Financial Management

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FINANCIAL MANAGEMENT OVERVIEW A. INTRODUCTION TO FINANCIAL MANAGEMENT B.COST OF CAPITAL C. LEVERAGE ANALYSIS D.CAPITAL STRUCTURE PLANNING E.DIVIDEND POLICY F. CAPITAL BUDGETING EVALUATION OF SECURITIES G. RISK & RETURN PROF. Tapash Ranjan Saha M . Com MBA M. Phil FICWA
A. INTRODUCTION TO FINANCIAL MANAGEMENT Financial Manaqement is a subject which deals with the ways and means of maneuvering finance in such a way , so as to maximize the return and attain the organizational objectives . Functions of FM : l.lnvestment Decision 2. Financing Decision • 3.Dividend Decision
Objectives Of FM : 1.Maximising Profit 2.0ptimizing Profit 3.0ptimision Shareholders Value • Finance Begins where accounting ends Finance and accounts are not the same Accounting and financing are complementary by nature
Functions & Objectives of FM INANCIAL MANAGEMENT Maximization Of Share Value Investment Decision Return Financial Decision Liquidity Management Trade off Financing Decisions Dividend Decisions isk
Sources of Finance Broadly speaking , sources of finance are two : l.lnternal Sources : Reserves — Profits — Provisions • 2.ExternaI : It is again of two types a. Ownwes b. Lenders • a.Owner — Equity Share , Preference Share b.Lenders — Debenture , Loans , Leasing , Hire Purchase , Bank OD , Bank CC , Creditors , etc. Important Financing Instruments :Shares , Debentures , CD , CP , LC , LOC , Bonds , TD , ICD , Call Money , BOD , CC etc.
Sources Of Corporate Finance Internal External Retained Earnin s Depreciation , Provisions , earer Registered Owners Share Equity Ri hts Lenders Share Cumulative Non Cumulative Convertible Nonconvertible Participating Non artici atin Debenture Financial Institutions Others NDC PCD IDBI IFCI SIDBI NABARD SFCs IPO, SEO , Bonus Bu Back Leasing , HP , Public FD, Factor , Bills , Creditors, Other Ca ital Market Instruments
B.COST OF CAPITAL Cost of Capital is the consideration that one is paid to the providers of capital , it is denoted by 1
va ua Ing Inves mentdecisions, • Designing a firm's debt policy, and Appraising the financial performance of top management.
T e opportunity cost is the rate of return foregone on the next best alternative investment opportunity of comparable ris occ quity shares reference shares Corporate bonds overnment bonds • isk-free security Risk
e cos o capl a o each source of capital is known as component, or specific, cost of capital. The overall cost is also called the weighted average cost of capital (WACC). Relevant cost in the investment decisions is the future cost or the marginal cost. Marginal cost is the new or the incremental cost that the firm incurs if it were to raise capital now, or in the near future. The historical cost that was incurred in the past in raising capital is not relevant in financial decision- making.
e ssue at ar INT • Debt Issued at Discount or INTt Premiunu = ± • Tax debt = —T)
s qui y ap•tal Free of Cost? No, it has an opportunity cost. • Cost of Internal Equity: The Dividend—Growth Model 0 Norma/ growth DIVO (1 + got 1 Supernormal growth DIVI EPSI (since g = 0) Zero-growth
os o x ernal Equity: The Dividend—Growth Model DIVI • Earnings—Price Ratio and the Cost Of EquitYEpsl(1-b) (g = br) EPSI
• Irredeemable Preference Share PDIV k • Redeemable Preference Share PDIVt
As per the CAPM, the required rate of return on equity is given by the following relationship: Ice = R +(Rm-R Equation requires the following three parameters to estimate a firm's cost of equity: • The risk-free rate (Rf) • The market risk premium (Rm — Rf) • The beta of the firm's share (ß)
T e ivi en -growth approach has limited application in practice • It assumes that the dividend per share will grow at a constant rate, g, forever. • The expected dividend growth rate, g, should be less than the cost of equity, ke, to arrive at the simple growth formula. • The dividend—growth approach also fails to deal with risk directly.
e o owing s eps are involved for calculating the firm's WACC: Calculate the cost of specific sources of funds Multiply the cost of each source by its proportion in the capital structure. Add the weighted component costs to get the WACC. +kdWe WACC is in fact the weighted marginal cost of capital (WMCC); that is, the weighted average cost of new capita/ given the firm' target capita/ structure.
anagers pre er t e book value weights for calculating WACC: • Firms in practice set their target capital structure in terms of book values. • The book value information can be easily derived from the published sources. • The book value debt—equity ratios are analysed by investors to evaluate the risk of the firms in practice.
ar e -va ue waghtsare theoretically superior to book-value weights: They reflect economic values and are not influenced by accounting policies. They are also consistent with the market- determined component costs. The difficulty in using market-value weights: The market prices of securities fluctuate widely and frequently. • A market value based target capital structure means that the amounts of debt and equity are continuously adjusted as the value of the firm changes.
frdebeorshares will invariably involve flotation costs in the form of legal fees, administrative expenses, brokerage or underwriting commission. One approach is to adjust the flotation costs in the calculation of the cost of capital. This is not a correct procedure. Flotation costs are not annual costs; they are one-time costs incurred when the investment project is undertaken and financed. If the cost of capital is adjusted for the flotation costs and used as the discount rate, the effect of the flotation costs will be compounded over the life of the project. The correct procedure is to adjust the investment project's cash flows for the flotation costs and use the weighted average cost of capital, unadjusted for the flotation costs, as the discount rate.
tjcalGpproach to incorporate risk differences in projects is to adjust the firm's WACC (upwards or downwards), and use the adjusted WACCto evaluate the investment project. Companies in practice may develop policy guidelines for incorporating the project risk differences. One approach is to divide projects into broad risk classes, and use different discount rates based on the decision-maker's experience.
or examp e, projec s may be classified as: • Low risk projects discount rate < the firm's WACC Medium risk projects discount rate = the firm's WACC • High risk projects discount rate > the firm's WACC
Computation of WACC Ko = keW1+KpW2+KdW3+KrW4 • SOURCES AMOUNT Equity 100000 • Preference 200000 Debenture 300000 Retai ned 400000 Total 1000000 1
• From the following data find out the WACC • Equity dividend for the year 10% - MP of Eq = Rs.25.t0tal 200000 10 % Preference Share @100 issued at a discount of 5 %. Total value Rs. 100000 12 % Debenture @ Rs 1000 Each , Flotation cost Total 400000 Retained Earning Rs. 250000 Tax rate 50%
C. LEVERAGE ANALYSIS Leverage in general means Advantage In FM it means Advantage in relation to business - cost - finance . • It should be understood — Risk and return goes hands in hands . • Leverage occurs due to fixed cost in cost and capital structure of an organisation.
Lets take the following example to understand the concept of leverage O tionA With FC in Cost structure Sales Less VC Contribution : Less FC Profit : Change in Profit RIGINAL 100 30 70 20 50 100= 500/0 +50 0/0 Sales 150 45 105 20 85 650/0 (85-50)/50 -700/0 50 Sales 50 15 35 20 15 300/0 (50-
It follows a 50 %increase in Sales is giving raise to a 70 % increase ( more than 50 %) in profit and voice versa It happens due to the presence of leverage — which occurs due to the presence of Fixed Cost in the capital structure . Now lets take the same example without FC in the capital structure and see what happens
Lets take the following example to understand the concept of leverage O tion B Without FC in Cost Structure Sales Less VC Contribution : Less FC Profit : Change in Profit RIGINAL 100 50 50 50 100= 500/0 +50 0/0 Sales 150 75 75 75 500/0 (75-50)/50 =500/0 50 Sales 50 25 25 25 500/0 (50-
Thus we see the 50 0/0 change in Sales + or — is giving exactly a 50 % Increase or decrease in Profit as there is no fixed cost. No risk no gain . so we understand the leverage exist only if there is a fixed cost element.
• Leverage may be of three types . 1. Operating leverage : denoted as DOL =C/ EBIT. It arises of operating Fixed Cost and measure operating risks 2.FinanciaI Leverage : denoted as DFL = EBIT/EBT. It arises due to financial fixed cost and measure the financial risk . • 3.Combind leverage : Denoted as DOCL =C/EBT. It arises out of total fixed cost and measure overall risk of the concern . DOI , DFI , DOCL > 1 means leverage exist and it signifies that a change in 100 % sale shall give arise to more than 100 % change in profit . • Lets have a look for the following further analysis of leverage and relevant concepts :
leverage affects a firm's operating profit (EBIT). The degree Of operating leverage (DOL) is defined as the percentage change in the earnings before interest and taxes relative to a given percentage % Change in EBIT DOL % Change in Sales A EBIT/EBIT DOL A Sales/Sales
Debt—equity ratio Interest coverage The first two measures of financial leverage can be expressed either in terms of book values or market values. These two measures are also known as measures of capital gearing. The third measure of financial leverage, commonly known as coverage ratio. The reciprocal of interest coverage is a measure of the firm's income gearing.
The use of the fixed-charges sources of funds, such as debt and preference capital along with the owners' equity in the capital structure, is described as financial leverage or gearing or trading on eq u ity. The financial leverage employed by a company is intended to earn more return on the fixed-charge funds than their costs. The surplus (or deficit) will increase (or decrease) the return on the owners'
Company 1. Indian Oil 2. HPCL 3. BPCL 4. SAIL 5. ONGC 6. TELCO 7. TISCO 8. BHEL 9. Reliance 10. 11. HLL 12. Infosys 13. Voltas Capital Gearing Debt ratio Debt—equity ratio Income Gearing Interest coverage Interest to EBIT ratio 0.556 0.350 0.490 0.858 0.106 0.484 0.577 0.132 0.430 0.522 0.027 0.000 0.430 1.25:1 0.54: 0.96:1 6.00:1 0.12:1 0.94:1 1.37:1 o. 15:1 0.75:1 1.09:1 0.03:1 0.00:1 0.72:1 4.00 5.15 5.38 - ve 53.49 0.99 1.62 8.36 3.46 2.31 264.92 2.64 0.250 0.194 0.186 - ve 0.019 1.007 0.616 0.120 0.289 0.433 0.004 0.378
ry m twe of acompany in using financial leverage is to magnify the shareholders' return under favourable economic conditions. The role of financial leverage in magnifying the return of the shareholders' is based on the assumptions that the fixed-charges funds (such as the loan from financial institutions and banks or debentures) can be obtained at a cost lower than the firm's rate of return on net assets (RONA or ROI). EPS, ROE and ROI are the important figures for analysing the impact of financial leverage.
Profit after tax per share of share s CEBIT P rofit after tax e qumity ROE • For calculating ROE either the book value or the market value equity may be used.
Financial Plan considering two alternative financial plans: (1) either to raise the entire funds by issuing 50,000 ordinary shares at Rs 10 per share, or • (D) to raise Rs 250,000 by issuing 25,000 ordinary shares at Rs 10 per share and borrow Rs 250,000 at 15 per cent rate of interest. 1. Earnings before interest and taxes, EBIT 2. Less: interest, INT 3. Profit before taxes, PBT = EBIT INT 4. Less: Taxes, T (EBIT INT) 5. Profit after taxes, PAT = (EBIT INT) (1 T) 6. Total earnings of investors, PAT + INT 7. Number of ordinary shares, N 8. EPS = (EBIT INT) (1 0/N 9. ROE = (EBIT - INT) (1 T)/S Debt- equit 120,000 0 120,000 60,000 60,000 60,000 50,000 1.20 12.0% All- equi ty 120,000 37,500 82,500 41,250 41,250 78,750 25,000 1.65 16.5%
Favourable Unfavourable Neutral ROI > i ROI < i ROI = i
pera •ng leverage affects a firm's operating profit (EBIT), while financial leverage affects profit after tax or the earnings per share. • The degrees of operating and financial leverages is combined to see the effect of total leverage on EPS associated with a given change in sales.
e vana Il o EBITand EPS distinguish between two types of risk—operating risk and financial risk. Operating risk can be defined as the variability of EBIT (or return on total assets). The environment—internal and external—in which a firm operates determines the variability of EBIT The variability of EBIT has two components: • variability of sales • variability of expenses The variability of EPS caused by the use of financial leverage is called financial risk.
e egree o combined leverage (DCL) is given by the following equation: % Change in EBIT % Change in EPS % Change in EPS % Change in Sales % Change in EBIT % Change in Sales another way of expressing the degree of combined leverage is as follows: Q(s — v) DCL x Q(s — v) -INT -INT
Indifference analysis in leverage • It is an analysis which states that , at what EBIT the EPS shall be same , irrespective of the combination of Debt / Equity . • It can be studied under 2 situations . Situation 1 : Equity Vs. Debt and Equity NI= No.of Eq. When no debt cap & N2=no.of Eqwhen EQ &Debt • Situation 2 : Debt —Equity Vs .Debt — Preference - Equity Pl>/N3
Indifference Analysis for Leverage Plan 11 Debt Adv EPS Indifference Point Eq -Advt EBIT Plan 11
Problem on indifference point From the following particulars find out the indifference point in leverage analysisi PARTICULARS Equity Share 10 % Preference Share 15 % Debenture total OPTION 1 500000 500000 OPTION 11 300000 200000 500000 OPTION 111 200000 100000 200000 500000
Sol ; • ??? ( 1-.5) /20000= .5)/10000 .SOL:EBIT = 20000 &EPS .5 • ??? (???- SOL: ??? 60000, EPS
D.CAPITAL STRUCTURE PLANNING It means having the optimum combination of debt , equity and other sources which shall give minimum ko and maximum V for a firm. For capital structure planning , all capitals are classified as either Equity or Debt
The term capital structure is used to represent the proportionate relationship between debt and equity. The various means of financing represent the financial structure of an enterprise. The left- hand side of the balance sheet (liabilities plus equity) represents the financial structure of a company. Traditionally, short-term borrowings are excluded from the list of methods of financing the firm's capital expenditure.
ering-tw alternative financial plans: (1) either to raise the entire funds by issuing 50,000 ordinary shares at Rs 10 per share, or • (D) to raise Rs 250,000 by issuing 25,000 ordinary shares at Rs 10 per share and borrow Rs 250,000 at 15 per cent rate of interest. The tax rate is 50 per cent. Financial Plan Debt-equity All-equity 1. Earnings before interest and taxes, EBIT 2. Less: interest, INT 3. Profit before taxes, PBT = EBIT INT 4. Less: Taxes, T(EBIT INT) 5. Profit after taxes, PAT = (EBIT INT) (1 T) 6. Total earnings of investors, PAT + INT 7. Number of ordinary shares, N 8. EPS = (EBIT INT) (1 T)/N 9. ROE = (EBIT INT) (1 T)/S 120,000 o 120,000 60,000 60,000 60,000 50,000 1.20 12.0% 120,000 37,500 82,500 41,250 41,250 78,750 25,000 1.65 16.5%
_j 75.00 —12.50* 37.50 37.50 50.00 —0.25 —2.50 75.00 18.75 18.75 18.75 18.75 18.75 Economic Conditions 31.25 56.25 Probability —21.88 15.63 28.13 50.63 70.63 Sales (Rs) 15.62 28.12 50.62 70.62 Costs: 37.50 37.50 37.50 37.50 37.50 —0.58 —5.80 13.50 1 8.80 75.00 37.50 37.50 37.50 37.50 37.50 12.50 37.50 82.50 18.75 41.25 61.25 18.75 41.25 61.25 25.00 25.00 25.00 25.00 25.00 —1.25 16.50 24.50 Ian I: NO debt EBIT Less: Interest PBT Less: tax, 50% PAT No. of shares (000) EPS (Rs) ROE (070) Plan 11: 25% debt EBIT —25.00 0.00 50.00 0.00 50.00 25.00 25.00 50.00 0.50 5.00 50.00 75.00 0.00 120.00 0.00 120.00 60.00 60.00 50.00 1.20 12.00 120.00 160.00 0.00 160.00 80.00 80.00 50.00 1.60 16.00 160.00 Ve oor 0.05 510 255 280 535 -25 -5% Less: PBT Less: PAT Interest tax, Variable (Rs) Fixed (Rs) Total Costs (Rs) EBIT (Rs) ROI (r) 0.10 660 330 280 610 50 Poor 0.15 710 355 280 635 75 Normal 0.35 800 400 280 680 120 0.30 880 440 280 720 160 Good 0.05 1,160 580 280 860 300 No. of share (000) EPS (Rs) ROE Plan 111: 50% EBIT Less: Interest PBT Less: tax, 50% PAT debt No. of shares (000) EPS (Rs) ROE (070) —25.00 —12.50 —25.00 —43.75 —21.87 —25.00 —62.50 —31.25 —12.50 0.42 4.20 50.00 6.25 6.25 0.25 2.50 50.00 0.75 7.50 0.75 7.50 0.75 7.50 101.25 1.35 120.00 1.65 141.25 1.88 160.00 122.50 2.45 300.00 0.00 300.00 150.00 150.00 50.00 3.00 30.00 300.00 18.75 281.25 140.63 140.62 37.50 3.75 37.50 300.00 37.50 262.50 131.25 131.25 25.00 5.25 52.50
Popular theories of Capital structure planning • 1.Net Income approach ( NI) — By David Durand • 2. Net Operating Income ( NOI ) — By David Durand 3. Traditional Approach — rational approach • 4. Modigliani — Miller Approach
According to NI approach both the cost of debt and the cost of equity are Cost independent of the capital structure; they remain constant regardless of how much debt the firm ke, ko uses. As a result, the overall cost of capital declines and the firm kd value increases with debt. This approach has no basis in reality; the optimum capital structure would be 100 per cent debt financing under NI approach. ko kd Debt
approach the value of the firm and the weighted average cost of capital are independent of the firm's capital the structure. absence of taxes, an individual holding all the debt and equity securities will receive the same cash flows regardless of the capital structure and therefore, value of the company is the same. Cost ko kd Debt
radi Ional approach argues that moderate degree of debt can lower the firm's overall cost of capital and thereby, increase the firm value. The initial increase in the cost of equity is more than offset by the lower cost of debt. But as debt increases, shareholders perceive higher risk and the cost of equity rises until a point is reached Cost ko kd Debt
evere Irm + DI = = 110,000 k d = interest rate = 6%; NOI = X = 10,000 al — shares held by an investor in L = 10% Unlevered Firm vu = su = 100,000 NOI = X = 10,000
eturn rom evere Irm: Investment = (110, 000 - 50, 000) = (60, 000) = 6, 000 Return = [10, 000 - (6% x 50, 000)] = 1, 000 - 300 = 700 Alternate Strategy: 1. sell shares in L: x 60,000 = 6,000 2. Borrow (personal leverage): 10% x 50,000 = 5,000 3. Buy shares in U: 10% x 100,000 = 10,000 Return from Alternate Strategy: Investment = 10,000 Return = x 10,000 = 1,000 Less: Interest on personal borrowing = 6% x 5,000 Net return = 1,000 - 300 = 700 Cash available = 11,000 -10,000 = 1,000 = 300
ity-fo a levered firm equals the constant overall cost of capital plus a risk premium that equals the spread between the overall cost of capital and the cost of debt multiplied by the firm's debt-equity ratio. For financial leverage be to irrelevant, the overall cost of capital must Cost MM's Proposition Il ko kd Debt
roposltzon MM Proposition 11 : X -kdD
n er curren aws •n most countries, debt has an important advantage over equity: interest payments on debt are tax deductible, whereas dividend payments and retained earnings are not. Investors in a levered firm receive in the aggregate the unlevered cash flow plus an amount equal to the tax deduction on interest. Capitalising the first component of cash flow at the all- equity rate and the second at the cost of debt shows that the value of the levered firm is equal to the value of the unlevered firm plus the interest tax shield which is tax rate times the debt (if the shield is fully usable). It is assumed that the firm will borrow the same amount of debt in perpetuity and will always be able to use the tax shield. Also, it ignores bankruptcy and agency costs.
LEVERAGE BENEFIT UNDER CORPOATE AND PERSONAL TAXES eor tax on div Pers tax on div Pers tax on int PBIT Int PBT Corp tax Div Div tax Tol corp tax Div income Pers tax on div AT div income Int income Pers tax on int AT int income AT total income Net leverage benifit Unlev 2500 o 2500 o 2500 2500 o o 2500 o 2500 o o o 2500 2500 700 1 800 o 1 800 1 800 o o 1 800 o 1 800 700 o 700 2500 o Unlev 35 % 10 % 2500 o 2500 875 1 625 1 477 1 48 1 023 1 477 o 1 477 o o o 35 % 10 % 250 700 1 800 1170 106 10 73 1 064 O 106 700 O 700 1 76 28
e urn Risk Flexibility Capacity Control
approach for analyzing the impact of debt on EPS. Valuation approach for determining the impact of debt on the shareholders' value. Cash flow approach for analyzing the firm's ability to service debt.
Widely-held Companies Closely-held Companies • Flexibility Loan Covenants Early Repay ability Reserve Capacity Marketability Market Conditions Hotation Costs • Capacity of Raising Funds • Agency Costs
E.DIVIDEND POLICY • Dividend is the portion of distributable profit given to the shareholders. • Dividends can be paid either in cash or as bonus share • Dividends can be paid out of : l.current profits 2.reserves 3.money provided by central government / state government Dividends may be a. interim dividend b. final / annual dividend
Dividend policies constant percentage of earning Amount Years Earnings dividends
Constant dividend policy Earnings Dividends in Rs. Dividends
Dividend Theories 1.TraditionaI Model - B. Graham & D. L Dodd • 2.Walters Model • 3.Gordons Model 4. M — M Hypothesis • 5.Radical Position 6.Residual Theory • 7. Linters Model
1. Traditional Model — Dodd B. Graham & D. L • As per this model the share price is more responsive in relation to payment of Dividends than retained earnings • Dividends are given 4 weight age in relation to retention P = m ( D + E/3) Where , Market Price Per Share D=Dividend Per Share E =Earning per Share m=Multiplier
2.WaIters Model • As per it : • If : Growth Firm : Less Dividend • If R=K: Normal Firm : Indifferent • If R
3.Gordons Model More or less like Walters model — Just is done from the point of view of retention As per it : • If R>K : Growth Firm : Less Dividend • If : Normal Firm : Indifferent • If R
4. M - M Hypothesis • According to M-M, under a perfect market situation, the dividend policy of a firm is irrelevant as it does not affect the value of the firm. They argue that the value of the firm depends on firm earnings which results from its investment policy. Thus when investment decision of the firm is given, dividend decision is of no significance.
PO = (DI + PI ) / (1+1
5. Radical Position • As per radical position the dividend is paid as per the tax implication on the dividend and retention Particulars • EPS DPS Capital Gain Tax@400/oonDiv Tax on Capital Gain@24 Net after Tax FirmA 10 10 2.4 7.6 Price per Share ( 8 % capitalization) 95 FirmB 10 10 04 oo 06 75
6. Residual Theory • As per this theory , dividend is only paid once all the possible investment opportunity are exhausted .
MCC Return New Investment
7. Linters Model • As per this model dividend policy depend on past dividend present earning and future earning potentials Divt — Divt-l=p(
F. CAPITAL BUDGETING It is the long term investment plans
I I ill tmenedecisions of a firm are generally known as the capital budgeting, or capital expenditure decisions. The firm's investment decisions would aenerally include expansion, acquisition, modernisation and replacement of the long-term assets. Sale of a division or business (divestment) is also as an investment decision. Decisions like the change in the methods of sales distribution, or an advertisement campaign or a research and development programme have long-term implications for the firm's expenditures and benefits, and therefore, they should also be evaluated as investment decisions.
e exc ange of current funds for future benefits. The funds are invested in long-term assets. The future benefits will occur to the firm over a series of years.
rowt • Risk Funding Irreversibility • Complexity
ne c assi Ica Ion IS as follows: Expansion of existing business Expansion of new business Replacement and modernisation • Yet another useful way to classify investments is as follows: Mutually exclusive investments • Independent investments Contingent investments
ree s eps are Invo ved in the evaluation of an investment: • Estimation of cash flows • Estimation of the required rate of return (the opportunity cost of capital) • Application of a decision rule for making the choice
he-shareholders' wealth. • It should consider all cash flows to determine the true profitability of the project. • It should provide for an objective and unambiguous way of separating good projects from bad projects. • It should help ranking of projects according to their true profitability. • It should recognise the fact that bigger cash flows are preferable to smaller ones and early cash flows are preferable to later ones. • It should help to choose among mutually exclusive projects that project which maximises the shareholders' wealth. • It should be a criterion which is applicable to any conceivable investment project independent of others.
scoun ed Cash How (DCF) Criteria Net Present Value (NPV) Internal Rate of Return (IRR) Profitability Index (PI) • 2. Non-discounted Cash How Criteria Payback Period (PB) Discounted Payback Period (DPB) Accounting Rate of Return (ARR)
the-investment project should be forecasted based on realistic assumptions. Appropriate discount rate should be identified to discount the forecasted cash flows. The appropriate discount rate is the project's opportunity cost of capital. Present value of cash flows should be calculated using the opportunity cost of capital as the discount rate. The project should be accepted if NPV is positive (i.e., NPV > 0).
• Net present value should be found out by subtracting present value of cash outflows from present value of cash inflows. The formula for the net present value can be written as follows: NPV NPV = t=l
Assume that Project X costs Rs 2,500 now and is expected to generate year-end cash inflows of Rs 900, Rs 800, Rs 700, Rs 600 and Rs 500 in years 1 through 5. The opportunity cost of the capital may be assumed to be 10 per cent. Rs 900 Rs 800 Rs 700 Rs 600 Rs 500 -Rs 2,500 NPV (1+0.10) (1+0.10) 2 ( 1+0.10) 3 (1+0.10)4 (1+0.10)5 NPV = [Rs 900(PVF ) + 800(PVF ) + 700(PVF ) 1, 0.10 2, 0.10 3, 0.10 + Rs 600(PVF ) + 500(PVF 2,500 4, 0.10 5, 0.10 NPV = [Rs + Rs + Rs + Rs + Rs 500 x 0.620] -Rs 2,500 NPV = Rs 2,725 -Rs 2,500 = + Rs 225
ccep e project&dhen NPV is positive NPV > O • Reject the project when NPV is negative NPV < O May accept the project when NPV is zero NPV = O • The NPV method can be used to select between mutually exclusive projects; the one with the higher NPV should be ected.
t-acceptable•investment rule for the following reasons: Time value Measure of true profitability Value-additivity Shareholder value Limitations: Involved cash flow estimation • Discount rate difficult to determine Mutually exclusive projects • Ranking of projects
te-ofrreturn (IRR) is the rate that equates the investment outlay with the present value of cash inflow received after one period. This also implies that the rate of return is the discount rate which makes NPV = 0. t=l Co t=l
neven as lows: Calculating IRR by Trial and Error The approach is to select any discount rate to compute the present value of cash inflows. If the calculated present value of the expected cash inflow is lower than the present value of cash outflows, a lower rate should be tried. On the other hand, a higher value should be tried if the present value of inflows is higher than the present value of outflows. This process will be repeated unless the net present value becornes zero.
eve ows • Let us assume that an investment would cost Rs 20,000 and provide annual cash inflow of Rs 5,430 for 6 years. • The IRR of the investment can be found out as follows: NPV = -Rs 20,000 + Rs = O Rs 20,000 = Rs r) Rs 20,000 - 3.683 PVAF6 r Rs 5,430
D 1 2 3 4 5 6 7 8 9 PV Profile Cash Flow -20000 5430 5430 5430 5430 5430 5430 Discount rate c 12,580 7,561 3,649 550 (l ,942) (3,974) Discout rate
ccep e projecewhen r > k. Reject the project when k, • May accept the project when r = k. • In case of independent projects, IRR and NPV rules will give the same results if the firm has no shortage of funds.
me o as following merits: • Time value • Profitability measure • Acceptance rule • Shareholder value IRR method may suffer from: • Multiple rates Mutually exclusive projects • Value additivity
In ex IS the ratio of the ro I a Il present value of cash inflows, at the required rate of return, to the initial cash outflow of the investment.
PV NPV PI e la cas ou ay o a projectäsRs 100,000 and it can generate cash inflow of Rs 40,000, Rs 30,000, Rs 50,000 and Rs 20,000 in year 1 through 4. Assume a 10 per cent rate of discount. The PV of cash inflows at 10 per cent discount rate is: Rs 1,0.10) + Rs 2,0.10) + Rs 3,0.10) + Rs 4,0.10) = 40,000 x 0.909 + Rs 30,000 x 0.826 + Rs 50,000 x 0.751 + Rs 20,000 x 0.68 Rs 112,350 -Rs 100,000 = Rs 12,350 1.1235 .
e o owing are he Placceptance rules: • Accept the project when PI is greater than one. • Reject the project when PI is less than one. • May accept the project when PI is equal to one. PI = 1 • The project with positive NPV will have PI greater than one. PI less than means that the project's NPV is negative.
he-time value of money. It is consistent with the shareholder value maximisation principle. A project with PI greater than one will have positive NPV and if accepted, it will increase shareholders' wealth. In the PI method, since the present value of cash inflows is divided by the initial cash outflow, it is a relative measure of a project's profitability. Like NPV method, PI criterion also requires calculation of cash flows and estimate of the discount rate. In practice, estimation of cash flows and discount rate pose problems.
berofyearsrequired to recover the original cash outlay invested in a project. • If the project generates constant annual cash inflows, the payback period can be computed by dividing cash outlay by the annual cash inflow. That is: Initial Investment Co Payback = Annual Cash Inflow C Assume that a project requires an outlay of Rs 50,000 and yields annual cash inflow of Rs 12,500 for 7 years. The payback period for the project is: Rs 50,000 = 4 years Rs 12,000
Unequal cash flows In case of unequal cash inflows, the payback period can be found out by adding up the cash inflows until the total is equal to the initial cash outlay. Suppose that a project requires a cash outlay of Rs 20,000, and generates cash inflows of Rs 8,000; Rs 7,000; Rs 4,000; and Rs 3,000 during the next 4 years. What is the project's payback? 3 years + 12 x (1,000/3,000) months 3 years + 4 months
e projec would beaccepted if its payback period is less than the maximum or standard payback period set by management. As a ranking method, it gives highest ranking to the project, which has the shortest payback period and lowest ranking to the project with highest payback period.
r I vir ues: • Simplicity • Cost effective • Short-term effects • Risk shield • Liquidity Serious limitations: • Cash flows after payback • Cash flows ignored • Cash flow patterns • Administrative difficulties • Inconsistent with shareholder value
e reciproca o pay ack will be a close approximation of the internal rate of return if the following two conditions are satisfied: • The life of the project is large or at least twice the payback period. • The project generates equal annual cash inflows.
iscounted-paybackperiod is the number of periods taken in recovering the investment outlay on the present value basis. The discounted payback period still fails to consider the cash flows occurring after the payback period. 3 DISCOUNTED PAYBACK ILLUSTRATED Cash Flows co -4,000 -4,000 -4,000 -4,000 3,000 2,727 0 0 1,000 826 4,000 3 , 304 1,000 751 1,000 751 1 ,ooo 683 2,000 1,366 Simple 2 yrs 2 yrs Discounted 2.6 yrs 2.9 s NPV at 987 PV of cash flows PV of cash flows
e accoun Ing ra eo return is the ratio of the average after-tax profit divided by the average investment. The average investment would be equal to half of the original investment if it were depreciated constantly. Average income ARR = Average investment A variation of the ARR method is to divide average earnings after taxes by the original cost of the project instead of the average cost.
IS me od Will accept all those projects whose ARR is higher than the minimum rate established by the management and reject those projects which have ARR less than the minimum rate. This method would rank a project as number one if it has highest ARR and lowest rank would be assigned to the project with lowest ARR.
me o may claim some merits • Simplicity • Accounting data • Accounting profitability Serious shortcoming • Cash flows ignored • Time value ignored • Arbitrary cut-off
conventional investment has cash flows the pattern of an initial cash outlay followed by cash inflows. Conventional projects have only one change in the sign of cash flows; for example, the initial outflow followed by inflows, i.e., A non-conventional investment, on the other hand, has cash outflows mingled with cash inflows throughout the life of the project. Non- conventional investments have more than one change in the signs of cash flows; for example,
onven Iona n ependent Projects: In case of conventional investments, which are economically independent of each other, NPV and IRR methods result in same accept-or-reject decision if the firm is not constrained for funds in accepting al/ profitable projects.
Cash Flows (Rs) Project x co -100 100 IRR 120 -120 NPV at 9 _9
projec may ave both lending and borrowing features together. IRR method, when used to evaluate such non-conventional investment can yield multiple internal rates of return because of more than one change of signs in cash flows. NPV (Rs) 250 -250 -500 -750 50 Rs 63 IOO 150 Discount Rate (%) 200 250
Investment projects are said to be mutually exclusive when only one investment could be accepted and others would have to be excluded. Two independent projects may also be mutually exclusive if a financial constraint is imposed. The NPV and IRR rules give conflicting ranking to the projects under the following conditions: The cash flow pattern of the projects may differ. That is, the cash flows of one project may increase over time, while those of others may decrease or vice-versa. The cash outlays of the projects may differ. The projects may have different expected lives.
Cash Flows (Rs) Project co 1,680 1,680 C3 140 1,510 NPV at 9% 301 321 IRR 1 ,400 700 840
Cash Flow (Rs) Project co -1,000 -100,000 NPV at 10% 364 9,080 IRR 1,500 120,000
Project x co - 10,000 10,000 12,000 O Cash Flows (Rs) O 20,120 NPV at 908 2,495 IRR O O
T e IRR met o is assumed to imply that the cash flows generated by the project can be reinvested at its internal rate of return, whereas the NPV method is thought to assume that the cash flows are reinvested at the opportunity cost of capital.
The modified internal rate of return (MIRR) is the compound average annual rate that is calculated with a reinvestment rate different than the project's IRR. The modified internal rate of return (MIRR) is the compound average annual rate that is calculated with a reinvestment rate different than the project's IRR.
ere IS no pro em in using N method when the opportunity cost of capital varies over time. • If the opportunity cost of capital varies over time, the use of the IRR rule creates problems, as there is not a unique benchmark opportunity cost of capital to compare with IRR.
con may arise between the two methods if a choice between mutually exclusive projects has to be made. Follow NPV method: PV of cash inflows Initial cash outflow NPV PI Project C 100,000 50,000 50,000 2.00 Project D 50,000 20,000 30,000 2.50
Other issues in Capital Budgeting • 1.Sensitivity Analysis • 2.Capital Rationing • 3.Capital Budgeting Under Risk 4.Capital Budgeting Under Uncertainty
ow s a FCh01ce be made between investments with different lives? Should a firm make investment now, or should it wait and invest later? When should an existing asset be replaced? • How shall choice be made between investments under capital rationing?
e c be ween projects With different lives should be made by evaluating them for equa/ periods of Cash 000) 0 60 0 60 120 1 40 0 40 30 2 40 60 IOO 30 3 0 40 40 30 4 0 40 40 30 129.42 106.96 236.38 215.10
e me o or andling the choice of the mutually exclusive projects with different lives, as discussed in last slide, can become quite cumbersome if the projects' lives are very long. We can calculate the annual equivalent value (AEV) of cash flows of each project. shall select the project that equivalent cost.
e-assume that projects can be replicated at constant scale indefinitely, we imply that an annuity is paid at the end of every n year startin from the first periQdv -1 where N PVT is the present value Of the investment indefinitely, NPVn is the present value of the investment for the original life, n and kis the opportunity cost of capital.
Machines Year 2 3 4 )iscount rate WAF kEC x Real Cash Flows (Rs 000) x x Nominal Cash Flows (Rs 000) Inflation 5% 120.00 30.00 30.00 30.00 30.00 .06 215.10 l. 7355 67.86 60.00 40.00 40.00 .06 129.42 3.1699 74.57 120.00 31.20 32.45 33.75 35.10 .144 215.10 1.6382 74,43 60.00 41.60 43.26 . 144 129.42 2.8900 79.00 Inflation 15% 120.00 40.50 54.68 73.81 99.65 .265 215.10 1.4154 93.52 60.00 54.00 72.90 .265 129.42 2.2999 91.44
e r u e IS straightforward: undertake the project at that point of time, which maximizes the NPU Project Undertaken at Period 1 2 NPV -100 + 150 x 0.909 -120 x 0.909 + 180 0.826 -140 x 0.826 + 205 0.751 36.35 39.60 38.32
tion-ofrthe-investment's NPV would depend on when we harvest trees. The net future value of trees increases when harvesting is postponed; but the opportunity cost of capital is incurred by not realising the value by harvesting the trees. The NPV will be maximised when the trees are harvested at the point where the percentage increase in value equals the opportunity cost of capital. • Suppose the net future value obtained over the years from harvesting the trees is At and if the opportunity cost of capital is k, then the net present value (NPV) of the net realisable value of trees is given by:
e optimum harvesting time, which maximizes the NPV, we set the derivative of the NPV with respect to tin Equation equal to zero. Land may have value since the trees can be replanted. Therefore, the correct formulation of the problem will be to assume that once the trees are harvested, the land will be replanted. Thus, if we consider a constant replication of the tree- harvesting investment indefinitely, then the NPV NPV = —C + kt -1
equivalent value (AEV) of the old and new equipment as given below. It is indicated that a chain of new machines is equivalent to an annuity of Rs 9,630 - 3.605 = Rs 2,671 a year for the life of the chain. The existing machine is still capable of providing an annuity of: Rs 7,390 + 2.402 = Rs 3,076. So long as the existing machine generates a cash inflow of more than Rs 2,671 there does not seem to be an economic justification for replacing it. Equipment New co -12 6 4 2.67 3.08 6 3 2.67 3.08 6 2 2.67 3.08 6 2.67 6 2.67 NPVat 9.63 7.39 9.63 7.39
Capital rationing refers to a situation where the firm is constrained for external, or self- imposed, reasons to obtain necessary funds to invest in all investment projects with positive NPV. Under capital rationing, the management has not simply to determine the profitable investment opportunities, but it has also to decide to obtain that combination of the profitable projects which yields highest NPV within the available funds.
There are two types of capital rationing: External capital rationing. • Internal capital rationing.
hould-bæmodified while choosing among projects under capital constraint. The objective should be to maximise NPV per rupee of capita/ rather than to maximise NPV. Projects should be ranked by their profitability index, and top-ranked projects should be undertaken until funds are exhausted. The Profitability Index does not always work. It fails in two situations: Multi-period capital constraints. • Project indivisibility.
mear rogrammmg (LP) • Integer Programming (IP) • Dual variable
ALTERNATIVE PRESENTATION OF CAPITAL BUDGETING Should we build this plant? O
What is capital budgeting? expenditures. important to firm's future. Very
Steps Estimate CFS (inflows & outflows). 1. Assess riskiness of CFS. 2. Determine k = WACC for project. 3. 4. Find NPV and/or IRR. 5. Accept if NPV > O and/or IRR > WACC.
What is the difference between independent and mutually exclusive projects? Projects are: independent, if the cash flows of one are unaffected by the acceptance of the other. mutually exclusive, if the cash flows of one can be adversely impacted by the acceptance of the other.
An Example of Mutually - Exclusive Projects 00000 lääiö6Évs. OAT to get products across a river.
Norma Cash low P Sect: Cost (negative CF) followed by a series of positive cash inflows. One change of signs. Nonnormal Cash Flow Project: Two or more changes of signs. Most common: Cost (negative CF), then string of positive CFS, then cost to close project. Nuclear power plant, strip mine.
Inflow (+) or Outflow (-) in Year
What is the paybaceperiod? The number of years required to recover a project's cost, or how long does it take to get the business's money back?
Payback for Project L Most CFS in out years) Cumulative PaybackL -100 -100 -2 1 10 -90 2.4 2 60 100 0/80 -3 3 80 50 5 yea s
Project come quickly) 1 -100 Cumulative -100 Paybacks 162 100 50 0 20 1.6 ears 3 20 40
Strengths of Payback: . Pr vi es an indication of a project's is and i uidit 2. as to calculat and understand. Weaknesses of Payback: 1. Ignores the TVM. 2. I nores CF occurring after the payback period.
Discounted Pa back: ther than raw CFS. 1 100/0 Uses discounted PVCFt -100 -100 10 9.09 -90.91 2 60 49.59 41.3 3 80 60.11 18.79 Cumulative -100 Discounted 2 payback lÄiää/60.ll Recover invest. + cap. costs in 2.7 yrs.
NPV Sum of the PVs of inflows and outflows. NPV= E t=O (1 + k) t Cost often isoand NPV= t=l (1 + k)
roject L: 1 100/0 What's Project L's NPV? 18.79 = NPV 2 60 NPV - 3 80 -100.00 9.09 49.59 60.11 10 s - $19.98.
Calculator Solution Enter in CFI-O for L: -100 10 NPV = 18.78 = NPV
Rationale for the NPV Method N cost = Net gain in wealth. Accept project if NPV > O. Choose between mutually exclusive projects on basis of higher NPV. Adds most value.
Using NPV method, which project(s) should be -accepted? -lus- , accept S because NPVs > NPVL . • accept both; NPV > O.
Internal Rate of Return: 1 IRR 3 Cost 2 Inflows IRR is the discount rate that forces PV inflows = cost. This is the same as forcing NPV = O.
NPV: Enter k, solve for NPV. n t=O (1 + IRR Enter NPV = O, solve for IRR. (1 +1!BD
What's Project L's IRR? 1 IRR = ? 2 60 3 80 -100.00 PVI PV2 PV3 O = NPV 10 Enter CFs in CFLO, then press IRR: 18.13%. IRR = 23.56%.
Find IRR if CFs are constant: 3 40 -100 INPUTS UTPU 40 3 2 40 40 9.70% Or, with CFLO, enter CFS and press IRR = 9.70%.
Q. How is a project's IR related to a bond'sIfiW? heyare-the same thing. A bond's Y TM is the IRR if you invest in the bond. 1 -1 ,134.2 90 IRR = 7.08% 2 90 10 1 ,090 (use TvM or CFLO).
Rationale for the IRR Method If IRR@WACC, then the project's rate of return is greater than its cost-- some return is left over to boost stockholders' returns. Example: WACC = 10%, IRR = 15%. Profitable.
IRR Acceptance Criteria acc pt project. If IRR < k, reject project.
Decisions on Projects S and L per IRR If S and L are independent, accept both. IRRs > k = 10%. • If S and L accept S because IRRs > IRRL
Construct NPV Profiles ter CFs in CFI-O and find NPVL and NPVs at different discount rates: 20 NPVL 50 33 (4) NPVs 40 20
NPV ($) 40 30 20 10 Crossover Point = 8.7% k 20 NPVL 50 33 (4) NPVs 40 29 20 IRRs = 23.6% Discount Rate (%) 23.6 IRR - L - 18.1%
NPV and IRR always lead to the same åcce t/re•ect decision for Inde endent - projects: NPV ($) IRR>k and NPV > O Accept. IRR k > IRR and NPV < O. Reject.
Mutually Exclusive Projects NPV k k < 8.7: NPVL> NPVs, IRRs> IRRL CONFLICT k > 8.7: NPVs> NPVL, IRRs> IRRL NO CONFLICT 'RRs 8.7 IRRL
1. 2. 3. 4. To Find the Crossover Rate Find cash flow differences between the projects. See data at beginning of the case. Enter these differences in CFLO register, then press IRR. Crossover rate = 8.68%, rounded to 8.7%. Can subtract S from L or vice versa, but better to have first CF negative. If profiles don't cross, one project dominates the other.
1. 2. Two Reasons NPV Profiles Cross Size scale differences. Smaller project frees up funds at t = O for investment. The higher the opportunity cost, the more valuable these funds, so high k favors small projects. Timin differences. Project with faster payback provides more CF in early years for reinvestment. If k is high, early CF especially good, NPVs > NPVL.
Reinvestment Rate Assumptions PV assumes reinvest at k (op RR assumes reinvest at IRR. • Reinvest at opportunity cost, k, is more realistic, so NPV method is best. NPV should be used to choose between mutually exclusive projects.
Managers like rates--prefer IRR to NPV comparisons. Can we give them a better IRR? R is the discount rate which causes the PV of a project's terminal value (TV) to equal the PV of costs. TV is found by compounding inflows at WACC. Thus, MIRR assumes cash inflows are reinvested at WACC.
MIRR for Project L (k = 10%) -100.0 2 60.0 10.0 MIRR = 16.5% 3 80.0 66.0 12.1 158.1 TV inflows $158.1 - (1+MlRRLl)3 PV outflows MIRRL = 16.5%
T find TV with 10B, enter in CFLO: CFO = 0, CFI = 10, CF2 = 60, CF3 = 80 NPV = 118.78 = PV of inflows. Enter PV = -118.78, N = 3, I = 10, PMT = O. Pres FV = 158.10 = FV of inflows. Enter FV = 158.10, PV = -100, PMT = O, Press I
why use MIRR versus IRR? MIRR correctly assumes reinvestment at opportunity cost = WACC. MIRR also avoids the problem of multiple IRRs. Managers like rate of return comparisons, and MIRR is better for this than IRR.
Pavilion Project: IRR? -800 1 5,000 NPV and 2 -5,000 Enter CFs in CFLO, enter I = 10. NPV = -386.78 IRR = ERROR. Why?
We got IRR = ERROR because there re 2 IRRs. Nonnormal CFs--two sign NPV 450 100 IRR - -800 picture: NPV Profile IRR2 = 4000/0 400 k
1. 2. 3. 4. Logic of Multiple IRRs At very low discount rates, the PV of CF2 is large & negative, so NPV < O. At very high discount rates, the PV of both CFI and CF2 are low, so CFO dominates and again NPV < O. In between, the discount rate hits CF2 harder than CFI, so NPV > O. Result: 2 IRRs.
COUId find IRR with calculator: 1. Enter CFS as before. 2. Enter a "guess" as to IRR by storing the guess. 10 STO IRR = = lower IRR Now guess large IRR, say, 200: 200 STO IRR = 4000/0 = upper IRR
When there are nonnormal CFS and more than one IRR, use MIRR: 1 2 -800,000 PV outflows @ 100/0 = TV inflows @ 100/0 = MIRR = 5.6%
Accept NO. Reject because MIRR = 5.6% < k = 10%. Also, if MIRR < k, NPV will be negative: NPV = -$386,777.
S and L are mutually exclusive and will be repeated. k = 10%. Which is better? (000s) 1 Project S: (100) 60 Project L: (100) 33.5 2 60 33.5 3 33.5 4 33.5
NPV -100 000 60,000 2 10 4,132 -1 oo,ooo 33,500 4 10 6,190 NPVL> NPVs. But is L better? Can't say yet. Need to perform common life analysis.
could be repeated after 2 years to generate additional profits. Can use either replacement chain or equivalent annual annuity analysis to make decision.
Replacement Chain Approach (000s) Replication: Project S: (100) 60 (100) 60 NPV = $7,547. 2 60 (100) 3 60 60 4 60 60
Or, use NPVs: 2 4,132 3 $6,190. 4 4,132 34415 7 547 1 100/0 Compare to Project L NPV
If the cost to repeat S in two years rises to $105,000, which is best? (000s) 1 Project S: (100) 60 2 60 3 60 4 60 (105) NPVs $3,415 NPVL $6,190. Now choose L.
Consider another project with a 3-year life. If terminated prior to Year 3, the -l machinery will have positive salvage value. Year O 1 2 3 ($5,000) 2,100 2,000 1 ,750 Salvaqe Value $5,000 3,100 2,000
CFs Under Each Alternative (000s) 1. No termination 2. Terminate 2 years 3. Terminate 1 year O (5) (5) (5) 1 2.1 2.1 5.2 2 2 4 3 1.75
Assuming a 10% cost of capital, what is the project's optimal, or economic life? NPV(2) = $215. NPV(I) = -$273. NPV (no) = -$123.
Conclusions The project is acceptable only if operated for 2 years. • A project's engineering life does not always equal its economic life.
Choosing the Optimal Capital udget • Finance theory says to accept all positive NPV projects. Two problems can occur when there is not enough internally generated cash to fund all positive NPV projects: An increasing marginal cost of capital. • Capital rationing
Increasing Marginal&st of apital • Externally raised capital can have large flotation costs, which increase the cost of capital. • Investors often perceive large capital budgets as being risky, which drives up the cost of capital. (More...)
ex erna unds willbe raised, then the NPV of all projects should be estimated using this higher marginal cost of capital.
Capital Rationing Capital rationing occurs when a company chooses not to fund all positive NPV projects. The company typically sets an upper limit on the total amount of capital expenditures that it will make in the upcoming year. (More...)
Reason-æ-companies waneto avoid the direct costs (i.e., flotation costs) and the indirect costs of issuing new capital. Increase the cost of capital by Solution: enough to reflect all of these costs, and then accept all projects that still have a positive NPV with the higher cost of capital. (More...)
Q-easopr:---Companies-don'thave enough managerial, marketing, or engineering staff to implement all positive NPV projects. Solution: Use linear programming to maximize NPV subject to not exceeding the constraints on staffing. (More...)
) -e.a.SO.n.:.........CO.mpanies believe that the project's managers forecast unreasonably high cash flow estimates, so companies "filter" out the worst projects by limiting the total amount of projects that can be accepted. Implement a post-audit process Solution: and tie the managers' compensation to the subsequent performance of the project.
Birds Eye View of Risk Analysis in capital Budgeting Technique used are as follows : 1.Higher Discounting Rate • 2.Lower Pay Back Period • 3.Certainty Equivalent Coefficient : Certain Cash Flow / Uncertain Cash Flow . To take a conservative approach Certain cash flow is multiplied with certain cash flow
• 4.Attach Probability to different cash flow as estimated and find out the Expected Cash Value : • 5000 x .2 = 1000 . 4000 x .3 = 1200 • 3000 x .5 = 1500 3700 • EVA
• 5.0ptimistic — Most Likely — Pessimistic Cash Flow = (0 + 4M + p ) / 6 • 6. Risk Adjuster Discounting Factors : • Particulars No Risk • Low Risk High Risk D.F. Risk Premium = D Factors 100/0 100/0 100/0 500/0 1000/0 100/0 200/0
N/A
EVALUATION OF SECURITIES
sse s can e rea or financial; securities like shares and bonds are called financia/ assets while physical assets like plant and machinery are called rea/ assets. The concepts of return and risk, as the determinants of value, are as fundamental and valid to the valuation of securities as to that of physical assets.
00 a ue • Replacement Value Liquidation Value Going Concern Value • Market Value
ace a ue Interest Rate—fixed or floating Maturity • Redemption value • Market Value
on s ma unty • Pure discount bonds • Perpetual bonds
resent value Of interest + on va ue = Present value of maturity value: t=l
e y•eld- o-maturity (YTPO is the measure of a bond's rate of return that considers both the interest income and any capital gain or loss. YTMis bond's internal rate of return. A perpetual bond's yield-to-maturity: INT INT
urren Yle IS he annual interest divided by the bond's current value. • Example: The annual interest is Rs 60 on the current investment of Rs 883.40. Therefore, the current rate of return or the current yield is: 60/883.40 = 6.8 per cent. Current yield does not account for the capital gain or loss.
heyield tocall, the call period would be different from the maturity period and the call (or redemption) value could be different from the maturity value. Example: Suppose the 10% 10-year Rs 1,000 bond is redeemable (callable) in 5 years at a call price of Rs 1,050. The bond is currently selling for Rs 950. The bond's yield to call is 12.7%. 1, 050 100 950 = E (1+ YTC)t (1+ YTC)
A bond (debenture) may be amortised every year, i.e., Of principal every year rather at maturity. The formula for determining the value of a bond or debenture that is amortised every year, can be written as follows: t 1 (I-kkd)t • Note that cash flow, CF, includes both the interest and repayment of the principal.
ure discount bond do not carry an explicit rate of interest. It provides for the payment of a lump sum amount at a future date in exchange for the current price Of the bond. The difference between the face value of the bond and its purchase price gives the return or YTMto the investor.
• Example: A company may issue a pure discount bond of Rs 1,000 face value for Rs 520 today for a period Of five years. The rate Of interest can be calculated as follows: 1, 000 520 = (1 + YTM)5 1, 000 (1 + YTM)5 = 1.9231 520 = 1.92311/5 —I 0.14 or i
ure 'scoun bOndsare called deep- discount bonds or zero-interest bonds or zero-coupon bonds. • The market interest rate, also called the market yield, is used as the discount rate. Value of a pure discount bond = PV of the amount on maturity:
erpe ua onds, also called conso/s, has an indefinite life and therefore, it has no maturity value. Perpetual bonds or debentures are rarely found in practice.
haEa-10 per cent Rs 1,000 bond will pay Rs 100 annual interest into perpetuity. What would be its value of the bond if the market yield or interest rate were 15 per cent? The value of the bond is determined as follows: INT 100 = Rs 667 0.15
bond declines as the market interest rate (discount rate) increases. The value of a 10- year, 12 per cent Rs 1,000 bond for the market interest rates ranging from 0 per cent to 30 per cent. 1200.0 1000.0 800.0 600.0 400.0 200.0 0.0 5% Interest Rate
risk would be higher on bonds with long maturities than bonds with short maturities. The differential value response to interest rates changes between short and long-term bonds will always be true. Thus, two bonds of same quali in terms of the risk of eault) would have different exposure to interest rate risk. Present Value (Rs) Discount rate 5•Year bond 10•Year bond Per etual bond 5 15 20 25 30 1,216 I ,OOO I ,386 I ,OOO 464 2,000 I ,OOO 400
-x- - - 5-year bond 1 0-year bond -............e.............-perpetual bond > 2000 1750 1500 1250 1000 750 500 250 5 10 -x 30 15 Discount rate 20 25
T e ongert e maturity of a bond, the higher will be its sensitivity to the interest rate changes. Similarly, the price of a bond with low coupon rate will be more sensitive to the interest rate changes. However, the bond's price sensitivity can be more accurately estimated by its duration. A bond's duration is measured as the weighted average of times to each cash flow (interest payment or repayment of principal).
8.5 per cent rate bond of Rs 1,000 face value that has a current market value of Rs 954.74 and a YTM of 10 per cent, and the 12 per cent rate bond of Rs 1,000 face value has a current market value of Rs 1,044.57 and a yield to maturity of 10.8 per cent. Table shows the calculation of duration for the two bonds. Year 1 2 3 4 5 Year 1 2 3 4 5 Cash Flow 85 85 85 85 1,085 Cash Flow 115 115 115 115 1,115 8.5 Percent Bond Present Value at 10 % 77.27 70.25 63.86 58.06 673.70 943.14 11.5 Percent Bond Present Value at 10.2% 103.98 94.01 85.00 76.86 673.75 1 033.60 Proportion of Bond Price 0.082 0.074 0.068 0.062 0.714 1.000 Proportion of Bond Price 0.101 0.091 0.082 0.074 0.652 1.000 Proportion of Bond Price x Time 0.082 0.149 0.203 0.246 3.572 4.252 Proportion of Bond Price x Time 0.101 0.182 0.247 0.297 3.259 4.086
latility-orthe-interes&ate sensitivity of a bond is given by its duration and YTM. A bond's volatility, referred to as its modified duration, is given as follows: Duration Volatility of a bond — (1 + YTM) The volatilities of the 8.5 per cent and 11.5 per cent bonds are as follows: Volatility of 8.5% bond = = 3.87 (1.100) 4.086 Volatility of 11.5% bond — - 3.69 (1.106)
-curve-shows the relationship between the yields to maturity of bonds and their maturities. It is also called the term structure of interest rates. Yield Curve (Government of India Bonds) Meld (070) 7.5% 7.0% 6.5% 6.0% 5.90% 5.5% 5.0% 0-1 1-2 3-4 4-5 5-6 6-7 7-8 8-9 7.18% Maturity (Years ) 9-10
e upwar sopng Yield curve implies that the long-term yields are higher than the short-term yields. This is the norma/shape of the yield curve, which is generally verified by historical evidence. However, many economies in high-inflation periods have witnessed the short-term yields being higher than the long-term yields. The inverted yield curves result when the short-term rates are higher than the long- term rates.
e expec a Ion theory supports the upward sloping yield curve since investors always expect the short-term rates to increase in the future. This implies that the Iona-term rates will be higher than the short-term rates. But in the present value terms, the return from investing in a long-term security will equal to the return from investing in a series of a short-term security.
theomassumes • capital markets are efficient • there are no transaction costs and • investors' sole purpose is to maximize their returns The long-term rates are geometric average of current and expected short-term rates. A significant implication of the expectation theory is that given their investment horizon, investors will earn the same average expected returns on all maturity combinations. Hence, a firm will not be able to lower its interest cost in the long-run by the maturity structure of its debt.
bonds are more sensitive than the prices of the short-term bonds to the changes in the market rates of interest. Hence, investors prefer short-term bonds to the long-term bonds. • The investors will be compensated for this risk by offering higher returns on long-term bonds. This extra return, which is called liquidity premium, gives the yield curve its upward bias.
e 'qui y premium theory means that rates on long-term bonds will be higher than on the short-term bonds. From a firm's point of view, the liquidity premium theory suggests that as the cost of short-term debt is less, the firm could minimize the cost of its borrowings by continuously refinancing its short-term debt rather taking on long-term debt.
tedmarkets theory assumes that the debt market is divided into several segments based on the maturity of debt. In each segment, the yield of debt depends on the demand and supply. Investors' preferences of each segment arise because they want to match the maturities of assets and liabilities to reduce the susceptibility to interest rate changes.
e segmen e marketstheory approach assumes investors do not shift from one maturity to another in their borrowing— lending activities and therefore, the shift in yields are caused by changes in the demand and supply for bonds of different maturities.
e au IS he risethat a company will default on its promised obligations to bondholders. • Default premium is the spread between the promised return on a corporate bond and the return on a government bond with same maturity.
Hi ves tnme nt Gr ades ate p ay r-nen t are judged to offer highes t s afety Of Of interes t and princip al- Thou gh the AA (Do u ble A) : Fligh Safety In tnment Gr ades A : Adequate Safety BBB (Triple B): de ra te Safe ty S peculati Gra&s BB (Double B): Inadequate Safety B: fligh Risk Substantial Risk In Defa u I t No te : circu tances providing this degree Of s afety are likely to change, such changes as can be envis aged are rnost unlikely to affect adversely the fundarnental_ly strong position Of such issues - Debentures rated 'AA' are judged to offer high s afety Of tirnely payrnent Of interest and principal. They differ in s afety fro AAA' is s u es only n•arginally- Debentures rated are judged to offer adequate safety Of payrnent Of interes t and princip al; ho ch an g es circu rms tances can adversely affect such issues m-nore than those in the higher rated categories - Debentures rated are judged to offer sufficient safety Of Of interest and principal for the pres ent; ho».zever, changing circunms tances are rmmore likely to lead to a ».zeakened capacity to pay interest and repay principal than for debentures in higher rated categories Debentures rated are judged to carry inadequate s afety Of tin•ely pay n•ent Of interest and principal; ».zhile they are les s ceptible to default than other speculative grade debentures in the immrn-rediate future, the uncertainties that the is suer faces could lead to inadequate capacity to n•ake interest and principal payr-nents - Debentures rated are judged to have greater susceptibility to default; »./hile currently interest and principal are adverse bus iness or econon•ic conditions lead to lack Of ability or ».zillingness to pay interest or principal- Debentures rated are judged to have factors present that n•ake vulnerable to default; tin•ely Of interest and principal is pos sib le only if favourable c tances continue- Debentures rated are judged to have greater susceptibility to default; »./hile currently interest and principal payn•ents are adverse bus iness or econon•ic conditions ».zould lead to lack Of ability or ».zillingness to pay interest or principal- (n-zinus) signs for ratings fron-z AA to D to reflect cornparative standing 7. 2- 3- CRISIL n-zay apply " + " (plus) or vvithin th e category- The contents vvithin parenthesis are a guide to the pronuncia tion of the rating syn-zbo Is- Preference share rating syrnbols are identical to deben ture rating syn-zbols except that the letters ' 'pf' are prefixed to the debenture rating syrnbols, e.g- p.fAAAA ( "pfTripIe "
company may Issue two types of shares: • ordinary shares and preference shares Features of Preference and Ordinary Shares • Claims • Dividend • Redemption • Conversion
e ue o e preference share would be the sum of the present values of dividends and the redemption value. A formula similar to the valuation of bond can be used to preference shares with a maturity period: PDIVI t=l
Suppose an investor is considering the purchase of a 12-year, 10% Rs 100 par value preference share. The redemption value of the preference share on maturity is Rs 120. The investor's required rate of return is 10.5 percent. What should she be willing to pay for the share now? The investor would expect to receive Rs 10 as preference dividend each year for 12 years and Rs 110 on maturity (i.e., at the end of 12 years). We can use the present value annuity factor to value the constant stream of preference dividends and the present value factor to value the redemption payment. 1 PO = 10 X 1 120 12 12 0.105 0.105 x (1.105) (1.105) = 10 x 6.506 +120 x 0.302 = 65.06 + 36.24 = Rs101.30 Note that the present value of Rs 101.30 is a composite of the present value of dividends, Rs 65.06 and the present value of the redemption value, Rs 36.24. The Rs 100 preference share is worth Rs 101.3 today at 10.5 percent required rate of return. The investor would be better off by purchasing the share for Rs 100 today.
e va ua Ion o or inary or equity shares is relatively more difficult. • The rate of dividend on equity shares is not known; also, the payment of equity dividend is discretionary. • The earnings and dividends on equity shares are generally expected to grow, unlike the interest on bonds and preference dividend.
rdln ry share is determined by capitalising the future dividend strBqo•n abthe opportunity cost of capital PO • Single Period Valuation: • If the share price is expected to grow at g per cent, then PI: PI = Po(l+g) We obtain a simple formula for the share valuation as follows: DIVI Ice —g
e Ina peno IS n, we can write the general formula for share value as follows: DIY t=l • Growth in Dividends Growth = Retention ratio x Return on equity g = b x ROE • Normal Growth DIVI Ice —g Share value = PV of dividends during finite super-normal growth period + PV of dividends during indefinite normal growth period • Super-normal Growth
n e r wo cases, e value Of the share can be determined by capitalising the expected earnings: When the firm pays out 100 per cent dividends; that is, it does not retain any earnings. When the firm's return on equity (ROE) is equal to its opportunity cost of capital.
For firms for which dividends are expected to grow at a constant rate indefinitely and the current market price is given DIVI
stirnatlon errors Unsustainable high current growth • Errors in forecasting dividends
e va ue o a growth opportunity is given as follows: NPVI Ice —g b x EPSI(ROE -ke) ke(ke — g)
P/E ratio is calculated as the price of a share divided by earning per share. • Some people use P/E multiplier to value the shares of companies. Alternatively, you could find the share value by dividing EPS by E/P ratio, which is the reciprocal of P/E ratio.
es are price IS a so given by the following formula: EPSI The earnings price ratio can be derived as follows: EPSI
autions: • E/P ratio will be equal to the capitalisation rate only if the value of growth opportunities is zero. • A high P/E ratio is considered good but it could be high not because the share price is high but because the earnings per share are quite low. • The interpretation of P/E ratio becomes meaningless because of the measurement problems of EPS.
G. RISK & RETURN
oa re urn = Dividend + capital gain Year-to-year Total Returns on HLL Share Rate of return = Dividend yield + Capital gain yield DIVI PI-PO 160.00 140.00 120.00 100.00 80.00 60.00 40.00 20.00 0.00 1992 70.54 1993 16.52 1994 22.71 1995 92.33 49.52 1996 1997 Year 36.13 1998 52.64 1999 7.29 2000 12.95 2001
e average ra e of return is the sum of the various one-period rates of return divided by the number of period. Formula for the average rate of return is as follows:
ormu ae or ca culating variance and standard deviation: Standard deviation = Variance 1
10 0 Index 1969-70 1 970 ? 71 1971 -72 1972-73 1973-74 91-day TB + Inf lation ? Long-term Govt. Bonds —g— Call Money Bkrket ? Stock N/hrket Return 1974-75 1975-76 1976-77 1977-78 1978-79 1979 ? 80 1980-81 1981 ? 82 1982-83 1983 ? 84 1984 ? 85 1985 ? 86 1986 ? 87 1987 ? 88 1988-89 1989-90 1990-91 1991 -92 1992-93 1993-94 1994 ? 95 1995-96 1996-97 1997-98 Year 57.16 4.41 0 0 0
Securities Ordinary shares (RBI Index) Call money market Long-term governnent bonds 91-Day treasury bills Inflation Il Arithmetic mean 17.50 9.93 8.74 5.46 8.80 Standard deviation 22.34 3.49 2.59 2.05 5.82 Risk premium* 12.04 4.47 3.28 Risk premium# 8.76 1.19 Relative to 91 -Days T-bills. # Relative to long-term government bonds.
elfi Ill rate of return [E (R)] is the sum of the product of each outcome (return) and its associated probability: RETURNS UNDER VARIOUS ECONOMIC CONDITIONS Economic Conditions (1) High growth Expansion Stagnation Decline Economic Conditions (1) Growth Bpansion Stagnation Decline Share Price (2) 305.50 285.50 261.25 243.50 Dividend Dividend Yield Capital Gain (3) 4.00 3.25 2.50 2.00 (4) 0.015 0.012 0.010 0.008 (5) o. 169 0.093 0.000 - 0.068 Return 0.185 0.105 0.010 - 0.060 RETURNS AND PROBABILITIES Rate of Return (%) (2) 18.5 10.5 1.0 - 6.0 Probability (3) 0.25 0.25 0.25 0.25 1.00 Expected Rate of Return (%) 4.63 2.62 0.25 - 1.50 6.00
The following formula can be used to calculate the variance of returns: RI + ...+ Rn-E(R2 -E(R2 i=l
k-averseinvestorwill choose among investments with the equal rates of return, the investment with lowest standard deviation. Similarly, if investments have equal risk (standard deviations), the investor would prefer the one with higher return. A risk-neutral investor does not consider risk, and would always prefer investments with higher returns. A risk-seeking investor likes investments with higher risk irrespective of the rates of return. In reality, most (if not all) investors are risk-averse.
orma IS rl u Ion is an important concept in statistics and finance. In explaining the risk-return relationship, we assume that returns are normally distributed. Normal distribution is a population- based, theoretica/ distribution.
lio-isa-bundle-oracombination of individual assets or securities. The portfolio theory provides a normative approach to investors to make decisions to invest their wealth in assets or securities under risk. • It is based on the assumption that investors are risk-averse. • The second assumption of the portfolio theory is that the returns of assets are normally distributed.
e return o a portfolio is equal to the weighted average Of the returns Of individual assets (or securities) in the portfolio with weights being equal to the proportion of investment value in each asset. Expected return on portfolio = weight of security X x expected return on security X + weight of security Y x expected return on security Y
e po 0/0 vanance or s andarddeviation depends on the co- movement of returns on two assets. Covariance of returns on two assets measures their co-movement. The formula for calculating covariance of returns of the two securities X and Yis as follows: Covariance X Y = Standard deviation X' Standard deviation Y Correlation XY The variance of two-security portfolio is given by the following equation: -k 2M' x Wy CO var + 2w w c c Cor
IS e op 'mum proportion of investment in security X Investment in Y will be: 1— c —Cov xy + —2Cov xy
en corre aton coefficient of returns on individual securities is perfectly positive (i.e., = 1.0), then there is no advantage of cor diversification. The weighted standard deviation of returns on individual securities is equal to the standard deviation of the portfolio. We may therefore conclude that diversification always reduces risk provided the correlation coefficient is less than 1.
Portfolio Risk, cp (%) Correlation Weight Ingrow 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 02 Rapidex 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Portfolio Return (%) 12.00 12.60 13.20 13.80 14.40 15.00 15.60 16.20 16.80 17.40 18.00 +1.00 16.00 16.80 17.60 18.40 19.20 20.00 20.80 21.60 22.40 23.20 24.00 -1.00 16.00 12.00 8.00 4.00 0.00 4.00 8.00 12.00 16.00 20.00 24.00 0.00 16.00 14.60 13.67 13.31 13.58 14.42 15.76 17.47 19.46 21.66 24.00 Mnimum Variance Portfolio 1.00 0.00 256 16 0.60 0.40 0.00 0.00 0.692 0.308 177.23 13.31 0.50 16.00 15.74 15.76 16.06 16.63 17.44 18.45 19.64 20.98 22.44 24.00 0.857 o. 143 246.86 15.71 -0.25 16.00 13.99 12.50 11.70 11.76 12.65 14.22 16.28 18.66 21.26 24.00 0.656 0.344 135.00 11.62
20 15 10 Cor 1.0 Cor = - 0.25 Cor = + 1.0 Cor 1.0 Cor = 25 + 0.50 10 Porfolio risk (Stdev, 20 070) 30
ris -averse Investor will prefer a portfolio with the highest expected return for a given level of risk or prefer a portfolio with the lowest level of risk for a given level of expected return. In portfolio theory, this is referred to as the principle of dominance.
An efficient portfolio is one that has the highest expected returns for a given level of risk. The efficient frontier is the frontier formed by the set of efficient portfolios. All other portfolios, which lie outside the efficient frontier, are inefficient portfolios. Return c Risk, o
Systematic risk arises on account of the economy-wide uncertainties and the tendency of individual securities to move together with changes in the market. This part of risk cannot be reduced through diversification. It is also known as market risk. Unsystematic risk arises from the unique uncertainties of individual securities. It is also called unique risk. Unsystematic risk can be totally reduced through diversification. Total risk = Systematic risk + Unsystematic risk Systematic risk is the covariance of the individual securities in the portfolio. The difference between variance and covariance is the diversifiable or unsystematic risk.
- ree asset or security has a zero variance or standard deviation. Return and risk when we combine a risk-free and a risky asset: E(Rp)
RISK-RETURN ANALYSIS FOR A PORTFOLIO OF A RISKY AND A RISK-FREE SECURITIES Weights (%) Expected Return, R Risky security 120 100 80 20 Risk-free security 20 20 40 60 80 100 f, risk-free rate Standard Deviation (01)) 7.2 6.0 4.8 3.6 2.4 1.2 0.0 20 17.5 15 12.5 10 7.5 2.5 1.8 3.6 5.4 17 15 13 11 7.2 Standard Deviation
rlie figures to illustrate the feasible portfolios consisting of the risk-free security and the portfolios of risky securities. We draw three lines from the risk-free rate (5%) to three portfolios. Each line shows the manner in which capital is allocated. This line is called the capital allocation line (CAL). The capital market line (CML) is an efficient set of risk-free and risky securities, and it shows the risk-return trade-off in the market equilibrium. Return Capital Market Line (CML) Capital Allocation Lines (CALs) Risk,
e s o the best price of a given level of risk in equilibrigmeofcw The expected return on a portfolio on CML is defined by the following equation:
e capl a assetpricing model (CAPM) is a model that provides a framework to determine the required rate of return on an asset and indicates the relationship between return and risk of the asset. Assumptions of CAPM • Market efficiency • Risk aversion and mean-variance optimisation • Homogeneous expectations • Single time period
epo e com Ina Ions o four possible returns of Alpha and market. They are shown as four points. The combinations of the expected returns points (22.5%, 27.5% and - 12.5%, 200/0) are also 200 -15.0 shown in the figure. We join these two points to form a line. This line is called the characteristics line. The slope of the characteristics line is the sensitivity coefficient, which, as stated earlier, is referred to as beta. -10.0 Alpha's Return 35.0 30.0 25.0 20.0 15.0 10.0 5.0 -5.0 - -10.0 -15.0 -20.0 -25.0 -30.0 5.0 10.0 15.0 20.0 25.0 Market "turn 30.
mount of systematic risk (ß), SML shows the required rate of return. E(Rj) 0 E(RJ) = Rf + [(Rm) SLM ß = (covarj m/02m) 1.0
•Il-always-combine a risk-free asset with a market portfolio of risky assets. They will invest in risky assets in proportion to their market value. • Investors will be compensated only for that risk which they cannot diversify. This is the market-related (systematic) risk. • Beta, which is a ratio of the covariance between the asset returns and the market returns divided by the market variance, is the most appropriate measure of an asset's risk. • Investors can expect returns from their investment according to the risk. This implies a linear relationship between the asset's expected return and its beta.
IS ase on unrealistic assumptions. • It is difficult to test the validity of CAPM. Betas do not remain stable over time.
In APT, the return of an asset is assumed to have two components: predictable (expected) and unpredictable (uncertain) return. Thus, return on asset j will be: where Rfis the predictable return (risk-free return on a zero-beta asset) and UR is the unanticipated part of the return. The uncertain return may come from the firm specific information and the market related information: +(ßlFl+ß2F2+ß3F3+.
ac ors: • industrial production • changes in default premium • changes in the structure of interest rates • inflation rate • changes in the real rate of return • Risk premium Factor beta
Reference books : 1.Management Accounting — Monilal Das — Rabindra Library 2.Financial management — I M Pandey — Vikas • 3.Financial Policy & Management Accounting -B . Banaerjee - PHI 4.Basic Financial Management —T R Saha — World Press 5.Financial Accounting For Manager -T R Saha - G J . Book Society 6. Management Accounting — Gokul Sinha
.THANKS

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