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Discount Rate, Yield to Maturity, Value of the Share, E/P Ratio and Ke

Discount Rate: - It is the rate of return that investors expect from securities of comparable risk.

Bonds or Debentures: - These are debt instruments or securities. In case of abond/debenture the stream of cash flows consists of annual interest payments and repayment of principal. These flows are fixed and known.

The Value of the Bond: - It can be found by capitalising cash flows at a rate of return, which reflects their risk. The market interest rate or yield is used as the discount rate in case of bonds (or debentures). The basic formula for the bond value is as follows:


Yield to Maturity: - A bond’s yield to maturity or internal rate of return can be found by equating the present value of the bond’s cash outflows with its price in the above equation.

Zero-Interest Bonds (called zero-coupon bonds in USA) do not have explicit rate of interest. They are issued for a discounted price; their issue price is much less than the face value. Therefore, they are also called deep-discount bonds.
The basic discounting principles apply in determining the value or yield of these bonds.

Preference shares have a preference over ordinary shareholders with regard to dividends. The preference dividend is specified and known. Similarly, in the case of redeemable preference share the redemption or maturity value is also known. Preference share value can be determined in the same way as the bond value. Here the discount rate will be the rate expected by the preference shareholders given their risk. This risk is more than the risk of bondholders and less than the equity shareholders.

Value of the Share (General) Cash flows of an ordinary (or equity) shareconsist of the stream of dividends and terminal price of the share. Unlike the case of a bond, cash flows of a share are not known. Thus, the risk of holding a share is higher than the risk of a bond. Consequently, equity capitalisation rate will be higher than that of a bond. The general formula for the share valuation is as follows:

As the time horizon, n, becomes very large (say, extends to infinity) the present value of future price approaches zero. Thus the term Pn disappears from the formula, and we can use the following equation to find the value of a share today:

Value of the Share (Zero Growth) If dividends do not grow, then capitalisingearnings can determine the share value. Under no-growth situation, earnings per share (EPS) will be equal to dividends per share (DIV) and the present value is obtained by capitalizing earnings per share:

Value of the Share (Constant Growth) In practice, dividends do grow over years. If we assume dividends to grow at a constant rate, g, then DIV1 = DIV0 (1 + g), DIV2 = DIV1 (1 + g), DIV3 = DIV2 (1 + g)..., and the share price formula can be written as follows:
This formula is useful in calculating the equity capitalisation rate (ke) when the price of the share (P0) is known.
Under the assumption of constant growth, the share value is equal to the capitalized value of earnings plus the value of growth opportunities as shown
below:
Value of Growth Opportunities (Vg) Given a firm’s EPS, ROE, the equity capitalisation rate, retention ratio and constant growth, the growth opportunities can be valued as follows:
E/P Ratio and Ke Relationship between the earnings-price ratio and capitalisation rate as follows:
The E/P ratio will equal the capitalisation rate only when growth opportunities are zero, otherwise it will either overestimate or underestimate the capitalisation rate.

Time Value For Money, Risk Premimum, Interest Rate, Capital Recovery

Time Value for Money : - Individual investors generally prefer possession of a given amount of cash now, rather than the same amount at some future time. This time preference for money may arise because of
(a) uncertainty of cash flows,
(b) subjective preference for consumption, and
(c) availability of investment opportunities.
The last reason is the most sensible justification for the time value of money.

Risk Premium: - Interest rate demanded, over and above the risk-free rate as compensation for time, to account for the uncertainty of cash flows.

Interest Rate or Time Preference Rate: - Rate which gives money its value, and facilitates the comparison of cash flows occurring at different time periods.

Required Interest Rate: - A risk-premium rate is added to the risk- free time preference rate to derive required interest rate from risky investments.

Compounding: - It means calculating future values of cash flows at a given interest rate at the end of a given period of time.

Future Value (F) of a Lump Sum: -  Today (P) for periods at rate of interest is given by the following formula:
 
The compound value factor, CVFn ,i can be found out from Table A given at the end of the book.

Future Value of an Annuity: - that is, the same amount of cash each year for periods at rate of interest is given by the following equation



The compound value of an annuity factor (CVAFn,i) can be found out from Table B given in Annexure at the end of the book.

Sinking Fund: -  An annuity to be deposited for periods at rate of interest to accumulate to a given sum. The following equation can be used:




Sinking Fund factor (SFFn, i) is a reciprocal of CVAFn, i.


Discounting: - It means calculating the present value of cash flows at a given interest rate at the beginning of a given period of time.

 Present Value (P) of a Lump Sum (F): - It occured at the end of period at rate of interest is given by the following equation:
The present value factor (PVFn, i) can be obtained from Table C given in Annexure at the end of the book.

Present Value of an Annuity (A) occurring for periods at rate of interest can be found out as follows:

Table can be used to find out the present value of annuity factor (PVAFn, i).

Capital Recovery: - It determined annual cash flows to be earned to recover a given investment. The following equation can be used:

Notice that the capital recovery factor (CRFn,i) is a reciprocal of the present value
annuity factor, PVAFn, i.


Wealth or Net Present Value: - It is defined as the difference between the present value of cash inflows (benefits) and the present value of cash outflows (costs). Wealth maximisation principle uses interest rate to find out the present value of benefits and costs, and as such, it considers their timing and risk. The following formula can be used to calculate NPV or wealth of any pattern of cash
flows:


Multi-period Compounding:  When interest compounds for more than once in a given period of time, it is called multi-period compounding. If is the nominal interest rate for a period, the effective interest rate (EIR) will be more than the nominal rate in multi-period compounding since interest on interest within a
year will also be earned, EIR is given as follows:
where is the number of compounding in a year and is number of years.


Internal Rate of Return (IRR):  IRR is the rate, which equates the present value of cash flows to the initial investment. Thus in operational terms, in the present value equation, all variables are known except rcan be found out by trial and error method:

Finance Functions

Finance Functions
The finance functions can be divided into three broad categories:
(1) Investment decision,
(2) Financing decision,
(3) Dividend decision.
In other words, the firm decides how much to invest in short-term and long-term assets and how to raise the required funds.

Shareholders’ Wealth Maximisation (SWM):  In making financial decisions, the financial manager should try to increase the value of the stake of the shareholder in the firm. This is referred to as the principle of Shareholders’ Wealth Maximisation (SWM).

Wealth:  Wealth is precisely defined as net present value and it accounts for time value of money and risk.

Agency Problem and Agency Costs: Shareholders and managers have the principal-agent relationship. In practice, there may arise conflict between the interests of shareholders and managers. This is referred to the agency problem and the associated costs are called agency costs. if any agency offer ownership rights  to the manager in the form of stock options, it will mitigate the agency costs.

Financial Manager:  The main duty of a financial manager is to raise capital from the capital markets. They should therefore well know about the functioning of capital markets to properly allocate capital to the competing firms and how security prices are determined in the capital markets.


Chief Financial Officer: A number of companies in India either have a finance director or a vice-president of finance as the Chief Financial Officer (CFO). Most companies have only one CFO. But a large company may have both a treasurer and a controller, who may or may not operate under the CFO.

Treasurer and Controller: The main function of a treasurer is to raise and manage company or firms funds. On the other hands it is the responsibility of the controller to look whether this fund are correctly applied or not.  

List of top MBA Schools in USA for the year 2017-2018 with tution fees

Sl. No.
Name of the Management College
City / State
Test  Required
 For admission
Tuition Fees per year in $ (approx)
1
Harvard University
Boston, MA
GMAT, GRE, IELTS, TOEFL, PTE
$63,675
2
University of Pennsylvania (Wharton)
Philadelphia, PA
GMAT, GRE, TOEFL, PTE
$67,516
3
University of Chicago (Booth) 

Chicago, IL
GMAT, GRE, IELTS, TOEFL, PTE
$66,540
4.
Massachusetts Institute of Technology (Sloan)
Cambridge, MA
GMAT, GRE
$67,938
5.
Northwestern University (Kellogg)
             

Evanston, IL
GMAT, GRE, IELTS, TOEFL
$66,462
6.
Stanford University
Stanford, CA
GMAT, GRE, IELTS, TOEFL, PTE
$66,540
7
University of California—Berkeley (Haas)

Berkeley, CA
GMAT, GRE, IELTS, TOEFL
$56,009
8
Dartmouth College (Tuck)

Hanover, NH
GMAT, GRE, IELTS, TOEFL, PTE
$66,390
9
Columbia University  

New York, NY
GMAT, GRE, IELTS, TOEFL, PTE
$68,792
10
Yale University
New Haven, CT
GMAT, GRE
$64,200
11
University of Michigan—Ann Arbor (Ross)
Ann Arbor, MI
GMAT, GRE, TOEFL, PTE
$59,350
12
Duke University (Fuqua)

Durham, NC
IELTS
$63,200
13
New York University (Stern)  

New York, NY
GMAT, GRE, IELTS, TOEFL
$66,588
14
University of Virginia (Darden)

Charlottesville, VA
GMAT, GRE, IELTS, TOEFL, PTE
$57,790
15
University of California—Los Angeles (Anderson)  

Los Angeles, CA
GMAT, GRE, IELTS, TOEFL
$52,272
16
Cornell University (Johnson)

Ithaca, NY
GMAT, GRE, IELTS, TOEFL
$61,584
17
University of Texas—Austin (McCombs)  

Austin, TX
GMAT, GRE, IELTS, TOEFL
$34,296
18
University of North Carolina—Chapel Hill (Kenan-Flagler)

Chapel Hill, NC
GMAT, GRE, IELTS, TOEFL, PTE
$40,015
19
Carnegie Mellon University (Tepper)  

Pittsburgh, PA
GMAT, GRE, IELTS, TOEFL
$61,440
20
Emory University (Goizueta)

Atlanta, GA
GMAT, GRE, IELTS, TOEFL, PTE
$57,000
21
Georgetown University (McDonough)

Washington, DC
GMAT, GRE, IELTS, TOEFL, PTE
$55,050
22
Indiana University (Kelley)

Bloomington, IN
GMAT, GRE, IELTS, TOEFL
$25,500
23
Washington University in St. Louis (Olin)
St. Louis, MO
GMAT, GRE, IELTS, TOEFL
$55,400
24
University of Southern California (Marshall)
Los Angeles, CA
GMAT, GRE, IELTS, TOEFL, PTE
$55,474
25
Arizona State University (Carey)
Tempe, AZ
GMAT, GRE, IELTS, TOEFL, PTE
$26,080
26
Vanderbilt University (Owen)
Nashville, TN
GMAT, GRE, IELTS, TOEFL, PTE
$51,900
27
Ohio State University (Fisher)
Columbus, OH
GMAT, GRE, IELTS, TOEFL
$30,120
28
University of Washington (Foster)

Seattle, WA
TOEFL
$31,335
29
Georgia Institute of Technology (Scheller)
Atlanta, GA
GMAT, GRE, TOEFL,
$28,896
30
Rice University (Jones)

Houston, TX
GMAT, GRE, IELTS, TOEFL, PTE
$53,000
31
University of Notre Dame (Mendoza)
Notre Dame, IN
GMAT, GRE, IELTS, TOEFL, PTE
$50,326
32
Temple University (Fox)
Philadelphia, PA
GMAT, GRE, IELTS, TOEFL, PTE
$31,293
33
University of Minnesota—Twin Cities (Carlson)
Minneapolis, MN
IELTS, TOEFL, PTE
$37,100
34
Brigham Young University (Marriott)

Provo, UT
GMAT, IELTS, TOEFL
$12,310
35
University of Wisconsin—Madison

Madison, WI 
IELTS, TOEFL, PTE
$15,894