Assignment Ist 562 FM Spring 2010

8/8/2019 Assignment Ist 562 FM Spring 2010

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Financial Management (562)

2/20By: M. Hammad Manzoor, MBA HRM-III, 508, 5

thFloor, Continental Trade Centre (CTC), Clifton 08, Karachi. (Roll No. 508195394)

Email: [email protected], Cell: 0321-584 2326

Q. No. 1 (a): Read the following case carefully, and then gives the answer

of the questions given below. The case: Management V/s Shareholder:

The annual shareholders meeting at the Mustafa Company brought some shock to themanagement and the board of directors, when a group of shareholders complained

vigorously about the company's financial policies. However, expressions of

dissatisfaction by one or two shareholders had not been, uncommon in the past, the

company's senior executives were surprised by the degree of support for the protest group

voice by other stockholders.

Shareholder Complaints:The initial target of the complaints was the company's policy of not paying dividend in almost

two years. The chairman of the board, Mr. Salman Mustafa, responded that the company

had been experiencing poor profitability and had needed all available funds to

maintain its investments. Other shareholders rose to complain that the company's policy of

not using borrowed money limited its ability to make investments and pay dividends. Again

the chairman responded, this time citing the need for caution in the way the company was

financed. He gave several examples of multinational companies that had been heavy

borrowers and had recently gone bankrupt. To this another shareholder complained that, if

the company were more aggressive in its investment policies, there would be enough

money for everything. "Until you start taking some chances of new ideas and new products,

our stock prices will continue to go down instead of up. I could have earned more by putting my

money in government bonds", complained the shareholder.

"Admit it", another shareholder shouted, "You increase your wealth with your fancy salariesand fancy offices couldn't careless about us little investors. But then why would you?.Most

of you don't even own stock in the. Company." Losing his temper, the Chairman replied

angrily that his own ancestors had founded the business and still owned almost 10 percent

of the shares outstanding. He added that the company, adding, "And I'm not saying that just

because my son, Ahmed is president. After all, nobody forced you to buy your stock and

nobody's forcing you to keep it. In fact, I would personally be more than happy to buy your

stock from you with my own money. Now I ask the rest of you shareholders", concluded the

Chairman broadly, "would you rather have your company be safe and secure or bankrupt?"

1. Identify the principal financial policies being debated.

2. Considering the perspective of management only, what tendencies do you see in

each of these financial policies?3. Considering the perspective of shareholders only, what tendencies do you sec in

each of these financial policies?

4. The Mustafa Company's creditors are not directly mentioned in the case, but

what do you think their preferences would be with regard to each of the

financial policies?

5. Use some ideas of your own to indicate how Mustafa Company's shareholders


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might persuade management to move in the direction of shareholders'

preferences.

Answer)

The essence of the debate is whether economic recovery and stabilization of the financial

system are two distinct and unconnected events. The prevailing view is something like the

framework within which we need to engineer a global economic recovery is macroeconomics.

Since current macroeconomic theory deals only with Keynesian policy (fiscal and monetary

policy), the only tools we have are fiscal and monetary expansion.

The disposal of non-performing assets and injection of capital are necessary steps in

stabilizing the financial system, but to the best of our knowledge there is no clear link

between this and a macroeconomic recovery. However, if we achieve an economic recovery

through fiscal and monetary policy, the volume of non-performing assets will ease,

eliminating the need for policies specifically designed to dispose of bad assets.

Signs of economic recovery are now emerging and fears of the crisis overwhelming the world

economy are starting to fade. Yet if the policy responses of US and European governments

toward the disposal of non-performing assets begin to falter, the financial systems of Europe

and the US will once again be vulnerable to recurring financial crises, There have been those

who have recognized that cleaning up banks balance sheets and rehabilitating debtors are

necessary preconditions for an economic recovery, but this recognition has been based purely

on empirical principles. The existing theoretical structure of macroeconomics is incapable of

addressing macroeconomic performance and the stability of the financial system in an

integrated context. For example, in the standard New Keynesian or Neoclassicalmacroeconomic models, the economic agents are the household, corporate, and government

sectors, and the financial sector is simply treated as an innocuous veil between these three

sectors. The issue of non-performing assets is invariably viewed as a microeconomic issue

related to the banking industry.

In fact, the crisis we are currently experiencing may call for a change in the theoretical

structure of macroeconomics. In my view, a macroeconomic approach that encompasses

financial intermediaries and places them at the centre of its models is necessary. The new

approach should satisfy three requirements:

The focus should be on the function of financial institutions as media of exchange andthe conditions that might cause payment intermediation to malfunction. Perhaps this

kind of macro model can be built on the framework of the monetary theory of Lagos

and Wright (2005), which explicitly considers the role of money as a medium of

exchange.


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The new macroeconomic approach should provide a unified framework for discussingthe cost and effectiveness of various policy responses to the current global crisis in an

integrated context, in which fiscal policy, monetary policy, and bad asset disposal can

be compared and relative weightings can be given to all three.

To provide a unified framework for policy analysis, the new approach should make iteasy to embed a model of financial crises into the standard business cycle models (i.e.,

the dynamic stochastic general equilibrium models).

I have elsewhere attempted to construct a theoretical model that satisfies these

requirements, in which I assume that assets such as real estate now function as media of

exchange given the development of liquid asset markets but are unable to fulfil this function

during a financial crisis (see Kobayashi 2009a). With a model like this, we can regard a

financial crisis as the disappearance of media of exchange, which triggers a sharp fall in

aggregate demand. In this case, both macroeconomic policy (fiscal and monetary policy) and

bad asset disposals can be understood as responses targeting the same goal restoring theamounts of media of exchange (inside and outside monies).

Thus we can compare and analyze these policies in an integrated context.

Article: Bad asset Disposal should not be left to Financial Community Insiders

If macroeconomic policy and financial stabilization through bad asset disposals are designed to

eradicate the same externality, financial stabilization is not just a problem for the financial

community it is crucial for the recovery of the overall economy.

Therefore, the design and execution of policies capable of disposing of non-performing assets

are not tasks that should be left to financial community insiders. We need to openly discuss

what financial stabilization policies should look like (for practical lessons on the policy package

from Japans experience, see Kobayashi 2008, 2009b). Bad asset disposals including capital

injections for financial institutions (or temporary nationalization) and the rehabilitation of debt-

ridden borrowers must be considered alongside fiscal stimuli and monetary easing, with a new

awareness that they also constitute macroeconomic policies. Perhaps, we need to adopt a new

paradigm of economic thought.

Shareholders or stockholders own parts or shares of companies. In large corporations,shareholders are people and institutions that simply invest money for future dividends and for

the potential increased value of their shares, whereas in small companies they may be the

people who established the business or who have a more personal stake in it. When investors

buy shares of companies, they receive certificates that say how many shares they own. Owning

shares of a company often entitles an investor to a part of the company's profits, which is

issued as a dividend. In addition, shareholders are typically offered a fixed payout per share if

the company is bought out. Because they are partial owners of a company, shareholders are


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receive cash for part or all of their shares. Companies may sell their stocks either through

private placement or public offerings. Private placement is usually limited to large institutions

or a small group of individuals.

Before the rise of the publicly traded corporation, often the families that founded companies

were the shareholders, managers, and members of the board of directors. But because thesecompanies needed to raise increasing amounts of capital to expand, they eventually had to turn

to outside investors. As a result, outside parties quickly became managers and members of the

board. After offering shares to the public, founding family members still retained control of

their corporations in many cases; however, shares also were dispersed among a variety of

investors who had small holdings.

Mustafa Companys shareholders might persuade management to move in the direction of

shareholders preferences.

Managers of a company that focuses on shareholder value will strive to remain abreast of

share-holder interests. Consequently, Andrew Black et al. suggest in In Search of Shareholder

Value that managers must think like entrepreneurs in order to meet shareholders' needs and

add to shareholder value, which may require some refocusing if managers are accustomed to

simply following the directions of their superiors. To create additional shareholder value,

managers must concentrate on a company's primary revenue-generating functions and running

a company as efficiently as possible, which should help a company become a product or service

leader and establish closer ties with consumers. Consequently, managers must begin their

effort to increase shareholder value by identifying the key revenue-generating functions and

then by promoting them.

Furthermore, managers must distinguish between the interests of shareholders who have long-

term interests in a company's worth and those who have short-term interests. Then they muststrive to implement growth strategies that will benefit both kinds of investors insofar as

possible, even though these interests may be in conflict with each other, according to J.P.

Donlon and John Gutfreund. However, this approach has come under the attack of employee

advocates and other critics. In corporate theory, companies traditionally have been viewed

according to the stakeholder model. This model suggests that a company can improve its

financial conditions by attending to the needs and desires of its stakeholders, which include not

only shareholders but also employees, distributors, customers, and so on. Shareholder and

employee interests are sometimes viewed as being at odds with each other, especially around

issues such as layoffs. According to the stake-holder model, managers should weigh the

interests of one group of stakeholders against the interests of another in order to manage acompany fairly. Hence, the shareholder value approach is controversial in that it gives priority

to shareholder needs.

Supporters of the shareholder value approach defend their position by arguing that if a

company is beholden to more than one interest group, then it will face the dilemma of having

to decide between the different groups. If it must decide between competing interests, then

the company must base this decision on some additional reason, but companies are hard-


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pressed to determine what the deciding criterion should be if not increasing shareholder value.

The stakeholder model offers no suggestions. Without a decisive criterion, a company would

constantly face this kind of dilemma, which would drastically slow-down the decision-making

process. Such a dilemma could manifest itself, for example, as a proposal that would increase

shareholder value and meet customer needs, but would result in the reducing the workforce.

However, a company does not ignore the interests of other stakeholders while concentrating

on shareholder value. For example, employees will quit if their interests are not attended to

and customers will patronize the competition if their needs are not met, and so management

inevitably must take their needs into consideration. Finally, advocates of this approach contend

that if a company fails to be profitable, then it will have to close, which would benefit none of

the stakeholders.


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Q. 2 (a) Critically examine the relationship between ROE and ROA. Give

example in support of your answer.

Answer)

Since ROE = ROA (Equity Multiplier) in order for ROE to equal ROA the equity multiplier must be

one. In other words, the total assets to total shareholders' equity ratio must be one. The return

on assets (ROA) percentage shows how profitable a company's assets are in generating

revenue.

ROA can be Computed as:

This number tells you what the company can do with what it has, i.e. how many dollars of

earnings they derive from each dollar of assets they control. It's a useful number for comparing

competing companies in the same industry. The number will vary widely across different

industries. Return on assets gives an indication of the capital intensity of the company, which

will depend on the industry; companies that require large initial investments will generally have

lower return on assets.

Return on Equity:

Return on equity (ROE) measures the rate of return on the ownership interest (shareholders'

equity) of the common stock owners. It measures a firm's efficiency at generating profits from

every unit of shareholders' equity (also known as net assets or assets minus liabilities). ROE

shows how well a company uses investment funds to generate earnings growth.

The Formula:

ROE is equal to a fiscal year's net income (after preferred stock dividends but before commonstock dividends) divided by total equity (excluding preferred shares), expressed as a

percentage. As with many financial ratios, ROE is best used to compare companies in the same

industry. High ROE yields no immediate benefit. Since stock prices are most strongly

determined by earnings per share (EPS), you will be paying twice as much (in Price/Book terms)

for a 20% ROE company as for a 10% ROE company. The benefit comes from the earnings

reinvested in the company at a high ROE rate, which in turn gives the company a high growth

rate. ROE is presumably irrelevant if the earnings are not reinvested.


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Q. 2 (b) What are the five groups of ratios? Give two or three examples of each

kind.

Answer:

These essential financial ratios give you a powerful insight into how your business is doing.Financial ratios help you to measure where your business stands, where its been and where its

heading. They also help you measure yourself against industry benchmarks, and see how youre

tracking against your business plans. There are plenty of ratios to choose from. Here are our top

five.

Gross profit margin Net profit margin Current ratio Inventory turnover Return on owners equity

GROSS PROFIT MARGIN

Your gross profit margin tells you the average gross profit on each dollar of sales before

operating expenses. The equation is simple:

Your gross profit margin will depend on the industry youre in, so its important to measure

yourself against industry benchmarks. Its an essential starting point for assessing theprofitability of each product but it still doesnt tell you whether your business is making a profit

over all. For that you need the net profit margin.

NET PROFIT MARGIN

Your net profit margin is the percentage profit your business makes for every dollar of revenue

whether youre making a profit after covering allof your costs.

Again, your target net profit margin will be at least partly determined by your industry. Some

retailers, for example, run high-volume, low-margin businesses, while others sell a small

number of expensive items with plenty of margin built in.


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Again, your target net profit margin will be at least partly determined by your industry. Some

retailers, for example, run high-volume, low-margin businesses, while others sell a small

number of expensive items with plenty of margin built in.

CURRENT RATIO

Youre making profitable sales but are they enough to cover short term liabilities? To answer

that, you need the current ratio. It helps to measure the solvency of your business by

comparing your current assets (like unpaid invoices) to your current liabilities (unpaid bills and

the like):

As a rule of thumb, you want your current ratio to be 2 or more. In other words, your assets

should be at least double your liabilities, meaning you have plenty of capacity to meet them. If

sales are growing and you have a short operating cycle, a lower number may be OK. But if you

have a long operating cycle, you might want your current ratio to be higher, to make sure

liabilities dont get out of control.

INVENTORY TURNOVER

If you have trading stock, then inventory turnover is an incredibly useful number. It shows you

how many times your business inventory is sold and replaced over a particular period:

So, if youve spent $200,000 buying stock over the year, and you keep an average of $20,000

worth of stock on hand, then your inventory turnover is 10 times a year.

Inventory turnover varies by industry but as a rule of thumb the higher it is the better. A low

turnover indicates you have a lot of money tied up in stock for long periods of time, which is

not good for cash flow. Too high a figure could indicate youre not keeping enough stock on

hand!

RETURN ON OWNERS EQUITY

Return on owners equity compares your net business income to the equity youve invested in

the business. It reveals how much youre making from your investment:


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So if youve invested $200,000 of your own money in the business, but its generating a net

income of $100,000 a year, then your return on owners equity is 50%. This ratio is a great way

to compare what youve earned from your business to what you might have earned from

another investment. If youre just starting up, it might not be as high as youd like, but it tends

to increase over time as your business grows, especially if your personal investment remains

the same.

Q. 2 (c) The most recent income statement of Allied Chemical Ltd is given below.

Prepare a common-size income statement based on this information. Give

interpretation to the standardized net income. What percentage of sales goes to

cost of goods sold?

Allied Corporation

2008 Income Statement

(Rs. In millions)

Sales Rs. 4,053Cost of goods sold 2,780

Depreciation 550___

Earning before interest and taxes Rs. 723

Interest paid 502___

Taxable income Rs. 221

Taxes (34%) 75____

Net income Rs. 146

Dividends Rs. 47

Allied Corporation

Income Statement

For the period Ended 2008Sale 4053 100%

-C.G.S 2780 68.59%

=G.P 1273 31.41%

-Depreciation 550

=Earning before Interest Tax 723

-Interest 502

-Taxable Income 221

-Taxes (34%) 75

=Net Income 146

-Dividends 47=Addition to Retained Earning 99


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Q. 3 (a) Find the amount to which Rs.500 will grow under each of the following

Conditions:

i. 12 percent compounded semi-annually for 5 years.

ii. 12 percent compounded quarterly for 5 years.

Answer)

Given Data:

PV = 500

i = 12%

n = 5%

Fv = Pv (1 + i)n

i. 12% Compounded Semi-Annually for 5 year

Fv = Pv (1 + i )

n

= 500 (1+12/2)5x2

= 500 (1+6 %)10

=500 (1.06)10

= 500 (1.7908)

Fv = 895.40

ii. 12% Compound quarterly for 5 Year

Fv = Pv (1 + i %)nx4

=500 (1+12/4)5x4

=500 (1+.3)20

=500 (1.03)20=500 (1.8061)

Fv = 903.05

iii. 12% Compounded Monthly for 5 Year

Fv =Pv (1 + i %)nx12

=500 (1 + 12/12)5x12

=500 (1 + 1)60

=500 (1.8167)

Fv=908.35

Q. 3 (b) Setup an amortization schedule for Rs.25000 loan to be repaid in equal

installments at the end of the next 5 years. The interest rate is 10 percent.

Pv = 25000

i = 10%

n = 5%


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PvA = FvA (Pvi FAi% ny)

25000 = FvA (Fvi FA10% 5y)

25000 = FvA (3.791)

25000 = FvA

3.791

6595 = FVA (Amortization)

The amortization schedule is as follow:

Year

Balance

Installment

Interest (10 %

x Amount or

Reaming

Balance)

Repayment

of principal

(Payment

Interest)

Principle Ending

0 25000

1 6595 2500 4095 20905

2 6595 2090 4505 16400

3 6595 1640 4955 11445

4 6595 1144 5451 5994

5 6595 601 5994 0

Q. 3 (c) The Moonless Corporation has just paid a dividend of Rs.3 per share. The

dividend of this company grows at a steady rate of 8 percent per year. Based on

this information, what will the dividend be in 5 years?

AnswerDiv = 3

g = 8%

What will the dividend be in 5 Year.

Future Value Dividend

FV=D (1+i)n

Do = 3

D1 = 3 (1.08) = 3.24

D2 = 3.24 (1.08) = 3.50

D3 = 3.50 (1.08) = 3.78

D4 = 3.78 (1.08) = 4.08

D5 = 4.08 (1.08) = 4.41


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Q. 4 (a) Stock A and B have the following probability distributions of expected

future returns:

Probability km kj

0.3 15% 20%0.4 9 5

0.3 8 12

i. Calculate the expected rate of return for the market and Stock A.

ii. Calculate the standard deviations for the market and Stock A.

iii. Calculate the coefficients of variation for the market and Stock A.

STOCK A

Probability

(P)

km (r) Pxr r-r~ (r-r~) (r-r~)x P

0.3 0.15 0.045 0.045 0.002025 0.0006075

0.4 0.09 0.036 -0.015 0.000225 0.00009

0.3 0.08 0.024 -0.0025 0.000625 0.0001875

Pxr = r~0.105=r~ 0.000885

0.000885 = 0.020

STOCK B

Probability(P)

km (r) Pxr r-r~ (r-r~)2 (r-r~)2 x P

0.3 0.20 0.06 0.084 0.007056 0.0021168

0.4 0.05 0.02 -0.066 0.004356 0.0017424

0.3 0.12 0.036 0.004 0.000016 0.0000048

Pxr = r~

0.116=r~ 0.003864

0.003864 = 0.062

STOCK A = r~=0.105, 2=0.000885, =0.02STOCK B = r~=0.116, 2=0.003864, =0.062


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Q. 4 (b)

Rehman has Rs.100,000 to invest in a portfolio containing stock A, stock B, and a

risk free asset. He must invest all of his money. Rehmans goal is to create a

portfolio that has an expected return of 13% and that has only 70% of the

overall market. If A has an expected return of 20%, a beta of 1.3 and the risk-free rate is 7%, how much money will he invest in stock A? Also give

interpretation to the answer.

Answer:

Investment 100000

Expected Return 13%

20%

B = 1.30

R7 = 7%Ki = Rf + B ( Rm - Rf )

20% = 7% + 1.30 ( Rm - 7%)

20% - 7% = 1.30 ( Rm 9.1% )

13% + 9.1% = 1.30 Rm

22-1% = Rm

1.30

20.8% = 20.8% = Rm

Expected Return is small differed from the Market Rate of Return. In stock A invest Rs. 100000.


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Q. 5 (a)

What is the relationship between the required rate of return on an investment

and the cost of capital associated with that investment?

Answer;

Return on capital calculated in a way that takes into account the risks associated with income.

Example: Being able to compare a high-risk, potentially high-return investment with a low-risk,

lower-return investment helps to answer a key question that confronts every investor: is it

worth the risk? There are several ways to calculate risk-adjusted return. Each has its strengths

and shortcomings. All require particular data, such as an investment's rate of return, the risk-

free return rate for a given period, and a market's performance and its standard deviation. The

choice of calculation depends on an investor's focus: whether it is on upside gains or downside

losses.

The two most-used measures for evaluating an investment are the net present value and the

internal rate of return. (Two earlier tutorials discussed these concepts. See the tutorials list for

links to tutorials for discounting future income and the internal rate of return.) It is often

assumed that higher is better for both of the net present value and the internal rate of return.

In particular, it is usually stated that investments with higher internal rates of return are more

profitable than investments with lower internal rates of return. However, this is not necessarily

so. In some situations, an investment with a lower internal rate of return may be better, even

judged on narrow financial grounds, than an investment with a higher internal rate of return.

This interactive lecture explores why and when this reversal takes place. To review, both the

net present value and the internal rate of return require the idea of an income stream, so let's

start there. An income stream is a series of amounts of money. Each amount of money comesin or goes out at some specific time, either now or in the future. The income stream represents

the investment; the income stream is all you need to know for financial evaluation purposes. In

real life, individuals, charitable institutions, and even for-profit businesses have social or other

goals when selecting investments. For businesses, the benefits of community good will are no

less real for being difficult to measure precisely. For enterprises with social as well as financial

goals, the measures discussed here are still useful: They tell you how much it costs you to

advance your social goals. Here is an income stream example, from the interactive lecture

about the internal rate of return.

Year 0 1 2 3 4 5 6

Income amounts -$1000 $200 $200 $200 $200 $200 $200

Here we see seven points in time and, for each, a dollar inflow or outflow. At year 0 (now), the

income amount is negative. Negative income is cost, or outgo. In this example, the negative

income amount in year 0 represents the cost of buying and installing the machine. In the future,


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at years 1 through 6, there will be net income of $200 each year. All of the amounts in the

income stream are net income, meaning that each is income minus outgo, or revenue minus

cost. In year 0, the cost exceeds the revenue by $1000. In years 1 though 6, the revenue will

exceed the cost by $200. This investment evidently has no salvage value. That is, there is

nothing that can be sold in year 6, the last year. If there were, the amount that could be

realized from the sale would be added to the income amount for year 6. For simplicity, all my

examples have the incomes and outgoes at one-year intervals. Real-life investments can have

income and expenses at irregular times, but the principles of evaluation are the same. Now let's

discuss our two measures in connection with this income stream:

Net Present Value

The net present value of an income stream is the sum of the present values of the individual

amounts in the income stream. Each future income amount in the stream is discounted,

meaning that it is divided by a number representing the opportunity cost of holding capital

from now (year 0) until the year when income is received or the outgo is spent. The opportunity

cost can either be how much you would have earned investing the money someplace else, or

how much interest you would have had to pay if you borrowed money. See the interactive

lecture on discounting future income for more explanation. That tutorial has a nifty

spreadsheet setup for calculating present values that you can copy and use in your own

spreadsheet. The word "net" in "net present value" indicates that our calculation includes the

initial costs as well as the subsequent profits. It also reminds us that all the amounts in the

income stream are net profits, revenues minus cost. In other words, "net" means the same as

"total" here. The net present value of an investment tells you how this investment compares

either with your alternative investment or with borrowing, whichever applies to you. A positive

net present value means this investment is better. A negative net present value means your

alternative investment, or not borrowing, is better.Consider again this income stream:

Year 0 1 2 3 4 5 6

Income amounts -$1000 $200 $200 $200 $200 $200 $200

Let's assume that the discount rate (the interest rate that you could earn elsewhere or at which

you could borrow) will not change over the life of the project. This makes the calculation

simpler. With this assumption, we can use the usual formula:

Present Value of any one income amount = (Income amount) / ((1 + Discount Rate)to the a power)

a is the number of years into the future that the income amount will be received (or spent, if

the income amount is negative). The net present value (NPV) of a whole income stream is the

sum of these present values of the individual amounts in the income stream. If we still assume

that income comes or goes in annual bursts and that the discount rate will be constant in the

future, then the NPV has this formula:


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Varying Future Interest Rates

The future interest rate does not have to be constant for this theory to apply. The interest rate

can vary, but that makes the formulas messier. For example, if r1 is the expected interest rate

next year, and r2 is the expected interest rate the year after that, then the present value today

of I2 income in year 2 is I2/(1+r1)(1+r2). The I 's are income amounts for each year. The

subscripts (which are also the exponents in the denominators) are the year numbers, starting

with 0, which is this year. The discount rate assumed to be constant in the future is r. The

number of years the investment lasts is n.

Three properties of the net present value of an income stream are:

1. Higher income amounts make the net present value higher. Lower income amounts make the

net present value lower.2. If profits come sooner, the net present value is higher. If profits come later, the net present

value is lower.

Internal Rate of Return

In the example we've been using, if you keep the income amounts at their original -1000, 200,

200, 200, 200, 200, and 200, and set the discount rate to 0.0547, the net present value

becomes 0. This discount rate, 0.0547 or 5.47%, is the internal rate of return for this investment

it is the discount rate that makes the net present value equal 0. You can try this below, by

setting the discount rate to 0.0547. If you now raise any of the income amounts in years 1

through 6 (feel free to edit an income amount and see for yourself), you will need a higherdiscount rate to bring the net present value back to 0. That would seem to imply that projects

with higher incomes have higher internal rates of return. Similarly, if you lower any of the

income amounts in years 1 through 6, then a lower discount rate will be needed to bring the

net present value back up to 0. That would seem to imply that projects with lower incomes

have lower internal rates of return. These seeming implications are actually often true, if the

projects being compared have about the same shape, with the costs coming early and the

benefits coming late, and if the projects being compared switch from net outgo to net income

at about the same time. Otherwise, though, the implications might not be true.

The NPV Curve

One way to understand how the net present value and the internal rate of return can give

seemingly different advice is to use what I will call the net present value curve, or NPV curve.

The NPV curve shows the relationship between the discount rate and the net present value for

a range of discount rates. The present value at a given discount rate, such as 5%, and the

internal rate of return are each points on the NPV curve. The NPV curve, the relationship

between the discount rate and the net present value has a formula that can be written like this:


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This, of course, is the formula we saw already for the net present value, for annualized costs

and revenues and a constant discount rate. Each I is an income amount for a specific year. The

subscripts (which are also the exponents in the denominators) are the year numbers, startingwith 0, which is this year. The constant discount rate is r. The number of years the investment

lasts is n. In Weeks's study of professionals' incomes, n was about 44, because costs and

incomes were calculated from age 21 to age 65. We'll use an example with an n of 6, so the

formula fits on your screen:

This is our machine investment example that we have been using all along. The NPV is a

function ofr. Graphed, it looks like this:

The blue curve shows the net present value for discount rates (r) from 0 to 0.1 (0% to 10%). The

red dots are the two points we get from our measures. The left red dot shows the net present

value at the discount rate of 0.05 (5%). The right red dot shows the internal rate of return,

because it is where the curve crosses the horizontal line indicating an NPV of 0. That right reddot is between the 0.05 and 0.06 marks on the raxis, so the internal rate of return is between

0.05 and 0.06. (The actual internal rate of return is about 0.0547, as we saw earlier.) Imagine

we have another possible investment, which has this NPV equation:


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This investment is like the first, except that the net profit in years 1 through 6 is $220 per year,

rather than $200. I would say that this investment has a similar "shape" to the first, because the

costs and profits come at the same times. Also, the size of the initial outlay is the same for both.

The only difference is the amount of profit. Here's a graph with both investments on it:

The green curve is the second investment. It is above and parallel to the first investment's blue

curve. The left orange dot shows the net present value of the second investment at the

discount rate of 0.05. The net present value there is a little over $100. This is higher than the

left red dot, so the net present value at r=5% of the green-line investment is higher than the net

present value at r=5% for the blue-line investment. The right orange dot shows where the

second investment's curve crosses the NPV=0 line. This is well to the right of the first

investment's internal rate of return dot. The internal rate of return for the second investment is

much higher (further to the right).

Q. 5 (b)

The earnings, dividends and stock price of Ehsaan technologies Inc. are expected

to grow at 7% per year in the future. Ehsaans common stock sells for Rs.23 per

share, its last dividend was Rs.2.00, and the company will pay a dividend of

Rs.2.14 at the end of the current year.i. What is companys cost of equity?

ii. If the firms beta is 1.6, the risk-free rate is 9%, and the expected return on

the market

is 13%, what will be the firms cost of equity using the CAPM approach?


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Assignment Ist 562 FM Spring 2010

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Transcript of Assignment Ist 562 FM Spring 2010