Financial Management

11 - 1

Copyright © by R. S. Pradhan. All rights reserved.

WELCOME TO

CHAPTER 2: FINANCIAL STATEMENTS, CASH FLOWS & TAXES

11 - 2


CHAPTER 2: FINANCIAL STATEMENTS, CASH FLOWS & TAXES

Financial statements report the historical performance of a firm and provide a basis for making projections and forecasts for the future.

Scorecard for recording performance.The financial statements are:

1. The Balance Sheet2. Income Statement3. A statement of Cash Flows

The Balance Sheet : Shows financial position as of a certain date (Dec. 31, 2005)

11 - 3


NEPAL BRICK FACTORY LTD. (‘000 Rs.) P.24Liabilities and equity Year 1 Year 2Accounts payable 1,200 2,000Notes payable 400 400Accrued wages 400 800Other accruals 200 800Current Liabilities 2,200 4,000

Long-term debt 6,600 6,000Preferred stock 0 0Stockholder’s equity: Com. Stock (Rs.100 par) 2,000 2,000Paid in Capital 2,000 2,000Retained Earnings 5,200 6,000Total Stockholders’ eq. 9,200 10,000Total liab.& eq. 18,000 20,000

11 - 4


Assets Year 1 Year 2Cash 800 1,000Marketable securities 200 1,000A/cs receivable, net 3,000 2,400Inventories 3,000 3,600Prepaid expenses 0 0Current assets 7,000 8,000Gross fixed assets:Land 1,000 1,000Building 5,000 5,500Plant & machinery 9,000 9,500Other fixed assets 3,000 4,000Gross fixed assets 18,000 20,000Less accu. depreciation -7,000 -8,000Net fixed assets 11,000 12,000Total assets 18,000 20,000

11 - 5


g In assets side, the assets are arranged in order of liquidity (convertibility into cash).The balance sheet figures are book values & not necessarily the same as market values.Total Assets = Total liabilities + Owner’s equityTA = TL + OECA + FA = CL + LTL + OEC + AR + I + FA = CL + LTL + OE Net working capitalNWC1 = CA– CL= Rs.7,000–2,200 =4,800NWC2 = CA– CL= Rs.8,000–4,000 =4,000

11 - 6


Operating assets and operating capital

g Managers must be judged and compensated for those things that are under their control.g Operating capital is the sum of the ‘net

operating working capital’ & ‘net operating fixed assets’.g NOWC1 =Non-intt. bearing CA – Non- intt.

bearing CLg = (800+3,000+3,000) – (1,200+400+200)g = Rs.6,800 – 1,800 = Rs.5,000.

11 - 7


g(Note that marketable securities & notes payables are not included in non-interest bearing CA & CL respectively.)NOWC2

=(1,000+2,400+3,600)–(2,000+800+800)= 7,000 – 3,600 = Rs. 3,400.

Operating capital = NOWC + Net operating fixed assetsOC1 = Rs. 5,000 + 11,000 = Rs. 16,000.OC2 = Rs. 3,400 + 12,000 = Rs. 15,400.Incremental OC = 15,400 –16,000= - 600.NOWC decreased though NOFA increased.

11 - 8


g It shows revenues, costs and net profits.g Or the net results of the firm’s

operations over a specified time period such as a year. g Figures are not as of a certain date.g Nepal Brick Factory, Income Statement

(p.30)

2. The Income Statement

11 - 9


Particulars Year 1 Year 2Revenues 20,000 24,000Cost of sales -11,000 -13,600Gross income 9,000 10,400Marketing expenses -5,000 -6,000General & adm. exps. -1,000 -1,200EBDIT 3,000 3,200Depreciation -1,000 -1,000Net ope. income (NOI) 2,000 2,200Other income, net +300 +240EBIT 2,300 2,440Interest expenses -500 -440EBT 1,800 2,000Income taxes @ 40% -720 -800Net income 1,080 1,200

11 - 10


Income Statement EquationsNet income = Total Revenue – Total CostNI = Total revenue – Cost of sales – Mktg.

exps.– Gen. & admn. exps. – Dep. + Other income, net - interest - taxes.

EBIT = Total revenue – Cost of sales – Mktg. exps. – Gen. & adm. exps. – Dep. + Other income, net

EBT = EBIT – InterestNet income = EBIT – Interest – Tax

11 - 11


Net operating profit after taxes (NOPAT)g Net income cannot be used to evaluate

managers. g NOPAT = EBIT (1 – Tax rate)

NOPAT1 = Rs. 2,300 (1 – 0.4) = Rs. 1,380.g NOPAT2 = Rs. 2,440 (1 – 0.4) = Rs. 1,464.Free Cash Flow: Cash flow actually

available for distribution to investors after the company has made all the investments in fixed assets and working capital. g FCF2= NOPAT– Net investment in OC

= Rs. 1,464 – (–600) = Rs. 2,064.

11 - 12


g Neither balance sheet nor income statement shows cash flows of the firm.g Cash + mkt. securities increased from

Rs. 1,000 in year 1 to Rs. 2,000 in year 2. Reasons?g Uses or applications of funds: Rules:

- Increase in assets- Decrease in liabilitiesSources of funds:- Decrease in assets.- Increase in liabilities.

3. The Statement of Cash Flows

11 - 13


Statement of cash flows (Year 2)- P.33 I. Cash flows from operating activities: 4,000

Net income 1,200 Add depreciation 1,000Changes in working capital:Decrease in accounts receivable 600Increase in inventories - 600Increase in accounts payable 800Increase in accrued wages 400Increase in other accruals 600

II. Cash flows from long-term invest. activities: -2,000Increase in gross fixed assets - 2,000

III. Cash flows from financing activities: -1,000 Incr./decrease in notes payables 0 Decrease in long-term debt – 600 Dividend payment (assume) – 400 Net increase in cash & cash equiv. 1,000

Cash & cash equiv., begin. of yr. 1,000Cash & cash equiv., end of yr. 2,000

11 - 14


g MTR: Marginal tax rate: Tax rate on the last unit of income. g ATR: Average tax rate: Actual tax payment

divided by taxable income, or % income that goes out in taxes.

Table 2.7: Typical corp. tax brackets/rates Taxable income Tax rate Upto Rs. 200,000 15%200,000 to 300,000 25% 300,000 to 400,000 34%> 400,000 39%Firm A: Taxable income = Rs. 260,000. Tax bill =? (Rs. 30,000+15,000)=45,000, ATR =? 17.3%, MTR = ? 25%)

4. Taxes: Marginal & average tax rates

11 - 15


5. Common size statements Difficult to directly compare the financial

statements of two firms because of size differences.

Also difficult for the same firm if size has changed.

Difficult if it is to be compared with a foreign firm.

Common size analysis consists of computing percentages of each item over total assets in case of balance sheet.

In case of income statement, percentages are computed over sales.

11 - 16


The Balance Sheet : NEPAL BRICK FACTORY LTD. (‘000 Rs.)Liabilities and equity Year 2 % of TAAccounts payable 2,000 10Notes payable 400 2Accrued wages 800 4Other accruals 800 4Current Liabilities 4,000 20

Long-term debt 6,000 30Preferred stock 0 0Stockholder’s equity: Com. Stock (Par Rs.100) 2,000 10Paid in Capital 2,000 10Retained Earnings 6,000 30Total Stockholders’ eq. 10,000 50

Total liab.& eq. 20,000 100

11 - 17


Assets Year 2 % of TACash 1,000 5Marketable securities 1,000 5A/cs. receivables, net 2,400 12Inventories 3,600 18Prepaid expenses 0 0Current assets 8,000 40Gross Fixed Assets:

Land 1,000 5Building 5,500 27.5Machinery & equip. 9,500 47.5Other fixed assets 4,000 20

Total Fixed Assets 20,000 100Less Depreciation -8,000 40Net Fixed Assets 12,000 60Total Assets 20,000 100

11 - 18


2.The Income StatementParticulars Year 2 % of SalesRevenues 24,000 100

Cost of sales -13,600 56.7Gross income 10,400 43.3

Marketing expense -6,000 25General & adm. exps. -1,200 5

EBDIT 3,200 13.3Depreciation -1,000 4.2

Net ope.income (NOI) 2,200 9.1Other income, net +240 +1.0

EBIT 2,440 10.1Interest expenses -440 1.8

EBT 2,000 8.3Income taxes @ 40% -800 3.3

Net income 1,200 5.0

11 - 19


Solve problems (Chap.2)

SP 1 & SP 2

P1 & P 2

Quiz

Thanking you

11 - 20


WELCOME TO

CHAPTER 3: FINANCIAL ANALYSIS

11 - 21


CHAPTER 3: FINANCIAL ANALYSIS Difficult to directly compare the financial

statements of two firms because of size differences.

Also difficult for the same firm if size has changed.

Difficult if it is to be compared with a foreign firm.

Common size analysis consists of computing percentages of each item over total assets in case of balance sheet.

In case of income statement, percentages are computed over sales.

11 - 22


The Balance Sheet : NEPAL BRICK FACTORY LTD. (‘000 Rs.)Liabilities and equity Year 2 % of TAAccounts payable 2,000 10Notes payable 400 2Accrued wages 800 4Other accruals 800 4Current Liabilities 4,000 20

Long-term debt 6,000 30Preferred stock 0 0Stockholder’s equity: Com. Stock (Par Rs.100) 2,000 10Paid in Capital 2,000 10Retained Earnings 6,000 30Total Stockholders’ eq. 10,000 50

Total liab.& eq. 20,000 100

11 - 23


Assets Year 2 % of TACash 1,000 5Marketable securities 1,000 5A/cs. receivables, net 2,400 12Inventories 3,600 18Prepaid expenses 0 0Current assets 8,000 40Gross Fixed Assets:

Land 1,000 5Building 5,500 27.5Machinery & equip. 9,500 47.5Other fixed assets 4,000 20

Total Fixed Assets 20,000 100Less Depreciation -8,000 40Net Fixed Assets 12,000 60Total Assets 20,000 100

11 - 24


2.The Income StatementParticulars Year 2 % of S.Revenues 24,000 100

Cost of sales -13,600 56.7Gross income 10,400 43.3

Marketing expense -6,000 25General & adm. Exps. -1,200 5

EBDIT 3,200 13.3Depreciation -1,000 4.2

Net ope.income (NOI) 2,200 9.1Other income, net +240 +1.0

EBIT 2,440 10.1Interest expenses -440 1.8

EBT 2,000 8.3Income taxes @ 40% -800 3.3

Net income 1,200 5.0

11 - 25


Financial Ratio Analysis Why bother with a ratio? Why not simply look

at the raw numbers. Raw numbers are not very informative.

Ratios prove more useful than the raw numbers. Net profit of Rs. 1 million?

A ratio is simply a one number divided by another number. Hence, one may compute a large number of fin. ratios.g Why compute ratios?- assess the financial strengths & weaknesses of

the firm- serve as a basis for decision-making - whether

to extend the loan to a firm?

11 - 26


g How it is computed?g What is it intended to measure?g What is the unit of measurement?g What does a high or low ratio mean?Uses of financial ratios:g Internal uses:

-comparison over time (Improvement?) -performance evaluation: managers-performance of multiple divisions -planning for the future.g External uses:- Comparison with similar firms.- Comparison with industry average.

11 - 27


Users of financial ratios: Creditors, owners, management, employees,

consumers, government, etc. g 1.Short term creditors: liquidity ratios.g 2.Long-term creditors: debt ratios, interest

coverages, & profitability ratios.g 3.Equityholders: profitability, growth, &

valuation.g 4.Management: all ratios. g 5.Credit rating agencies: Purpose?

11 - 28


Different groupings of financial ratios. Actual ratios would remain the same.

A. Liquidity ratiosB. Asset mgmt. or efficiency ratiosC. Debt mgmt. or leverage ratiosD. Profitability ratiosE. Market value ratios Compute ratios for Nepal Brick (Year 2): A. Liquidity ratios 1.Current ratio = CA/CL =Rs.8,000/Rs.4,000=2x.

(Ind. Aver. Or Comp. Co. = 2x) Comment: OK2.Quick, or acid test =(CA - Inv.)/ CL

=(Rs.8000-3600)/4000 =1.1x. (IA or CC=1.0x) OK

11 - 29


B Asset Management (Efficiency or Turnover ) ratios

3. Inventory turnover = Sales or COGS/ Inv. = Rs. 24,000/ 3,600 = 6.67x.(IA or CC=8x).Poor.

4.Days sales outstanding (DSO) = Receivables/ (Annual sales/360)= Rs.2,400/(Rs.24,000/360) = 36 Days.(IA or CC = 30 days). Poor.

5.Fixed assets turnover = Sales/Net fixed assets = Rs. 24,000/Rs. 12,000 = 2x.(IA or CC = 2x). OK.

6.Total assets turnover = Sales/ Total assets = Rs. 24,000/Rs. 20,000 =1.2x.(IA or CC=1.5x). Somewhat low.

11 - 30


7.Capital requirement = Operating capital / Sales = (Rs.15,400)/ Rs. 24,000 = 64.2%(IA or CC =40%) Poor

C. Debt Mgmt. or Leverage ratios8.Total debt to total assets = Total debt/Total

assets = Rs.10,000 /Rs.20,000 =50%(IA or CC = 40%) High (Risky)

9.Long-term debt to total assets = Long-term debt/Total assets = Rs.6,000/20,000 =30% (IA or CC =30%) OK

10.Times-interest-earned (TIE) = EBIT/ Interest charges = Rs.2,440/Rs.440 = 5.55x.(IA or CC = 8x). Low (risky)

11 - 31


D. Profitability ratios11.Net profit margin = Net income/ Sales

= Rs.1,200/24,000 = 5%. (IA or CC =8%). Poor.

12. Basic earning power = EBIT/Total assets =Rs.2,440/20,000 =12.2%.(IA or CC =15%). Poor.

13. Return on total assets (ROA) =Net income/ total assets =1,200/20,000 = 6%.(IA or CC = 9%). Poor.

14. Return on equity (ROE) = Net Income / Equity = Rs.1,200/Rs.10,000 = 12%.(IA or CC =15%). Poor.

11 - 32


E. Market value ratios15. EPS = NI/ No. of shares = Rs. 1200/20

= Rs.60. (IA or CC = Rs.75). Poor.16. Price-earning (P/E) = MPS/ EPS

= Rs.200/Rs. 60 =3.33x. (Assume MPS=Rs. 200) (IA or CC = 6x). Low.

17. Book value per share = Book equity/ No. of shares = Rs. 10,000/ 20 = Rs. 500.

(IA or CC = Rs.700). Low.18. Market/Book values = MPS/ Book value per

share = Rs. 200/ Rs. 500 =0.4x. (IA or CC = 1.5 times). Low.

11 - 33


g The two measures of profitability, ROA and ROE, is the reflection of use of debt financing, or financial leverage.g Du Pont Corporation developed a famous way

of decomposing ROE into its component parts. Net income

ROE= ------------------ = 12 percent.Equity

Multiply the ratio by Assets/AssetsNet income Assets

ROE = ----------------- x ----------------Equity Assets

2. The Du Pont Identity

11 - 34


Net income AssetsROE = ---------------- x ----------------

Assets EquityROE = ROA x Equity Multiplier

Rs.1200 Rs.20,000g = ------------ x ---------------

Rs.20,000 Rs.10,000= 0.06 x 2.0 = 0.12 or 12%. Same as before.

Further decompose ROE by multiplying numerator and denominator by sales:

Sales NI AssetsROE=--------- x ---------- x --------------

Sales Assets EquityNI Sales Assets

= --------- x -------------- x ---------Sales Assets Equity

11 - 35


= Profit margin x Assets turnover x Equity multiplier

= 0.05 x 1.2 x 2.0 =0.06 x 2.0 =0.12 or 12% Again, it is the same as before. The Du Pont

Identity tells us that ROE is affected by three things:

1.Operating efficiency as measured by profit margin.

2. Asset use efficiency as measured by assets turnover.

3. Financial leverage as measured by equity multiplier.

If ROE is unsatisfactory, the Du Pont Identity tells us where to start looking for the reasons.

11 - 36


Empirical evidence: Prediction of corporate bankruptcy

Altman (1968) used discriminant analysis of fin. ratios in the prediction of corp. bankruptcy.

Only 5 out of 22 ratios were finally considered as predictors. Altman’s model appeared as follows:

Z=0.012 X1 +0.014 X 2 +0.033 X3+0.006 X4+0.999 X5

X1 = (CA-CL)/ TAX2 = Retained Earnings/ Total AssetsX3 = EBIT / Total AssetsX4 = ME / Book Value of Total Debt (market value

of equity includes both pref. & com. shares, and debt includes CL + LTL).

X5 = sales/total assets

11 - 37


A Z-score of less than 1.8 indicates a very high probability of failure, while a Z-score larger than 3 indicates a high probability of nonfailure.

Z-scores between 1.8 and 3 fall in the “gray zone” where it is not possible to predict with confidence whether the firm will or will not fail.

Group meansRatio Bankrupt NonbankruptX1 - 6.1% 42.4%X2 - 62.6% 35.5%X3 - 31.8% 15.4%X4 40.1% 247.7%X5 1.5 times 1.9 times A case of Nepal Brick Factory, X1=0.2, X2=0.04,

X3=0.122, X4= 0.4, X5=1.2ZNBF = 0.012(0.2) + 0.014(0.04) + 0.033(0.122) +

0.006(0.4) + 0.999(1.2) = 1.21 (High probability of failure)

11 - 38


Limitations of ratio analysis 1.Different depreciation methods 2.Different inventory valuation methods (LIFO,

FIFO, etc.) 3.Different fiscal years 4.Treatment of research & development

expenditure 5.Treatment of pre-operating expenditure 6.Seasonality in businessSOLVE PROBLEMSPage 71 Self-test Problems: SP 3 & 7 Page 77 Problems: P1, 2, 3, 5, & 6.Quiz

Thanking you.

11 - 39


WELCOME TO

CHAPTER 5 TIME VALUE OF MONEY

11 - 40


A rupee received today is worth more than a rupee expected in the future.

Financial managers must have clear understanding of the time value of money.

Of all the concepts in finance, none is more important than time value of money.

Also called discounted cash flow analysis.

CHAPTER 5: TIME VALUE OF MONEY

11 - 41


Time value of money is concerned with the following: 1. Future value (Value at a future date?)2. Present value (Value today?)3. Rates of return: ‘i’ or ‘r’=?

(Rate of interest or return?) 4. Finding time: ‘n’ or ‘t’ =?

(No. of time periods?) Four ways to find:1. Solve the equation with a regular calculator.2. Use financial tables.

A1: PVIF valuesA2: PVIFA valuesA3: FVIF valuesA4: FVIFA values

3. Use a financial calculator.4. Use a spreadsheet.

11 - 42


FV = ?

0 1 2 3i = 10%

gFinding FVs means moving to the right. gHow much do we get at t=3 on simple and/or compound interest basis?

PV= -100

1. FUTURE VALUE (FV)gAmount of money / investment that will grow to over a period of time at some given interest rate.gFinding FV is called compounding.gWhat’s the FV of an initial Rs.100 after 3 years if i = 10%?

11 - 43


After 3 years

gFV3 = PV(1 + i)3 = Rs.100(1.10)3

= 100 x 1.331 = 133.10. OR gUsing the FVIF (Future Value of Interest Factor) Table:Table A3 Page 422): FV3 = PV x FVIF10%,3yrs

= Rs. 100 x 1.331 = 133.10gHigher the ‘i’, higher would be FV or vice versa (See Fig 5.1 in page 125).

FVn = PV(1 + i)n

11 - 44


gTable A4: How to use FVIFA (Future Value Interest Factor of Annuity) table?

What’s the FV of a 3-year ordinary annuity of Rs.100 at 10%?

100 100100

0 1 2 310%

110 121FV = 331

11 - 45


Table method: What is the FV of a 3-year ordinary annuity of

Rs. 100 at 10 percent?Yr. Cash Flow FVIF@10%FV

(Page 422)1 100 1.21 1212 100 1.1 1103 100 1 100Total 3.31 331(Future Value Interest Factor of Annuity : Table

A4 Page 425): FV = PMT x FVIFA10%3yrs FV = Rs.100 x 3.31 = Rs. 331 How do we find FV if the cash flows are not

even? Change CFs in the above table.

11 - 46


Effect of compounding is not great over short time periods.

If one of our ancestors had invested Rs.10 for us at a 10 percent interest rate 150 years ago, how much we would have today?

FV150 = PV(1 + i)150 = ?

11 - 47


FV = Rs. 16,177,178.

We would have become a millionaire.

11 - 48


i = 10%

2. PRESENT VALUES (PV)

FV=100

0 1 2 3

PV = ?

t = 3 yrs.

PV is the current value of future cash flows discounted at the appropriate rate.

Discounting is the process of finding out present value of some future amount.

Finding PV is the discounting which is the reverse of compounding.

What’s the PV of Rs.100 due in 3 years if i = 10%?

11 - 49


We know, FVn = PV(1 + i )n

( )PV =

FV

1+ i = FV

11+ i

nn n

n

PV = Rs.1001

1.10

=100*0.7513 =75.13

3

gPVIF (Table A1: Present Value Interest Factor - Page 416).

gPV = FV*PVIF10%3yrs=Rs.100(0.7513) = Rs. 75.13.gHigher the discount rate, lower would be PV or vice versa (Fig 5.3 in page 128).

11 - 50


Table A2: How to use PVIFA (Present Value Interest Factor of Annuity) table?

What is the PV of this ordinary annuity?

100 100100

0 1 2 310%

90.9

82.6

75.1248.6 = PV

11 - 51


Table method: What is the PV of a 3-year ordinary annuity of Rs.100 at 10 percent?

Year Cash Flow PVIF@10% PVPage 416

1 100 0.909 90.92 100 0.826 82.63 100 0.751 75.1Total 2.486 248.6Using PVIFA table: PV = (PVIFAi%,n yrs) PMT

= PVIFA (10%, 3 yrs) = (2.4869)100 = 248.69. How do we find PV if the cash flows are not

even? (Change CFs in the above table).

11 - 52


3. Finding discount rate or rates of return:

gSuppose we would like to retire in 40 years as a millionaire. If we have Rs. 20,000 today, what rate of return do we need to earn?

FV=PV(1+i)n

Or Rs.1000,000=Rs.20,000(1+i)40

Or Rs. 20,000 (1+i)40 = Rs.1000,000 Or (1+i)40 = 50 OR (1+i) = 501/40 =50.025 =10.2%Using Table method: FV = PV (FVIFi, n yrs) FVIFi,40 = 5010% = 45.259? = 5011% = 65.0009 i = 10.24%

Orig.value - LR value i =LR + ----------------------------- Diff. in rates HR value - LR value

11 - 53


Orig.value - LR value i =LR + ------------------------------- Diff. in rates HR value - LR value

50 - 45.259 i =10 + --------------------------- (0.11-0.10) 65.0009 - 45.259

i = 10.24 =10.24%

11 - 54


4. Finding the Time (t or n?) How long does it take to double Rs. 1 million, if

the appropriate interest rate is 10 percent?

i = 10%

Rs.2m

0 1 2 ?

-Rs. 1m

FV= PV(1 + i)n

gOr Rs. 2m = Rs.1m(1 + 0.10)n

gOr (1.1)n = 2gOr n ln (1.1) = ln (2)gOr n = ln (2) / ln (1.1)gOr n = 0.693 / 0.0953 = 7.3 yrs.

t = ?

11 - 55


Using Table Method: FV = PV (FVIFi, n yrs)

Or (FVIFi, n yrs) = FV / PV Or FVIF10%, n =2m/1m = 2. Or Find ‘n’ for “2 in 10% column” It lies between 7 and 8 years. Value of 7 year = 1.9487 ? = 2Value of 8 year = 2.1436 By interpolation,

Orig. Value - LY ValueLY+ -------------------------------- (Diff. in yrs)

HY Value - LY Value = 7.3 years

11 - 56


Ordinary Annuity (end of the year)

PMT PMTPMT

0 1 2 3i%

PMT PMT

0 1 2 3i%

PMT

Annuity Due (beginning of the year)

What’s the difference between an ordinary annuity and an annuity due?

PV FV

11 - 57


gWhat is the FVA & PVA if the interest rate is 5%, PMT = Rs.100, & t = 3 years? Assume payment has to be made at the beginning of the year.FVADue = PMT (FVIFA5%,3yrs) x 1.05FVADue = Rs.100 x 3.1525 x1.05 = Rs.331PVADue = PMT (PVIFA5%, 3yrs) x 1.05= Rs. 100 x 2.7232 x 1.05 = Rs. 285.9 If you have to receive, negotiate for beginning of the period payment. If you have to pay, negotiate for end of the period payment. Since ordinary annuities are more common, we confine to payment at the end of each period.

11 - 58


More Frequent compounding? (P.130 last para)

gWill the FV of a lump sum be larger or smaller if we compound more often, holding the stated i% constant? Why?gLARGER! If compounding is morefrequent than once a year - for example, semiannually, quarterly, or daily - interest is earned on interest more often.

11 - 59


0 1 2 310%

0 1 2 3

5%

4 5 6

134.01

100 133.10

1 2 30

100

Annually: FV3 = Rs.100(1.10)3 = 133.10.

Semiannually: FV6= Rs.100(1.05)6 =134.01(Divide rate by 2 and multiply ‘t’ by 2.)

11 - 60


gBy using Table: Annual basis: FV3 = FVIF(10%, 3yrs.)Rs.100 = 1.331x100 = 133.1Semiannually: FV6 = FVIF(5%,6 pds) Rs.100 =1.3401x100 =134.01(Again, divide rate by 2 and multiply ‘t’ by 2) Comparison of different types of interest rates: (P.131)People in finance often work with three types of interest rates:iNom = nominal/ stated/ quoted rate per year.iPer = periodic rate.EAR (EFF%) = Effective annual rate.

11 - 61


Nominal or quoted rate: the rate quoted by the banks, brokers and other fin. insts. Also known as annual percentage rate (APR).Periodic rate: the rate charged by a lender or paid by a borrower each period. It can be a rate per year or per quarter or per month, etc. Effective Annual Rate (EAR = EFF%)The annual rate which causes PV to grow to the same FV as under multi-period compounding.

11 - 62


How do we find EFF% for a nominal rate of 10%, compounded semiannually?

EFF% = - 1(1 + )iNom

m

nm

= - 1.0(1 + )0.102

1x2

= (1.05)2 - 1.0 = 0.1025 = 10.25%.m = no. of periods

11 - 63


EAR = EFF% of 10%

EARAnnual = 10%.

EARS = (1 + 0.10/2)1x2 - 1 = 10.25%.

EARQ = (1 + 0.10/4)1x4 - 1 = 10.38%.

EARM = (1 + 0.10/12)1x12 - 1 = 10.47%.

EARD(360) = (1 + 0.10/360)1x360- 1= 10.52%.

11 - 64


AmortizationgConstruct an amortization schedule for a Rs.1,000, 10% annual rate 3 year loan with 3 equal payments.

PV of annuityAnnual pmt = --------------------------

PVIFA(10%, 3 yrs)= Rs.1000/2.4869 = Rs.402

Year Payment Interest Prin. pmt. End Bal.1 402 100 302 6982 402 70 332 3663 402 37 366 -

Total 1206 206 1000

11 - 65


Solve Problems

Chapter 5: Time Value of Money

Self-test problems: Page 136

SP 3,4,6,7,11,13,14 & 15.

Problems: Page 139

P1 to P4, & P9 to P15.

Quiz

11 - 66


WELCOME TO

CHAPTER 6:BONDS AND THEIR

VALUATION

11 - 67


CHAPTER 6: BONDS AND THEIR VALUATION

What is a bond?

Key features of bonds

Bond valuation method

Measuring yield

11 - 68


What is a bond?

A bond is a long-term contract under which a borrower agrees to make payments of interest and principal, on specific dates, to the holders of the bond.

Bonds may be classified as treasury bonds, municipal bonds, foreign bonds, and corporate bonds.

11 - 69


Key Features of a Bond1. Par value & number of bonds: Face amount, e.g., Rs.1000. About 2 years ago, BOK issued:General public: 50,000 debentures @ Rs.1000 =Rs. 5 CroresPvt placement: 150,000 debentures @ Rs.1000= Rs.15 Crores.

2. Coupon interest rate: Stated interest rate. Generally fixed. (6%, every 6 months)3. Maturity: Years until bond be repaid. (7 years)4. Default risk: Risk that issuer will not make interest or principal payments.5. Indenture: Document containing terms and conditions of bond issue.6. A call provision: a provision to call in the bond before maturity. Most bonds have call provisions.

11 - 70


7.Call premium: Premium to be paid if called before maturity.

8.Refunding operation: Issuer can refund if rates decline. That helps the issuer but hurts the investor.

9. Sinking Fund: It is an orderly retirement of bonds. Provision to pay off a loan over its life rather

than fall due at maturity. Sinking funds are generally handled in 2 ways.

- Call a certain % at par per year through lottery method.- Open market operation.

11 - 71


Financial Asset Valuation The value of any financial asset – a stock, a

bond, a lease, or even a physical asset such as an apartment building or a piece of machinery – is simply the present value of the cash flows the asset is expected to produce.

Floating rate bonds have floating interest payments depending on the level of interest rates over time.

A zero coupon bonds have no interest payments.

A regular bond will have the following situation.

11 - 72


Cash flows for regular bondThe discount rate (ki) is the opportunity cost of

capital, i.e., the rate that could be earned on alternative investments of equal risk.

( ) ( ) ( )Bond value =

INT

1 + k. . +

INT

1 + k1 21

INT

k n

0 1 2 nk%

Int1 Intn+ MInt2Bond Value=?

...

+ ++

M + --------- (1+k)N

11 - 73


What’s the value of a 10-year, 10% coupon (Rs.1000) bond if kd = 10%?

( ) ( ) ( )V

k kB

d d

= Rs.100 Rs.1,

1

.1000

11 10 10 . . . +

Rs.100

1+ kd

100 100

0 1 2 10kd=10%

100 + 1,000VB = ?

...

= Rs.90.91 + . . . + Rs.38.55 + Rs.385.54= Rs.1,000.

++++

11 - 74


Rs. 614.46 385.54

Rs. 1,000.00

PV annuity (interest) PV maturity value Value of bond

===

Table Method:= (PVIFAi%,n yrs)C + (PVIFi%,n

thyr) M”

= (PVIFA10%,10Yrs)Rs.100 +

(PVIF10%,10th

yr) Rs.1000= (6.1446 x Rs. 100) + (0.3855 x Rs. 1000)= 614.5 + 385.5 = 1000

11 - 75


Suppose 10% bond was issued for 20 years and now has 10 years to maturity. What would happen to its value over time (t = 10 years) if the required rate of return remained at 7%, 13%, or at 10%?

11 - 76


M

Bond Value (Rs.)

Years remaining to Maturity

1,318

1,211

1,000

837

789

0 10 20

kd = 7%.

kd = 13%.

kd = 10%.

Premium bond

Discount bond

11 - 77


The value of a discount bond increases to Rs.1,000 at maturity.

The value of a premium bond decreases to Rs.1,000 at maturity.

At maturity, the value of any bond must equal its par value.

A par bond stays at Rs.1,000 if kd remains constant.

- If kd < coupon rate, bond sells at a premium. - If kd > coupon rate, bond sells at a discount.- If kd = coupon rate, bond sells at its par

value.

11 - 78


Yield to maturity (YTM): is the rate of return earned on a bond held to maturity. Also called “promised yield.” What’s the YTM on a 10-year, 9% annual coupon, Rs.1,000 par value bond that sells for Rs.887? Guess?

90 90 90

0 1 9 10kd=?

1,000PV1

. . .PV10

PVM

887 Find kd that “works”!

...

11 - 79


Finding the YTM (Guess try rate first):Try 10%:VB = (PVIFAi,n)C +(PVIFi,n)M”Rs.887 =(PVIFA 10%,10yrs)Rs.90 +

(PVIF 10%, 10th Year) Rs.1000 Rs.887 = (6.1446)Rs. 90+ (.3855) Rs.1000 Rs.887 = Rs.553.01 + Rs. 385.5Rs.887 = Rs. 939 Try 12%:Rs.887 = (PVIFA 12%, 10yrs)Rs. 90 + Rs.1000

(PVIF 12%, 10th Year)887 = (5.6502)Rs.90+Rs.1000(0.322)887 = 509 + 322887 = 831

11 - 80


PV of LR - Market valueLR + -------------------------------- Diff. In rates PV of LR - PV of HR

939 - 887 = 10 + -------------------- 2 939 - 831= 10+ 0.96 =10.96 or 11.0%

Find YTM if price were Rs.1,134.2?It means kd < coupon rate. YTM= 7.08%.Bond sells at a premium.

11 - 81


Approximate methodFV – MV 1000-887

CI + ------------- 90 + ------------- n 10YTM = -------------------------- = ----------------------

FV + MV 1000+887------------ --------------

2 2= 101.3/943.5 = 0.107 or 10.7 percent. Earlier this YTM was 10.96 percent.

CI : Coupon interest in rupees.FV : Face value or maturity value of a bond.MV : Market value of a bondn : Maturity period of a bond

11 - 82


gOf course, the bond's price will be less affected by a change in interest rates if it has been outstanding for a long time and matures shortly.

gIf the bond is purchased and held to maturity, the bondholder's YTM will not change, regardless of what happens to interest rates.

11 - 83


Current yield = Annual coupon pmtCurrent price

Current yield

gIt shows cash income.gFind current yield and capital gains yield for a 9%, 10-year, Rs.1000 bond when the bond sells for Rs.887.

Rs.90 Rs.887

Current yield = = 10.15%

gYTM = Current yield + capital gains yieldg11% = 10.15% + capital gains yieldgHence the capital gains yield is 0.85%.

11 - 84


Yield to Call (YTC). It refers to the return the investors receive if it is called before maturity period which is known as the yield to call (YTC) or realised rate of return. Example: An 8-year, 10 percent annual coupon bond, with a par value of Rs.1,000 is likely to be called in 2 years at a call price of Rs.1,050. The bond sells for Rs.1080. Assume that the bond has just been issued. What is the bond’s yield to call?

11 - 85


a)Try 6%VB = (PVIFAi%,n yrs.)C + (PVIFi%, n

th yr) Call Price

Rs.1,080=(PVIFA6,2)Rs.100+(PVIF6,2)Rs. 1050Rs.1,080 = (1.8344)100 + (0.89)1050Rs.1,080 = 1118Try 8%Rs.1,080=(PVIFA8,2)Rs.100+(PVIF8,2)Rs.1050Rs.1,080 = (1.7833)100 + (0.8573)1050Rs.1,080 = 1078By interpolation,YTC=6+[(1118-1080)x(2)/(1118-1078)] =7.9%.

11 - 86


Semiannual bondFind the value of 10-year, 10% coupon,Rs.1000 semiannual bond if kd = 14%.

1. Multiply years by 2 to get periods = 2n.2. Divide nominal rate by 2 to get periodic rate = kd/2.3. Divide annual INT by 2 to get PMT = INT/2.Bond Value (VB)=PVIFA(7%,20pds)Rs.100/2 + Rs.1000 PVIF(7%,20th pd)= (10.5940 x Rs.50) + (.2584xRs.1000)=Rs. 788.

11 - 87


You could buy, for Rs.1,000, either a 10%, 10-year, annual payment bond or an

equally risky 10%, 10-year semiannual bond. Which would you prefer?

The semiannual bond’s EFF% is:

10.25% > 10% EFF% on annual bond, so buy semiannual bond.

EFFi

mNom

nm

%.

.= +

− = +

− =1 1 1

0 10

21 10.25%

1x2

.

11 - 88


Solve Problems: Chapter 6

Self-Test Problems: SP2 to SP6. Problems: P1, P2 & P3.

Thanking you

11 - 89


Should we build thisplant?

WELCOME TOCHAPTER 9: CAPITAL BUDGETING

11 - 90


Importance of capital budgeting Financial decisions: Investment, financing &

dividend decisions. Capital budgeting is treasurer’s function. Decisions involve substantial amount of money. Decisions have implications for a longer period. Loss of flexibility. Shows direction in which firm goes. Timing: Capital assets must be available when

they are needed.

11 - 91


Categories of investment proposals or project classifications

Replacement of obsolete assets: machine, equipment, plant, production processes, existing technology, etc.

Replacement for cost reduction: equipment is serviceable but old.

Expansion project: Expansion of existing products/ markets.

Safety and/or environmental projects: government compliance, insurance company compliance, etc.

Research & development. Others: Office building, parking lots etc.

11 - 92


Ranking investment proposals Capital budgeting approach stresses thedevelopment of systematic procedures & rules forevaluating investment proposals.

g1. Payback period(i) Ordinary payback period(ii)Discounted payback period

g2. Accounting rate of returng3. Net present valueg4. Internal rate of returng5. Modified internal rate of returng6. Profitability indexg7. Replacement chain methodg8. Equivalent annuity method

11 - 93


1.Payback period: Number of years required to recover the initial capital outlay on a project.

If cash flows are equal or even: Original investment

Payback period = ----------------------------- Annual cash flow

Consider the following two projects:Project X Project Y

Original Invest. -Rs.12,000 -Rs.12,000Cash flows (Rs.) Year 1 3,000 3,000

Year 2 3,000 3,500Year 3 3,000 4,000Year 4 3,000 4,500Year 5 3,000 5,000

Payback period: Project X = Rs.12,000/Rs.3000 = 4 years

11 - 94


Payback period: Project Y

Cash flows Cum.CFs Or Cum.CFsRupees Rupees Rupees

Original Investment -12,000 -12,000Cash flows: Year 1 3,000 -9,000 3,000

Year 2 3,500 -5,500 6,500 Year 3 4,000 -1,500 10,500 Year 4 4,500 3,000 15,000 Year 5 5,000

Payback = 3+ (Rs.1500/Rs.4500) = 3.33 years

11 - 95


Year Project A B C D0 (Rs.3,000) (Rs.3,000) (Rs.3,000) (Rs.3,000)1 300 0 300 6002 2,700 0 600 9003 300 900 900 1,5004 -300 2,100 1,200 1,5005 -1,200 3,900 3,750 1,800Payback 2 yrs. 4 yrs. 4 yrs. 3 yrs. Merits- Simple and easy to compute/understand. - It is a widely used method.- Provides an indication of a project’s liquidity.Demerits- Not a measure of profitability.- Fails to consider all the cash flows. - Ignores cash flows after the payback period.- Fails to consider time value of money.

11 - 96


Discounted Cash Payback (Assume that cost of capital is 10%)

Discounted Pay Back Period (Project D)

Year CFs, D, Rs. PVIF@ 10% PV Rs. Cum. CF 0 -3,000Cum CFs, Rs. Or Cum CFs0 -3000 1 (3,000.0) (3,000.0) (3,000.0) 1 600 0.909 545.4 (2,454.6) 545.4 2 900 0.826 743.4 (1,711.2) 1,288.8 3 1,500 0.751 1,126.5 (584.7) 2,415.3 4 1,500 0.683 1,024.5 439.8 3,439.8 5 1,800 0.621 1,117.8 1,557.6 4,557.6

Discounted cash payback:= 3 + [(Rs.3,000 - Rs.2,415.3) / 1,024.5]= 3 + (584.7 / 1,024.5) = 3.57 years.

11 - 97


2. Accounting rate of return (ARR)

ARR may be computed in different ways. One of such methods may be indicated as under:

Average Net IncomeARR = ----------------------------

Investment outlay

Where: Cash Flow = Net income + depreciation Net income = Cash Flow – Depreciation Straight line depreciation Life of the project = 5 years

11 - 98


ARR for Project D

Year CFs Net Inc. Depreciated ARR = CF- Dep. value of inv.

0 Rs.- 3,000 - Rs. 3,000 -1 600 0 2,400 02 900 300 1,800 16.67%3 1,500 900 1,200 75%4 1,500 900 600 150%5 1,800 1,200 0 ∞

gAnother definition of ARR calculates a single average return for the whole project.

11 - 99


It is computed as average net income divided by investment.

(0+300+900+900+1200)/5 ARR for D = ----------------------------------- = 22%

3000 ARR for all four projects are:Projects A B C DARR -8% 26%. 25% 22%

Merits: - Simple to understand and use.- Can readily be calculated by using accounting

data.- Uses all items of cash flows Demerits:- Does not consider time value of money.- Use of profits rather than cash flows.- ARR rises with the age of assets.

11 - 100


3. NPV Method

gPeople began to search for methods that would recognize time value of money. gThis recognition led to the development of discounted cash flow (DCF) techniques. One such method is NPV method. n

NPV = Σ CFt/(1+k)t – Io t=1CF = cashflows, Io= original investmentk = discounting factor, n = life of the project.OR n

NPV= Σ CFt/(1+k)t t=0

11 - 101


Calculation of NPV for Project D. Assume that cost of capital is 10%.

Year CFs (D) Rs. PVIF@ 10% PV Rs. 0 -3,000 1.000Rs. -3,000 1 600 0.909 545.42 900 0.826 743.43 1,500 0.751 1,126.54 1,500 0.683 1,024.55 1,800 0.621 1,117.8NPV: 1,557.6gNPV is Positive, i.e., NPV > 0. The project is acceptable. gNPV= PV inflows – Cost= Net gain in wealth. gChoose between mutually exclusive projects on the basis of higher NPV.

11 - 102


Mutually Exclusive Projects

BRIDGE vs. BOAT to get products across a river.

NPV for all four projects are:Projects A B C DNPV –1,221.9 1,532.1 1,592.6 1,557.6•If projects are independent, accept B,C & D.•If projects are mutually exclusive, accept C.

11 - 103


4. Internal Rate of Return (IRR)gIn NPV method, discount rate is given. How sure we are that it truly represents COC? COC is based on number of assumptions. Hence we compute IRR.gIRR is the interest rate that equates the PV of the expected future cash flows to the initial cost outlay. n

NPV = Σ CFt/(1+IRR)t – Io= 0 t=1

gIf IRR is greater than cost of capital, then the project’s rate of return is greater than cost of capital. Accept project. gIt means some return is left over to boost stockholders’ returns.

11 - 104


IRR is discount rate that forces PV of inflows = cost. This is the same as forcing NPV=0.Decision rule: If IRR > k, accept project.

If IRR < k, reject project.

0 1 2 3

CF0 CF1 CF2 CF3

Cost Inflows

gHow is a project’s IRR related to a bond’s YTM?gThey are the same thing. A bond’s YTM is the IRR if we invest in the bond.gHow to compute IRR? Trial & error method if cash flows are not even.

k=?

11 - 105


Calculation of IRR for Project D

Try 10%:Year CFs(D) Rs. PVIF@ 10% PV Rs.0 -3,000 1.000 Rs.-3,0001 600 0.909 545.42 900 0.826 743.43 1,500 0.751 1,126.54 1,500 0.683 1,024.55 1,800 0.621 1,117.8NPV : Rs. 1,557.6

11 - 106


Try 25% Try 26%Year CFs,Rs. PVIF PV Rs. PVIF PV Rs.

Proj.D @ 25% @26% 0 -3,000 1.000 Rs.-3,000 1.000 Rs.-30001 600 0.800 480 0.794 476.42 900 0.640 576 0.630 567.03 1,500 0.512 768 0.500 750.04 1,500 0.410 615 0.397 595.55 1,800 0.328 590.4 0.315 567.0NPV : Rs.29.6 Rs.-44.1

NPV of LRIRR = Lower Rate + ------------------------------- (HR – LR)

NPV of LR - NPV of HR= 25.4%

11 - 107


g If cash flows are equal or even: IRR=?g PVIFAi,n = Investment outlay / PMTg Example: Investment outlay = Rs.52,125,

Payment or cash flow = Rs.12,000 per year, Life of the project = 8 yearsIRR = ?

g PVIFAi,8= Rs.52,125/Rs.12,000 = 4.3438.Using PVIFA Table, 8th year row shows that 4.3438 lies in the 16% column.Therefore, IRR is approximately 16 percent.

g IRR for all projectsProjects A B C DIRR -200% 20.9% 22.8% 25.4%Decision rule: If IRR > k, accept project.

11 - 108


Summary results

Project A B C D

Payback 2 yrs 4 yrs 4 yrs 3 yrs

ARR -8% 26% 25% 22%

NPV Rs.1222 Rs.1532 Rs.1592 Rs.1558

IRR -200% 20.9% 22.8% 25.4%

To be continued ...Solve problems: Chapter 9: Capital budgetingSelf-Test Problems: SP1, 2, & 3. Problems: P3, & 4.

11 - 109


WELCOME TO

CHAPTER 7: STOCKS AND THEIR

VALUATION

11 - 110


CHAPTER 7: STOCKS AND THEIR VALUATION

Features of common stockDetermining common stock values

- For dividend paying firms, &

- For non-dividend paying firms.Valuation of Preferred stock

11 - 111


True owners of business. No fixed maturity period. No fixed return. Country laws specify rights &

responsibilities. Key features:1. Αmend the charter of the company2. Αdopt and amend bylaws3. Elect the directors of the company4. Enter into acquisition and merger

Common Stock

11 - 112


5. Authorize the sale of fixed assets6. Authorize change of capital 7. Authorize issue of securities.8. Right to vote9. Right to inspect the corporate books10. Apportionment of income11. Apportionment of control 12. Apportionment of risk.

11 - 113


Financial Asset Valuation

The value of any financial asset – a stock, a bond, a lease, or even a physical asset such as an apartment building or a piece of machinery – is simply the present value of the cash flows the asset is expected to produce.

11 - 114


( ) ( ) ( ) ( )PD

k

D

k

D

k

D

ke e e e

01

12

23

31 1 1 1

=+

++

++

+ ++

∞∞. . .

gBut dividends may grow at different rates. gThere can be three cases:

1. Normal/ Constant growth case2. Zero growth case 3. Supernormal growth case

Stock Value = PV of Dividends

11 - 115


1. Normal or Constant growth stock

Po

D0 (1+g)

=

If g is constant at 5 percent, D0 = Rs. 10, ke = 10%, What is stock’s current market value, P0?

Ke - g=

D1

Ke - g

Rs. 10.5

0.10 - 0.05= Rs.210=

P1

What is the stock’s market value one year from now, P1?

=D1 (1+g)

Ke - g=

D2

Ke - g=

Rs.10.5 x 1.05

0.10 - 0.05

Rs.220.5=Or P1= P0 (1+g) = Rs.210(1.05)= Rs.220.5.P2, P3, P4, P5?

11 - 116


Find the expected dividend yield & capital gains yield (or total return) during the first year.

Dividend yield = = = 5.0%.Rs.10.5

Rs.210

D1

P0

CG Yield = =P1 - P0

P0

Rs.220.5 - Rs.210

Rs.210= 5.0%.

Total return = Dividend yld + Capital gains yld.

Total return, ke = 5% + 5% = 10%.

11 - 117


P0

D1

=

Then, ke = Rs. 10.5/Rs.210 + 0.05= 0.05 + 0.05 = 10%.

gD1/P0 is known as dividend yield.gke has been computed by using DCF method

Ke - g

Or Ke = D1

P0

+ g

11 - 118


2. Zero growth case: What would P0 be if g = 0?

The dividend stream would be a perpetuity.

Rs. 10 Rs.10Rs.10

0 1 2 3ke=10%

P0 = = = Rs.100D1

Ke- g

Rs.10

0.10 - 0

Po=?

11 - 119


3. Super-normal growth case: (Nonconstant growth followed by constant growth): If the firm has supernormal growth of 30% for 3 years, then a long-run constant growth of 5%, what is P0? ke is still 10%. Can no longer use constant growth model.

0

11.82

13.97

16.51

346.63

1 2 3 4ke=10%

388.92 = P0

g = 30% g = 30% g = 30% g = 5%

D0 = Rs. 10 D1=13 D2=16.9 D3=21.97 D4= 23.0685

461.37Rs.05.010.0

23.0685P̂3

=−

=

P3=D4/(Ke- g)

11 - 120


Super-normal growth

Yr. Div.(Rs.) [email protected] PV(Rs.)

1 13.00 0.9091 11.82

2 16.90 0.8264 13.97

3 21.97 0.7513 16.51

P3 461.37 0.7513 346.63

Current stock value (Po) = Rs. 388.92

where, P3=D4/(Ke- g)

=Rs. 23.0685/(0.1-0.05) = Rs. 461.37

11 - 121


Method of computing intrinsic value of the stock- super normal growth

Find the PV of dividends during the period of non-constant growth.

Find the price of the stock at the end of the non-constant growth period, and discount this price back to the present.

Add these two components to find the intrinsic value of the stock.

11 - 122


Suppose g = 0 for t = 1 to 3, and then g is a constant 5%. Ke=10%. D0=Rs.10. What is P0?

0

9.098.267.51

157.77

1 2 3 4ke=10%

Po=182.63

g = 0% g = 0% g = 0% g = 5%

10 10 10 10.5

10.5.

$P3 0.10 - 0.05210= =

...

D0=Rs.10

11 - 123


Expansion Plan: Valuing the entire firm In the previous section we assumed that all

firms pay dividends. Although most larger firms do pay a dividend,

some firms, even highly profitable ones such as Microsoft, have never paid a dividend.

How can the value of such a company be determined?

Similarly, suppose you start a business, and someone offers to buy it from you. How could you determine its value?

In such cases, we cannot use the dividend growth model. However we could use the total company, or corporate valuation model.

For the purpose, we need to compute free cash flow.

11 - 124


Free cash flow is the cash flow actually available for distribution to investors after the company has made all the investments in fixed assets and working capital.

FCF2= NOPAT– Net investment in OC= Rs.1,464 – (–600) = Rs. 2,064 (See Chap 2).

Suppose, free cash flows (FCF) are:Year 1 FCF = - Rs. 5 million.Year 2 FCF = Rs. 10 million.Year 3 FCF = Rs. 20 million.

FCF grows at constant rate of 6% after year 3. The corporate cost of capital, ko, is 10%. The company has 10 million shares of stock

outstanding. Debt Rs. 40 million

11 - 125


Vop at 3

Find the value of operations by discounting the free cash flows at

the cost of capital.0

-4.545

8.264

15.026

398.197

1 2 3 4kc=10%

416.942 = Vop

g = 6%

FCF= -5m 10m 20m 21.2m

Rs.21.2

. . Rs.530.

10 0 06=

−=

0

Vop3=FCF4/(Ko- g)

11 - 126


Year FCF (M.Rs.) PVIF@ 10% PV, M.Rs. 1 –5 0.9091 – 4.552 10 0.8264 8.263 20 0.7513 15.03

Vop at 3 530 0.7513 398.19Total 416.93 Find the price per share of common stock?Value of eq. = Value of operations - Value of debt

= Rs.416.94 - Rs.40 = Rs.376.94 million.

Price per share = Rs. 376.94 m / 10 m = Rs. 37.69.

11 - 127


Preferred Stock Valuation

Hybrid security: Similar to bonds as well as common stock.

Features: A fixed rate of dividend (> bond interest). A fixed maturity period A fixed par value Postponement of dividend - not a default Cumulative dividends Call provision Sinking fund provision Refunding operation

11 - 128


Valuation of preferred stock: If the dividend on preferred stock is Rs. 10 per share and required return on preferred stock is 11 percent, what is the value of a preferred stock? (Par value =Rs. 100).

Vps = = =Rs.10

0.11Rs. 90.90

Dps

Kps

What’s the expected return on preferred stock with Vps=Rs.120 and annual dividend = Rs.10?

Kps = Dps / Vps =Rs. 10/ Rs. 120 = 8.3%.

11 - 129


If 10% preferred dividend is paid on quarterly basis, find the Eff % or Effective Annual Rates (EAR).

Knom nm

EARps = 1+ ----------- - 1 m

0.1 1x4

Eff% or EARps= 1+ -------- - 1 = 10.38%. 4

Solve problems: Chap 7: Stock Valuation Self-test: SP- 6, 7, 8, 11, 12, & 13. Problems: P8, 10, 12 & 13. Quiz

Thanking you

11 - 130


WELCOME TO

CHAPTER 8: THE COST OF CAPITAL

11 - 131


CHAPTER 8: THE COST OF CAPITAL It is the minimum rate of return required from

an investment to maintain or increase the value of the firm in the market place.

It is not really a cost as such, it is a required return on new capital projects. It is a hurdle rate or cutoff point for new proposals.

Which of the following projects be chosen?Project A - 30%Project B - 28%Project C - 26%Project D - 24%Project E - 22%

11 - 132


If COC is 25 percent, choose projects A,B & C. Without the knowledge of the firm’s cost of

capital, the firm will have difficulties in two areas:

- It will not be able to select the cutoff point for new capital investment projects.

- It will not have a complete picture when it is deciding which securities should be used to raise additional funds.

Suppose the cost of debt is 8% and the cost of equity is 12%. In the first year, the firm borrows heavily to finance the project yielding 9%.

In the second year, it has the project yielding 11%. It cannot accept the project because the debt capacity is already exhausted & it has to be financed with 12% equity.

11 - 133


To avoid the problem, the cost of capital should be calculated as weighted average or composite cost of the various types of capital.

The weighted average approach assumes that the debt has one cost, preferred stock has another, & common stock a third, and, therefore, the overall required return is weighted average of the individual components of capital structure.

Cost of Capital Components:h 1. Debth 2. Preferredh 3. Common Equityh 4. WACCBefore-tax or after-tax capital costs? Most firms incorporate tax effects in the cost of

capital. Therefore, focus is on after-tax costs. Only cost of debt is affected. Dividends are not tax deductible.

11 - 134


Should we focus on historical (embedded) costs or new (marginal) costs?

gThe cost of capital is used primarily to make decisions which involve raising and investing new capital. So, we should focus on marginal costs. Component Cost of DebtInterest is tax deductible, so kd = kb (1 - T) = 10% (1 - 0.40) = 6%.Flotation costs are small & ignored.

11 - 135


What’s the cost of preferred stock? Vps=Rs.113; 10% dividend; Par=Rs.100; Floatation cost=Rs.2.

0.09 = 9% 111

10

Rs.113 - Rs.2

(Rs.100)0.1 x

==

=ps

ps

psV

Dk =

Flotation costs for preferred are significant, so are reflected. Use net price.Preferred dividends are not tax deductible, so no tax adjustment.

11 - 136


Two ways of raising common equity? Retained earnings (cost of RE). External equity (cost of ext. equity)Why is there a cost for retained earnings? It is an opportunity cost of retained earnings. The cost of equity, ke can be computed under DCF

method as: ke = (D1/P0)+ gGiven: D0= Rs.10; g = 5%, P0= Rs.150

D1 D0 (1+g) Rs.10(1.05)Ke=------- + g =------------- + g =------------------- + 0.05

P0 P0 Rs.150 =0.07+0.05 = 0.12 = 12%

g If float. cost is 10%, Ke=? Ke=10(1.05)/150(0.9)+5% =12.8%. Also known as cost of external equity.

Cost of common stock

11 - 137


Assume target or optimal capital structure is 30 percent debt, 10 percent preferred stock, & 60 percent equity. What’s the WACC based on kd = 6%, kps=9%, ke=12%? Tax =40%.

WACC = wdkd + wpskps + wceke

= 0.3(6%) + 0.1(9%) + 0.6(12%)= 1.8% + 0.9% + 7.2% = 9.9%.Calculation of WACCCapital Prop./Weight AT Cost Wtd. CostDebt 0.3 0.06 0.018Pref. 0.1 0.09 0.009Equity 0.6 0.12 0.072

Total 1.0 0.099WACC = 9.9%.

11 - 138


Some additional considerations

g Cost of debt is constant up to a certainlimit, after which, it increases at an increasingrate with the increase in leverage. Tax=50%.(D/TA,%) (kb) kd = kb(1 – T)10% 10% 5%20% 10% 5%30% 10.8% 5.4%35% 11% 5.5%40% 13% 6.5%50% 16% 8%

11 - 139


Leverage (D/TA, %)

Kd (%)

Kd

(D/TA,%) kd = kb(1 – T)10% 5%20% 5%30% 5.4%35% 5.5%40% 6.5%50% 8%

11 - 140


Optimal or target capital structureS.no. Cap.str. % total Cost, % WACC1. Debt 10 5 0.5

Equity 90 12.3 11.1/11.62. Debt 20 5 1.0

Equity 80 12.75 10.2/11.23. Debt 30 5.4 1.6

Equity 70 13.29 9.3/10.94. Debt 35 5.5 1.9

Equity 65 13.5 8.3/10.25. Debt 40 6.5 2.6

Equity 60 15.51 9.3/11.96. Debt 50 8.0 4.0

Equity 50 18.0 9.0/13.0Ke increases curvilinearly because:g Smaller the size of common stock issue, higher would

be floatation cost.g Increase in debt means increase in equity

capitalization rate.

11 - 141


After tax cost of capital, %

35%

10.7%

Leverage (Debt/TA, %)

ke

kO

kd

Optimal capital structure is given by the lowest point in Ko curve.

11 - 142


Marginal cost of capitalg The moment there is a change incomponent cost of capital, WACC will change.The new WACC is known as MCC. Suppose:Earnings avail. to stockholders: Rs. 59mLess dividends paid 27mRetained earnings 32mg Now suppose we want to undertake a project

costing Rs. 100m.g What would be WACC?

11 - 143


g Suppose, kb=11%, T=46%, kps=11%, g=5%, Div.Yld. Or D1/Po=10%, Po= Rs. 100.

g kd= kb(1-T) = 0.11(1-.46) =5.94%, g ke=D1/Po+g=10%+5%=10/100+5%=15%. Also

known as cost of RE or internal equity.g If float. cost is 10%, Ke=? Ke=10/90+5% =16.11%.

Also known as cost of external equity.Capital Target cap str. ATCost Wtd. costDebt 0.29 Rs. 29m 5.94 1.72Preferred 0.01 Rs. 1m 11.00 0.11Ret. earn. 0.32 Rs. 32m 15.00 4.8Ext. eq. 0.38 Rs. 38m 16.11 6.12

1.0 Rs.100m 12.75%g Retained earnings are not enough to provide

equity portion of capital. g There is a need to go for external financing.

Hence WACC or MCC would increase to 12.75%

11 - 144


g How big is the project we can undertake with the current level of retained earnings?

Break in MCC Retained earningsOr = ------------------------------New capital Percent equity

Rs. 32 million=---------------------- = Rs. 45.7 million 0.70Capital Target cap str. ATCost Wtd. costDebt 0.29 Rs.13.2m 5.94 1.72Preferred 0.01 Rs. 0.5m 11.00 0.11Common 0.70 Rs. 32.0m 15.00 10.50

1.00 Rs. 45.7m 12.33%g Retained earnings are enough to provide equity

portion of capital. g There is no need to go for external financing. Hence

WACC = 12.33%g If the project cost is less or more than Rs.45.7m, what

would be the cost of capital?

11 - 145


g Now suppose, after undertaking Rs. 45.7m or Rs.100m project, there is another project costing Rs.100m. What would be the MCC?

g The retained earnings are already exhausted. We need to go for external equity to provide equity portion of capital there by incurring floatation cost.

g It will increase cost of equity.

g Increase in cost of equity will increase WACC beyond 12.75%.

11 - 146


Some Mistakes to Avoid

g When estimating the cost of debt, use the current interest rate on new debt, not the coupon rate on historical debt.

g Use the target capital structure to determine the weights.

g If you don’t know the target weights, then use the current market value of debt & equity. If they are not known, then only use book values. (More ...)

11 - 147


Factors affecting WACC

Controllable & uncontrollable:g Level of interest rates. If rises, WACC

increases.g Tax rates: If tax rate increases, WACC

decreases.g Capital structure policy: more debt

means lower WACC.g Dividend policy: If dividend increases,

WACC increases due to ext. equity. g Investment policy: If the firm

undertakes more risky project, WACC would increase.

11 - 148


Some problem areas in COC

g Privately owned firmsg Small businessesg Measurement problemsg Costs of capital for projects of differing

risksg Capital structure weightsSolve problems: Chap.8g Self-test problems:SP 1 to 4.g Problems:P1 & 7.

*** Thanking you ***

11 - 149


WELCOME TO

Chapter 11

Breakeven Analysis

11 - 150


The breakeven analysis, or cost volume profit analysis shows the relationship between costs, sales volume & profitability.

BEP is a point at which sales will just cover costs - i.e., the point at which the firm will break even.

Also shows the magnitude of the firm’s profits or losses if sales exceed or fall below that point.

Fixed and variable costs Fixed costs are those that do not increase with

the increase in output. Examples include depreciation on plant &

machinery, rentals, salaries, office expenses, etc.

Chapter 11: Breakeven Analysis

11 - 151


gVariable costs are those costs that increase directly with the increase in output. gExamples include factory labour, raw materials, sales commissions, etc.gSome of the above costs (Salaries & office expenses) may contain both, fixed & variable components.gIf all costs were variable, the subject of breakeven volume would not come up.

11 - 152


Determination of BEP

1. Table Method

2. Formula Method

3. Graphic Method

Suppose,

Fixed costs (F) = Rs.80,000

Variable costs per unit (v) = Rs.2.4

Selling price per unit (p) = Rs.4

11 - 153


Table method: TABLE 11.1: p=Rs.4, v=Rs.2.4, F=Rs.80,000 BEP=?Units sold(Q)

40,000 50,000 80,000 100,000 Sales revenue (TR), Rs.

160,000 200,000 320,000 400,000 Less variable costs (v),Rs.

96,000 120,000 192,000 240,000 Contribution Margin ( C),Rs.

64,000 80,000 128,000 160,000 Less fixed operating expenses (F), Rs.

80,000 80,000 80,000 80,000 Net operating income (X), Rs.

(16,000) zero 48,000 80,000gBEP=50,000 units or Rs.200,000

11 - 154


Formula Method: BEP in units?

Breakeven quantity (Q*)

F Rs. 80,000

= ------------- = -------------------- = 50,000 units.

(p - v) or c Rs.4 - Rs. 2.4

c = contribution margin

Breakeven point in Rs. (S*)

= BEP in Units x Selling price

= 50,000 x Rs 4

= Rs. 200,000. OR

11 - 155


Breakeven point in Rupees or Breakeven revenues (TR*): F F Rs. 80,000BEP in Rs. = --------- = ----------- = ----------------------- CR (1 - v/p) 1 - (Rs.2.4/Rs.4) CR = contribution ratio

= Rs. 80,000/0.4 = Rs. 200,000.

TR=TC Or TR=PQ, & TC=F+VQ,

If TC=TR,Q=?

Or PQ=F+VQ, Or PQ-VQ = F, Or Q(P-V)=F F

Q = ---------------(p–v)

11 - 156


120 Units (Q) '000 0

40

80

100

120

160

200

240

280

320

20 40 60 80 100 140

Total Revenue

Total Costs

Fixed Costs

Revenues and Costs: Firm B (Thousands of Rupees)

Net Profit

Total Variable Cost

Breakeven point

Loss

11 - 157


Cash BEP Firms that have fixed costs which include a

large amount of non-cash expenses often find it useful to compute the cash BEP.

Purpose is to determine the level of sales necessary to cover cash operating costs.

Fixed costs - Non-cash exps.(i.e.,dep.)Cash BEP =-------------------------------------------------- p - vIf Dep =Rs. 10,000, Cash BEP=?

(Rs. 80,000 - 10,000)= ----------------------------------- = 43,750 units

(Rs.4 - Rs.2.4)

11 - 158


Chap 11 SP1:(a) Page 279: p=Rs.15, F=700,000, v=Rs.10 per unit. Gain or loss?

Quantity 125,000 units 175,000 unitsIncome Rs.1,875,000 Rs.2,625,000Fixed costs 700,000 700,000Variable costs 1,250,000 1,750,000Total costs 1,950,000 2,450,000Gain (Loss) (75,000) 175,000 SP1:(b) BEP?Breakeven quantity (Q*)

F Rs.700,000= ------------- = -------------------- (p - v) or c Rs.15 - Rs.10= 140,000 unitsBEP in Rs. = Q* × P = (140,000)(Rs.15) = Rs.2,100,000

11 - 159


SP2:(a) p=Rs.45, F=Rs.175,000, Dep=Rs.110,000, v=Rs.20 per unit. Gain or loss?

Particular 5,000 units 12,000 unitsIncome Rs.225,000 Rs.540,000Fixed costs 175,000 175,000Variable costs 100,000 240,000Total costs 275,000 415,000Gain (loss) (Rs. 50,000) Rs.125,000 SP2:BEP?(b) Breakeven quantity (Q*)

F Rs. 175,000= ------------- = ------------------------------ = 7,000

units (p - v) or c Rs.45 - Rs.20BEP in Rs. = Q × P = (7,000)(Rs.45)=Rs. 315,000

11 - 160


SP2:(c) Cash BEP quantity (Q*)

F - Dep. Rs.175,000-110,000= -------------- = ---------------------------- = 2,600 units (p - v) or c Rs. 45 - Rs. 20

Cash BEP in Rs.= Q × P = (2,600)(Rs.45)=Rs.117,000.

Solve ProblemsP1: ‘a’ & ‘b’ only. (Page 336)

Financial Management

Education

Transcript of Financial Management