Financial Management.ppt -Pgdm2010 (2)

Financial Management

K.V.RAMESHAssistant ProfessorCoordinator MBA ( PE )Institute of Public Enterprise

Lay out Nature of Financial Management.

Investment & Financing Decisions.

Dividend Decisions.

Liquidity Decisions or Working Capital Management.

Financial management by Jonathan Berk / Peter DeMarzo & Ashok Thampy.Fundamentals of Financial Management by James C.Van Horne and John M. Wachowicz, Jr.Fundamentals of Financial management by Brigham & HoustonFinancial management by I M PandeyFinancial management by G. Sudarsana ReddyContemporary Financial management by Rajesh Kothari and Bobby duttaFinancial management by Shashi K. Gupta and R.K.SharmaFinancial management by Khan and JainCost accounting and Financial management Khan and JainFundamentals of Financial management by Prasanna Chandra.

What is Finance ? Finance stands for provision of money as and

when required. Process of raising, providing and administering

all money/funds to be used in a corporate enterprise.

Is concerned with the acquisition and conservation of capital funds in meeting the financial need and overall objectives of business enterprise.

Approaches to finance

Providing of funds needed by a business on most suitable terms.

Cash.

Concerned with raising of funds and their effective utilisation.

Financial Management

The ways and means of managing money.

Planning, acquisition, allocation, and utilisation of financial resources with the aim to achieve objectives of the firm.

Is the application of planning and controlling functions to the finance function.

Scope of Finance Function

Estimating financial requirements.

Capital structure decisions.

Selecting source of finance.

Selecting pattern of investment.

Proper Cash management.

Implementing financial controls.

Proper use of surpluses.

Aims of Finance function

Acquiring sufficient funds.

Proper utilisation of funds.

Increasing profitability.

Maximising firm’s value.

Financial plan Is a statement estimating the amount of capital and determining its composition.

Objectives:

Availability of adequate funds. Balancing of costs and risks. Flexibility. Simplicity. Long term view. Liquidity. Optimum use. Economy.

Considerations

Nature of Industry.

Credit rating of the concern.

Future plans- Expansion and diversification.

Availability of sources.

General economic conditions.

Government control.

Objectives of Financial managementProfit:

Profit earning.Profitability is a barometer for measuring efficiency and economic prosperity of a business.Economic and business conditions do not remain the same all the time.Profits are the main sources of finance for the growth of the business.Profitability is essential for fulfilling social goals.

Wealth: Maximizes the stockholders wealth.

Profit Vs Wealth The term profit is vague.

Ignores the time value of money.

Ignores Risk factor.

Dividend policy.

Its an prescriptive idea.

Not necessarily socially desirable.

Controversy objectives

Maximize stockholders wealth or wealth of firm.

Ownership and management are separated.

Functions of a Finance manager

Financial forecasting and planning.

Acquisition of funds.

Investment of funds.

Helping in valuation decisions.

Maintain proper liquidity.

Functional areas of FM

Determining financial needs.Selecting the source of funds.Financial analysis and Interpretation.C-V-P analysis.Capital budgeting.Working capital management.Profit planning and control.Dividend policy.

Organization of finance function

Board of directors

Managing Director/ Chairman

Director (F)/ VP (F)/ CFO

Treasurer and Controller ( Financial executives)

Responsibilities of FE

The basic responsibility of the treasurer is to provide, manage and protect the firm’s capital.

The basic responsibility of the controller is to check that the funds are used efficiently.

Functions of FE

Treasurer : Obtaining finance Banking relationship Investor relationship Short- term financing Cash management Credit administration Investments Insurance

Functions of FE

Controller: Financial Accounting Internal audit Taxation Management accounting and control Budgeting, planning and control Economic appraisal Reporting to Government

FM Process

FM is a dynamic decision-making process include a series of interrelated activities involving:Financial planningFinancial decision-makingFinancial analysisFinancial control

Concept of Time value of money Value of the money received today is more

than the value of the same amount of money received after a certain period.

Reasons for Time valueHigher preference for present consumption .Purchasing power of the currency declines with time.Money received today can be invested to earn suitable returns.

Reasons for Time Preference of Money

The future is always uncertain and involves risk.

People generally prefer spending than deferring for future.

Money has time value because of opportunities available to invest.

Timeline and Time travel Timeline is a linear representation of the timing of the expected

cash flows. Timelines are an important first step in organizing and then solving a financial problem.

A series of cash flows lasting several periods as a stream of cash flows.

Rules of Time travelOnly cash flows in the same units can be compared or combined at the same point in time.

To move a cash flow forward in time, must compound it.

To move a cash flow backward in time, must use discounting.

Techniques of Time Value of Money

Compounding Technique Interest is compounded when the amount earned on an initial deposit

becomes part of the principal at the end of the first compounding period. Principal refers to the amount of money on which interest is received. n Vn = Vo(1+i) Where Vn = Future value at the period. Vo = Value of money at time 0. i = Interest rate.

Note: If calculations becomes difficult, the future value of money can be calculated with the help of Compound factor tables.

Vn = Vo (CFi,n)

Where CFi,n is compound factor at i percent and n periods.

Simple Interest vs Compound Interest

Interest paid/earned on original amount or on principal borrowed is called the simple interest.

Symbolically P0(i)(n)Where P0 refers to deposit today i.e., t = 0

i refers to interest rate per periodn refers to number of time periods

Compound Interest is the interest paid/earned on any previous interest earned as well as on the principal borrowed.

nSymbolically Po(1+i) - Po

Multiple Compounding Periods

In case the interest is payable on quarterly basis, compounding of interest twice a year say 30th June and 31st December every year. The future value of money in the above said case/cases

mn

Vn = Vo ( 1 + i/m)

Where Vn = Future value of money after n years.

Vo = Value of money at time 0

i = Interest rate

m = Number of times of compounding per year

Multi Period Compounding

The actual rate of interest realised called effective rate in case of multi period compounding is more than the apparent annual rate of interest called nominal rate.

Effective rate of interest is calculated with the following formula:

m

( 1 + i/m) – 1

Where i refers to nominal rate of interest

m refers to frequency of compounding per year

Compounded value of Annuity

Annuity is a series of equal payments lasting for some specified period. When cash flows occur at the end of each period the annuity is called a Regular Annuity or Deferred Annuity. If the cash flows occur at the beginning of each period instead of at the end it is called Annuity Due.

Future value of Annuity:Vn = (R)(ACFi,n)

Future value of Annuity Due: Vn = (R)(ACFi,n)(1 + i)

Problems1. What will be the value of Rs.100 after two years at 10% p.a. Rate of interest if

neither the principal sum of Rs.100 nor interest is withdrawn at the end of one year.

2. From the above calculate the value of Rs.100 @ 10% after ten years.3. If you deposit Rs.1000 in an account earning 7% simple interest for two years.

What is the accumulated interest at the end of the second year?4. Calculate the compound value of Rs.10,000 at the end of third year @ 12%

rate of interest when interest is calculated on yearly and quarterly basis.5. A company offers 12% rate of interest on deposits. What is the effective rate

of interest if the compounding is done half yearly, quarterly and monthly?6. Mr. A deposits Rs.1000 at the end of every year for four years and the deposit

earns a compound interest @ 10% p.a. Determine how much money he will have at the end of four years.

7. year for five years in a bank and the deposit earns a compound Mr. B deposits Rs.5000 at the beginning of each interest @ 8% p.a. Determine how much money he will have at the end of five years?

Discounting or Present Value Technique

Present value shows what the value is today of some future sum of money. The Present Value Technique is known as discounting because the present value of money to be received in future will always be less.

V0 = Vn

1 + iWhere Vn is future value for n period

Vo is present valueNote: When we use discount factors, the present value is calculated by:

Present Value = Future Value x DFi,n

Present Value of an Annuity

If the amount of payment is R, the present value of an annuity can be calculated with the help of annuity discount factor tables.

Vo = (R)(ADFi,n)

Present value of an annuity due:If the cash flows occur at the beginning of each year, the present value of an annuity due is calculated by using present value tables:

Vo = (R)(ADFi,n)(1 + i)

Present value of an Infinite Life Annuity: Vo = R/i

Problems1. Calculate the present value of Rs.1000 to be received after

one year @ 10% time preference rate.2. Mr. X is to receive Rs.5000 after five years @ 10% p.a.

Calculate its present value.3. Calculate present value of the following five years cash

flows assuming a discount rate of 10%. The cash flows for each respective year are Rs.5000, Rs.10,000, Rs.10,000, Rs.3000 and Rs.2000.

4. Mr. X has to receive Rs.2000 per year for five years. Calculate the present value of annuity assuming that he can earn interest on his investment @ 10% p.a.

5. Mr. A has to receive Rs.10,000 at the beginning of each year for five years. Calculate the present value of annuity due assuming 10% rate of interest.

6. Calculate the present value of Rs.1000 received in perpetuity for an infinite period taking discount rate of 10%.

Valuation of SecuritiesBonds with a maturity period:

n

Vd = ∑ Rt + Mn

(1+ Kd)t (1+ Kd)nVd = Value of bondR1, R2 ----- = Annual interest in period 1, 2 & so on.Kd = Required rate of return M = Maturity value of bondn = Number of years to maturity

Note: If n becomes large we use present value tables, formula is Vd = (R)(ADFi,n) + (M)(DFi,n)

Bonds in Perpetuity/DDBsBonds which never mature or have infinite maturity period. The value of such bonds is the discounted value of infinite streams of interest (cash) flows.

Vd = R Kd

Deep Discount Bonds: n

Vddb = FV / ( 1 + r ) OrVddb = (FV) x (DFi,n)

Where Vddb = Value of a deep discount bond FV = Face value at maturity r = Required rate of return n = Number of years to mature / Life of DDB

Problems1. Mr.X is considering the purchase of a 8% Rs.1000 bond

redeemable after 5years at par, required rate of return is 10%. Calculate the amount to be paid for bond.

2. Xltd a company is proposing to issue a 5year debenture of Rs.1000 redeemable in equal instalments@14% interest p.a. If an investor has a minimum required rate of return of 12%, calculate the debentures present value.

3. Mr.A has a perpetual bond of the face value of Rs.1000. He receives an interest of Rs.60 annually. What would be its value if the required rate of return is 10%.

4. Mr.A has a perpetual bond of the face value of Rs.1000. He receives an interest of Rs.60 annually. Its current value is Rs.600. Calculate the yield to maturity.

5. IDBI issued deep discount bond for a maturity period of 20 years and having face value of Rs.100000. Calculate the value of DDB if the required rate of return is 10%.

Valuation of Preference share

1. Mr.A is considering the purchase of a 7% preference share of Rs.1000 redeemable after 5 years at par. What should be the pay now to purchase the share assuming that the required rate of return is 8%.

2. Mr.A has a irredeemable preference share of Rs.1000. He receives an annual dividend of Rs.80 annually. What will be its value if the required rate of return is 10%. ( d/kp)

Valuation of Equity Share Short term investor Po = D1/1+ke + P1/ 1+ke

where Po refers to Current value of the share. D1 Expected dividend P1 Expected price of share ke Required rate of return on equity

Mr.X is planning to buy an equity share for 1 year. The expected dividend is Rs.7 and expected sale proceeds Rs.200. Determine the value of the share assuming the discount rate of 15%.

Note: If in the above case expected dividend and selling price in the second year are Rs.7.50 and Rs.220. calculate value of share.

D is constant The value of share shall be calculated by using annuity

discount factor tables.

Po = (D) (ADFi,n) + (Pn ) (DFi,n)

Mr.X expects a dividend of Rs.5 per share for each of ten years and a selling price of Rs.80 at the end of ten years. Calculate the present value of share if his required rate of return is 12%.

Dividend Valuation Model The concept of this model is that many investors do not

contemplate selling their share in the near future. ∞ tPo = Σ Dt / (1+ke) t=1

No growth: Po = D/Ke

Constant growth: Po = D1 = Do(1+g) Ke - g Ke - g

Where Do is current dividend

D1 is expected dividend

Ke is required rate of return on equity

g is expected percent growth in dividend

Problems

1. A company is expected to pay a dividend of Rs.6 per share. The dividends are expected to grow perpetually at a rate of 9%. What is the value of its share, if the required rate of return is 15%?

2. The current price of a company’s share is Rs.200. The company is expected to pay a dividend of Rs.5 per share with an annual growth rate of 10%. If an investor’s required rate of return is 12%, should he buy the share?

3. The current price of a company’s share is Rs.75 and dividend per share is Rs.5. Calculate the dividend growth rate , if its capitalisation rate is 12%.

Rate of Return on Equity Share

D1 Po =

Ke - g

OR

D1

Ke = Po + g

The expected rate of return re, can be calculated with the following formula:

D1 P1-P0

re = + Po P0

The market price of a share is Rs.80. The company is expected to pay a dividend of Rs.4 and the share can be sold at Rs.88. Calculate return on share. Advise the investor to buy or not if his capitalisation rate is 10%.

What is Cost of Capital?

Is the minimum rate of return expected by its investors.

Is the rate of return that a firm requires to earn from its projects.

Is the minimum rate of return which will at least maintain value of the shares.

Definitions A cut-off rate for the allocation of capital to

investment of projects. It is the rate of return on a project that will leave unchanged the market price of the stock.

Is the minimum required rate of earnings or the cut-off rate of capital expenditures.

The rate of return the firm requires from investment in order to increase the value of the firm in the market price.

Components of Cost of Capital

The expected normal rate of return at zero risk level (ro).

Premium for business risk (b). The premium for financial risk on

account of pattern of capital structure (f).Symbolically: K = ro + b + f

Form of Capital

Debt

Preference Capital

Retained Earnings

Equity Capital

Computation of Cost of Capital

Debt: Cost of debt is the rate of interest payable on debt. Debt may be irredeemable or redeemable.Cost of debt before-tax: Kdb = I/P

Where ‘I’ is interest and ‘P’ is principal.Cost of debt after-tax :

Kda = Kdb(1-t) = I/NP (1-t)Where ‘NP’ refers to Net Proceeds

‘t’ refers to rate of tax

Debt issued at a premium or discount

Net proceeds received from the issue must be considered and not the face value of securities.

Kdb = I/NP 1.Compute cost of debt capital, rate of tax 50% where

X ltd issues Rs.50,000 8% debentures: a) at par.

b) at premium of 10%. c) at discount of 5%.

2. L&T Ltd issues Rs.1,00,000 9% debentures at a premium of 10%. The cost of floatation are 2%. The rate of tax is 60%.Compute cost of debt.

Redeemable debtBefore Tax

I + 1/n(RV-NP)Kdb =

½(RV+NP)

Where ‘I’ is Annual Interest ‘n’ is number of years in which debt

is to be redeemed. ‘RV’ is Redeemable value of debt ‘NP’ is Net proceeds of debentures.

3. A company issues Rs.10,00,000 10% redeemable debentures at a discount 5%. The cost of floatation Rs.30,000.The debentures are redeemable after 5 years. Calculate before –tax assuming tax rate 50%.

Note: calculate after-tax cost of debt.

After Tax I(1-t)+ 1/n(RV-NP)

Kdb = ½(RV+NP)

Cost of Preference Capital It is a function of dividend expected by its investors.

Perpetual Kp = D/P D refers to Annual Preference Dividend

P refers to proceeds

Issued at a discount or premium Kp = D/NP

Redeemable Kpr = D+MV-NP/n

½(MV+NP) MV refers to Maturity value of preference shares. NP refers to Net Proceeds of preference shares.

Problems Zee ltd issues 10,000 10% Preference shares of

Rs.100 each. Cost of issue is Rs.2 per share. Calculate cost of preference capital if these are issued at par, at a premium of 10% and at a discount of 5%.

Lakme ltd issues 10,000 10% preference shares of Rs.100 each redeemable after 10 years at a premium of 5%.The cost of issue is Rs.2 per share. Calculate the cost of preference capital.

Ponds India ltd issues 1,000 7% preference shares of Rs.100 each redeemable after 5years at par. Calculate the cost of preference capital.

Cost of Retained Earnings It is the rate of return which the existing shareholders

can obtain by investing the after-tax dividends in alternative opportunity of equal qualities.

D1

Kr = + G

NP or MP

Where D1 is expected dividend at the end of the year

G is Rate of growth

To make adjustment in the cost of retained earnings for tax and cost of purchasing new securities the following formula is adopted.

Kr = (D/NP + G) (1-t)(1-b) or

Kr = Ke(1-t)(1-b)

Where Ke is rate of return available to shareholders. ‘b’ is cost of purchasing new securities or brokerage costs.

A firm’s return available to shareholders is 15%, the average tax rate of shareholders is 40% and it is expected that 2% is brokerage costs. What is the cost of retained earnings.

Cost of Equity

It refers to the maximum rate of return that the company must earn on equity finance in order to maintain the present market price of the stock.

Dividend yield method: Ke = D/NP or MP

Dividend yield plus growth method:

Ke = (D1/NP + G) = Do(1+g)/NP+G

Problems1. A company issues 1000 equity shares for Rs.100

each at a premium of 10%. A company has been paying 20% dividend for the past five years and expects the same in near future. Compute the cost of equity capital. Will it make any difference if the market price of equity share is Rs.160?

2. A company plans to wish you 1000 new shares of Rs.100 each at par. The flotation costs are expected to be 5% of the share price. The company pays dividend of Rs.10 per share initially and growth in dividends is expected to be 5%. Compute the cost of new issue of equity shares.If the current price of an equity share is Rs.150. Calculate the cost of existing equity share capital.

Weighted average cost of capital

Is the average cost of the costs of various sources of financing.

It lies between the least and most expensive funds. It enables the maximization of profits and the wealth of

the equity shareholders by investing the funds in projects earning excess of the overall cost of capital.

Composite cost of capital or Overall cost of capital or average cost of capital.

Factors affecting WACC Controllable factors. Capital structure policy Dividend policy Investment policy Uncontrollable factors Tax rates Level of Interest rates Market risk premium

Steps involved in computation WACC

Determination of the source of funds to be raised and their individual share in the total capitalisation.

Computation of cost of specific source of funds.

Assignment of weight to specific source of funds.

Multiply the cost of each source by appropriate assigned weights.

Add individual source weight cost to arrive cost of capital.

Assignment of Weights Book value Weights assigned on the basis of values found on the

balance sheet. The book value of the source of fund divided by the book

value of total funds.Merits:1. Simple in calculation.2. Book values provide a usable base, when firm is not listed

or security are not actively traded.3. Analysis of capital structure i.e.,D-E ratioDemerits:1. No relationship between book values and present

economic value of various sources of capital.2. Book value proportions are not consistent with the concept

of cost of capital.

Assignment of Weights Market value:Weights assigned on the basis of market value of the

component of capital.Market value of the component of capital divided by the market

value of all components of capital.Merits:1. Values are closely approximate the actual amount to be

received from their sale, representing the true value of the investors.

2. Prevailing market prices are taken into account.Demerits:1. Very difficult to determine the market values because of

frequent fluctuations.2. Equity capital gets greater importance.3. If the market value of the share is higher than the book

value, WACC would be overstated and vice-versa.

Problems1. Following is the long-term capitalization of a company:

40,000 Equity Shares of Rs.200 each with a market value of Rs.160.

10% Preference Shares (10,000) of Rs.200 each with a market value of Rs.240.

9% Debentures 2000 of Rs.2000 each with a market value of Rs.2200.

Retained earnings Rs.20 Lacs.Additional Information:A flotation cost of 4% was incurred for cash instrument of financing.Redemption premium on debentures is 20%.The current dividend of Rs.10 is expected to grow at 10% to

infinity. The term of maturity of debentures is ten years.The company is taxed at 30%.Preference dividend and Interest are payable annually.Compute Weighted average cost of capital using Market Weights

and Book Weights.

2. A company has the following capital structure at the end of March, 2010.

12% 2007 debentures Rs.15 Lacs. 9% Preference shares Rs.10 Lacs. Equity Shares of Rs.10 each Rs. 12 Lacs.The company has the marginal tax rate of 50%. It

is expected to pay a dividend of Rs.1.50 per share this year and this dividend is expected to grow at the annual rate of 10% in the future.

You are required to find out the firm’s cost of capital from the above given information.

Marginal Cost of Capital Marginal Cost of Capital is calculation of the cost of

additional funds to be raised. Marginal Weights represent the proportion of various

sources of funds to be employed in raising additional funds.Demerits: It ignores the long-term implications of the new

financing plans. Fails in achieving the wealth maximization objective in

the long run.

Capital Asset Pricing Model

This model was developed by William F.Sharpe.

This model explains as to what kind of relationship exists between risk and return namely

Relationship between Risk and Return for an efficient portfolio.

Relationship between Risk and Return for an individual security.

Importance CAPM

It provides a bench mark for evaluating various investments.

It helps us to make an informed guess about the return that can be expected from an asset that has not yet been traded in the market.

Assumptions Investors have same information about securities. Security returns are normally distributed. There are no restrictions on investments. Investors can borrow and lend freely at a riskless rate

of interest. The market is perfect i.e., no taxes, no transaction

costs, securities are completely divisible and market is competitive.

Investors have homogeneous expectations. Investors seek to maximize the expected utility of

their portfolios over a single period planning horizon.

Value of Equity Share

It is a function of cash inflows expected by the investors and the risk associated with cash inflows.

It is calculated by discounting the future stream of dividends at the required rate of return called the Capitalization rate.

The required rate of return depends upon the element of risk associated with investment in shares and is equal to risk-free rate of interest plus the premium for risk.

CAPM The premium for risk is the difference between market

return from a diversified portfolio and the risk-free rate of return ie., beta co-efficient. Ke = Rf + β(Rm – Rf)Where Ke refers to Cost of equity capital

Rf refers to Risk-free rate of return Rm refers to Market return of a diversified portfolio

β refers to Beta co-efficient of the firm’s portfolio.

Problems

1. You are given the following facts about a firm:Risk-free rate of return is 11%.Beta co-efficient of the firm is 1.25.Compute the cost of equity capital using CAPM assuming a market return of 15% next year. What would be the cost of equity if beta rises to 1.75.

2. The Capital Ltd. wishes to calculate its cost of equity capital using CAPM. Company’s analyst found that its risk-free rate of return equals to 12%, beta equals 1.7 and the return on market portfolio equals to 14.5%.

Investment Decisions

Capital budgeting is the process of making investment decisions in capital expenditures.

It is that expenditure incurred at one point of time whereas benefits of expenditure are realised at different points of time in future.

It is concerned with the allocation of the firm’s scarce financial resources among the available market opportunities.

Distinction of capital budgeting decisions

Involves the exchange of current funds for the benefits to be achieved in future.

Future benefits are expected to be realised over a series of years.

Funds invested are in non-flexible and long term activities.

Involve huge funds and are irreversible decisions.

Are strategic investment decisions.

Nature of Investment decisionsLarge investments.

Long-term commitment of funds.

Irreversible in nature.

Long-term effect on profitability.

Difficulties of Investment decisions.

National importance.

Capital budgeting process

Identification on Investment proposals.Screening the proposals.Evaluation of various proposals.Fixing priorities.Final approval and preparation of capital expenditure budget.Implementing proposal.Performance review.

Techniques of Financial Evaluation

Pay-back period. Discounted pay-back. Accounting rate of return. Net present value. Internal rate of return. Profitability Index.

PAY-BACK PERIODThis method throws light as to the length of the period by

which the entire investment would be recouped from out of the future cash flows.

Cash flow means net profit after tax before depreciation. Advantages: Simple to understand and easy to calculate. A project with a shorter pay-back period is preferred

to the one having a longer pay-back period. This method is suited to a firm which has shortage of

cash.

Disadvantages It does not take into account the cash inflows earned

after the pay-back period and hence true profitability of the projects cannot be correctly assessed.

Ignores the time value of money. It does not take into consideration the cost of capital. It treats each asset individually in isolation with other

assets. Cash outlay of the project

PB = Annual Cash inflows

Problems1. There are two projects X and Y. Each project

requires an investment of Rs. 20,000. You are required rank these projects according to PB method. The following are the net profit before depreciation and after tax of the two projects for their respective years. Project X Rs.1000, Rs.2000, Rs.4000, Rs. 5000 and Rs.8000. Project Y, Rs.2000, Rs.4000, Rs.6000, Rs.8000.

2. Calculate discounted pay-back period from the following information:Cost of project Rs.6 Lacs, Life of project 5 years. Annual Cash inflow Rs.2 Lacs, Cut off rate 10%.

Accounting Rate of ReturnThis method takes into account the earnings expected

from the investments over their whole life. Under this method concept of profit is used rather than cash inflows. The term profit refers to net profit after tax and depreciation. The project with higher rate of return is selected.

Average annual profitARR =

Net investment in the project

Merits / DemeritsMerits:

This method is fairly a simple calculation of averages. This method takes calculations of average rate of

return for the entire life of the project by taking the terminal salvage / scrap value.Demerits:

Does not take into account time value of money. It does not take into account the quickness or the

rapidity with which the investment is recouped.

Problems1. A project requires an investment of Rs.5 Lacs and has a scrap

value of Rs.20,000 after five years. It is expected to yield profits after depreciation and taxes during the five years amounting to Rs.40,000, Rs.60,000, Rs.70,000, Rs.50,000 and Rs.20,000. Calculate the average rate of return on the investment.

2. Calculate the average rate of return for projects A and B from the following:

Project A Project BInvestments (Rs.) 20,000 30,000Expected Life (Years) 4 5Projected net income after tax and depreciation:Years 1 2,000 3,000 2 1,500 3,000 3 1,500 2,000 4 1,000 1,000 5 - 1,000If the required rate of return is 12%, which project should be undertaken?

Net Present ValueA rupee in hand today is certainly more valuable than the rupee which is received after a period of time. This method attempts to calculate the return on investments by introducing the factor of time element. The NPV method is based on the fact that the cash flow arising at different periods of time differ in value and are not comparable unless there equivalent present values are formed.Merits:

It recognizes the time value of money It takes into account the earnings over the entire life of the

project and true profitability of the investment proposal can be evaluated.

It takes into consideration the objective of maximum profitability.

Demerits: More difficult to understand and operate. While comparing projects with unequal

investment of funds, NPV may not give good results.

It is not easy to determine the appropriate discount rate.

Problems1. No project is acceptable unless the yield is 10%. Cash

inflows of a certain project along with cash outflows are give below:

Years Outflows Inflows Rs. Rs.

0 1,50,000 - 1 30,000 20,000 2 30,000 3 60,000 4 80,000 5 30,000

The salvage value at the end of the fifth year is Rs.40,000. Calculate NPV.

2. A company is considering investment in a project that costs Rs.2 Lacs. The project has an expected life of five years and zero salvage value. The company uses straight line method of depreciation. The company’s rate of tax is 40%. The estimated earnings before depreciation and before tax from the project are Rs.70,000, 80,000, 1,20,000, 90,000 and 60,000 respectively. You are required to calculate the net present value at 10% and advise the company.

Internal Rate of Return Time adjusted rate of return or discounted cash flow or

discounted rate of return or trial and error yield method.

It is defined as the rate of discount at which the present value of cash inflows is equal to the present value of cash out flows.

Accept the proposal if the IRR is higher than or equal to the minimum required rate of return.

In case of alternative proposals, select the proposal with the highest rate of return as long as the rates are higher than the cutoff rate.

Steps Determine the future net cash flows during the entire

economic life of the project.Net cash inflows are estimated future profits before depreciation but after taxes.

Determine rate of discount at which the PV of cash inflows is equal to PV of cash outflows.a) When annual cash flows are equal:

Calculate PV factor = initial outlay / annual cash flow

Refer PV annuity tables and find out the rate at which the calculated PV factor is equal to the PV given in the table.

Steps

b) When annual cash flows are unequal over the life of the asset. Prepare the cash flow table using an arbitrary assumed

discount rate to discount the net cash flow to the PV. Find out the NPV by deducing the PV of total cash flows. If NPV is positive, apply higher rate of discount. If higher discount rate still gives a positive NPV increase the

discount rate further until NPV becomes negative. If the NPV is negative at this higher rate, the IRR must be

between these two rates.

Merits / DemeritsMerits:

It takes into account time value of money. It considers the profitability of the projects over its

entire life. It provides for uniform ranking of various proposals. It is method which ensures reliable technique of

capital budgeting.Demerits:

It is difficult to understand. It is difficult method of evaluation of investment

proposals. This method assumes that the earnings are re-

invested in the project, which is not justified.

Differences between NPV & IRR

Size disparity Time disparity Projects with unequal lives Re-investment rate assumption

NPV method is a superior to that of IRR.

Profitability Index OR Benefit-Cost Ratio

It is the relationship between present value of cash inflows and outflows. A proposal is acceptable if the PI is greater than one

Problems

1. A company is considering an investment proposal to purchase a machine costing Rs.2,50,000. The machine has life expectancy of five years and has no salvage value. The company’s tax rate is 40%. The firm uses straight line method of depreciation. The estimated cash flows before tax after depreciation are as follows: Rs.60,000, 70,000, 90,000, 1,00,000 and 1,50,000. Calculate pay-back period, average rate of return, NPV and profitability index at 10% discount rate.

2. A company has investment opportunity costing Rs.40,000 with the following expected net cash flow after taxes and before depreciation.

Year Net Cash flow (Rs.)

1 7,000 2 7,000 3 7,000 4 7,000 5 7,000 6 8,000 7 10,000 8 15,000 9 10,000 10 4,000

Using 10% as the cost of capital, determine the following:Pay-back period, NPV and PI at 10% discount factor, IRR with the help of 10% and 15% discount factor.

3. A company can make either of two investments at the beginning of 2010. Assuming required rate of return @ 10% per annum. Evaluate the investment proposals under pay-back period, NPV, IRR, PI and discounted pay-back period.The forecast particulars are given below:

Proposal A Proposal BCost of Investment (Rs.) 20,000 28,000Life (Years) 4 5Scrap Value Nil NilNet Income (after dep & tax) Rs.End of 2010 500 NilEnd of 2011 2,000 3,400End of 2012 3,500 3,400End of 2013 2,500 3,400End of 2014 - 3,400

It is estimated that each of the alternative proposals will require additional networking capital of Rs.2,000 which will be received back in full after the expiry of each project life. Depreciation is provided under straight line method. The present value of Re.1 to be received at the end of each year, at 10% and 14% may be utilized.