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10
Valuation and Rates
of Return
Chapter
McGraw-Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.
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.
10-2
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.
10-3
Valuation of Financial Assets
10-4
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.
10-5
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.
10-6
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)
10-7
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:
10-8
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.
10-9
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.
10-10
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%.
10-11
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.
10-12
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.
10-13
Risk Premium (cont’d)
• Assuming the risk premium is 3%, an overall
required rate of return of 10% can be computed;
10-14
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%;
10-15
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.
10-16
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
10-17
Decrease in Inflation Premium
(cont’d)
– Present value of principal payment at maturity
– Total present value
10-18
Bond Price Table
10-19
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.
10-20
Impact of Time to Maturity on Bond
Prices
10-21
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:
10-22
Relationship Between Time to
Maturity and Bond Price
10-23
Example - 13% Discount Rate
• Present value of interest payments:
• Present value of principal payment at maturity
• Total present value
10-24
Example – 12% Discount Rate
• Present value of interest payments
• Present value of principal payment at maturity
• Total present value
10-25
Formula for Bond Yield
• Weighted average is used to get the average investment
over 15 year holding period.
10-26
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.
10-27
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
10-28
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.
10-29
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:
10-30
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:
10-31
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:
10-32
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.
10-33
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.
10-34
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:
10-35
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).
10-36
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%.
10-37
Constant Growth Dividend Valuation
Model
• Where:
•
•
•
• g
= Price of the stock today;
= Dividend at the end of the first year;
= Required rate of return (discount rate);
= Constant growth rate in dividends.
• Based on the current example;
computed as:
= $2.00;
= .12; g = .07.
is
10-38
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:
10-39
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
10-40
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.
10-41
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.
10-42
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.
10-43
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.
10-44
Stock Valuation under Supernormal
Growth Analysis
10-45