AssignmentFINANCIAL MANAGEMENT

SET - 1

Q.1 Explicit cost and implicit cost are the two dimensions of cost.What role does cost play in financial decisions?

Ans: - Financing decisions relate to the acquisition of funds at the least cost. Here cost has two dimensions viz explicit cost and implicit cost.

Explicit cost refers to the cost in the form of coupon rate, cost of floating and issuing the securities etc.

Implicit cost is not a visible cost but it may seriously affect the company’s operations especially when it is exposed to business and financial risk. For example, implicit cost is the failure of the organization to pay to its lenders or debenture holders loan installments on due date on account of fluctuations in cash flow attributable to the firms business risk. In India if the company is unable to pay its debts, creditors of the company may use legal means to sue the company for winding up. This risk is normally known as risk of insolvency. A company which employs debt as a means of financing, normally faces this risk especially when its operations are exposed to high degree of business risk.

In all financing decisions a firm has to determine the proportion of equity and debt. The composition of debt and equity is called the capital structure of the firm.

Debt is cheap because interest payable on loan is allowed as deductions in computing taxable income on which the company is liable to pay income tax to the Government of India. For example, if the interest rate on loan taken is 12 %, tax rate applicable to the company is 50 %, and then when the company pays Rs.12 as interest to the lender, taxable income of the company will be reduced by Rs.12.

In other words when actual cost is 12% with the tax rate of 50 % the effective cost becomes 6% therefore, debt is cheap. But, every installment of debt brings along with it corresponding insolvency risk.

Another thing notable in this connection is that the firm cannot avoid its obligation to pay interest and loan installments to its lenders and debentures.

On the other hand, a company does not have any obligation to pay dividend to its shareholders. A company enjoys absolute freedom not to declare dividend even if its profitability and cash positions are comfortable. However, shareholders are one of the stakeholders of the company. They are in reality the owners of the company. Therefore well managed companies cannot ignore the claim of shareholders for dividend. Dividend yield is an important determinant for stock prices. Dividend yield refers to dividend paid with reference to the market price of the shares of the company. An investor in company’s shares has two objectives for investing:

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1. Income from Capital appreciation (i.e. Capital gains on sale of shares at market price)

2. Income from dividends.

It is the ability of the company to give both these incomes to its shareholders that determines the market price of the company’s shares.

The most important goal of financial management is maximisation of net wealth of the shareholders. Therefore, management of every company should strive hard to ensure that its shareholders enjoy both dividend income and capital gains as per the expectation of the market. But, dividend is declared out of the profit earned by the company after paying income tax to the Govt of India.

For example, let us assume the following facts:

Dividend = 12 % on paid up value

Tax rate applicable to the company = 30 %

Dividend tax = 10 %

When a Company pays Rs.12 on paid up Capital of Rs.100 as dividend, the profit that the company must earn before tax is:

Since payment of dividend by an Indian Company attracts dividend tax, the company when it pays Rs.12 to shareholders, must pay to the Govt of India

10 % of Rs.12 = Rs.1.2 as dividend tax. Therefore dividend and dividend tax sum up to 12 + 1.2 = Rs.13.2.

Since this is paid out of the post tax profit, in this question, the company must earn:

Therefore, to declare a dividend of 12 % Company has to earn a pre tax profit of 19 %. On the other hand, to pay an interest of 12 % Company has to earn only 8.4 %. This leads to the conclusion that for every Rs.100 procured through debt, it costs 8.4 % where as the same amount procured in the form of equity (share capital) costs 19 %. This confirms the established theory that equity is costly but debt is a cheap but risky source of funds to the corporate.

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The challenge before the finance manager is to arrive at a combination of debt and equity for financing decisions which would attain an optimal structure of capital. An optimal structure is one that arrives at the least cost structure, keeping in mind the financial risk involved and the ability of the company to manage the business risk. Besides, financing decision involves the consideration of managerial control, flexibility and legal aspects. As such it involves quite a lot of regulatory and managerial elements in financing decisions.

2. Assume you are newly appointed as Finance Executive in a Manufacturing firm. What guidelines you need to follow in financial planning?

Ans: - Financial Planning is a process by which funds required for each course of action is decided. It must consider expected business Scenario and develop appropriate courses of action. A financial plan has to consider Capital Structure, Capital expenditure and cash flow. In this connection decisions on the composition of debt and equity must be taken.

Financial planning generates financial plan. Financial plan indicates:

1. The quantum of funds required to execute business plan

2. Composition of debt and equity, keeping in view the risk profile of the existing business, new business to be taken up and the dynamics of capital market conditions.

3. Formulation of policies for giving effect to the financial plans under consideration.

A financial plan is at the core of value creation process. A successful value creation process can effectively meet the bench marks of investor’s expectations.

Benefits that accrue to a firm out of the financial planning

1. Effective utilization of funds: Shortage is managed by a plan that ensures flow of cash at the least cost. Surplus is deployed through well planned treasury management. Ultimately the productivity of assets is enhanced.

2. Flexibility in capital structure is given adequate consideration. Here flexibility means the firms ability to change the composition of funds that constitute its capital structure in accordance with the changing conditions of capital market. Flexibility refers to the ability of a firm to obtain funds at the right time, in the right quantity and at the least cost as per requirements to finance emerging opportunities

3. Formulation of policies and instituting procedures for elimination of all types of wastages in the process of execution of strategic plans.

4. Maintaining the operating capability of the firm through the evolution of scientific replacement schemes for plant and machinery and other fixed assets.

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This will help the firm in reducing its operating capital. Operating capital refers to the ratio of capital employed to sales generated. A perusal of annual reports of Dell computers will throw light on how Dell strategically minimized the operating capital required to support sales. Such companies are admired by investing community.

5. Integration of long range plans with the shortage plans.

As a Finance Executive I will follow the following Guidelines for financial planning:

1. Never ignore the coordinal principle that fixed asset requirements be met from the long term sources.

2. Make maximum use of spontaneous source of finance to achieve highest productivity of resources.

3. Maintain the operating capital intact by providing adequately out of the current periods earnings. Due attention to be given to physical capital maintenance or operating capability.

4. Never ignore the need for financial capital maintenance in units of constant purchasing power.

5. Employ current cost principle wherever required.

6. Give due weightage to cost and risk in using debt and equity.

7. Keeping the need for finance for expansion of business, formulate plough back policy of earnings.

8. Exercise thorough control over overheads.

9. Seasonal peak requirements to be met from short term borrowings from banks.

Q.3. Due to over capitalization the company may collapse which would certainly affect it Employees, society, consumers and its Shareholders. What remedies you would suggest? Give suitable Example.

Ans:-A company is said to be overcapitalized, when its total capital (both equity and debt) exceeds the true value of its assets. It is wrong to identify overcapitalization with excess of capital because most of the overcapitalized firms suffer from the problems of liquidity. The correct indicator of overcapitalization is the earnings capacity of the firm. If the earnings of the firm are less then that of the market expectation, it will not be in a position to pay dividends to its shareholders as per their expectations. It is a sign of overcapitalization. It is also possible that a company has more funds than its requirements based on current operation levels, and yet have low earnings.

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Overcapitalization may be on account of any of the following:

1. Acquiring assets at inflated rates

2. Acquiring unproductive assets.

3. High initial cost of establishing the firm

4. Companies which establish their new business during boom condition are forced to pay more for acquiring assets, causing a situation of overcapitalization once the boom conditions subside.

5. Total funds requirements have been over estimated.

6. Unpredictable circumstances (like change in import – export policy, change in market rates of interest, changes in international economic and political environment) reduce substantially the earning capacity of the firm. For example, rupee appreciation against U.S.dollar has affected earning capacity of firms engaged mainly in export business because they invoice their sales in US dollar.

7. Inadequate provision for depreciation adversely affects the earning capacity of a company , leading to overcapitalization of the firm.

8. Existence of idle funds.

Effects of over capitalization

1. Decline in the earnings of the company.

2. Fall in dividend rates.

3. Market value of company’s share falls, and company loses investors confidence.

4. Company may collapse at any time because of anemic financial conditions – it will affect its employees, society, consumers and its shareholders. Employees will lose jobs. If the company is engaged in the production and marketing of certain essential goods and services to the society, the collapse of the company will cause social damage.

Remedies for Overcapitalization:

Restructuring the firm is to be executed to avoid the situation of company becoming sick.

It involves

1. Reduction of debt burden.

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2. Negotiation with term lending institutions for reduction in interest obligation.

3. Redemption of preference shares through a scheme of capital reduction.

4. Reducing the face value and paid-up value of equity shares.

5. Initiating merger with well managed profit making companies interested in taking over ailing company.

4. a. Mr.Avinash aged 40 years, needs 50000 after 5 years. If the interest rate is 10% how much should he save now to get Rs.50000 at the end of 5 years.

Ans:

PV = FV n or FV (PVIF)

(1+i) 5.10

= 50000(0.621)

= 31,050

Mr.Avinash has to Invest Rs.31,050/- now to get Rs.50,000/- after 5 years

4. b. Senior citizen intents to deposit Rs.1000 annually in ICICI bank for 3 years. The prevailing interest rate is 10%. What is the maturity value of the deposit?

Year AmountNo. of Yrs. Compounded

CVIF @ 10% FV

1 1000 4 1.466 14642 1000 3 1.331 13313 1000 2 1.210 12104 1000 1 1.100 11005 1000 0 1.000 1000  5000     6105

OR

FV= PV (FVIFA)5.10%

= 1000(6.105)

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= 6105=00

So, the Maturity value is MV=Rs.6,105/- after 5 yrs

Q.5. Explain various types of bonds

Ans: - Types of BondsBonds are of three types: (a) Irredeemable Bonds (also called perpetual bonds) (b) Redeemable Bonds (i.e., Bonds with finite maturity period) and (c) Zero Coupon Bonds.

Irredeemable Bonds or Perpetual Bonds

Bonds which will never mature are known as irredeemable or perpetual bonds. Indian Companies Acts restricts the issue of such bonds and therefore these are very rarely issued by corporate these days. In case of these bonds the terminal value or maturity value does not exist because they are not redeemable. The face value is known; the interest received on such bonds is constant and received at regular intervals and hence the interest receipts resemble perpetuity. The present value (the intrinsic value) is calculated as:

V0=I/id

If a company offers to pay Rs. 70 as interest on a bond of Rs. 1000 par value, and the current yield is 8%, the value of the bond is 70/0.08 which is equal to Rs. 875

Redeemable Bonds :

There are two type’s viz., bonds with annual interest payments and bonds with semi-annual interest payments.

Bonds with annual interest payments;

Basic Bond Valuation Model:

The holder of a bond receives a fixed annual interest for a specified number of years and a fixed principal repayment at the time of maturity. The intrinsic value or the present value of bond can be expressed as:

This can also be stated as folloows

V0=I*PVIFA(kd, n) + F*PVIF(kd, n)

Where V0 = Intrinsic value of the bond

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P0 = Present Value of the bond

I = Annual Interest payable on the bond

F = Principal amount (par value) repayable at the maturity time

N = Maturity period of the bond

Kd = Required rate of return

Example: A bond whose face value is Rs. 100 has a coupon rate of 12% and a maturity of 5 years. The required rate of interest is 10%. What is the value of the bond?

Solution:

Interest payable = 100*12% = Rs. 12

Principal repayment is Rs. 100

Required rate of return is 10%

V0=I*PVIFA (kd, n) + F*PVIF (kd, n)

Value of the bond = 12*PVIFA (10%, 5y) + 100*PVIF (10%, 5y)

= 12*3.791 + 100*0.621

= 45.49+62.1

= Rs. 107.59

Example: Mr. Anant purchases a bond whose face value is Rs. 1000, maturity period 5 years coupled with a nominal interest rate of 8%. The required rate of return is 10%. What is the price he should be willing to pay now to purchase the bond?

Solution:

Interest payable=1000*8%=Rs. 80

Principal repayment is Rs. 1000

Required rate of return is 10%

V0=I*PVIFA(kd, n) + F*PVIF(kd, n)

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Value of the bond = 80*PVIFA(10%, 5y) + 1000*PVIF(10%, 5y)

= 80*3.791 + 1000*0.621

= 303.28 + 621

= Rs. 924.28

This implies that the company is offering the bond at Rs. 1000 but is worth Rs. 924.28 at the required rate of return of 10%. The investor may not be willing to pay more than Rs. 924.28 for the bond today.

Bond Values with Semi-Annual Interest payment:

In reality, it is quite common to pay interest on bonds semi-annually. With the effect of compounding, the value of bonds with semi-annual interest is much more than the ones with annual interest payments. Hence, the bond valuation equation can be modified as:

It is to be kept in mind that the required rate of return is halved (12%/2) and the period doubled (6y*2) as the interest is paid semi-annually.

Valuation of Zero Coupon Bonds:

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In India Zero coupon bonds are alternatively known as Deep Discount Bonds. For close to a decade, these bonds became very popular in India because of issuance of such bonds at regular intervals by IDBI and ICICI. Zero-coupon bonds have no coupon rate, i.e. there is no interest to be paid out. Instead, these bonds are issued at a discount to their face value, and the face value is the amount payable to the holder of the instrument on maturity. The difference between the discounted issue price and face value is effective interest earned by the investor. They are called deep discount bonds because these bonds are long term bonds whose maturity some time extends up to 25 to 30 years.

Example:

River Valley Authority issued Deep Discount Bond of the face value of Rs.1,00,000 payable 25 years later, at an issue price of Rs.14,600. What is the effective interest rate earned by an investor from this bond?

Solution:

The bond in question is a zero coupon or deep discount bond. It does not carry any coupon rate. Therefore, the implied interest rate could be computed as follows:

Step 1. Principal invested today is Rs.14600 at a rate of interest of “r”% over 25 years to amount to Rs.1,00,000.

Step 2. It can be stated as A = P0 (1+r)n

1,00,000 = 14,600 (1+r)25

Solving for ‘r’, we get 1,00,000/14600 = (1+r)25

6.849 = (1+r)25

Reading the compound value (FVIF) table, horizontally along the 25 year line, we find ‘r’ equals 8%. Therefore, bond gives an effective return of 8% per annum

Q.6. Sushma Industries wishes to issue bonds with Rs.100 as par value, 5 years to maturity, coupon rate 11% and YTM of 11%

a) What the value of the bond?b) If the YTM is 10% what would be the value of the bond?c) If the YTM is 13% what is the value of the bond?

Ans: a)F = 100n = 5Kd = 11%I = 11%

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VB = Value of Bond = I X PVIFA (Kd.n) + F X PVIF (Kd. N) 11 5 11 5

= 11*3.696 + 100*0.593

= 40.65 + 59.30 = 99.96 or 100

So, Bond Value is Rs.100/-

b)

F = 100n = 5Kd = 10%I = 11%

VB = Value of Bond = I X PVIFA (Kd.n) + F X PVIF (Kd. N) 10 5 10 5

= 11*3.791 + 100*0.621

= 41.70 + 62.10 = 124.20 or 124

So, Bond Value is Rs.124/-

c)

F = 100n = 5Kd = 13%I = 11%

VB = Value of Bond = I X PVIFA (Kd.n) + F X PVIF (Kd. N) 13 5 13 5

= 11*3.517 + 100*0.543

= 38.687 + 54.30 = 92.98 or 93

So, Bond Value is Rs.93/-

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AssignmentFinancial Management

Set - 2

Q.1. Is Equity Capital Free of cost? Substantiate your statement.

Ans: - Equity shareholders do not have a fixed rate of return on their investment. There is no legal requirement (unlike in the case of loans or debentures where the rates are governed by the deed) to pay regular dividends to them. Measuring the rate of return to equity holders is a difficult and complex exercise. There are many approaches for estimating return – the dividend forecast approach, capital asset pricing approach, realized yield approach, etc. According to dividend forecast approach, the intrinsic value of an equity share is the sum of present values of dividends associated with it.

Ke = (D1/Pe) + g

This equation is modified from the equation Per= {D1/Ke-g}. Dividends cannot be accurately forecast as they may sometimes be nil or have a constant growth or sometime supernormal growth periods.

Is Equity Capital free of cost?

Not legally bound to pay dividends and also the rate of equity dividend is not fixed like Some people are of the opinion that equity capital is free of cost for the reason that a company is preference dividends. This is not a correct view as equity shareholders buy shares with the expectation of dividends and capital appreciation. Dividends enhance the market value of shares and therefore equity capital is not free of cost.

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Example: Suraj Metals are expected to declare a dividend of Rs. 5 per share and the growth rate in dividends is expected to grow @ 10% p.a. The price of one share is currently at Rs. 110 in the market. What is the cost of equity capital to the company?

Solution:

Ke = (D1/Pe) + g

= (5/110) + 0.10

= 0.1454 or 14.54%

Q.2.a. What is the rate of return for a company if the β is 1.25, risk free rate of return is 8% and the market rate of return is 14%. Use CAPM model.

b. Sundaram Transports has the following capital structure.

Equity capital Rs.10 par value 250 lakhs12% preference share capital Rs.100 each

100 lakhs

Retained earnings 150 lakhs12% Debentures (Rs.100 each) 350 lakhs14% Term loan from SBI 150 lakhsTotal 1000 lakhs

The market price per equity is Rs 54. The company is expected to declare a dividend per share of Rs.2 per share and there will be a growth of 10% in the dividends for the next 5 years. The preference shares are redeemable at a premium of Rs.5 per share after 8 years. The current market price of preference share is Rs.92. Debenture redemption will take place after 7 years at a discount of 2% and the current market price is Rs.91 per debenture. The corporate tax rate is 40%. Calculate WACC.

Ans: (a)

β=1.25RFR=8%RRR=18%What is the rate of return of the Company?E(rp = rf + β (rm-rf)where, rm= Expected rate of return of the Portfolio rf= Risk free return rp= Required rate of return18%= 8% + 1.2 (rm-8%)

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rm = 8 %+( 18%-8%)  

1.2 = 8%+10%

= 18%

= 15%

1.2 1.2So, rm = 15%

2 (b):

(a)

Cost of Equity Capital

Ke = D1

+gwhere D1=2

Pe Pe=Mp=54 g = 10%

= 2 +10%

54

=0.0370+0.10 = 0.1370X100 (%)

= 13.70%(b)

Cost of Debt/Preference Capital

Kp =

D+(F-P/N)(F+P/2)where D= Dividend = 12% F=100+5=105

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P = MP/NP = 92 N= 8 Yrs

Kp =

12+(105-92/8)

(105+92/2)

=

12+1.625 = 0.1383 X 100 =13.83%

98.5(c)

Cost of Debt/Debenture

Kd = I(1-T)+(F-P/N)(F+P/2)where T= Corp.tax = 40% N= 7 Yrs F=MP=100-2=98 P = 91 I = 12%

Kd = 12(1-40%)+(98-91/7)

(98+92/2)

=12(1-0.40)+1 =

7.2+1/97.5= 0.0841 X100

97.5 = 8.41%(d)

Cost of Term LoanKt = i(1-T) where, T = cost of tax - 40% & i= Interest 14%

= I ( 1-0.40) = 14% (0.60) = 0.14+(0.60 ) = 0.14 x 100 = 14%Calculate the weights if each source & multiply by cost of each sourcea) 250/1000 = 0.25 X 0.1370 = (0.03425)

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b) 100/1000 = 0.10 X 0.1383 = (0.01383)c) 350/1000 = 0.35 X 0.0841 = (0.02943)d) 150/1000 = 0.15 X 0.1400 = (0.02100)

= (0.09851) = 0.9851 X 100

= 9.85% The WACC= 9.85%

Q.3. the effective cost of debt is less than the actual interest payment made by the firm. Do you agree with this statement? If yes/no substantiate your views.

Ans:-The debentures carry a fixed rate of interest. Interest qualifies for tax deduction in determining tax liability. Therefore the effective cost of debt is less than the actual interest payment made by the firm.

The cost of term loan is computed keeping in mind the tax liability.

The cost of preference share is similar to debenture interest. Unlike debenture interest, dividends do not qualify for tax deductions.

The calculation of cost of equity is slightly different as the returns to equity are not constant.

The cost of retained earnings is the same as the cost of equity funds.

Solved Problems

1. Deepak steel has issued non-convertible debentures for Rs. 5 Cr. Each debenture is of a par value of Rs. 100 carrying a coupon rate of 14%. Interest is payable annually and they are redeemable after 7 years at a premium of 5%. The company issued the NCD at a discount of 3%. What is the cost of debenture to the company? Tax rate is 40%.

Solution:

= 0.094 or 9.4%

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Q.4. Why capital budgeting decision very crucial for finance managers?

Ans:-There are many reasons that make the Capital budgeting decisions the most crucial for finance managers

1) These decisions involve large outlay of funds now in anticipation of cash flows in future. For example, investment in plant and machinery. The economic life of such assets has long periods. The projections of cash flows anticipated involve forecasts of many financial variables. The most crucial variable is the sales forecast.

a. For example, Metal Box spent large sums of money on expansion of its production facilities based on its own sales forecast. During this period, huge investments in R & D in packaging industry brought about new packaging medium totally replacing metal as an important component of packing boxes. At the end of the expansion Metal Box Ltd found itself that the market for its metal boxes had declined drastically. The end result is that metal box became a sick company from the position it enjoyed earlier prior to the execution of expansion as a blue chip. Employees lost their jobs. It affected the standard of living and cash flow position of its employees.

This highlights the element of risk involved in these type of decisions.

b. Equally we have empirical evidence of companies which took decisions on expansion through the addition of new products and adoption of the latest technology creating wealth for shareholders. The best example is the Reliance group.

c. Any serious error in forecasting Sales and hence the amount of capital expenditure can significantly affect the firm. An upward bias may lead to a situation of the firm creating idle capacity, laying the path for the cancer of sickness.

d. Any downward bias in forecasting may lead the firm to a situation of losing its market to its competitors. Both are risky fraught with grave consequences.

2. A long term investment of funds some times may change the risk profile of the firm. A FMCG company with its core competencies in the business decided to enter into a new business of power generation. This decision will totally alter the risk profile of the business of the company. Investor’s perception of risk of the new business to be taken up by the company will change his required rate of return to invest in the company. In this connection it is to be noted that the power pricing is a politically sensitive area affecting the profitability of the organization. Therefore, Capital budgeting decisions change the risk dimensions of the company and hence the required rate of return that the investors want.

3. Most of the Capital budgeting decisions involve huge outlay. The funds requirements during the phase of execution must be synchronized with the flow of funds. Failure to achieve the required coordination between the inflow and outflow

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may cause time over run and cost over run. These two problems of time over run and cost over run have to be prevented from occurring in the beginning of execution of the project. Quite a lot empirical examples are there in public sector in India in support of this argument that cost over run and time over run can make a company’s operations unproductive. But the major challenge that the management of a firm faces in managing the uncertain future cash inflows and out flows associated with the plan and execution of Capital budgeting decisions.

4. Capital budgeting decisions involve assessment of market for company’s products and services, deciding on the scale of operations, selection of relevant technology and finally procurement of costly equipment. If a firm were to realize after committing itself considerable sums of money in the process of implementing the Capital budgeting decisions taken that the decision to diversify or expand would become a wealth destroyer to the company, then the firm would have experienced a situation of inability to sell the equipments bought. Loss incurred by the firm on account of this would be heavy if the firm were to scrap the equipments bought specifically for implementing the decision taken. Sometimes these equipments will be specialized costly equipments. Therefore, Capital budgeting decisions are irreversible.

5. The most difficult aspect of Capital budgeting decisions is the influence of time. A firm incurs Capital expenditure to build up capacity in anticipation of the expected boom in the demand for its products. The timing of the Capital expenditure decision must match with the expected boom in demand for company’s products. If it plans in advance it may effectively manage the timing and the quality of asset acquisition. But many firms suffer from its inability to forecast the future operations and formulate strategic decision to acquire the required assets in advance at the competitive rates.

6. All Capital budgeting decisions have three strategic elements. These three elements are cost, quality and timing. Decisions must be taken at the right time which would enable the firm to procure the assets at the least cost for producing the products of required quality for customer. Any lapse on the part of the firm in understanding the effect of these elements on implementation of Capital expenditure decision taken, will strategically affect the firm’s profitability.

7. Liberalization and globalization gave birth to economic institutions like World Trade organization. General Electrical can expand its market into India snatching the share already enjoyed by firms like Bajaj Electrical or Kirloskar Electric Company. Ability of G E to sell its products in India at a rate less than the rate at which Indian Companies sell cannot be ignored. Therefore, the growth and survival of any firm in today’s business environment demands a firm to be pro-active. Pro-active firms cannot avoid the risk of taking challenging Capital budgeting decisions for growth. Therefore, Capital budgeting decisions for growth have become essential characteristics of successful firms today.

8. The social, political, economic and technological forces generate high level of uncertainty in future cash flows streams associated with Capital budgeting decisions. These factors make these decisions highly complex.

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9. Capital expenditure decisions are very expensive. To implement these decisions, firms will have to tap the Capital market for funds. The composition of debt and equity must be optimal keeping in view the expectation of investors and risk profile of the selected project.

Q.5 A road project require an initial investment of Rs.10,00,000. It is expected to generate the following cash flow in the form of toll tax recovery.

Year Cash Inflows

d) 4,50,000

e) 4,25,000

f) 3,00,000

g) 3,50,000

What is the IRR of the project?Ans:Year Cash Flows (Rs.)

1 4,50,0002 4,25,0003 3,00,0004 3,50,000

Total 14,75,000

Average of 4 yeas = 14,75,000/4 = 3,68,750/-

Divide the initial outlay by Avg. Cash flow-i.e.- 10,00,000/3,68,750 = 2.711 

As per PVIFA Table for 4 years, the annuity factor is very near to 29% on 2.711, try this for ACF

Year Cash Flow PV factor 29%PV of Cash

flow1 4,50,000 0.775 3,48,7502 4,25,000 0.601 2,25,4253 3,00,000 0.466 1,39,8004 3,50,000 0.361 1,26,350

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8,40,325

Since PV C 29% comes only to 8, 40,325/-, lower rate of discount is to be considered.i.e.- 25% and 22%

Year Cash Flow PV factor 25% PV factor 22%PV of Cash flow

PV of Cash flow

1 4,50,000 0.800 0.820 3,60,000 3,69,0002 4,25,000 0.640 0.672 2,72,000 2,85,0003 3,00,000 0.512 0.551 1,53,600 1,65,300

4 3,50,000 0.410 0.451 1,43,500 1,57,8509,29,100 9,77,150

Since PV C 22% comes only to 9,29,100/-, lower rate if Discount to be considered

Year Cash Flow PV factor 20%PV of Cash

flow1 4,50,000 0.833 3,74,8502 4,25,000 0.694 2,94,9503 3,00,000 0.579 1,73,7004 3,50,000 0.482 1,68,700

10,12,200

The PV at 20% comes to 10,12,200 which is more or less equal to the initial investment,the Internal Rate of Return (IRR) may be taken as 20%In order to have the exactness of IRR can be interpolated as done here:

PV required = 10,00,000

PVC 20% = 10,12,000 -i.e.-+(12,000)

PVC 22% = 9,77,150 -i.e.--(22,850)

Therefore, Actual IRR = 20 + 12,200X 212,200-(-

22850)

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= 20 + 12,200 X 235,050

= 20 + (.348X 2)

= 20 + 0.696 =20.69%

So, IRR = 20.69%

Q.6.What is sensitivity analysis? Mention the steps involved in it.

Ans: - There are many variables like sales, cost of sales, investments, tax rates etc which affect the NPV and IRR of a project. Analyzing the change in the project’s NPV or IRR on account of a given change in one of the variables is called Sensitivity Analysis. It is a technique that shows the change in NPV given a change in one of the variables that determine cash flows of a project. It measures the sensitivity of NPV of a project in respect to a change in one of the input variables of NPV.

The reliability of the NPV depends on the reliability of cash flows. If fore casts go wrong on account of changes in assumed economic environments, reliability of NPV & IRR is lost. Therefore, forecasts are made under different economic conditions viz pessimistic, expected and optimistic. NPV is arrived at for all the three assumptions.

Following steps are involved in Sensitivity analysis:

1. Identification of variables that influence the NPV & IRR of the project.

2. Examining and defining the mathematical relationship between the variables.

3. Analysis of the effect of the change in each of the variables on the NPV of the project.

Example: A company has two mutually exclusive projects under consideration viz project A & project B.Each project requires an initial cash outlay of Rs. 3, 00,000 and has an effective life of 10 years. The company’s cost of capital is 12%. The following four costs of cash flows are made by the management

Economic Project A Project BEnvironment Annual cash

inflowsAnnual cash in flows

Pessimistic 65,000 25,000Expected 75,000 75,000Optimistic 90,000 1,00,000

What is the NPV of the project?

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Which project should the management consider?

Given PVIFA = 5.650

Answer / Solutions

NPV of project A

Economic Project PVIFA PV of cash in flows

NPV

Environment

cash inflows

at 12% 10 years

   

Pessimistic 65,000 5.650 3,67,250 67,250Expected 75,000 5.650 4,23,750 1,23,750Optimistic 90,000 5.650 5,08,500 2,08,500

NPV of Project B

Pessimistic 25,000 5.650 1,41,250 (1,58,750)

Expected 75,000 5.650 4,23,750 1,23,750Optimistic 1,00,000 5.650 5,65,000 2,65,000

Decision

1. Under pessimistic conditions project A gives a positive NPV of Rs. 67,250 and Project B has a negative NPV of Rs. 1,58,750 Project A is accepted.

2. Under expected conditions, both gave some positive NPV of Rs. 1, 23,000. Any one of two may be accepted.

3. Under optimistic conditions Project B has a higher NPV of Rs 2, 65,000 compared to that of A’s NPV of Rs 2,08,500.

4. Difference between optimistic and pessimistic NPV for Project A is Rs. 1, 41,250 and for Project B the difference is Rs 4, 23,750.

5. Project B is risky compared to Project ‘A’ because the NPV range is of large difference.

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