Financial Management (Valuation and rates of return)

profilekukuda34
Chap0102.ppt
Home>Business & Finance homework help>Management homework help>Financial Management (Valuation and rates of return)

Chapter

McGraw-Hill/Irwin

Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.

Valuation and Rates of Return

10

10-*

Chapter Outline

  • Valuation of assets, based on the present value of future cash flows.
  • The required rate of return in valuing an asset is based on the risk involved.
  • Bond valuation and its determination.
  • Stock valuation and its determination.
  • Price-earnings ratio.

10-*

Valuation of Financial Assets

  • Helps in evaluating financial commitment a firm needs to make to:
  • Stockholders and bondholders.
  • Attract investment.
  • Cost of corporate financing (capital) is used in analyzing the feasibility of an investment on an ensuing project.

10-*

Valuation of Financial Assets

10-*

Valuation Concepts

  • Valuation of a financial asset is based on determining the present value of future cash flows.
  • Required rate of return (the discount rate)
  • Depends on the market’s perceived level of risk associated with the individual security.
  • It is also competitively determined among companies seeking financial capital.
  • Implying that investors are willing to accept low return for low risk and vice versa.
  • Efficient use of capital in the past results in a lower required rate of return for investors.

10-*

Valuation of Bonds

  • A bond provides an annuity stream of interest payments and a principal payment at maturity.
  • Cash flows are discounted at Y (yield to maturity).
  • Value of Y is determined in the bond market.
  • The price of the bond is:
  • Equal to the present value of regular interest payments.
  • Discounted by the yield to maturity added to the present value of the principal.

10-*

Valuation of Bonds (cont’d)

  • Assuming interest payments ( ) = $100; principal payments at maturity ( ) = $1,000; yield to maturity (Y) = 10% and total number of periods (n) = 20. Thus, the price of binds ( );
  • Where:
  • = Price of the bond; = Interest payments; = Principal payment at maturity; t = Number corresponding to a period (running from 1 to n); n = Number of periods; Y = Yield to maturity (or required rate of return)

10-*

Present Value of Interest Payments

  • To determine the present value of a $100 annuity for 20 years, with a discount rate of 10%.
  • We have:

10-*

Present Value of Principal Payment (Par Value) at Maturity

  • Principal payment at maturity is used interchangeably with par value or face value of the bond.
  • Discounting $1,000 back to the present at 10%, we have:

  • The current price of the bond, based on the present value of interest payments and the present value of the principal payment at maturity:

  • Here, the price of the bond is essentially the same as its par, or stated value to be received at maturity of $1,000.

10-*

Concept of Yield to Maturity

  • The yield to maturity or the discount rate is the required rate of return required by bondholders.
  • Three factors influence the required rate of return:
  • Required real rate of return.
  • Inflation premium.
  • Risk premium.

10-*

The Real Rate of Return

  • Demanded by the investor against current use of the funds on a non-adjusted basis.
  • The financial ‘rent’ the investors charges for the usage of their funds for a given period.
  • Usually about 2 to 3%.

10-*

Inflation Premium

  • Compensation towards the negative effect of inflation on the value of a dollar.
  • Premium added to the real rate of return:
  • Ensures that the investor will not ‘pay’ the borrower to use his or her funds.
  • The risk-free rate of return can be determined.

10-*

Risk Premium

  • Towards special risks of an investment.
  • Business risk: inability of the firm to retain its:
  • Competitive position.
  • Maintain stability and growth.
  • Financial risk: inability of the firm to meet its:
  • Debt obligations as and when due.
  • Is relative to the type of investments.

10-*

Risk Premium (cont’d)

  • Assuming the risk premium is 3%, an overall required rate of return of 10% can be computed;

10-*

Increase in Inflation Premium

  • Assume this goes up from 4 to 6%, with everything else being constant.

  • Present value of interest payments:

$100 annuity for 20 years at a discount rate of 12%;

10-*

Increase in Inflation Premium (cont’d)

  • Present value of principal payment at maturity:

Present value of $1,000 after 20 years at a discount rate of 12%;

  • Total present value:

Assuming that increase inflation increases required rate of return and decreases the bond price by $150 approximately.

10-*

Decrease in Inflation Premium

  • Assuming that the inflation premium declines:
  • The required rate of return (yield to maturity) decrease to 8%, where the 20 year bond with a 10% interest rate would now sell for;
  • Present value of interest payments

10-*

Decrease in Inflation Premium (cont’d)

  • Present value of principal payment at maturity

  • Total present value

10-*

Bond Price Table

10-*

Time to Maturity

  • Influences the impact of a change in yield to maturity on valuation.
  • Longer the maturity, the greater the impact of changes in yield.

10-*

Impact of Time to Maturity on Bond Prices

10-*

Determining Yield to Maturity from the Bond Price

  • The yield to maturity (Y), that will equate the interest payments ( ) and the principal payments ( ) to the price of the bond ( ).

  • Assuming that a 15 year bond pays $110 per year (11%) in interest and $1,000 after 15 years in principal repayment.
  • Choosing an initial percentage to try as a discount rate, we have:

10-*

Relationship Between Time to Maturity and Bond Price

10-*

Example - 13% Discount Rate

  • Present value of interest payments:

  • Present value of principal payment at maturity

  • Total present value

10-*

Example – 12% Discount Rate

  • Present value of interest payments

  • Present value of principal payment at maturity

  • Total present value

10-*

Formula for Bond Yield

  • Weighted average is used to get the average investment over 15 year holding period.

10-*

Semiannual Interest and Bond Prices

  • A 10% interest rate may be paid as $50 twice a year in the case of semiannual payments.

  • To make the conversion:
  • Divide the annual interest rate by two.
  • Multiply the number of years by two.
  • Divide the annual yield to maturity by two.

  • Assuming a 10%, $1,000 par value bond has a maturity of 20 years, the annual yield at 12%:
  • 10%/2 = 5% semiannual interest rate; hence 5% X $1,000 = %50 semiannual interest.
  • 20 X 2 = 40 periods to maturity
  • 12%/2 = 6% yield to maturity, expressed on a semiannual basis.

10-*

Semiannual Interest and Bond Prices (cont’d)

  • At a present value of a $50 annuity for the 40 periods, at discount rate of 6%:
  • Present value of interest payments

  • Present value of principal payment at maturity

  • Total present value

10-*

Valuation and Preferred Stock

  • Preferred stock represents a perpetuity, having no maturity date.
  • It has a fixed dividend payment.
  • It has no binding contractual obligation of interest on debt.
  • Being a hybrid security, it does not have:
  • The ownership privilege of a common stock.
  • The legal provisions that could be enforced on debt.

10-*

Perpetuity of a Preferred Stock

  • Where,
  • = the price of the preferred stock; = the annual dividend for the preferred stock (constant); = required rate of return (discount rate) applied to preferred stock dividends.

  • A more usable formula is:

  • Assuming, the annual dividend is $10, and the stockholder requires a 10% rate of return, the price of the preferred stock would be:

10-*

Perpetuity of a Preferred Stock (cont’d)

  • If the rate of return required by security holders change, the value of the preferred stock also changes.
  • The longer the period of an investment, the greater the impact of a change in the require rate of return.
  • With perpetual security, the impact is at a maximum.
  • Assuming that the required rate of return has increased to 12%. The value of the preferred stock would be:

  • If it were reduced to 8%, the value of the preferred stock would be:

10-*

Determining the Rate of Return (Yield) from the Market Price

  • Assuming the annual preferred dividend ( ) is $10 and the price of the preferred stock ( ) is $100, the required rate of return (yield):

  • A higher market price provides quite a decline in the yield:

10-*

Valuation of Common Stock

  • Interpreted by the shareholder as the present value of an expected stream of future dividends.
  • The ultimate value of any holding lies with:
  • The distribution of earnings in the form of dividend payments.
  • The earnings must be translated into cash flow for the stockholder.

10-*

Dividend Valuation Model

  • Where,
  • = Price of stock today;
  • D = Dividend for each year;
  • = the required rate of return for common stock (discount rate).

  • This formula, with modifications is generally applied to three different situations:
  • No growth in dividends.
  • Constant growth in dividends.
  • Variable growth in dividends.

10-*

No Growth in Dividends

  • The common stock pays a constant dividend as in the case of a preferred stock.
  • This is not a very popular option.

  • Where,
  • = Price of the common stock; = Current annual common stock dividend (constant); = Required rate of return for common stock.

  • Assuming = $1,86 and = 12%, the price of the stock would be:

10-*

Constant Growth in Dividends

  • The general valuation process is shown:

  • Where,
  • = Price of common stock today;
  • = Dividend in year 1, ;
  • = Dividend in year 2, , and so on;
  • g = Constant growth rate in dividends;
  • = Required rate of return for common stock (discount rate).

10-*

Constant Growth in Dividends (cont’d)

  • Assuming:

  • = Last 12 month’s dividend (assume $1.87);
  • = First year, $2.00 (growth rate, 7%);
  • = Second year, $2.14 (growth rate, 7%);
  • = Third year, $2.29 (growth rate, 7%) etc;
  • = Required rate of return (discount rate), 12%.

10-*

Constant Growth Dividend Valuation Model

  • Where:

  • = Price of the stock today;
  • = Dividend at the end of the first year;
  • = Required rate of return (discount rate);
  • g = Constant growth rate in dividends.

  • Based on the current example; = $2.00; = .12; g = .07. is computed as:

10-*

Stock Valuation Based on Future Stock Value

  • Assumption: To know the present value of an investment.
  • Stock is held on for three years and then sold.
  • Adding the present value of three years of dividends, and the present value of the stock price after three years gives the present value of the benefits.
  • The appropriate formula to be used is:

10-*

Determining the Required Rate of Return from the Market Price

  • Determining the required rate of return, knowing the first year’s dividend, the stock price, and the growth rate (g):

  • Assuming;

= Required rate of return (to be solved);

  • = Dividend at the end of the first year, $2.00;
  • = Price of the stock today, $40;
  • g = Constant growth rate 7%, we have:

= $2.00 + 7% = 5% + 7% = 12%

$40

10-*

Determining the Required Rate of Return from Market Price (cont’d)

  • The stockholder is receiving a current dividend plus anticipated growth in the future.
  • If the dividend yield is low, the growth rate must be high to provide the necessary return.
  • If the dividend rate is low, a high dividend yield will be expected.

  • The first term represent the dividend yield the stockholder will receive.
  • The second represents the anticipated growth in dividends, earnings, and stock price.

10-*

Price-Earnings Ratio Concept and Valuation

  • A multiplier applied to current earnings to determine the value of a share of stock in the market.
  • Influenced by:
  • Earnings and sales growth of a firm.
  • Risk (or volatility in performance).
  • The debt-equity structure of the firm.
  • The dividend policy.
  • The quality of management.

10-*

Variable Growth in Dividends – Supernormal Growth

  • Present value of dividends during the exceptional growth is observed.
  • Present value of the normal, constant dividends that follow the supernatural growth period:
  • Is used to determine the price of the stock at the end of the supernatural growth period.
  • Discounting this price to the present and adding it to the present supernormal value:
  • Gives us the current price of the stock.

10-*

Variable Growth in Dividends – No Dividends

  • Approach 1: though no dividend is paid currently
  • The stockholders will be paid a cash dividend at a later date.
  • The present value of their deferred payments may be used.
  • Approach 2:
  • Take the present value of earnings per share for a number of periods.
  • Add that to the present value of the future anticipated stock price.

10-*

Stock Valuation under Supernormal Growth Analysis