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Shareholders

  • Buyer of share are called share holders or stock holders and they are the legal owner of the firm whose shares they hold share represent ownership right of their holders.Buyer are the legal owner of the firm whose shares they hold.

Share holders invest their money in the shares of a company in the expectation of a return on their invested capital.The return of shareholders consist of dividend and capital gain share holder make capital gain share hikder make capital gain or loss by selling their shares.

Type of shareholder

1)Preference shareholder 2)Ordinary shareholder

Preference shareholder

Preference share is often  considerd to be a hybrid security.Since it has many features of both ordinary shares and debenture.

Preference share is senior security as compared to ordinary share it has a prior claim or the company’s income in the sense that the company must first pay preference dividend before paying ordinary dividend.

In preference share dividend rate is fixed and preference dividend are not tax deductible preference shareholder.

Ordinary shareholder

Ordinary shares represent the ownership position in a company.The holders of ordinary shares called ordinary share holder are the legal owners of the company ordinary shares are the source of permanent capital since they do not have a maturity date.

The capital shares is by ordinary shares is called share capital or equity capital.It appears on the left-hand side of a firm account form balance sheet or on the top of sources of capital are generally contained in holders attached to the balance sheet.

Ordinary share holders have a residual ownership claim.They have a claim to the residual income which is earning available for ordinary shareholder after paying expenses interest charges taxes and preference dividend.

Ordinary shareholders also have a residual claim on the company’s assets in the case of liquidation.This share holder are required to vote on a number of important matters.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cash flow

  • A statement of change financial position on a cash basis commonly known as the cash flow statement, Summarises the causes of change in cash position between dates of the two balance sheet, It indicates the source and uses of cash.
    Thus, this is statement analysis changes in non-current accounts as well as current accounts.

Sources and uses of cash

Sources of cash.

->The profitable operation of the firm.
->Decrease in assets(except cash)
->Increase in liabilities (including) debenture or bonds.
->Sale proceeds from an ordinary or preference share issue.

Uses of cash

->The loss from an operation
->increase in assets(except cash)
->decrease in liabilities
->redemption of redeemable preference share.
->Cash dividends

The easiest and the direct method of preparing a statement of changes in cash position is to only record inflow and outflow of cash and find out the net change during a given period.

The rupee received minus the rupees paid during a period is the cash position has to be found out from the income statement and comparative balance sheet. Adjustment for the no cash items is made.

Change in current assets

An increase is current assets reduce the cash flow from operations while a decrease in current assets. that is, the beginning balance exceeding and of the year balance increase cash flow.

i)Increase in debtors implies that cash collection from customers or less them sales figure shown in the profit and loss statement while a decrease in debtors indicates that cash collections are greater than the sales figures.

ii)Increase or decrease in inventory adjusted to the cost of goods sold. An increase in inventory implies that cash outflow is greater than the cost of goods sold figure(shown in the profit and loss statement), while a decrease in inventory means that cash outflow is 100 than the cost of goods sold figure.

iii)Increase in prepaid expenses implies that cash outflow is more than the amount of actual expenses(shown in profit and loss statement, while a decrease in prepaid expenses means that cash outflow is less than the amount of actual expenses.

Change in current liabilities

increases in current liabilities increase cash flow from operation while a decrease in current liabilities reduces it.

i)Increase in creditors implies that cash payments to creditors are less than the purchase figure.
While a decrease in creditors indicates that cash payments to creditors are greater than purchase.

ii)Increase in ‘income in advance’ implies greater cash inflow than shown in the profit and loss statement as income, while a decrease in ‘income in advance’ means less cash inflow than shown as income.

Component of cash flow

i)Initial investment
ii)Annual net cash flows
iii)Terminal cash flow

Initial Investment

The initial investment is the net cash outlay in the period in which an asset is purchased. A major element of the initial investment is gross outlay or original value(ov) of the asset, which comprises of its cost (including accessories and spare parts) and freight and installation charges.

The original value included in the existing block of assets for computing annual depreciation. Original value minus depreciation is the assets’ book value(BV). It may require a lump sum investment in net working capital also.

Thus initial investment will be equal to gross investment plus an increase in networking capital also.

ii)Net Cash flows

An investment expected to generate annual cash flows from operations after the initial cash outlay has been made. Cash flows should always be estimated on an after-tax basis. Some people advocate the computing of cash flows before taxes and discounting them at the before-tax discount rate to find NPV.

Unfortunately, this will not work in practice since there does not exist an easy and meaningful way for adjusting the discount rate on a before-tax basis.

We shall refer to the after-tax cash flow as net cash flows(NCF) and use the term C_{1},C_{2},C_{3}....C_{n} respectively for NCF in period 1,2,3,……n.

Net cash flow =Revenue-Expenses-Taxes
NCF=REV-EXP-TAX

3)Terminal cash flow

Salvage value (SV) is the most common example of terminal cash flows. Salvage value  defined as the market price of an investment at the time of its sale. The cash proceeds net of an investment at the time of its sale. The cash proceeds net of taxes from the sale of the assets treated as cash inflow in the terminal (last) year.

The effect of the salvage value of existing and new assets summarised as follows.

i)Salvage value of the asset-It will increase cash inflow in the terminal(last) period of the new investment.
ii)Salvage value the existing asset now-It will reduce the initial cash outlay of the new asset.
iii)Salvage value of the existing asset at the end of its normal life-It will reduce the cash flow of the new investment of in the period in which the existing asset sold.

 

 

Banker to an issue

The bankers to an issue engaged in activities such as acceptance of applications along with application money from the investor. In respect of an issue of capital and refund of application money.

The term issue means an offer of sales purchase of a security by and body corporate person/group of persons on his/its/their behalf to or form the public the holders of securities of the body corporate person group of persons.

Registration process of banker an issue

To carry on the activity as a banker to issue a person must obtain a certificate of registration from the SEBI

The SEBI grants registration on the basis of call the activities relating to bankers to an issue in particular with reference to the following requirements.

a)The application has the necessary infrastructure communication and data processing facilities and manpower to effectively discharge his activities.

b)The application any of the directors of the applicant not involved in any litigation connected with the securities market. It has not been convicted of any economic offense.

c)The applicant is a scheduled bank.

d)Grant of certificate is in the interest of the investors.

e)The applicant is a fit and proper person.

A banker to an issue can apply for the renewal of his registration three months before the expiry of the certificate.

Condition of registration

The registration of a banker to an issue would be subject to the same condition as are applicable to the merchant.

                      Obligation and Responsibilities

Furnish information -> When required a banker to an issue has to furnish to the SEBI the following information.

a) The number of issues for which he engaged as a banker to an issue.

b)The number of applications/details of the application money received.

c)The dates on which applications from investors forwarded to the issuing company 100 issues.

d)The dates amount of refund to the investor.

2)Books of account document->A banker to an issue is required to maintain books of accounts/records documents for a minimum period of three years in respect of interalia, the number of applications received, the names of the investor, the time within which the applications received were forwarded to the issuing of the investor to the issue and dates and amounts of refund money to  investor.

3)Agreement with issuing companies:-Every banker to an issue enters into an agreement with the issuing company. The agreement provides for the number of collection centers at which applications received forwarded to the issuing company.

4)Discounting action by the RBI-If the RBI takes any disciplinary action against a banker to an issue in relation. To the issue payment, the latter should immediately inform the SEBI. If the bankers prohibited from carrying on his activities as a result of the disciplinary action.

                        Code of conduct

1)Make all efforts to protect the interest of investors.

2)In the conduct of its business, observe high standards of integrity and fairness in the conduct of its business.

3)Fulfill its obligation in a prompt, ethical, and professional manner.

4)At all times exercise due diligence ensures proper care and exercise independent professional judgment.

5)Endeavour to ensure that

(a)Inquires from an investor adequately dealt.

(b)Grievances of investors redressed in a timely and appropriate manner.

c)Where a complaint not remedied promptly, the investor advised of any further steps which may be available to the investor. It is under the regulatory.

6)Be prompt in disbursing dividends, interest, or any such accrual income received or collected by him on behalf of his clients.

7)Not make any exaggerated statement of whether oral written to the client, either about its qualification or capability to render certain services or its achievements in regard to service rendered to other clients.

8)Always endeavor to render the best possible advice to the clients having regard to the client’s needs and the environments and his own professional skill.

9)Avoid conflict of interest and make adequate disclosure of his interest.

10)Put in place a mechanism to resolve any conflict of interest situation that may arise in the conduct of its business or where any conflict of interest arises, should take reasonable steps to resolve the same in an equitable manner.

11)Make appropriate disclosure to the client of its possible source or potential areas of conflict of duties and interest. While it is acting as a banker which would impair its ability to render a fair, objective, and unbiased services.

12)Not discriminate amongst its clients, save and except on ethical and commercial considerations.

13)Ensure that the SEBI  promptly informed about any action, legal proceedings,etc. Initiated against it in respect of any material breach of non-compliance by it, of any law, rules direction of the SEBI.

14)Not make any untrue statement or suppress any material fact in any document. Reports, papers, or information furnished to the SEBI.

15)Not neglect or fail or refuse to submit to the SEBI or other agencies with which it registered. It like document correspondence, and paper or any part thereof as demanded requested from time to time.

16)Provide adequate freedom and powers to its compliance officer for the effective discharge of its duties.

17)Ensure that any person it employs or appoints to conduct a business is fit and power and otherwise qualified to act. In the capacity so employed or appointed.

18)Ensure that the senior management, particular decision-makers have access to all relevant information about the business on a timely basis.

19)Not be a party to or instrumental for
(a) creation of a false market
(b)price rigging or manipulation or
(c)the passing of unpublished price sensitive information in respect of securities listed and proposed to be listed in  stock exchange.To any person or intermediary.

 

 

 

Over-the-counter market

The over-the-counter market is an important alternative to exchange and measured in terms of the total volume of trading has become much larger than the exchange-traded market.

The OTC market is a negotiated market. Transaction not handled on an organized exchange is handled in this market. The OTC  market is not a place it has no central location but it is rather a way of doing business. It consists of a network of dealers, linked together by communication devices including the latest technological equipment these dealers can deal directly with each other and with the customer.

The third term market describes over-the-counter trading of shares listed on an exchange, Although most transaction inlisted stock takes place on an exchange. An investment firm that is not a member of the exchange can make a market in the listed stock. The success or failure of the third market depends on whether the OTC market in these stocks is a good as the exchange market and whether the relative cost of the OTC transaction compares favorably with the cost on the exchange.

Future exchange arose to solve some of the problems associated with over-the-counter trading of forward that had existed previously, similarly the establishment of exchange-traded options led to an explosion of trading and resulted in markets that are much larger and more robust than the over-the-counter option market that came before.

The function of the Over-the-counter market

->Dealers arrive at the prices of securities in the OTC market by both negotiating with customers specifically and making competitive bids.

->Dealers match the forces of supply and demand with each dealers making a market in certain securities.

->Dealers quote bid and ask prices for each security the bid price is the highest price offer by the dealers,and the ask price is the lowest price at which the dealers making a market in certain securities.

->Dealers quote bid and ask prices for each security,the bid price is the highest price is the lowest price at which the dealer is willing to sell

-> Actively traded stocks on the OTC market have a many us to 10 to 20 market makers(dealers functions must as the specialist does for an exchange-listed stock.

Clearing of OTC

The marketing process for OTC trades is similar to that of the exchange-traded option. After the trade occurs, the firm’s back-office its paper processing center, Confirms the details of the trade.

1)Who bought and who sold
2)Put or call
3)Strike price
4)exercise date
5)Quantity of option
6)Underlying security
7) Identification of traders and firms
8)The timing of the premium payment
9)If upon exercise, the long is to receive a cash payment, determined by the difference between the security’s price and the strike price.

If the two firms have a master option agreement covering all such option trades, then need not be confirmed between back office for this information is specified in the master agreement.If all information fields match the back office of the respective firms agree that the trade is good, and each sends a paper confirmation to the other.

Since an OTC trade does not take place under the auspices of an exchange, there is no third party to guarantee the financial performance of the counter-parties to the trade. This requires that each party to the trade has some knowledge of the creditworthiness of the opposite party.

 

 

Criteria of investment Evaluation

Investment  consist of these three steps
->Estmation of cash flow
->Estimation of the required rate of return
->Application of a decision rule for making the choice

Investment decision rule

i)Investment decision rule may be referred to as a capital budgeting technique or investment criteria. To measure the economic worth a sound appraisal technique is that it should maximize the shareholders shareholders‘ wealth for a sound investment.

ii)It should consider all cash flows to determine the true profitability of the period.

iii) It should provide an objective way of separating good projects from bad projects.

iv)It should help the ranking of projects according to their true profitability.

v) It should help to choose among mutually exclusive projects that project where maximize the shareholder wealth.

vi)It should be a criterion that is applicable to any conceivable investment project independent of others.

                                                               Evaluation criteria
Two type of investment criteria are in use in practice.
i) Discounted cash flow criteria
ii)Non-discounted cash flow criteria.

Discounted cash flow included
->Net present value(NPV)
->Internal rate of return
->Profitability Index

1)Net present value(NPV)-NPV is a DCF technique that explicitly recognizes the time value of money it correctly postulates that cash flows arising at different time periods differ in value.
The following steps are involved in the calculation of NPV
->Cash flows of the investment project should be forecasted based on realistic assumption.

->Present value of cash flows should be calculated using the opportunity cost of capital as the discount rate.

->Net present value should be found out by subtracting present value of cash outflow from the present value of cash inflows.
Project should be accepted if NPV is positive NPV>0

Importance of NPV
NPV valuation supposes that the opportunity cost of capital is 10% percent and project X cost rs.2000 now and is expected to generate year-end cash inflow of Rs.900,800,700,600,500.

NPV=                         [\frac{900}{(1+0.10)}+\frac{800}{(1+0.10)^{2}}+\frac{700}{(1+0.10)^{3}}+\frac{600}{(1+0.10)^{4}}+\frac{500}{(1+0.10)^{5}}]-2500

NPV=2725-2500=+225

How to except NPV
i)Accept the project when NPV is positive NPV>0
ii)Reject the project when NPV is negative NPV<0
iii)May accept the project when NPV is zero NPV=0

2)Internal rate of return method-The internal rate of return method is another discounted cash flow technique which takes account of the magnitude and timing of cash flow. The concept of internal is quite simple to understand in the case of one project.
Suppose that 10000 Rs.deposit in a bank and would get back Rs.100800

\frac{10800-10000}{ 10000}

1.08-1=0.08
0.08 or 8%

r=\frac{C_{1}-C_{0}}{C_{0}}

r=\frac{C_{1}}{C_{0}}-L

How to except IRR
i)Accept the project when r>k
ii)Reject the project when r<k
iii)May Accept the project when r=k

3)Profitability Index-Profitability index is the ratio of the present value of cash inflows , at the required rate of return ,to the initial cash outflow of the investment. The formula for calculating the benefit-cost ratio or profitability index as follows.

PI=

Pv of cash inflowsInitial cash outlay

\frac{PV(C_{1})}{C_{0}} = \sum_{t=1}^{n}\frac{C_{1}}{(1+k)^{t}}/C_{0}

Suppose that initial cash outlay is Rs.100000 and it can generate cash inflow of rs.40000,30000,50000 and rs.20000 in a year.

PV= 40000(PVF _{1.0.10})+30000(PVF_{2.0.10})+50000(PVF_{3.0.10})+20000(PVF_{4.0.10})

=40000\times 0.909+30000\times0.826+50000\times 0.751+20000\times 0.68

NPV =112350-100000=12350

PI  =\frac{112350}{100000}=11235

How to except profitability Index
i)Accept the project when PI is greater than one PI>1
ii)Reject the project when PI is less than one PI<1
iii)May accept the project when PI is equal to one PI=I

                     Non-discounted cash flow criteria

1)Payback -The payback (PB) is one of the most popular and widely recognized traditional methods of  evaluating investment proposals. Payback is the number of years required to recover the original cash outlay invested in a project.
If the project generator constant annual cash inflow the payback period can be computed by dividing cash outlay.

    =

Initial InvestmentAnnual cash Inflow

=         \frac{C_{0}}{C}

How to except payback
Many firms use the payback period as an investment evaluation criteria and a method of ranking project.

->The project would be accepted if its payback period is less than the maximum or standard payback period set by management.

->As ranking method it gives the highest ranking to the project.

->If the firm has to choose between two mutually exclusive projects, the project with a shorter payback period will be selected.

2)Discounted payback period-Payback method is that it does not discount the cash flows for calculating the payback period. The discounted payback period is the number of periods taken in recovering the investment outlay on the present value basis.
The discount payback period still fails to consider the cash flows occurring after the payback period.

Project P and Q involve the same outlay of Rs.4000 each opportunity cost of capital is 10%.

3)Accounting rate of return-The accounting rate of return (ARR), also known as the return on investment(ROI) .I uses accounting information on as revealed by financial statements to measure the profitability of an investment.
The accounting rate of return is the ratio of the average after-tax profit divided by the average  investment.

The average investment would be equal to half of the original investment if it were depreciated constantly.

ARR=\frac{Average income}{Average investment}

ARR=\frac{\sum_{t=1}^{n}(I-t)}{(I_{0+I_{n}})/2}
Where
EBIT=Earning before interest and tax
T=tax
I0=book value
In=Book value of investment at the end of the number of years

How to except ARR
This method will accept all those projects whose ARR is higher than the minimum rate established by the management.
Reject these project which has ARR less than the minimum rate.

 

 

 

 

Perpetuities

A perpetuity is a stream of equal cash flows that occur at regular intervals for example. Perpetual bonds promise the owner a fixed cash flow every year forever.

Here is the timeline of perpetuity.
From the timeline that the first, cashflow does not occur immediately,it arrives at the end of the first period. This timing is sometimes referred to as payment in arrears and is a standard convention that we adopt.

            The present value of a perpetuity

Perpetuity is an annuity that occurs indefinitely perpetuities are not very common in financial decision making. But one can find a few examples for instance in the case of irredeemable preference share(i.e.preference shares without a maturity. The company expected to pay preference dividend perpetuity.
By definition, in perpetuity, time period n,  is so large C mathematically n approaches infinity that the expression(1+i^)^{n}, and the formula for perpetuity simply becomes.
Present value of a perpetuity

Perpetuity formula
\frac{Perpetuity}{Interest rate}

P=\frac{A}{i}
Using the formula for the present value. The present value of a perpetuity with payment C and interest rate r is given by

PV= \frac{C}{(1+r)}+\frac{C}{(1+r)2}+\frac{C}{(1+r)^{3}}+....=\sum _{n=1}^{\infty }\frac{C}{(1+r)^{n}}

Notice that C=C in the present value formula because the cash flow for perpetuity is constant. Also because the first cash flow is in one period.

To find the value of perpetuity one cash flow at a time would take forever.
The term of an infinite number of positive terms could be finite. The answer is that the cash flows in the future. One discounted for an ever-increasing number of periods, so their contribution to the sum eventually becomes negligible.
To derive the shortcut. We calculate the value of perpetuity by creating our own perpetuity, We can then calculated the present value of the perpetuity because of the perpetuity, By the law of one price, the value of the perpetuity must be the same as the cost.

We incurred to create our own perpetuity. Suppose that you withdraw $5  and reinvest the $100 for a second year again you will have $105 after one year and you can withdraw $5 and reinvest $100 for another year.
By doing this year after year, you can withdraw $5 every year in perpetuity.

By investing $100 in the bank today. You can in effect, create a perpetuity paying $5 per year

 

Annuity

An annuity is a stream of N equal cash flows paid at regular intervals. The difference between an annuity and perpetuity is that an annuity ends after some fixed number of payments.

Not surprisingly, annuities are the most common kinds of financial instruments. The pensions that people receive when they retire are often in the form of. Most car loans, mortgages, leases, some bonds, and pension plans are also annuities.

We represent the cash flow of an annuity on a timeline as follows.
With perpetuity, we adopt the convention that the first payment take place at date, one period from today.

The present value of N-period annuity with payment C and interest rate is
PV=\frac{C}{(1+r)}+\frac{C}{(1+r)^{2}}+\frac{C}{(1+r)^{3}}+----+\frac{C}{(1+r)^{N}}=\sum_{n=1}^{N}\frac{C}{(1+r)^{n}}

                                 Types of annuity

1)The present value of an annuity
2)Future value of an annuity

1)The present value of a growing annuity:-In financial decision-making there are a number of situations where cash flows may grow at a constant rate. For example, Suppose that deposit 1000 rs.at 10 percent  for 5 years will the amount after 5 year

Year-End Amount of       salary      PVF@12% PV of salary(Rs)
1 1000 0.893 893
2 1100 0.797 877
3 1210 0.712 862
5 1331 0.636 847
5 1464 0.567 830
6105 4309

We can write the formula for calculating the present value of a growing annuity as follows:

Formula of annuity
P=\frac{A}{(1+i)}+\frac{A(1+g)^{1}}{(1+i)^{2}}+\frac{A(1+g)^{2}}{(1+i)^{3}}+....+\frac{A(1+g)^{n-1}}{(1+i)^{n}}

P=A[\frac{1}{(1+i)}+\frac{(1+g)^{1}}{(1+i)^{2}}+\frac{(1+g)^{2}}{(1+i)^{3}}+...+\frac{(1=g)^{n-1}}{(1+i)^{n}} ]

2)Future value of an annuity

How can we compute the compound value of an annuity due? The compound value of an annuity because it earns extra interest for one year. If you multiply the compound value of an annuity by(1+i), You would get the compound value of an annuity due.

The formula for the compound value of an annuity due is as follows.
Future value of an annuity\times (1+i)
=A\times CVFA_{n,i}\times (1+i)
=A[\frac{(1+i)^{n}-1}{i}](1+i)

Some tricks were also available to calculate annuity. Presents four tricks below.

Trick#1 A delayed annuity:-One of the trick in working with annuities or properties is getting the timing exactly right. This is particularly true. When an annuity or perpetuity begins at a date many periods in the future.

For example:-Mr.A will receive a four-year annuity of rs.500 per year Begining at date of 6. If the interest rate is 10 percent. What is the present value of her annuity?
This situation can be graphed.

This analysis involves two steps
1) Present value calculation.
The present value of annuity on date 5
$500[\frac{1}{0.10}-\frac{1}{0.10(1.10)^{4}}]=$500\times A_{0.10}^{4}
=$500\times 3.1699
=$1584.95
Note that $1584.95 represents the present value on date 5
$1584.95 is the present value at date 6, because the annuity begins on date 6, However, our formula values the annuity as of one period prior to the first payment. This can be seen in the most typical case where the first payment occurs at date 1.

2) Discount the present value of the annuity back to date 0. That is
Present value at date 0:
\frac{1584.95}{(1.10)^{5}}=$984.13

The annuity formula brings Mr. Annuity back to 5, the second calculation must discount over the remaining 5 periods. Two-step procedure graphed in the figure below .

Date
cash  flow

 

Trick#2 Annuity in advance:-If first payment of annuity received immediately. for example, Mr.B received first payment from the lottery immediately. The total number of payments remains 20.

Under this new assumption. We have a 19-date annuity with the first payment occurring at date 1  plus an extra payment at date 0. The present value is

$50000 payment at date 0+$50000\times A_{0.08}^{19}
19-year annuity
=$50000+$50000\times 96036
=$530180

$530180, the present value in this example. This is to be expected because the annuity of the current example begins earlier. An annuity with an immediate initial payment is called an annuity in advance.

Trick#3The infrequent annuity: An annuity with payments occurring less frequently than once a year.
For example, Mr.C receives an annuity of $450.Payable once every two years. The annuity stretches out over 20 years. The first payment occurs at date 2 that is, two years from today. The annual interest rate is 6 percent.
The trick is to determine the interest rate over a two-year period. The interest rate  over two years is
1.06\times 1.06-1=12.36%
That is,$100 invested over two years will yield $112.36

Present value of a $450 annuity over 10 periods, with an interest rate of 12.36 percent per period. This is
$450  [\frac{1}{0.1236}-\frac{1}{0.1236\times(1.1236)^{10} }]=$450\times A_{0.1236}^{10}=$2,505.57

Trick#4 Equating presents the value of two annuities: If a parent estimates college education for their new born daughter. They estimated that college expenses will run $30000 per year when their daughter reaches college in 18 years. The annual interest rate over the next few decades will 14 percent.How much money they deposit in the bank each year so that their daughter will completely supported through four years of college.

We assume that the child born today. Her parents will make the first of her four annual tuition payments on her 18th birthday. They will make equal bank deposits on each of her first 17 birthdays. But no deposit at date 0.

This calculation requires 3 steps. The first two determine the present value of the withdrawals. The final step determines yearly deposits that will have a present value equal to that of the withdrawals.
1. Calculation of the present value of the four years at college using the annuity formula.
$30000\times [\frac{1}{0.14}]-\frac{1}{0.14\times (1.14)^{4}} =$30000\times A_{0.14}^{4}
=$30000\times 2.9137=$87,411

2.Calculation the present value of the college education at date 0 as
\frac{87411}{(1.14)^{17}}=$9,422.91
3. Assuming that child’s parents make a deposit to the bank at the end of each of the 17 years, We calculate the annual deposit that will yield a present value of all deposit. This is calculated as
C\times A_{0.14}^{17}=$9,422.91
SinceA_{0.14}^{17}=6.3729
C=\frac{9422.91}{6.3729}=$1478.59

Thus, deposit of $1478.59 made at the end of each of the first 17 years and in other words invested at 14 percent will provide enough money to make tuition payments of $30000 over the following four years.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Discounted cash flow

Discounted cash flow (DCF) approach is theoretically the most appropriate valuation approach. The value of a firm depends on the expected cash flows and the discount rate. The expected cash flow of the firm depends on the operating efficiencies and market conditions.
The discounted rate depends on the risk of the expected cash flows. Firm’s generating specify target capital structure in terms of fixed debt-to-value ratio. In conculsion, Wacc is the appropriate discount rate for valuing a firm.
To estimate a continuation value in year T using discounted cash flow. We assume a constant expected growth rate and constant debt-equity ratio.
V=\sum_{t=1}^{n=\infty }\frac{FCF_{t}}{(1+k_{0})^{t}}

Where,
FCF=free cash flow
K_{0} = weighted average  cost of capital(WACC)
If FCF remains constant forever, that is FCF is a perpetuity,  the value of the firm
V=\frac{FCF}{K_{0}}

Earnings are the basics for estimating fre cash flows of firm cash flows include an adjustment for depreciation, capital expenditure and working capital.

                  Earning depends on capital

If we assume constant relation of earnings depends on sales.If we assume constant relation of earnings working capital and capital expenditure to sales.
NCF=FCF
=SALES\times P\times (1-t)+DEP-(w+f)SALES
Where,
P=EBIT
T=Corporate tax rate
DEP=depreciation
w=net working capital
f=capital expenditure

How to calculate covariance

The covariance of returns on two assets measures their co-movement.
When we consider two assets, we are concerned with the co-movement.
Determine the expected returns on assets, the deviation of possible returns from the expected return for each asset.
Determine the sum of the product of each deviation of the return of two assets and respective probability.
The covariance of any asset with itself is represented by its variance(covar_{j,j})=\sigma ^{2}_{j}. The return on the market portfolio should depend on its own risk, which is given by the variance of the market return(\sigma ^{2}_{m}).

Required rate of return

Opportunity cost of capital called the required rate of return. The opportunity of cost of capital is the expected rate of return. An investor could earn by investing his or her money in financial assets of equivalent risk.

Risk in investment arises because of the uncertain returns investment proposals. Investment evaluated in terms of both expected return and risk. Besides the decision to commit funds in new investment proposals. Capital budgeting also involves replacement decisions. The decision of recommitting funds when an asset becomes less productive or non-profitable.