Return
Bought 100 shares of Apple stock for $97.34 on January 1st 2016.
Sold the stock the stock for $225.74 on September 1st 2018.
Assume no dividends were paid.
Shares
Pt
Pt+1
What is your initial investment?
What was your return on investment?
Bought 100 shares of Apple stock for $97.34 on January 1st 2016.
Sold the stock the stock for $225.74 on September 1st 2018.
Assume no dividends were paid.
What was your dollar, and cumulative, return on investment?

TVM I
Berkshire-B shares are around $200 right now. Analysts expect the price to be $250 in 2 years.
If the appropriate discount rate is 8%, what is the value of Berkshire-B shares today? Should you buy the stock?
?

If you hold on to that account for 40 years, what is it going to be worth?

What about 50 years?
Formula
TVM Function

If you have $12,000 saved towards a new car and expect the car to cost $18,000, how long will you have to save
PV
$12,000
FV
$18,000
r
8%
n
?
TVM Function
What sort of return do you have to earn to grow $5,000 to $10,000 in 7 years?
PV
$5,000
FV
$10,000
r
?
n
7
TVM Function
TVM II
Hear a rumor that grandma wants to gift you $5,000 at your graduation in 2 years.
What’s that worth today if the discount rate is 9%?
?
?

Have $20,000 to invest. Decide to invest in the S&P 500, which earns an average annual return of 10%.
What is that savings expected to be if you save until retirement in 40 years? 50 years?
?
?
PV
FV

n
?
n
?
n
Interest at 4.5%
Interest at 9%
Interest at
What interest rate is needed to grow $7,500 into $10,000 in 3 years?

Expect a portfolio to earn 7.5%. How long to double your investment in that portfolio?

You bought 1,000 shares of Netflix stock for $4.2
You sold all your shares for $356.56 on March 1s
Assume no dividends were paid.
Shares
Pt
What is your initial investment?
What was your return on investment?
?