Financial Management

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Copyright © by R. S. Pradhan. All rights reserved.
WELCOME TO
CHAPTER 2: FINANCIAL STATEMENTS,
CASH FLOWS & TAXES

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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 Sheet
2. Income Statement
3. A statement of Cash Flows
The Balance Sheet : Shows financial
position as of a certain date (Dec. 31,
2005)

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NEPAL BRICK FACTORY LTD. (‘000 Rs.) P.24
Liabilities and equity Year 1 Year 2
Accounts payable 1,200 2,000
Notes payable 400 400
Accrued wages 400 800
Other accruals 200 800
Current Liabilities 2,200 4,000
Long-term debt 6,600 6,000
Preferred stock 0 0
Stockholder’s equity:
Com. Stock (Rs.100 par) 2,000 2,000
Paid in Capital 2,000 2,000
Retained Earnings 5,200 6,000
Total Stockholders’ eq. 9,200 10,000
Total liab.& eq. 18,000 20,000

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

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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
equity
TA = TL + OE
CA + FA = CL + LTL + OE
C + AR + I + FA = CL + LTL + OE
 Net working capital
NWC1 = CA– CL= Rs.7,000–2,200 =4,800
NWC2 = CA– CL= Rs.8,000–4,000 =4,000

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

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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 assets
OC1 = 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.

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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

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

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Income Statement Equations
Net income = Total Revenue – Total Cost
NI = 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 – Interest
Net income = EBIT – Interest – Tax

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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.

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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 liabilities
Sources of funds:
- Decrease in assets.
- Increase in liabilities.
3. The Statement of Cash Flows

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 Statement of cash flows (Year 2)- P.33
 I. Cash flows from operating activities: 4,000
Net income 1,200
Add depreciation 1,000
Changes in working capital:
Decrease in accounts receivable 600
Increase in inventories - 600
Increase in accounts payable 800
Increase in accrued wages 400
Increase in other accruals 600
 II. Cash flows from long-term invest. activities: -2,000
Increase 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. 1,000
Cash & cash equiv., end of yr. 2,000

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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

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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.

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 The Balance Sheet :
NEPAL BRICK FACTORY LTD. (‘000 Rs.)
Liabilities and equity Year 2 % of TA
Accounts payable 2,000 10
Notes payable 400 2
Accrued wages 800 4
Current Liabilities 4,000 20
Long-term debt 6,000 30
Preferred stock 0 0
Com. Stock (Par Rs.100) 2,000 10
Paid in Capital 2,000 10
Retained Earnings 6,000 30
Total Stockholders’ eq. 10,000 50
Total liab.& eq. 20,000 100

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 Assets Year 2 % of TA
Cash 1,000 5
Marketable securities 1,000 5
A/cs. receivables, net 2,400 12
Inventories 3,600 18
Current assets 8,000 40
Gross Fixed Assets:
Land 1,000 5
Building 5,500 27.5
Machinery & equip. 9,500 47.5
Other fixed assets 4,000 20
Total Fixed Assets 20,000 100
Less Depreciation -8,000 40
Net Fixed Assets 12,000 60
Total Assets 20,000 100

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2.The Income Statement
Particulars Year 2 % of Sales
Revenues 24,000 100
Cost of sales -13,600 56.7
Gross income 10,400 43.3
Marketing expense -6,000 25
General & adm. exps. -1,200 5
EBDIT 3,200 13.3
Depreciation -1,000 4.2
Net ope.income (NOI) 2,200 9.1
Other income, net +240 +1.0
EBIT 2,440 10.1
Interest expenses -440 1.8
EBT 2,000 8.3
Income taxes @ 40% -800 3.3
Net income 1,200 5.0

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Solve problems (Chap.2)
SP 1 & SP 2
P1 & P 2
Quiz
Thanking you

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WELCOME TO
CHAPTER 3:
FINANCIAL ANALYSIS

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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.

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 The Balance Sheet :
NEPAL BRICK FACTORY LTD. (‘000 Rs.)
Liabilities and equity Year 2 % of TA
Accounts payable 2,000 10
Notes payable 400 2
Accrued wages 800 4
Current Liabilities 4,000 20
Long-term debt 6,000 30
Preferred stock 0 0
Com. Stock (Par Rs.100) 2,000 10
Paid in Capital 2,000 10
Retained Earnings 6,000 30
Total Stockholders’ eq. 10,000 50
Total liab.& eq. 20,000 100

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 Assets Year 2 % of TA
Cash 1,000 5
Marketable securities 1,000 5
A/cs. receivables, net 2,400 12
Inventories 3,600 18
Current assets 8,000 40
Gross Fixed Assets:
Land 1,000 5
Building 5,500 27.5
Machinery & equip. 9,500 47.5
Other fixed assets 4,000 20
Total Fixed Assets 20,000 100
Less Depreciation -8,000 40
Net Fixed Assets 12,000 60
Total Assets 20,000 100

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2.The Income Statement
Particulars Year 2 % of S.
Revenues 24,000 100
Cost of sales -13,600 56.7
Gross income 10,400 43.3
Marketing expense -6,000 25
General & adm. Exps. -1,200 5
EBDIT 3,200 13.3
Depreciation -1,000 4.2
Net ope.income (NOI) 2,200 9.1
Other income, net +240 +1.0
EBIT 2,440 10.1
Interest expenses -440 1.8
EBT 2,000 8.3
Income taxes @ 40% -800 3.3
Net income 1,200 5.0

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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?

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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.

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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?

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 Different groupings of financial ratios. Actual
ratios would remain the same.
A. Liquidity ratios
B. Asset mgmt. or efficiency ratios
C. Debt mgmt. or leverage ratios
D. Profitability ratios
E. 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: OK
2.Quick, or acid test =(CA - Inv.)/ CL
=(Rs.8000-3600)/4000 =1.1x.
(IA or CC=1.0x) OK

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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.

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7.Capital requirement = Operating capital /
Sales = (Rs.15,400)/ Rs. 24,000 = 64.2%
(IA or CC =40%) Poor
 C. Debt Mgmt. or Leverage ratios
8.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)

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 D. Profitability ratios
11.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%.
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%.

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 E. Market value ratios
15. 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.

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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/Assets
Net income Assets
ROE = ----------------- x ----------------
Equity Assets
2. The Du Pont Identity

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Net income Assets
ROE = ---------------- x ----------------
Assets Equity
ROE = ROA x Equity Multiplier
Rs.1200 Rs.20,000
g = ------------ 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 Assets
ROE=--------- x ---------- x --------------
Sales Assets Equity
NI Sales Assets
= --------- x -------------- x ---------
Sales Assets Equity

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= 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.

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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 X2 +0.033 X3+0.006 X4+0.999 X5
X1 = (CA-CL)/ TA
X2 = Retained Earnings/ Total Assets
X3 = EBIT / Total Assets
X4 = ME / Book Value of Total Debt (market value
of equity includes both pref. & com. shares,
and debt includes CL + LTL).
X5 = sales/total assets

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 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 means
Ratio Bankrupt Nonbankrupt
X1 - 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=1.2
ZNBF = 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

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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 business
SOLVE PROBLEMS
Page 71 Self-test Problems: SP 3 & 7
Page 77 Problems: P1, 2, 3, 5, & 6.
Quiz
Thanking you.

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WELCOME TO
CHAPTER 5
TIME VALUE OF MONEY

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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

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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 values
A2: PVIFA values
A3: FVIF values
A4: FVIFA values
3. Use a financial calculator.
4. Use a spreadsheet.

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FV = ?
0 1 2 3
i = 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%?

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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 = 133.10
gHigher the ‘i’, higher would be FV or vice
versa (See Fig 5.1 in page 125).
FVn = PV(1 + i)n

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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 3
10%
110
121
FV = 331

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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 1.21 121
2 100 1.1 110
3 100 1 100
Total 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.

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 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
= ?

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FV = Rs. 16,177,178.
We would have become a millionaire.

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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%?

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We know, FVn = PV(1 + i )n
( )
PV =
FV
1+i
= FV
1
1+i
n
n n
n


 


PV = Rs.100
1
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).

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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 3
10%
90.9
82.6
75.1
248.6 = PV

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Table method: What is the PV of a 3-year
ordinary annuity of Rs.100 at 10 percent?
Year Cash Flow PVIF@10% PV
Page 416
1 100 0.909 90.9
2 100 0.826 82.6
3 100 0.751 75.1
Total 2.486 248.6
Using 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).

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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 = 50
10% = 45.259
? = 50
11% = 65.0009
i = 10.24%
Orig.value - LR value
i =LR + ----------------------------- Diff. in rates
HR value - LR value

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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%

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

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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
? = 2
Value of 8 year = 2.1436
By interpolation,
Orig. Value - LY Value
LY+ -------------------------------- (Diff. in yrs)
HY Value - LY Value
= 7.3 years

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Ordinary Annuity (end of the year)
PMT PMTPMT
0 1 2 3
i%
PMT PMT
0 1 2 3
i%
PMT
Annuity Due (beginning of the year)
What’s the difference between an
ordinary annuity and an annuity due?
PV FV

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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 1.05
FVADue = Rs.100 x 3.1525 x1.05 = Rs.331
PVADue = 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 more
frequent than once a year - for example,
semiannually, quarterly, or daily - interest
is earned on interest more often.

11 - 59
0 1 2 3
10%
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 = 133.1
Semiannually:
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 + )0.10
2
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
Amortization
gConstruct an amortization schedule for a
Rs.1,000, 10% annual rate 3 year loan with 3
equal payments.
PV of annuity
Annual pmt = --------------------------
PVIFA(10%, 3 yrs)
= Rs.1000/2.4869 = Rs.402
Year Payment Interest Prin. pmt. End Bal.
1 402 100 302 698
2 402 70 332 366
3 402 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 Bond
1. 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 Crores
Pvt 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.

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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 bond
The 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 n
k%
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 k
B
d d
=
Rs.100 Rs.1,
1
.1000
1
1 10 10. . . +
Rs.100
1+ kd
100 100
0 1 2 10
kd=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
th
yr) M”
= (PVIFA10%,10Yrs)Rs.100 +
(PVIF10%,10
th
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

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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 9090
0 1 9 10
kd=?
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. 385.5
Rs.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 + 322
887 = 831

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PV of LR - Market value
LR + -------------------------------- 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 method
FV – MV 1000-887
CI + ------------- 90 + -------------
n 10
YTM = -------------------------- = ----------------------
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 bond
n : 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 pmt
Current 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 yield
g11% = 10.15% + capital gains yield
gHence the capital gains yield is 0.85%.

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

11 - 86
Semiannual bond
Find 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.
EFF
i
m
Nom
nm
%
.
.= +




 − = +

 

 − =1 1 1
0 10
2
1 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 this
plant?
WELCOME TO
CHAPTER 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 the
development of systematic procedures & rules for
evaluating investment proposals.
g1. Payback period
(i) Ordinary payback period
(ii)Discounted payback period
g2. Accounting rate of return
g3. Net present value
g4. Internal rate of return
g5. Modified internal rate of return
g6. Profitability index
g7. Replacement chain method
g8. Equivalent annuity method

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 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.12,000
Cash flows (Rs.)
Year 1 3,000 3,000
Year 2 3,000 3,500
Year 3 3,000 4,000
Year 4 3,000 4,500
Year 5 3,000 5,000
 Payback period: Project X
= Rs.12,000/Rs.3000 = 4 years

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 Payback period: Project Y
Cash flows Cum.CFs Or Cum.CFs
Rupees Rupees Rupees
Original Investment -12,000 -12,000
Cash 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 D
0 (Rs.3,000) (Rs.3,000) (Rs.3,000) (Rs.3,000)
1 300 0 300 600
2 2,700 0 600 900
3 300 900 900 1,500
4 -300 2,100 1,200 1,500
5 -1,200 3,900 3,750 1,800
Payback 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 CFs
0 -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 Income
ARR = ----------------------------
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 0
2 900 300 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 D
ARR -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=1
CF = cashflows, Io= original investment
k = 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 0.909 545.4
2 900 0.826 743.4
3 1,500 0.751 1,126.5
4 1,500 0.683 1,024.5
5 1,800 0.621 1,117.8
NPV: 1,557.6
gNPV 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.

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Mutually Exclusive Projects
BRIDGE vs. BOAT to get
products across a river.
NPV for all four projects are:
Projects A B C D
NPV –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.-3,000
1 600 0.909 545.4
2 900 0.826 743.4
3 1,500 0.751 1,126.5
4 1,500 0.683 1,024.5
5 1,800 0.621 1,117.8
NPV : 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.-3000
1 600 0.800 480 0.794 476.4
2 900 0.640 576 0.630 567.0
3 1,500 0.512 768 0.500 750.0
4 1,500 0.410 615 0.397 595.5
5 1,800 0.328 590.4 0.315 567.0
NPV : Rs.29.6 Rs.-44.1
NPV of LR
IRR = 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 / PMT
g Example: Investment outlay = Rs.52,125,
Payment or cash flow = Rs.12,000 per year,
Life of the project = 8 years
IRR = ?
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 projects
Projects A B C D
IRR -200% 20.9% 22.8% 25.4%
Decision rule: If IRR > k, accept project.

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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 budgeting
Self-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 stock
Determining 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 company
2. Αdopt and amend bylaws
3. Elect the directors of the company
4. Enter into acquisition and merger
Common Stock

11 - 112
5. Authorize the sale of fixed assets
6. Authorize change of capital
7. Authorize issue of securities.
8. Right to vote
9. Right to inspect the corporate books
10. Apportionment of income
11. 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
( ) ( ) ( ) ( )
P
D
k
D
k
D
k
D
ke e e e
0
1
1
2
2
3
3
1 1 1 1
=
+
+
+
+
+
+ +
+
∞
∞. . .
gBut dividends may grow at different rates.
gThere can be three cases:
1. Normal/ Constant growth case
2. 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.100
D1
Ke- g
Rs.10
0.10 - 0
Po=?

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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
23.0685
Pˆ
3
=
−
=
P3=D4/(Ke- g)

11 - 120
Super-normal growth
Yr. Div.(Rs.) PVIF@0.1 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
9.09
8.26
7.51
157.77
1 2 3 4
ke=10%
Po=182.63
g = 0% g = 0% g = 0% g = 5%
10 10 10 10.5
10.5
.
$P3
0.10 - 0.05
210= =
...
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 – 4.55
2 10 0.8264 8.26
3 20 0.7513 15.03
Vop at 3 530 0.7513 398.19
Total 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
0.11
Rs. 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. Debt
h 2. Preferred
h 3. Common Equity
h 4. WACC
Before-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 Debt
Interest 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
ps
V
D
k =
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)+ g
Given: 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 WACC
Capital Prop./Weight AT Cost Wtd. Cost
Debt 0.3 0.06 0.018
Pref. 0.1 0.09 0.009
Equity 0.6 0.12 0.072
Total 1.0 0.099
WACC = 9.9%.

11 - 138
Some additional considerations
g Cost of debt is constant up to a certain
limit, after which, it increases at an increasing
rate 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 structure
S.no. Cap.str. % total Cost, % WACC
1. Debt 10 5 0.5
Equity 90 12.3 11.1/11.6
2. Debt 20 5 1.0
Equity 80 12.75 10.2/11.2
3. Debt 30 5.4 1.6
Equity 70 13.29 9.3/10.9
4. Debt 35 5.5 1.9
Equity 65 13.5 8.3/10.2
5. Debt 40 6.5 2.6
Equity 60 15.51 9.3/11.9
6. Debt 50 8.0 4.0
Equity 50 18.0 9.0/13.0
Ke 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 capital
g The moment there is a change in
component cost of capital, WACC will change.
The new WACC is known as MCC.
Suppose:
Earnings avail. to stockholders: Rs. 59m
Less dividends paid 27m
Retained earnings 32m
g 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. cost
Debt 0.29 Rs. 29m 5.94 1.72
Preferred 0.01 Rs. 1m 11.00 0.11
Ret. earn. 0.32 Rs. 32m 15.00 4.8
Ext. 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 earnings
Or = ------------------------------
New capital Percent equity
Rs. 32 million
=---------------------- = Rs. 45.7 million
0.70
Capital Target cap str. ATCost Wtd. cost
Debt 0.29 Rs.13.2m 5.94 1.72
Preferred 0.01 Rs. 0.5m 11.00 0.11
Common 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 firms
g Small businesses
g Measurement problems
g Costs of capital for projects of differing
risks
g Capital structure weights
Solve problems: Chap.8
g 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 80,000
gBEP=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. 80,000
BEP 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) '0000
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 - v
If 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 units
Income Rs.1,875,000 Rs.2,625,000
Fixed costs 700,000 700,000
Variable costs 1,250,000 1,750,000
Total costs 1,950,000 2,450,000
Gain (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 units
BEP 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 units
Income Rs.225,000 Rs.540,000
Fixed costs 175,000 175,000
Variable costs 100,000 240,000
Total costs 275,000 415,000
Gain (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.20
BEP 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 Problems
P1: ‘a’ & ‘b’ only. (Page 336)

Financial Management

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