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.

Investing

Return On Investment

After the investment is made.

The returnis 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 ReturnExample : 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 ReturnDividends: 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 raten = 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 Value1) Congratulations! You have won a cash prize of $20,000! You have two

options:

Or

B. The choice is clear: most people will choose to take the money today. 2) Now, what if the options are:

Or

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.

A. Receive $20,000 now B. Receive $20,000 in three years

A. Receive $20,000 now A. Receive $23,000 in three years

An Application of the Time Money ValueSituation 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 = 3PV = 20,000*The formula can be adjusted to solve for any of the variables. FV = PV*(1+i)nFV = 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:

Interest = Principal*Interest Rate*Time

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 investmenti = Interest raten = 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 = 3P = 10,000M= 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 StocksComponents 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 = price of the stock todayi = expected rate of returnD1 = dividend year 1D2 = dividend year 2D3 = dividend year 3

= price of the stock in future

P0 = + + + … +

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) = 12201000i = 220 i = 0.22 = 22%The expected rate of return is 22%

Expected Rate of Return for BondsComponents of Bonds’ Expected Return

CouponA 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 semi-annually. 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

P0 = + + + … +

• 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.

0 1 2 3 4

Coupon 1 = $25 Coupon 1 = $25 Coupon 1 = $25

$1000 principal repayment Coupon 1 = $25

Investor pays $1000 for bond

6/1/11 12/1/11 6/1/12 12/1/12

Cash Flow of BondsYield 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 = 1,000P = 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+942.1842303P = $1,038.54

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?

C= 50F= 1,050P= 1000n= 5

YTM = C+ (F-P)/n (F+P)/2

YTM = 50+ (1050-1000)/5 (1050+1000)/2YTM = 5.85%

The yield to maturity is 5.85%

Solution YTM = Yield To Maturity