Objective: Students will be able to define and differentiate between
realized and expected return. Students will gain basic knowledge of
Time Value of Money and how compound and simple interest can
affect expected return.
 I.N. Vestor is the top plastic surgeon in Tennessee. He has
$10,000 to invest at this time. He is considering investing in
Frizzle Inc. What factors will influence his investment decision
to invest in Frizzle, Inc.?
 He wants to make money (return) on his investment.
 He wants to keep his money safe.
 Return: The percentage of the original investment either
gained or lost after the investment is made. In order to make
an educated investment decision, I.N. Vestor can research the
return that the investment has generated in the past (known as
the historical return).
 Historical Return (Realized Return): A historical measure of
what an investor has earned based on actual historical cash
flows during a specified holding period.
 The holding period of an investment is the time frame
starting when the initial investment in the stock/bond begins,
and ending on the day the stock or bond is sold.
P0 = Price at initial investment
P1 = Price at end of investment
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Components of Bonds’ Realized Return:
 Coupon:
 Periodic payments of interest that issuer is required to pay at
set intervals, (typically semiannually) until maturity.
 Capital gain:
 If the bond is held until maturity, the investor receives the full
principal value. However, if the bond is sold before maturity,
a capital gain or loss may be realized depending on the
bond’s market price at the time of the sale.
Time Value of Money
 The idea that a dollar received today is worth more than a
dollar received in the future. A dollar received today can
be either used for consumption purposes or be
reinvested, earning additional income from return or
interest.
 Time Value of Money is the principal that drives the
expected return model.
Present Value Formula:
 The Present Value Formula determines how much a sum
of money received in the future would be worth today.
The Future value of money is discounted using the
interest rate.
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PV = Present Value of the $
FV = Future Value of the $
i = interest rate
n = number of interest periods
 Discounting:
 Finding the present value of an investment by taking the
future value of that investment and discounting it by the
interest rate.
An Application of the Time Value of Money:
1) Congratulations! You have won a cash prize of $20,000! You have
two options:
A. Receive $20,000 now
OR
B. Receive $20,000 in three years
The choice is clear: most people will choose to take the money
today.
2) Now, what if the options are:
A. Receive $20,000 now
OR
B. Receive $23,000 in three years
Here, the choice is less clear. The option you would choose is
based on how much interest you think you can earn on $20,000
today.
 Solution: If the interest rate is 5% and it is compounded annually
then after three years you will have $23,152.50. So you would still
take the $20,000 today rather than the greater numerical amount in the
future?
Using the Present Value Formula:
PV = FV/( 1+ i ) n
i = 5%
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n =3
PV = 20,000
*the formula can be adjusted to solve for any of the variables.
FV = PV*( 1+ i ) n
FV = 20,000 ( 1 + .05 ) 3 = $23,152.50
So taking the $20,000 today would still be the best option.
Compound vs. Simple Interest
 Simple Interest:
 In the simple interest calculation, coupons or dividends
paid are not assumed to be reinvested and, thus, do not
generate additional interest.
 The formula for simple interest is:
Interest = Principal * interest rate * time
 Compound Interest:
 In the compound interest calculation, the coupons and
dividend payments are assumed to be reinvested. So,
the coupons and dividends generate additional interest
after they are paid to the investor because the investor
reinvests the payments. Compound interest causes your
money to grow at a faster rate
 The formula for compound interest is:
M = P( 1+ i ) n
M = the amount generated (including the initial principal)
P = principal, the initial investment
i = interest rate
n = number of interest periods
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Example: I.N. Vestor wants to know how much he will make in 3
years if he puts $10,000 into his savings account today. The
savings account interest rate is 4% compounded annually. How
much will I.N. Vestor have after 3 years?
Solution:
i = 4%
n=3
P = 10,000
M = 10,000 (1+.04) 3= $11,248.64
I.N. Vestor will have $11,248.64 after 3 years.
 Expected/ Required Return:
 Return an investor requires or expects for assuming a
certain amount of risk with the investment. The
expected/required return is based on future expected
cash flows for a set period of time.
 Holding period in the expected return calculation is based
on the period beginning today (n=0) and ending at an
established time in the future.
 Expected Rate of Return for Stocks
Components of Stocks’ Expected Returned:
 Future expected dividends.
 Expected price of stock at the end of the holding period.
 Unlike bonds, stocks have no maturity date. To recover
principal, an investor must sell stock in the stock market.
Formula for a Stock’s Expected Rate of Return
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P0 =
D1
+
(1+i)1
D2
(1+i)2
+
D3
+ … +
(1+i)3
Pn
( 1+ i )n
P0 = price of the stock today
i = expected rate of return
D1 = dividend year 1
D2 = dividend year 2
D3 = dividend year 3
Pn = price of the stock in future
Example: I.N. Vestor buys 1 share of XYZ stock at $1,000 per share.
It pays a 2% annual dividend ($20 per year). The price of the stock
after 1 year is expected to be $1,200. What is the expected rate of
return?
Solution:
1000 =
20 + 1200
( 1+ i )
( 1+ i )
1000 ( 1+ i ) = 1220
1000i = 220
i = 0.22 = 22%
The expected rate of return is 22%
Expected Rate of Return - Bonds
 Components of a Bond’s Expected Return:
 Coupon:
 A company that issues a bond must pay the coupons
to the bondholder.
 Principal:
 The par or face value of the bond that is returned to
the investor at maturity.
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Bond Cash Flows:
 A company that issues a bond must pay the coupons
(interest) to the bondholder for a scheduled time period.
 Coupon payments are paid to the bondholder, usually semiannually.
 When the bond matures, the issuer repays the principal to
the bondholder.
 Long-term bonds have higher coupon rates than short-term
bonds. This is because of risk. Bonds with longer maturities
have higher coupon rates because the longer time frame
makes them riskier to an investor because there is a greater
chance of default (all else equal).
Bond Price Formula:
P0
=
C1
(1+i)
+
C2
(1+i)
+
C3
(1+i)3
+ … +
Cn
(1+i)n
+
Mn
(1+i)n
C = coupon payment (usually semi-annually) in dollars, not %
n = number of periods
i = yield to maturity (expected return)
M = value at maturity, or par value (typically $1,000 per bond)
Example:
 On December 1, 2014, I.N. Vestor buys a $1,000 par value.
The interest rate is 3%. Assuming that I.N. Vestor holds the
bond to maturity, he will receive 4 coupon payments of $25 on
6/1/2013, 12/1/2013, 6/1/2014, and the last one on 12/1/2014.
At maturity, 12/1/2014, I.N. Vestor receives his principal
investment of $1,000 plus the last coupon also of $25. Over the
two-year period, I.N. Vestor has received $25 four times plus
his original investment at maturity of $1,000 = 1,000 + 100 =
$1,100. What would I.N. Vestor pay for this bond today?
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Cash Flows of the Bond
Investor pays
“Insert Price” for
bond
0
Coupon 1 = $25
Coupon 1 = $25
Coupon 1 = $25
$1000 principal
repayment
Coupon 1 = $25
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2
3
4
6/1/13
12/1/13
6/1/14
12/1/14
Solution using Formula:
i = 3% = 1.5% (because of semi-annual coupons)
n = number of periods= 4 (2 years*2 payments/year)
C = 25
M = par value = 1,000
P = 25/(1+.015)1 + 25 / (1+.015)2 + 25 / (1+.015)3 + 25 / (1+.015)4 +
1000 / (1+.015)4
P = 24.63054187 + 24.2665437 +
23.9079248+23.55460576+942.1842303
P = $1,038.54
In the bond market, expected return is known as yield to maturity.
 Yield to Maturity:
 In the bond market, this is the rate of return that an
investor would earn if he bought the bond at its
current market price and held it until maturity.
Formula for a Bond’s Yield to Maturity (Expected Return):
YTM =
C
+
P- F
9
n
F+P
2
C = Coupon Payment
F = Face Value of Bond
P = Price of Bond
n = Years until maturity
Example: Suppose your bond has a face value of $1,050 and has a
coupon rate of 5%. It matures in 5 years and the par value is $1,000.
What is the YTM?
Solution:
C = 50
F = 1,050
P = 1000
n=5
YTM = Yield to Maturity
YTM = C + ( P - F ) / n
(F+P)/2
YTM = 50 + ( 1050 – 1000 ) / 5
( 1050 + 1000 ) / 2
YTM = 5.85%
The Yield to Maturity is 5.85%
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Additional Resources
Pessin, Allan H. Fundamentals of the Securities Industry. New York,
NY:
New York Institute of Finance, 1978. Print.
http://www.federalreserve.gov/
http://www.tvmcalcs.com/calculators/apps/excel_bond_valuation
www.investopedia.com
www.investorwords.com
http://www.robertniles.com/stats/stdev.shtml
http://epp.eurostat.ec.europa.eu/statistics_explained/index.php/Excha
nge_rates_and_interest_rates
http://www.russell.com/us/glossary/analytics/standard_deviation.htm
http://www.kathylien.com/site/inflation/burger-king-perfect-exampleof-current-inflation-pressures
http://www.bls.gov/web/laus/lauhsthl.htm
http://www.wellsfargoadvantagefunds.com/wfweb/wf/education/choos
ing/bonds/rates.jsp
YouTube Videos:
http://youtu.be/t_LWQQrpSc4
http://youtu.be/RV2Plc5lrT4
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