Management the financial resources of firm

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Topic 1. Introduction to Management of Financial Resources

The field of finance. In business, financial guidelines determine how money is raised and spent. Although raising and spending money may sound simple, financial decisions affect every aspect of a business - from how many people a manager can hire, to what products a company can produce, to what investments a company can make.

Money continually flows through business. It may flow in from banks, from the government, from the sale of stock, and so on, and it may flow out for a variety of reasons - to invest in bonds, to buy new equipment, or to hire topnotch employees. Business must pay constant attention to ensure that the right amount of money is available at the right time for the right use.

Finance has three main career paths: financial management, financial markets and institutions, and investments. Financial management involves managing the finance of a business. It is essentially a combination of accounting and economics. First, financial managers use accounting information - balance sheets, income statements, and so on - to analyze, plan, and allocate financial resources for business firms. Second, financial managers use economic principles to guide them in making financial decisions that are in the best interest of the firm. In other words, finance is an applied area of economics that relies on accounting for input.

Because, finance looks closely at the question of what adds value to a business, financial managers are central to most businesses. They measure the firm's performance, determine what the financial consequences will be if the firm maintains its present course or changes it, and recommend how the firm should use the assets. Financial managers also locate external financing sources and recommend the most beneficial mix of financing sources, and they determine the financial expectations of the firm's owners.

The basic financial goals of the firm. The financial manager's basic job is to make decisions that add value to the firm. When asked what the basic goal of a firm is, many people will answer, “to make a lot of money” or “to maximize profits.” While no one will argue that profits aren't important, the single-minded pursuit of profits is not necessarily good for the firm and its owners. We will explain why this is so in the sections that follows. For now, let's say that a better way to express the primary financial goal of a business firm is to “maximize the wealth of the firm's owners.” Everything the financial manager does - indeed, all the actions of everyone in the firm - should be directed toward this goal.

Now, what do we mean by wealth? Wealth refers to value. If a group of people owns a business firm, the contribution that firm makes to that group's wealth is determined by the market value of that firm. This is a very important point: we have defined wealth in terms of value. The concept of value, then, is a fundamental importance in finance.

The next question is how to measure the value of the firm. The value of a firm is determined by whatever people are willing to pay for it. The more valuable people think a firm is, the more they will pay to own it. Then the existing owners can sell it to investors for more than their original purchase price, thereby increasing current stockholders wealth. The financial manager's job is to make decisions that will cause people to think more favorably about the firm and, in turn, to be willing to pay more to purchase the business.

Topic 2. The Instruments of Management of Financial Resources

The time value of money. When people undertake to set aside money for investment something has to be given up now. For instance, if someone buys shares in a firm or lends to a business there is a sacrifice of consumption. One of the incentives to save is the possibility of gaining a higher level of future consumption by sacrificing some present consumption. Therefore, it is apparent that compensation is required to induce people to make a consumption sacrifice. Compensation will be required for at least three things:

· Time. That is, individuals generally prefer to have $1 today than $1 in five years' time. To put this formally: the utility of $1 now is greater than $1 received five years hence. Individuals are predisposed towards impatience to consume, thus they need an appropriate reward to begin the saving process. The rate of exchange between certain future consumption and certain current consumption is the pure rate of interest - this occurs even in a world of no inflation and no risk. If you lived in such a world you might be willing to sacrifice $100 of consumption now if you were compensated with $104 to be received in one year. This would mean that your pure rate of interest is 4%.

· Inflation. The price of time (or the interest rate needed to compensate for time preference) exists even when there is no inflation, simply because people generally prefer consumption now to consumption later. If there is no inflation then the providers of finance will have to be compensated for that loss in purchasing power as well as for time.

· Risk. The promise of the receipt of a sum of money some years hence generally carries with it an element of risk; the payout may not take place or the amount may be less than expected. Risk simply means that the future return has a variety of possible values. Thus, the issuer of a security, whether it is a share, a bond or a bank account, otherwise no one will be willing to buy the security.

Take the case of Mr. Investor who is considering a $1000 one-year investment and requires compensation for three elements of time value. First, a return of 4% is required for the pure time value of money. Second, inflation is anticipated to be 10 % over the year. Thus, at time zero (n₀) $1000 buys one basket of goods and services. To buy the same basket of goods and services at time n₁ (one year later) $1100 is needed. To compensate the investor for impatience to consume and inflation the investments needs to generate a return of 14.4 %, that is: (1+0.04) (1+0.1) - 1 = 0.144.

The figure 14.4 % may be regarded here as the risk-free return (RFR), the interest rate which is sufficient to induce investment assuming no uncertainty about cash flows.

However, different investment categories carry different degrees of uncertainty about the outcome of the investment. Investors require different risk premiums on top of the RFR to reflect the perceived level of extra risk. Thus:

Required return (time value of money) = RFR + Risk Premium

Simple Interest is interest paid only on the original principal. Example: Suppose that a sum of $100 is deposited in a bank account that pays 12 % per annum. At the end of year 1 the investor has $112 in an account. That is:

F=P (1+r) =112=100(1+0.12)

At the end of 5 years:

F=P (1+rn) = 160=100(1+0.12 x 5)

Compound Interest is interest paid on the accumulated interest and principal. Example: An investment of $100 is made at an interest rate of 12 % with the interest being compounded. In one year the capital will grow by 12 % to 112$. In the second year the capital will grow by 12 %, but this time the growth will be on the accumulated value of $112 and thus will amount to an extra 13.44 at the end of two years:

F=P (1+r) (1+r)

F=112 (1+r)

F= 125.44

Present values.

There are many occasions in financial management when you are given the future sums and need to find out what those future sums are worth in present-value terms today. For example, you wish to know how much you would have to put aside today which will accumulate, with compound interest, to a defined sum in the future; or you are given the choice between receiving $200 in five years or $100 now and wish to know which is the better option, given anticipated interest rates; or a project gives a return of $1 mln. in three years for an outlay of $800 000 now and you need to establish if this is the best use of the $800 000 by the process of discounting a sum of money to be received in the future is given a monetary value today.

Determining the rate of interest.

Sometimes you wish to calculate the rate of return that a project is earning. For instance, a savings company may offer to pay you $10 000 in five years if you deposit $8 000 now, when interest rates on accounts elsewhere are offering 6% per annum. In order to make a comparison you need to know the annual rate being offered by the savings company. Thus, we need to find r in the discounting equation. To be able to calculate r it is necessary to rearrange the compounding formula.

The investment period.

Rearranging the standard equation so that we can find n, we create the following equation:

n=

Using the changing interest rates:

F=P(1+r)(1+r)...(1+r)

Example: You borrow $5 mln. at 10 % of interest on 5 years. Starting the second year the interest rate will increase on 2% every year. Calculate the future value of the sum.

F=5(1.11.121.141.161.18)=9.612

Discounting semi-annually, monthly and daily.

Sometimes financial transactions take place on the basis that interest will be calculated more frequently than once a year. For instance, if a bank account paid 12 % nominal return per year, but credited 6% after half a year, in the second half of the year interest could be earned on the interest credited after the first six month. This will mean that the true annual rate of interest will be grater than 12 %.

The greater the frequency with which interest is earned, the higher the future value of the deposit.

Example: If you put $10 in a bank account earning 12 % per annum then your return after one year is: 10(1+0.12)=11.20.

If the interest compounded semi-annually:

10(1+[0.12/2])(1+[0.12/2])=10(1+[0.12/2])² =11.236

If the interest is compounded quarterly:

10(1+[0.12/4])⁴ =11.255

Daily compounding:

10(1+[0.12/365])³⁶⁵ =11.2747

Continuous compounding.

If the compounding frequency is taken to the limit we say that there is continuous compounding. When the number compounding periods approaches infinity the future value is found by F = Pe^rn where e is the value of the exponential function. This is set as 2.71828 9 (to five decimal places, as shown on a scientific calculator).

So, the future value of $10 deposited in a bank paying 12 % nominal compounded continuously after 8 years is:

10 x 2.71828^{0.12 x 8} = 26.12

Converting monthly and daily rates to annual rates

Sometimes you are presented with a monthly or daily rate of interest and wish to know what that is equivalent to in terms of Annual Percentage Rate (APR) (or Effective Annual Rate (EAR)).

If m is the monthly interest or discount rate, then over 12 month:

(1+m)¹² = 1+r

Where r is the annual compound rate.

r = (1+m)¹² - 1

Thus, if a credit card company charges 1.5 % per month, the annual percentage rate (APR) is: r = (1 + 0.0015)¹² - 1 = 19.56 %

Topic 3. Cash Flow Appraisal

Uneven Cash Flows are series of payments that are unequal over time.

С; С;...С

For instance, a professional athlete may sign a contract that provides for an immediate $7 mln. signing bonus, followed by a salary of $2 mln. in year 1, $4 mln. in year 2, then $6 mln. in year 3 and 4. Whatis the present value of the promised payments that total $25 million? Assume a discount rate of 8 %.

$7 000 000 / 1.080	$ 7 000 000
$ 2 000 000 / 1.081	$ 1 851 851
$ 4 000 000 / 1.082	$ 3 429 355
$ 6 000 000 / 1.083	$ 4 762 993
$ 6 000 000 / 1.084	$ 4 410 179
	$ 21 454 379

Annuities: Quite often there is not just one payment at the end of a certain number of years. There can be a series of identical payments made over a period of years. For instance:

· Bonds usually pay a regular rate of interest;

· Individuals can buy, from saving plan companies, the right to receive a number of identical payments over a number of years;

· A business might invest in a project which, it is estimated, will give regular cash inflows over a period of years;

· A typical house mortgage is an annuity.

An annuity is a series of payments or receipts of equal amounts. We are able to calculate the present value of this set of payments.

Annuities where the cash flows occur at the end of each of the specified time periods are known as ordinary annuities.

Future value of an ordinary annuity.

Suppose Company A plans to invest $500 in a money market account at the end of each year for the next 4 years, beginning one year from now. The business expects to earn a 5 % annual rate of return on its investment. How much money will Company A have in the account at the end of five years?

FVA = A x or FVA = A x FVIFA (r, n) = FVA= 500 x = $2 155.05

FVA = 500 x 4.3101 = $ 2 155.05

The present value of annuity:

Assume, that the financial manager of Company B learns of an annuity that promises to make four annual payments of $500, beginning one year from now. How much should the company be willing to pay to obtain that annuity?



PVA = A x or PVA = A x PVIFA (r, n)

PVA = 500 x 3.5460 = $ 1 773

Future and present value of annuities due.

Annuity due is an annuity where the annuity payments occur at the beginning of each period.

Whenever you run intoan FVA or a PVA of an annuity due problem, adjustment needed is the same in both cases. Use the FVA or PVA of an ordinary annuity formula shown earlier, then multiply your answer by (1 + r) (because annuities due have annuity payments earning interest one period sooner).

In our example:

FVA= 500 x = $2 155.05

PVA = 500 x 3.5460 = $ 1 773

In case of annuity due:

FVA = 2 155.05 x 1.05 = 2 262. 81

PVA = 1 773 x 1.05 = 1 861. 62

Perpetuities:

Some contracts run indefinitely and there is no end to the payments. Perpetuities are rare in the private sector, but certain government securities do not have an end date; that is, the amount paid when the bond was purchased by the lender will never be repaid; only interest payments are made. Also, in a number of project appraisals or share valuation it is useful to assume that regular annual payments go on forever. Perpetuities are annuities which continue indefinitely. The value of perpetuity is simply the annual amount received divided by the interest rate when the latter is expressed as a decimal. PV= - Using the annuity in banking. When a company borrows money from a bank, and then the loan matures, company has to return money to the bank with the interest compounded. There are three types of loans are pure discount loans, amortized loans, and loans with constant total payment.

1. Pure discount loans

The Pure discount loans are simplest form of loan. With such a loan, the borrower receives money today and repays a single lump sum at some time in the future.

Where - amount of payment (total payment)

D - loan (principal paid)

Example:

D=500000;

g=10%;

r=15%;

n=5

FM3 (5, 15)=6.742

tengе

Repayment schedule.

Years	Interest	Payments to the fund	Total payments	Payments with the interest compounded
1 2 3 4 5	50000 50000 50000 50000 50000	74162 74162 74162 74162 74162	124162 124162 124162 124162 124162
				500000



2. Amortized loans are loans where the lender may require the borrower to repay parts of the loan amount over time. A simple way of amortizing a loan is to have borrower to pay the interest each period plus some fixed amount.

where D - loan balance of the year 1

D - loan balance of the year t

For example: suppose a business take out a $ 100 000, five-year loan at 10%. Prepare the loan amortization schedule.

Interest paid: 1000.1=10.

period	Beginning balance	Principle paid	Interest paid	Total payment
1 2 3 4 5	100 80 60 40 20	20 20 20 20 20	10 8 6 4 2	30 28 26 24 22

3. Loans with constant total payment:

Loans with constant total payment mean to have the borrower make a single, fixed payment every period.



For example: suppose a business take out a $ 100 000, five-year loan at 10%. Prepare the loan amortization schedule.

period	Beginning balance	Total payment	Interest paid	Principle paid
1 2 3 4 5	100 83.62 65.6 45.8 24.0	26.38 26.38 26.38 26.38 26.38	10 8.36 6.56 4.58 2.4	16.38 18.02 19.82 21.8 24.0

Because the loan balance decline to zero, the five equal payments do pay off the loan. Notice that the interest paid declines each period. This isn't surprising because the loan balance is going down. Given that the total payment is fixed, the principal paid must be rising each period.

Topic 4. Risk and Uncertainty

The world is risky place. In everything we do - or don't do - there is a chance that something will happen that we didn't expect. Risk is potential for unexpected events to occur.

Most people try to avoid risks if possible. Risk aversion is the tendency to avoid additional risk.

The relationship between risk and required rate of return is known as the risk-return relationship. It is a positive relationship because the more risk assumed, the higher the required rate of return most people will demand. It takes compensation to convince people to suffer.

Measuring risk.

We can never avoid risk entirely. That's why businesses must take sure that the anticipated return is sufficient to justify the degree of risk assumed. To do that, however, firms must first determine how much risk is present in a given financial situation. In other words, they must be able to answer the question, “How risky is it?”. Measuring risk quantitatively is a rather tall order. We all know when something fells risky, but we don't often quantify it. In business, risk measurement focuses on the degree of uncertainty present in a situation - the chance, or probability, of an unexpected outcome. The greater the probability of an unexpected outcome, the greater the degree of risk.

Using standard deviation to measure risk.

In statistics, distributions are used to describe the many values variables may have. A company's sale in future years, for example, is a variable with many possible values.

So the sales forecast may be described by a distribution of the possible sales values with different probabilities attached to each value. If this distribution is symmetric, its mean - the average of a set of values - would be the expected sales value.

Similarly, possible returns on any investment can be described by a probability distribution - usually a graph, table, or formula that specifies the probability associated with each possible return the investment may generate. The mean of the distribution is the most likely, or expected, rate of return.

The graphs below show the distributions of forecast sales for two companies, Company A and Company B.

Note how the distribution for Company A's possible sales values is clustered closely to the mean, and how the distribution of Company B's possible sales values is spread far above and far below the mean.

The narrowness or wideness of a distribution reflects the degree of uncertainty about the expected value of the variable in question (sales, in our example).

The distributions in graphs show, for instance, that while the most probable value of sales for both companies is $1000, sales for Company A could vary between $600 and $1400, while sales for Company B could vary between $200 and $1800.

Company B's relatively wide variations show that there is more uncertainty about its sales forecast than about Company A's sales forecast.

Company A:

Company B:

One way to measure risk is to compute standard deviation of a variable's distribution of possible values. The standard deviation is a numerical indicator of how widely dispersed the possible values are around a mean. The more widely dispersed a distribution is, the larger the standard deviation, and the greater the probability that the value of a variable will be greatly different than the expected value.

The standard deviation, then, indicates the likelihood that an outcome different than what is expected will occur.

Let's calculate the standard deviation of the sales forecast distributions for Company A and Company B to illustrate how the standard deviation can measure the degree of uncertainty, or risk, that is present.

At first, we should calculate the mean м - the average of a set of values.

м (D_b) =

Where м - the expected value, or mean.

D_i - the possible value for some variable.

P_i - the probability of the value D occurring.

Company A:

Possible sales value (Di)	Probability (Pi), %	Dix Pi
$ 600	5	30
$ 800	10	80
$ 1000	70	700
$ 1200	10	120
$ 1400	5	70
		м(Db) = 1000

Company B:

Possible sales value (Di)	Probability (Pi), %	Dix Pi
$ 200	4	8
$ 400	7	28
$ 600	10	60
$ 800	18	144
$ 1000	22	220
$ 1200	18	216
$ 1400	10	140
$ 1600	7	112
$ 1800	4	72
		м(Db) = 1000

We now know that the mean of Company A's and Company B's sales forecast distribution is $1000. We are ready to calculate the standard deviation of the distribution using the following formula:

у =

For Company A:

у = v(600-1000)²Ч0.05 + (800-1000)²Ч0.1 + (1000-1000)²Ч0.7 + (1200-1000)²Ч0.1 + (1400-1000)²Ч0.05 = v24000 = 155

For Company B:

у = v(200-1000)²Ч0.04 + (400-1000)²Ч0.07 + (600-1000)²Ч0.1 + (800-1000)²Ч0.18 + (1000-1000)²Ч0.22 + (1200-1000)²Ч0.18 + (1400-1000)²Ч0.1 + (1600-1000)²Ч0.07 + (1800-1000)²Ч0.04= v148000 = 385

As you see, Company B's standard deviation of 385 is over twice that of Company A. This reflects the greater degree of risk in Company B's sales forecast.

The greater the standard deviation value, the greater the uncertainty as to what the actual value of the variable in question will be. The greater the value of the standard deviation, the greater the possible deviation from the mean.

Whenever we want to compare the risk of investments that have different means, we use the coefficient of variation.

We were safe in using the standard deviation to compare the riskiness of Company A's possible future sales distribution with that of Company B because the mean of the two distributions was the same ($1000). Imagine, however, that Company A's sales were ten times that of Company B. If that were the case and all other factors remained the same, then the standard deviation of Company A's possible future sales distribution would increase by a factor of 10, to $1550. Company A's sales would appear to be much more risky than Company B's, whose standard deviation was only $385.

To compare the degree of risk among distributions of different sizes, we should use a statistic that measure relative riskiness. The coefficient of variation (CV) measures relative risk by relating standard deviation to the mean. The formula follows:

CV= у/ м

The higher the CV of a project, the higher the risk.

Topic 5. Risk and Return (part II)

Types of risk:

Business Risk refers to the uncertainty a company has with regard to its operating income (EBIT). The more uncertainty about a company's expected operating income, the more business risk the company has. For example, if we assume that grocery prices remain constant, the only grocery store in a small town probably has little business risk - the stores owners can reliably predict how much their customers will buy each month. In contrast, a gold mining firm has a lot of business risk.

Because the owners have no idea when, where, or how much gold they will strike, they can't predict how much they will earn an any period with any degree of certainty.

The degree of uncertainty about operating income (and therefore the degree of business risk in the firm) depends on the volatility of operating income. If operating income is relatively constant, as in the grocery store example, then there is relatively little uncertainty associated with it. If operating income can take on many different values, as is the case with the gold mining firm, then there is a lot of uncertainty about it.

We can measure he variability of company's operating income by calculating the standard deviation of the operating income forecast. A small standard deviation indicates little variability, and therefore little uncertainty. A large standard deviation indicates a lot of variability, and great uncertainty.

Some companies are large and others small. So to make comparisons among different firms, we must measure the risk by calculating the coefficient of variation of possible operating income values. The higher the coefficient of variation of possible operating income values, the greater the business risk of the firm.

Tables below show the expected value, standard deviation, and coefficient of variation of operating income for Company А and Company В, assuming that the expenses of both companies vary directly with sales (that is, neither company has any fixed expenses).

Example:

Company А:

	Probability
	5%	10%	70%	10%	5%
Sales	600	800	1000	1200	1400
VC	516	688	860	1032	1204
EBIT	84	112	140	168	196

м = 140

у = 21.69

СV = 15.5%

Company В:

	Probability
	4%	7%	10%	18%	22%	18%	10%	7%	4%
Sales	200	400	600	800	1000	1200	1400	1600	1800
VC	172	344	516	688	860	1032	1204	1376	1548
EBIT	28	56	84	112	140	168	196	224	252

м = 140

у = 53.86

СV = 38.5%

Sales volatility affects business risk - the more volatile company's sales, the more business risk the firm has. Indeed, when no fixed costs are present - as in the case of Company А and Company В - sales volatility is equivalent to operating income volatility. Tables above show that the coefficient of variation of Company А's and Company В's operating income are 15.5 percent and 38.5 percent, respectively. Note that these coefficient numbers are exactly the same numbers as the two companies' coefficients of variation of expected sales.

In the tables above we assumed that all of Company А's and Company В's expenses varied proportionately with sales. We did this to illustrate how sales volatility affects operating income volatility. In the real world, of course, most companies have some fixed expenses as well, such as rent, insurance premiums, and the like. It turns out that fixed expenses magnify the effect of sales volatility on operating income volatility. In effect, fixed expenses intensify business risk. The tendency of fixed expenses to magnify business risk is called operating leverage. To see how this works, refer to the tables below, in which we assume that all of Company А's and Company В's expenses are fixed.

Company А:

	Probability
	5%	10%	70%	10%	5%
Sales	600	800	1000	1200	1400
FC	860	860	860	860	860
EBIT	-260	-60	140	340	540

м = 140

у = 155

СV = 110.7%

Company В:

	Probability
	4%	7%	10%	18%	22%	18%	10%	7%	4%
Sales	200	400	600	800	1000	1200	1400	1600	1800
FC	860	860	860	860	860	860	860	860	860
EBIT	-660	-460	-260	-60	140	340	540	740	940

м = 140

у = 385

СV = 275.0%

As the tables show, the effect of replacing each company's variable expenses with fixed expenses increased the volatility of operating income considerably. The coefficient of variation of Company А's operating income jumped from 15.5 percent when all expenses were variable, to over 110 percent when all expenses were fixed. A similar situation exists for Company В.

The greater fixed expenses, the greater the change in operating income for a given change in sales.

Financial risk: When companies borrow money, they incur interest changes that appear as fixed expenses on their income statements. (For business loans, the entire amount borrowed normally remains outstanding until the end of the term of the loan. Interest on the unpaid balance, then, is a fixed amount that is paid each year until the loan matures.) Fixed interest charges act on a firm's net income in same way that fixed operating expenses acted on operating income - they increase volatility. The additional volatility of a firm's net income caused by the fixed interest expense is called financial risk. We measure financial risk by noting the difference between the volatility of net income when there is no interest expense and the volatility of net income when there is interest expense. To measure financial risk, we subtract the coefficient of variation of net income without interest expense from the coefficient of variation of net income with interest expense. The coefficient of variation of net income is the same as the coefficient of variation of operating income when no interest expense is present. Tables below show the calculation for Company А and Company В assuming: all variable operating expenses, and $40 in interest expense.

Financial risk, which comes from borrowing money, compounds the effect of business risk and intensifies the volatility of net income. Fixed operating expenses increase the volatility of operating income and magnify business risk. In the same way, fixed financial expenses (such as interest on debt) increase the volatility of net income and magnify financial risk.

Company А:

	Probability
	5%	10%	70%	10%	5%
Sales	600	800	1000	1200	1400
VC	516	688	860	1032	1204
EBIT	84	112	140	168	196
Interest exp.	40	40	40	40	40
Net Income	44	72	100	128	156

м = 100

у = 22

СV = 22%

Company В:

	Probability
	4%	7%	10%	18%	22%	18%	10%	7%	4%
Sales	200	400	600	800	1000	1200	1400	1600	1800
VC	172	344	516	688	860	1032	1204	1376	1548
EBIT	28	56	84	112	140	168	196	224	252
I	40	40	40	40	40	40	40	40	40
NI	-12	16	44	72	100	128	156	184	212



м = 100

у = 54

СV = 54%

Firms that have only equity financing have no financial risk because they have no debt on which to make fixed interest payments. Conversely, firms that operate primarily on borrowed money are exposed to a high degree of financial risk.

Portfolio Risk.

A portfolio is any collection of assets managed as a group. Most large firms employ their assets in a number of different investments. Together, these make up the firm's portfolio of assets. Individual investors also have portfolios containing many different stocks or other investments.

Firms (and individuals for that matter) interested in portfolio returns and the uncertainty associated with them. Investors want to know how much they can expect to get back from their portfolio compared to how much they invest (the portfolio's expected return) and what the chances are that they won't get that return (the portfolio's risk).

Investors who are dealing with an existing portfolio can usually estimate the expected return, or mean of the profitability distribution of possible returns of the portfolio, and its standard deviation and coefficient of variation (as we did earlier for the sales forecast distributions of Company А and Company В). Firms want to know whether adding another asset (or another portfolio) to an existing portfolio will change the overall risk of the firm. To find the riskiness of the new combined portfolio, we must find the expected return and standard deviation of possible returns of new portfolio.

Example: Company A merged with Company B to form a new firm called Company C.

	Company А	Company В
Expected return Re	10%	12%
Standard deviation у	2%	4%

Also assume the new combined Company C is made up of 50 % old Company A and 50 % old Company B.

To find the expected return use the formula:

R_e = (w_A x R_A ) + (w_B x R_B ),

Where:

w_A - the weight of asset А in the portfolio

R_A -the expectedrate of return of asset А

w_B - the weight of asset B in the portfolio

R_B - the expectedrate of return of asset B

R_e = (0.5 x 0.1) + (0.5 x 0.12) = 0.11 = 11%

Now let's turn to the standard deviation of possible returns of the new combined Company C portfolio. Determining the standard deviation of a portfolio requires special procedures. Why? Because gains from one asset in the portfolio may offset losses from another, lessening the overall degree of risk in the portfolio.Even though the returns of each company vary, the timing of the variations is such that when one company's returns increase, the other's decrease.

Therefore the net change in the new combined Company C portfolio returns is very small - nearly zero. The weighted average of the standard deviations of returns of the two individual assets, then, does not result in the standard deviation of the portfolio containing both firms. The reduction in the fluctuations of the returns of Company C (the combination of Company А and Company В) is called the diversification effect.

How successfully diversification reduces risk depends on the degree of correlation between the two variables in question. Correlation indicates the degree to which one variable is linearly related to another. Correlation is measured by the correlation coefficient, represented by the letter k. The correlation coefficient can take on values between + 1 (perfect positive correlation) to - 1 (perfect negative correlation). If two variables are perfectly positively correlated, it means they move together - that is, they change values proportionately in the same direction at the same time. If two variables are perfectly negatively correlated, it means that every positive change in one value is matched by a proportionate corresponding negative change in the other. The closer k is to + 1, the more the two variables will tend to move with each other at the same time. The closer k is to - 1, the more the two variables will tend to move opposite each other at the same time. An k value of zero indicates that the variables' values aren't related at all. This is known as statistical independence.

Determining the precise value of k between two variables can be extremely difficult. The process requires estimating possible values that each variable could take, and their respective probabilities, simultaneously.

We can make a rough estimate of the degree of correlation between two variables by examining the nature of the asset involved. If one asset is, for example, a firm's existing portfolio, and the other asset is a replacement piece of equipment, then the correlation between the returns of the two assets is probably close to +1. Why? Because there is no influence that would cause the returns of one asset to vary any differently than those of the other. A Coca-Cola Bottling company expanding its capacity would be an example of a correlation of about +1.

What if a company planned to introduce a completely new product in a new market? In that case we might suspect that the correlation between the returns of the existing portfolio and the new product would be something significantly less than +1. Why? Because the cash flows of each asset would be due to different, and probably unrelated, factors. To calculate the standard deviation of a portfolio, we must use the following formula:

у = v w_A² у_A² + w_B² у_B² + 2 w_A w_B k_{A, B} у_A у_B



Where:

w_A - the weight of asset А in the portfolio

у_A - the standard deviation of the returns of asset A

w_B - the weight of asset B in the portfolio

у_B - the standard deviation of the returns of asset B

k_{A, B}- the correlation coefficient of the returns of asset A and asset B

у = v 0.5² x 0.02² + 0.5² x 0.04² + 2 x 0.5 x 0.5 x (-1) x 0.02 x 0.04 = 1%

The diversification effect results in risk reduction. Why? Because we are combining two assets, Company А and Company В, that have returns that are negatively correlated (k = - 1). The standard deviation of the combined portfolio is much lower than that of either of the two individual companies (1% for Company C compared to 2% for Company А and 4% for Company В).

Nondiversifiable Risk:

Unless the returns of one-half the assets in a portfolio are perfectly negatively correlated with the other half - which is extremely unlikely - some risk will remain afterassets are combined into a portfolio. The degree of risk that remains is nondiversifiable risk, the part of a portfolio's total risk that can't be eliminated by diversifying.

Nondiversifiable risk is one of the characteristics of market risk because it is produces by factors that are shared, to a greater or lesser degree, by most assts in the market. These factors might include inflation and real gross domestic product changes.



Nondiversifiable risk is measured by a term called beta (). The ultimate group of diversified assets, the market, has a beta of 1. The betas of portfolios, and individual assets, relate their returns to those of the overall stock market. Portfolios with betas higher than 1 are relatively more risky than the market. Portfolios with betas less than 1 are relatively less risky than the market. (Risk-free portfolios have a beta of zero.) The more the return of the portfolio in question fluctuates relative to the return of the overall market, the higher the beta.

By definition, the market's beta is 1. The returns of the average-risk portfolio fluctuates exactly the same amount, so the beta of the average-risk portfolio is also 1. The low-risk portfolio's beta is 0.5, only half that of the market. In contrast, the high-risk portfolio's beta is 1.5, half again as high as the market.

Companies in low-risk stable industries like public utilities will typically have low beta values because returns of their stock tend to be relatively stable. (When the economy goes into a recession, people generally continue to turn on their lights and use their refrigerators; and when the economy is booming, people do not splurge on additional electricity consumption.) Recreational boat companies, on the other hand, tend to have high beta values. That's because demand for recreational boats is volatile. (When times are tough, people postpone the purchase of recreational boats. During good economic times, when people have extra cash in their pockets, sales of these boats take off.)

Dealing with Risk:

Once companies determine the degree of risk present, what do they do about it? There are two broad classes of alternatives for dealing with risk. First, you might take some action to reduce the degree of risk present in the situation. Second, (if the degree of risk can't be reduced), you may compensate for the degree of risk you are about to assume. We'll discuss these two classes of alternatives in the following sections.

Risk-Reduction Methods:

There are three main methods of risk-reduction: reducing sales volatility and fixed costs, insurance, and diversification.

Reducing sales volatility and fixed costs. Earlier we discussed how sales volatility and fixed costs contribute to a firm's business risk. Firms in volatile industries whose sales fluctuate widely are exposed to a high degree of business risk. That business risk is intensified even further if they have large amounts of fixed costs.

Reducing the volatility of sales, and the amount of fixed costs a firms pays, then, will reduce risk.

Reducing sales volatility. If a firm could smooth out its sales over time, then the fluctuation of its operating income (business risk) would also be reduced. Businesses try to stabilize sales in many ways. For example, retail sky equipment stores sell tennis equipment in the summer, summer vacation resorts offer winter specials and movie theatres offer reduced prices for early shows to encourage more patronage during slow periods.

Insurance. Insurance is a time-honored way to spread risk among many participants and thus reduce the degree of risk borne by any one participant. Business firms insure themselves against many risks, such as flood, fire, and liability. However, one important risk - the risk that an investment might fail - is uninsurable. To reduce the risk of losing everything in one investment, firms turn to another risk-reduction technique, diversification.

Diversification. We showed in previous discussion how the standard deviation of returns of Company A (2 %) and Company B (4%) could be reduced to 1 % by combining the two firms into one portfolio. The diversification effect occurred because the returns of the two firms were not perfectly positively correlated. Any time firms invest in ventures whose returns are not perfectly positively correlated with the returns of their existing portfolios, they will experience diversification benefits.

Compensating for the Presence of Risk:

In most cases it's not possible to avoid risk completely. Some risk usually remains after firms use the risk-reduction techniques. When firms assume risk to achieve an objective, they also take measures to receive compensation for assuming that risk. In the sections that follow, we discuss these compensation measures.

Adjusting the required rate of return. Most owners and financial managers are generally risk averse. So for a given expected rate of return, less risky investment projects are more desirable than more risky investment projects. The higher the expected rate of return, the more desirable the risky venture will appear. As we noted earlier, the risk-return relationship is positive. That is, because of risk aversion, people demand a higher rate of return for taking on a higher-risk project.

Although we know that the risk-return relationship is positive, an especially difficult question remains: How much return is appropriate for a given degree of risk? Say, for example, that a firm has all assets invested in a chain convenience stores that provides a stable return on investment of about 6 percent a year. How much more return should the firm require for investing some assets in a baseball team that may note provide steady returns - 8 percent? 10 percent? 25 percent? Unfortunately, no one knows for sure, but financial experts have researched the subject extensively.

One well-known model used to calculate the required rate of return of an investment is the Capital Asset Pricing Model (CAPM).

Relating return and risk: The Capital Asset Pricing Model. Financial theorists William F. Sharpe, John Lintner, and Jan Mossin worked on the risk-return relationship and developed the Capital Asset Pricing Model, or CAPM. We can use this model to calculate the appropriate required rate of return for an investment project given its degree of risk as measured by beta (). The formula for CAPM is the following:

R_e = R_f+ Ч(R_m - R_f)

Where: R_e - the expected rate of return appropriate for the investment project;

R_f - the risk free rate of return;

R_m - the required rate of return on the overall market;

The three components of the CAPM include the risk-free rate of return (R_f), the market risk premium (R_m - R_f), and the project's beta (). The risk-free rate of return (R_f) is the rate of return that investors demand from a project that contains no risk. Risk-averse managers and owners will always demand at least this rate of return from any investment projects.

The required rate of return on the overall market minus the risk-free rate (R_m - R_f) represent the additional return demanded by investors for taking on the risk of investing in the market itself. The term is sometimes called the market risk premium. In the CAPM, the term for the market risk premium, (R_m - R_f), can be viewed as the additional return over the risk-free rate that investors demand from an “average stock” or an “average-risk” investment project.

As discussed earlier, a project's beta represents a project's degree of risk relative to the overall stock market. In the CAPM, when the beta term is multiplied by the market risk premium term, (R_m - R_f), the result is the additional return over the risk-free rate that investors demand from that individual project. Beta is relevant risk measure according to the CAPM. High-risk (high-beta) projects have high required rates of return, and low-risk (low-beta) projects have low the required rates of return.

Topic 6. Bond and Stock Valuation

Bonds are essentially IOUs (I owe you) that promise to pay their owner a certain amount of money on some specified date in the future - and in most cases, interest payments at regular intervals until maturity.

Face value (par value, principal) is the amount that the bond promises to pay its owner at some date in the future.

Maturity date is the date on which the issuer is obligated to pay the bondholder the bond's face value.

Coupon interest is the interest payment made to the bond owner during the life of the bond.

Finding the present value of Zero-coupon bonds:

Finding the present value of Regular bonds:

,

Where: C - dollar amount of each periodic interest payment; F - Face value

The Yield to Maturity (YTM) represents the average rate of return on a bond if all promised interest and principal payments are made on time and if the interest payments are reinvested at the YTM rate given the price paid for the bond.



Where: C - dollar amount of each periodic interest payment; F - Face value

Preferred stock is so called because if dividends are declared by the board of directors of a business, they are paid the preferred stockholders first.

Finding the present value of preferred stock dividends: PV = D_p/r

D_p - amount of preferred stock dividend

The Yield of Preferred stock: r_p = D_p/PV

Common stock is so called because there is nothing special about it.

The holders of a company`s common stock are simply the owners of the company.

Their ownership entitles them to the firm's earnings that remain after all other groups having a claim on the firm (such as bondholders) have been paid.

Gordon Growth Model:

The yield of common stock:

r_s = D₁/PV + g

Topic 7. Capital Budgeting Decision Methods

Types of projects:

Independent projects are projects which do not compete with each other.

Mutually exclusive projects compete against each other.

Capital budgeting is a process of evaluating proposed large, long-term investment projects.

Incremental cash flows - cash flows that will occur if an investment is undertaken, but won't occur if it isn't.

Stages in the Capital budgeting process:

· Finding projects

· Estimating the incremental cash flows associated with projects

· Evaluating and selecting projects

· Implementing and monitoring projects

The Net Present Value (NPV) is the dollar amount of change in the value of the firm as a result of undertaking the project.

NPV= - C+

Where: C - Initial Investment

B_i - cash flows at the indicated times

r - Discount rate or required rate of return for the project

n - Number of the periods

If NPV >0 - accept the project

If NPV <0 - reject the project

If NPV = 0 - no profit, no loss

The profitability Index (PI) or benefit-cost ratio is the present value of an investment's future cash flows divided by its initial cost (investment)

Where: C - Initial Investment

B_i - cash flows at the indicated times

r - Discount rate or required rate of return for the project

n - Number of the periods

PI criteria:

If PI >1 - accept the project

If PI <1 - reject the project

If PI = 1 - no profit, no loss

The Internal Rate of Return (IRR) is the estimated rate of return for a proposed project, given the project's incremental cash flows. The required rate of return is often referred to as the hurdle rate. Trial-and-Error Method: Assume:

С=-800;

;

;

To solve the problem using the trial-and-error method we will fill out the following table:

r	0	10	20	30	40
NPV	400	224.8	88.9	-18.9	-106.1

Where: r1 - the required rate of return with positive NPV

r2 - the required rate of return with negative...