The financial statements of Matrix Limited are shown below:

Matrix Limited: Profit and Loss Account for the year ending 31st March 20X1

(Rs. In Million)20 X 1 20 X 0

Net Sales 1065 950Cost of goods sold 805 720 Stocks 600 520 Wages and salaries 120 110 Other manufacturing expenses 85 90Gross profit 260 230Operating expenses 90 75 Depreciation 50 40 Selling and general administration 40 35Profit before interest and tax 170 155 Interest 35 30Profit before tax 135 125Tax 50 45Profit after tax 85 80Dividends 35 30Retained earnings 50 50

Matrix Limited: Balance sheet as at 31st March 20X1

Rs. In million

20X1 20X0

I. Sources of Funds

1. Shareholder’s funds 505 455 (a) Share Capital 125 125 (b) Reserve and surplus 380 3302. 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 785 715

II. Application of Funds1. Net fixed assets 550 4952. Investments 30 25

(a) Long term investments 20 20(b) Current investments 10 5

3. Current 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 60

Less: Current Liabilities and provisions 150 138Net current assets 205 195Total 785 715

(ii) Prepare the classified cash flow statement(iii) Prepare the cash flow identity

Solution

(i) Classified Cash Flow StatementClassified Cash Flow Statement for Matrix Limited for period 1.4.20X0 to 31.3.20X1

A. Cash Flow from Operating Activities Net profit before tax and extraordinary items 135Adjustments for Interest paid 35 Depreciation 50Operating profit before working capital changes 220Adjustments for Debtors (5) Inventories (22) Loans and advances 10 Current Liabilities and provisions 12Cash generated from operations 215 Tax paid (50)Net cash flow from operating activities 165

B. Cash flow from Investing activities Purchase 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 financial 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

(ii) Cash Flow IdentityThe cash flow identity for the period 1.4.20X0 to 31.3.20X1 is as follows:

A. Cash flow from assets = Operating cash flow – Net capital spending – Net investment in marketable securities – Change in net working capitalOperating cash flow = PBIT – Taxes + Depreciation = 170 – 50 + 50 =

170Net capital spending = Ending net fixed assets – Beginning net fixed

Assets + depreciation = 550 – 495 + 50 = 105Net investment in = Ending Investments in marketable securities – Marketable securities beginning investment in marketable securities

= 30 – 25 = 5Change in net working = Ending net working capital – Beginning net Capital working capital = 205 – 195 = 10Cash flow from assets = 170 – 105 – 5 – 10 = 50Cash flow to lenders Interest – Net new borrowing = 35 – 20 = 15Cash flow to shareholders Dividend paid – Net new share capital raised =

35

1. A firm’s current assets and current liabilities are 1,600 and 1,000 respectively. How much can it borrow on a short- term basis without reducing the current ratio below 1.25?

Solution: Let the maximum short- term borrowing be B. The current ratio with this borrowing should be 1.25.

1,600+B1,000+B

=1.25

Solving this equation, we get B = 1,400. Hence the maximum permissible short -term borrowing is 1,400.

2. Determine the sales of a firm given the following information:Current ratio = 1.4Acid-test ratio = 1.2Current Liabilities = 1,600Inventory turnover ratio = 8

Solution: The sales figure may be derived as follows:Current assets = Current liabilities x Current ratio

= 1,600 x 1.4 = 2,240Current assets – Inventories = Current Liabilities x Acid -test ratio

= 1,600 x 1.2 – 1,920Inventories = 2,240 – 1,920 = 320Sales = Inventories x Inventories turnover ratio

= 320 x 8 = 2,560

3. The following ratios are given for Mintex CompanyNet profit margin ratio 4 percentCurrent ratio 1.25Return on net worth 15.23 percentTotal debt to total assets ratio 0.40Inventory turnover ratio 25

Complete the following statementsProfit and Loss Account

Rs. Sales Cost of goods sold Operating expenses 700 Profit before interest and tax Interest 45 Profit before tax

Tax provision (50 percent)Profit after tax

Balance SheetNet worth Fixed assetsLong-term debt Current Assets 180(10 percent interest)

CashShort-term debt Receivables 60(10.42 percent interest) Inventory

Solution: The blanks in the above statements may be filled as follows:(a) Short term debt: The value of short-term debt - the only current liabilities – is derived as

follows.

current ratio= Current assetsCurrent liabilities

=1.25

Current liabilities=Current assets1.25

= 1801.25

=144

So short-term debt is 144.(b) Long-term debt: The long-term debt carries 10 percent interest rate. Hence the long-

term debt is equal to Interest−.1042(144)

0.10=45−150.10

=300

(c) Total assets: As the ratio of total debt to total assets is 0.4, total assets (the total of the balance sheet) is simply:

Totaldebt0.4

=144+3000.4

=1110

(d) Net worth: The difference between total assets and total debt represents the net worth. Hence, it is equal to:

1100- (444) = 666(e) Fixed assets: The difference between total assets and current assets represents fixed

assets. So,Fixed assets = 1100 – 180 = 930

(f) Profit after tax: This is equal to: (Net worth) (Return on net worth) = (666) (0.1523) = 101.4

(g) Tax: As the tax rate is 50 percent, the tax provision is simply equal to the profit after tax, i.e., 101.4

(h) Profit before tax: The sum of the profit after tax and the tax provision is equal to the Profit before tax. So, it is equal to:

101.4 = 101.4 = 202.8(i) Profit before interest and taxes: This is equal to the profit before tax plus the interest

Payment. Hence, it is equal to:202.8 + 45 = 247.8

(j) Sales: The figure of the sales may be derived as follows:Profit after tax

Net profit marginratio=101.40.04

=2535

(k) Cost of goods sold: The figure of cost of goods sold may be derived from the following accounting identity:Sales – cost of goods sold – operating expenses = EBIT2535 – Cost of goods sold – 700 = 247.8Hence the cost of goods sold figure is 1587.2

(l) Inventory: This is equal to:Sales

Inventory turnover ratio=253525

=101.4

(m) Cash: This may be obtained as follows:Current assets – receivables – inventory = 180 – 60 – 101.4 =18.6

4. The financial statements of Matrix Limited are given below: Matrix Limited: Profit and Loss Account for the Year Ending 31st March 20X1

(Rs. In million) 20 X 1 20 X 0

Net Sales 1065 950Cost of goods sold 805 720 Stocks 600 520 Wages and salaries 120 110 Other manufacturing expenses 85 90Gross profit 260 230Operating expenses 90 75 Depreciation 50 40 Selling and general administration 40 35Profit before interest and tax 170 155 Interest 35 30Profit before tax 135 125

20 X 1 20 X 0Tax 50 40Profit after tax 85 80Dividends 35 30Retained earnings 50 50

Matrix Limited: Balance sheet as at 31st March 20X1

Rs. In million

20X1 20X0

I. Sources of Funds1. Shareholder’s funds 505 455 (a) Share Capital 125 125 (b) Reserve and surplus 380 3302. 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 30

Total 785 715

II. Application of Funds1. Net fixed assets 550 4952. Investments 30 25

(c) Long term investments 20 20(d) Current investments 10 5

3. Current assets, loans and advances 355 333(e) Inventories 160 138(f) Sundry debtors 120 115(g) Cash and bank balances 25 20(h) Loans and advances 50 60

Less: Current Liabilities and provisions 150 138Net current assets 205 195

Total 785 715

a. Calculate the following ratios Current ratio Acid-test ratio

Cash ratio Debt-equity ratio Interest coverage ratio Fixed charges coverage ratio Inventory turnover ratio Debtors turnover ratio Average collection period Fixed assets turnover Total assets turnover Gross profit margin Net profit margin Return on assets Earning power Return on equity

b. Set up the Dupont equation

Solution:

a. Current ratio=Current assets , loans∧advances+Current investmentsCurrent liabilities∧provisions+Short termdebt

=355+10150+90

=1.52

Acid-test ratio = Quick assets

Current liabilities=365−160

240=0.85

Cash ratio = Cash∧bank balanes+Current investments

Current liabilities=25+10240

=0.15

Debt-equity ratio = DebtEquity

=280505

=0.55

Interest coverage ration = PBITInterest=17035

=4.9

Fixed charges coverage ration = PBIT+Depreciation

Interest +Repayment of loan1−Tax rate

=170+5035+901−37

=1.24

Inventory turnover = Cost of goods soldAverageinventory

= 805(160+138) /2

=5.40

Debtors turnover = Net credit salesAverage debtors

= 1065(120+115) /2

=9.06

Average collection period = 365

Debtors turnover= 3659.06

=40.3days

Fixed assets turnover = Net sales

Average net fixesassets= 1065

(550+495)/2=2.04

Total assets turnover = Net sales

Average totalassets= 1065

(785+715)/2=1.42

Gross profit margin = Gross profitNet sales

= 2601065

=24.4%

Net profit margin = Net profitNet sales

= 851065

=7.98%

Return on assets = Net profit

Average totalassets= 85

(785+715)/2=11.3%

Earning power = PBIT

Average totalassets= 170

(785+715)/2=22.7%

Return on equity = Equity earningsAverage equity

= 85(505+455)/2

=17.7 %

b. Dupont equation

Return on equity = Net profit margin x Total assets turnover ratio x Leverage multiplier

= Net profitNet sales

x Net salesAveragetotal assets

x Average totalassetsAverage equity

= 851065

x 1065(785+715)/2

x (785+715)/2(504+455)/2

= 7.98% x 1.42 x1.5625

= 17.7%

5. The balance sheets of ABC for the past two years are as under:

Liabilities 31-3-X6 31-3-X7 Assets 31-3-X6 31-3-X7

Equity shares 50000 50000 Gross fixes assets 60000 72000

General reserves 10000 14000 Less accumulated 16000 21000

Depreciation

Liabilities 31-3-X6 31-3-X7 Assets 31-3-X6 31-3-X7

Surplus 4000 4800 Net fixes assets 44000 51000

Public deposits 8000 2000 Long term invest- 30000 32000

Debentures 15000 17000 Sundry debtors 16500 12000

Term loan 20000 18000 Inventories 32000 34000

Trade creditors 8000 10800 Miscellaneous exp 9500 10000

Short term bank 15000 20000

Borrowing

Provision for tax 2000 2400

Total 132000 139000 132000 139000

(i) One of the important ratios considered by a bank for lending purposes is the ratio of the

total outside liabilities to tangible net worth. What is the ratio for ABC for the year

ended 31-3-X7?

(ii) List out the sources and uses of funds for the year ended 31-3-X7 classifying them under

the heads long-term and short-term.

(iii) Comment on the uses of funds based on the above.

Solution:

(i) Total outside liability = Public deposits + Debentures + Term loan + Trade creditors +

Short term bank borrowing + Provision for tax.

= 2000 + 17000 + 18000 + 10800 + 20000 + 2400 = 70200.

Tangible Networth = Equity shares + General reserve + Surplus – Miscellaneous

expenses

= 50000 + 14000 + 4800 – 10000 = 58800

The required ratio is: 70200/58800 = 1.19

(ii) Long-term sources Long-term uses

Net profit 4800 Purchase of fixes assets 12000

(Increase in reserve & surplus) Additional investments 2000

Depreciation for the year 5000 Repayment of public deposits 6000

Increase in debentures 2000 Repayment of term loan 2000

Addition to miscellaneous expenses 500

Total of long-term sources 11800 Total of long-term uses 22500

Short-term sources Short-term uses

Increase in trade creditors 2800 Increase in inventories 2000

Increase in bank borrowing 5000

Increase in provision for tax 400

Decrease in sundry debtors 4500

Total of short-term sources 12700 Total of short-term uses 2000

(iii) Long-term deficit = 22500 – 11800 = 10700

(iv) Short-term surplus = 12700 – 2000 = 10700

ABC has diverted short-term funds amounting to 10700 raised mainly by resorting to

additional market credit and increased short-term bank borrowing, for long-term uses

like purchase of fixed assets and repayment of public deposits which is not prudent.

1. The income statements and balance sheets of Deepam silks for years 1 and 2 are as

follows:

Profit and Loss Account Year 1 Year 2

Net sales 600 720

Cost of goods sold 450 500

Gross Profit 150 220

Selling expenses 50 60

General and administration expenses 36 40

Depreciation 30 40

Operating profit 34 80

Non-operating surplus/deficit 10 (8)

Profit before interest and tax 44 72

Interest 10 12

Profit before tax 34 60

Tax 14 26

Profit after tax 20 34

Dividends 12 15

Retained earnings 8 19

Balance sheet Year 1 Year 2

Assets

Fixed Assets (net) 240 270

Investments 10 10

Current assets, loans and advances

Cash and bank 5 6

Receivables 80 90

Inventories 125 144

Loans and advances 25 30

Miscellaneous expenditures and losses 15 10

Total 500 560

Balance sheet Year 1 Year 2

Liabilities

Share capital

Equity 100 100

Preference 20 20

Reserves and surplus 150 169

Secured loans

Bank borrowings 60 80

Unsecured loans

Public deposits _ 11

Current liabilities and borrowings

Total Creditors 125 130

Provisions 45 50

500 560

Prepare the proforma income statement for year 3 and the proforma balance sheet as at the

end of year 3, based on the following assumptions:

(a) The projected sales for year 3 are 850

(b) The forecast values for the following profit and loss account items may be derived using

the percent of sales method (for this purpose, assume that the average of the

percentages for year 1 and 2 is applicable).

Cost of goods sold

Selling expenses

General and administration expenses

Non-operating surplus/deficit

Interest

(c) The forecast values for the other items of the profit and loss account are as follows:

Depreciation : 45

Tax : 50 percent of earnings before tax

Dividends : 21

(d) The forecast values of various balance sheet items may be derived as follows:

Fixed assets (net) : Budgeted at 300

Investments : No change over year 2

Current assets : Percent of sales method wherein the percentages

Are based on the average for the previous two

Years

Miscellaneous expenditures : Expected to be reduced to 5 and losses

Equity and preference capital : No change over year 2

Reserves and surplus : Proforma profit and loss account

Bank borrowings and current : Percent of sales method wherein the percentages

Are liabilities and provisions based on the average

For the previous two years

Public deposits : No change

External fund required : Balancing item

Solution

The proforma profit and loss account and the proforma balance sheet are shown below:

Pro forma Profit and loss account for Deepam Silks for Year 3

Historical data Average percent Proforma profit and

Year 1 Year 2 of sales loss account for year 3

Net sales 600 720 850

Cost of goods sold 450 500 72.0 612

Gross profit 150 220 @ 238

Selling expenses 50 60 8.3 70.6

General and administration 36 40 5.8 49.3

Expenses

Depreciation 30 40 Budgeted 45

Operating profit 34 80 @ 73.1

Non-operating surplus/deficit 10 -8 1.4 11.9

Profit before interest and tax 44 72 @ 85.0

Interest 10 12 1.7 14.5

Profit before tax 34 60 @ 70.5

Tax 14 26 Budgeted 35.3

Profit after tax 20 34 @ 35.2

Dividends 12 15 Budgeted 21

Retained earnings 8 19 @ 14.2

@ Based on accounting identity.

Pro forma Profit and loss account for Deepam Silks for Year 3

Historical data Average percent Proforma profit and

Year 1 Year 2 of sales loss account for year 3

Net sales 600 720 850

Assets

Fixed assets (net) 240 270 Budgeted 300

Investments 10 10 No change 10

Current assets, loans and

advances

Cash 5 6 0.8 6.8

Receivables 80 90 12.9 109.7

Inventories 125 144 20.0 170.0

Loans and advances 25 30 4.1 34.9

Miscellaneous expenditures

And losses 15 10 Budgeted 5.0

Total 500 560 636.4

Liabilities

Share capital

Equity 100 100 No change 100

Preference 20 20 No change 20

Reserves and surplus 150 169 Proforma profit 183.2

And loss account

Secured loans

Bank borrowings 60 80 10.6 90.1

Unsecured loans

Public deposits _ 11 No change 11.0

Current liabilities

Trade creditors 125 130 19.4 164.9

Provisions 45 50 7.2 61.2

External funds requirement Balancing item 6.0

500 560 636.4

2. The following information is available for Olympus Limited: A/S = 0.8, ∆S = Rs. 20

million, L/S = 0.40, m = 0.06, S1 = Rs. 100 million and d = 0.4. What is the external funds

requirement for the forthcoming year?

Solution:

The external funds requirement of Olympus is:

EFR = A*/SO (∆ S) – L*/ S (∆ S) – mS1(r)

= 0.8 x 20 – 0.4 x 20 – 0.6 x 100 x 0.6

= Rs. 4.4 million

3. The following information is available for Signal Corporation: m = 0.05, d = 0.30, A/E =

2.4, A/So = 1.0. What rate of growth can be sustained with internal equity?

Solution:

The sustainable growth rate for Signal is:

g=m(So/ Ao)(1+D /E)b1−m (So /Ao ) (1+D /E )b

= 0.05 x1 x2.4 x 0.71−0.05 x1 x2.4 x 0.7

= 9.17 percent.

1. If you invest Rs. 5,000 today at a compound interest of 9 percent, what will be its future

value after 75 years?

Solution: The future value of Rs. 5,000 after 75 years, when it earns a compound

interest of 9 percent is

Rs. 5,000 (1.09)75

Since the FVIF table given in Appendix A has a maximum period of 30, the future value

expression may be stated as

Rs. 5,000 (1.09)30 (1.09)30 (1.09)15

The above product is equal to

Rs. 5,000 (13.268) (13.268) (3.642) = Rs. 32, 05,685.1

2. If the interest rate is 12 percent, what are the doubling periods as per the rule of 72 and

the rule of 69 respectively?

Solution: As per the rule of 72 the doubling period will be

72/12 = 6 years

As per the rule of 69, the doubling period will be

0.35 + 6912

=6.1 years

3. A borrower offers 16 percent nominal rate of interest with quarterly compounding.

What is the effective rate of interest?

Solution: The effective rate of interest is

(1+0.164 )4 - 1 = (1.04)4 – 1

= 1.17 – 1

= 0.17 = 17 percent

4. Fifteen annual payments of Rs. 5,000 are made into a deposit account that pays 14

percent interest per year. What is the future value of this annuity at the end of 15

years?

Solution: The future value of this annuity will be:

Rs. 5,000 (FVIFA14%, 15) = Rs. 5,000 (43.842) = Rs. 2, 19,210

5. A finance company advertises that it will pay a lumpsum of Rs. 44,650 at the end of five

years too investors who deposit annually Rs. 6,000 for 5 years. What is the interest rate

implicit in this offer?

Solution: The interest rate may be calculated in two steps

(a) Find the FVIFA for this contract as follows:

Rs. 6,000 (FVIFA) = Rs. 44,650

So

FVIFA = Rs . 44.650Rs.6,000

=7.442

(b) Look at the FVIFA table and read the row corresponding to 5 years until 7.442 or a

value close to it is reached. Doing so we find that

FVIFA20%,5yrs is 7.442

So, we conclude that the interest rate is 20 percent.

6. What is the present value of Rs. 1,000,000 receivables 60 years from now, if the

discount rate is 10 percent?

Solution: The present value is

Rs. 1,000,000 (11.10 )60

This may be expressed as

Rs. 1,000,000 (11.10 )30 (

11.10 )30

= Rs. 1,000,000 (0.057) (0.057) = Rs. 3249

7. A 12 – payment annuity of Rs. 10,000 will begin 8 years hence. (The first payment occurs

at the end of 8 years.) What is the present value of this annuity if the discount rate is 14

percent?

Solution: This problem may be solved in two steps.

Step 1: Determine the value of this annuity a year before the first payment begins i.e., 7

years from now. This is equal to:

Rs. 10,000 (PVIFA14%,12years) = Rs. 10,000 (5.660)

= Rs. 56,600

Step 2: Compute the present value of the amount obtained in Step 1:

Rs. 56,600 (PVIFA14%,7years) = Rs. 56,600 (0.400)

= Rs. 22,640

8. What is the present value of the following cash stream if the discount rate is 14

percent?

Year 0 1 2 3 4

Cash flow 5,000 6,000 8,000 9,000 8,000

Solution: The present value of the above cash flow stream is:

Year Cash Flow (PVIFA14%,n) Present value

0 Rs. 5,000 1.000 Rs. 5,000

1 6,000 0.877 5,262

2 8,000 0.769 6,152

3 9,000 0.675 6,075

4 8,000 0.592 4,736

Rs. 27,225

9. Mahesh deposits Rs. 200,000 in a bank account which pays 10 percent interest. How

much can he withdraw annually for a period of 15 years?

Solution: The annual withdrawal is equal to:

Rs .200,000

PVIFA 10% ,15YRS= Rs.2000,000

7,606=Rs .26,295

10. You want to take a world tour which costs Rs. 1,000,000 – the cost is expected to remain

unchanged in nominal terms. You are willing to save annually Rs. 80,000 to fulfill your

desire. How long will you have to wait if your savings earn a return of 14 percent per

annum?

Solution: The future value of an annuity of Rs. 80,000 that earns 14 percent is Equated

to Rs. 1,000,000.

80,000 x FVIFAn=?,14% = 1,000,000

80,000 (1,14n−10.14 ) = 1,000,000

1.14n – 1 = 1,000,00080,000 x 0.14 = 1.75

1.14n – 1 = 1.75 + 1 = 2.75

n log 1.14 = log 2.75

n x .0569 = 0.4393

n = 0.4393/0.0569 = 7.72 years

You will have to wait for 7.72 years

11. Shyam borrows Rs. 80,000 for a musical system at a monthly interest of 1.25 percent.

The loan is to be repaid in 12 equal monthly instalments, payable at the enf of each

month. Prepare the loan amortization schedule.

Solution:

The monthly installment A is obtained by solving the equation:

80,000 = A x PVIFAn=12,r=1.25%

80,000 = A x 1− 1

(1+r )nr

80,000 = A x 1− 1

(1.0125)12.0125

= A x 11.0786

Hence A = 80,000 / 11.0786 = Rs. 7221

The loan amortization schedule is shown below:

Loan Amortisation Schedule

Month Beginning Monthly Interest Principal Remaining

Amount Installment Repayment Balance

(1) (2) (3) (2) – (3) = (4) (1) – (4) = (5)

1 80,000 7221 1000 6221 73779

2 73,779 7221 922.2 6298.8 67480.2

3 67,480.2 7221 843.5 6377.5 61102.7

4 61102.7 7221 763.8 6457.2 54645.5

5 54645.5 7221 683.1 6537.9 48107.6

6 48107.6 7221 601.3 6619.7 41487.9

7 41487.9 7221 518.6 6702.4 34785.5

8 34785.5 7221 434.8 6786.2 27999.3

9 27999.3 7221 350.0 6871.0 21128.3

10 21128.3 7221 264.1 6956.9 14171.4

11 14171.4 7221 177.1 7043.9 7127.1

12 7127.1 7221 89.1 7131.9 -4.8@

@Rounding off error

191