Investing
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
on Frizzle, Inc.?
 He wants to make money
(generate a return) on his
investment.
 He wants to keep his money
safe.
Return On Investment
 After the investment is made.
The return
is the percentage
either gained or
lost on the original
investment.
In order to make an educated investment
decision, I.N. Vestor can research the
return that the investment has generated in
the past. (also known as historical return)
Historical Return/Realized Return

Historical Return (Realized Return): Historical
measure of what an investor has earned based
on actual historical cash flows during a specific
holding period.
Holding Period
The time frame starting
when the initial
investment in the
stock/bond begins and
ending on the day the
stock/bond is sold.
Realized Return = Dividend + (P1 – P0)
P0
Historical/Realized Return
Example : I.N. Vestor purchased Stock ABC one year ago for $33. The stock paid a dividend of $1.75 and
now has a price of $37.25. What realized (historical) return did he earn over the one-year period?
Solution : If I.N. Vestor sells the stock now for $37.25 then he will collect
$37.25 plus the $1.75 dividend that was paid during the year
Realized return =
Dividend + (price @ end of period - price @ beginning of period)
Price @ beginning of the period
On his initial investment of $33, the realized (historical) return is
1.75 + (37.258 - 33) / 33 = 18.2%
The Realized Return is 18.2% in one year per share of ABC.
Questions to Consider:
• Is that a good return?
• Is that return better than the return a bank offers?
• Is it a good investment decision?
Components of Stocks’ Realized Return
Dividends: A portion of a company’s earnings distributed
to their stockholders.
– The issuer can elect to suspend payment of the dividend
and reinvest that amount into additional purchase of the
stock.
Capital gain: Profit that is realized when the security is
sold and the selling price of the security is greater than
the purchase price. If the price of the stock drops during
the period, a capital loss is realized.
Capital Gain (Loss) = P1 – P0
– A capital gain is realized when the outcome is positive.
– A capital loss will is realized when the outcome is negative.
Components of Stocks’ Realized Return
Capital gain: Profit that is obtained when the security is
sold and the price of a security is greater than the
purchase price. If the price of the stock drops during
the period, a capital loss is realized.
Capital Gain (Loss) = P1 – P0
– A capital gain is realized when the outcome is
positive.
– A capital loss will is realized when the outcome is
negative
Components of Bonds’ Realized Return
Coupon: Periodic payment of interest that the issuer is
required to pay at set intervals, (typically
semiannually) until maturity.
Components of Bonds’ Realized Return
Capital gain: If the bond is held to maturity, the investor
receives the full principal value.
– If the bond is sold prior to maturity, a capital gain or
loss may be realized depending on the bond’s
market price at the time of 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 principle that drives the
expected return model.
Present Value Formula
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. The Future value of
money is discounted using the interest rate.
PV = Present Value of the $
FV = Future Value of the $
i = interest rate
n = number of interest periods
Present Value
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 Money Value
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
B. 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
A. 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.
An Application of the Time Money Value
Situation 1: Assume the interest rate is 5%, compounded
annually. After three years you will have $23,152.50 so
you would still take the $20,000 today rather than the
$23,000 in the future.
 Using the Present Value Formula:
PV = FV/(1+i)n
I = 5%
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.
Situation 2: Now assume the
interest rate is 4%, compounded
annually. After three years, you
will have $22,497.28 so you would
rather take the $23,000 in the
future.
FV = PV*(1+i) n
FV = 20,000(1+.04)3 = $22,497.28
So taking the $23,000 in three
years would 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:
Compound vs. Simple 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
Compound vs. Simple Interest
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.
Return
Expected/Required Return: Return an investor
requires or expects for assuming a certain amount of
risk with the investment. The expected 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 Return
 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.
Expected Rate of Return Formula- Stocks
P0
i
D1
D2
D3
Pn
= price of the stock today
= expected rate of return
= dividend year 1
= dividend year 2
= dividend year 3
= price of the stock in future
Expected Rate of Return Formula- Stocks
Example: I.N. Vestor buys 1 share of stock XYZ at $1,000 per
share. It pays a 2% annual dividend ($20 per year). The price of
the stock after 1 year is $1,200. What is the expected rate of
return?
Solution: 1,000 = _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 for Bonds
Components of Bonds’ Expected Return
Coupon
A company that issues a bond
must pay the coupons or
coupon payments to the
bondholder.
Principal
The original investment.
Bond Cash Flows
 Company that issues a bond must pay the coupon payment
(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 change of default.
Bond Price Formula
C1
C2
C3
Pn
P0 =
+
+
+…+
2
3
(1+i ) (1+i ) (1+i )
(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 in the market is 3%.
Assuming that I.N. Vestor holds the bond
to maturity, he will receive 4 coupon
payments of $25 ($50 coupon payment
each year. Because the coupon is paid
semi annually (every 6 months), each
payment is $25) on 6/1/2013, 12/1/2013,
6/1/2014, and the last one on 12/1/2014.
At the maturity date, 12/1/2014,
I.N. Vestor receives his principal
investment of $1,000 plus the last
coupon 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.
Cash Flow of Bonds
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.
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
Investor pays
$1000 for bond
0
Coupon 1 = $25
Coupon 1 = $25
Coupon 1 = $25
$1000 principal
repayment
Coupon 1 = $25
1
2
3
4
6/1/11
12/1/11
6/1/12
12/1/12
Formula for a Bond’s Yield to Maturity
(Expected Return)
YTM
=
C
+
F-P
n
F+P
2
C = Coupon Payment
F = Face Value of Bond
P = Price of Bond
N = years until maturity
Ex.
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+ (F-P)/n
(F+P)/2
YTM = 50+ (1050-1000)/5
(1050+1000)/2
YTM = 5.85%
The yield to maturity is 5.85%