,311 PV of annuity 1,618,689Annuity amount 532,928 Depreciation charge under sinking fund methodCapital 2,000,000 1,707,072 1,378,992 1,011,543Capital charge 240000 204848.61 165479.1 121385.165Annuity amount 532,928 532,928 532,928 532,928Depreciation 292,928 328,080 367,449 411,543

Solved problem 33.4(Amounts in Rs.million)

NOPAT 21.085Investment in fixed assets 250Investment in current assets 50Economic life in years 14Salvage value of fixed assets 0Cost of capital 10%Annual depreciation 17.86End of year 1 2 3 4 5Net value of fixed assets 232.14 214.29 196.43 178.57 160.71Investment in current assets 50 50 50 50 50

282.14 264.29 246.43 228.57 210.71ROCE for year 5 9.22%ROGI for year 5 12.98%Economic depreciation 8.937 CVA for year 5 0

Total capital employed( book value)

Solved problem 34.1

Videsh Limitrd Swadesh LimitedEarnings per share 5 5Market price per share 60 50No. of shares 1,000,000 800,000Expected synergy gain 5%Target post-merger EPS 6Total earnings post-merger 9450000

1575000Exchange ratio 0.71875

Solved problem 34.2Black&Co White&Co.

Market price per share 70 32No. of outstanding shares 20,000,000 15,000,000PV of gains to be generated 200,000,000Exchange ratio agreed to 0.5

0.27273PV of Black&Co. post-merger 2,080,000,000True cost of merger 87,272,727.27

Solved problem 34.3Alfa Corporation Beta Corporation

Total current earnings(E) 50,000,000 20,000,000No.of outstanding shares(S) 20,000,000 10,000,000Market price per share(P) 30 20(a) & (b)P/E ratio of the combined entity 12 11Synergy gain 0 5%

0.8

0.657(c)Synergy gain 0

11.43

Total no.of post-merger shares for the EPS to be 6

Share of Black&Co.that will be owned by the shareholders of White &Co.

Maximum exchange ratio acceptable to Alpha shareholders

Minimum exchange ratio from the point of view Beta shareholders

Level of P/E multiple at which lines ER1 and ER2 will intersect

Solved problem 37.1

Spot 50Forward time in months 3 50.8Annualised premium 6.40%

Solved problem 37.2Period in days Interest rate

US 90 1.75%UK 90 1.25%

1.5

90

Required forward rate in USD per GBP 1.5074

Solved problem 37.3Current spot rate for USD in Rupees 51Expected inflation rate in India 6%Expected inflation rate in the US 2.50%

52.74

Solved problem 37.4One - year US nominal interest rate 5%

One - year Indian nominal interest rate 10%Current spot rate for USD in Rupees 49.5

51.86

Solved problem 37.5

70Risk-free rate of interest in India 10%Risk-free rate of interest in UK 6%Required rupee return 20%

Year0 -50 70.00 -35001 20 72.64 1452.82 30 75.38 2261.53 20 78.23 1564.54 10 81.18 811.8

NPV in rupees(million) 578.06

Forward period in months

Rate( Rupees per USD)

Current spot exchange rate in USD per GBP

Period in days for which forward rate is sought

Expected spot rate of USD in Rupees in one year

Expected spot rate of USD in Rupees in one year

Current spot exchange rate of GBP in Rupees

Cash flow in pounds(million)

Expected exchange

rate(Rs per GBP

Cash flow in

rupees(million)

Solved problem 40.1Amount of stock X owned(Rs. million) 2

2.5Hedge ratio 0.8

0.5

Solved problem 40.2Current stock index 1400Period in months 6Six-months stock index futures trading at 1500Risk-free annual interest rate 11%Average annual dividend yield on index stocks 3.86%

Solved problem 40.3Spot price per ton 4500Futures price per ton for a one year contract 5000Risk-free interest rate 12%PV of storage cost per ton 200PV of convenience yield per ton 235.71

Amount of Y that should be short sold to minimise the risk(Rs. million)

Amount that should be deposited in a bank to create a zero value hedge(Rs million)