2. Time Value of Money
Present value of any the amount of money today that would
future sum of money = be needed at current interest rates to produce that future sum
Compounding = interest remains in the bank and ALSO earns interest

3. Formulas Time value of money Time value of money one year
P = present value of dollars
F = Future value of money
r = interest rate in decimals
N = number of years
Time value of money
one year
Time value of money
Multiple years
$F = $P x (1 + r)
$F = $P x (1 + r)N
$P = __$F__
(1 + r)
$P = __$F__
(1 + r)N

4. Assume the interest rate is 10% in all of the examples below
If I lend $1 today how much will I be paid one year from now?
$F = $P x (1 + r)
$F = 1 x (1 + .1)
$F = 1 x 1.1
$F = $1.10

5. Assume the interest rate is 10% in all of the examples below
How much will I have to lend out today to have $1 a year from?
$P = __$F__
(1 + r)
  $P = ___1___
(1 + .1)
$P = _1_
1.1
$P = $.91

6. Assume the interest rate is 10% in all of the examples below
If I Deposit $50 in a bank account how much will I have one year from now?
$F = $P x (1 + r)
$F = 50 x (1 + .1)
$F = 50 x 1.1
$F = 55

7. Assume the interest rate is 10% in all of the examples below
How much do I need to deposit in a bank account today to have $50 one year from now?
$P = _$50_
(1 + .1)
1.1
$P = $45.45
$P = __$F__
(1 + r)

8. Suppose you have to choose one of three projects to undertake
Suppose you have to choose one of three projects to undertake. Project A costs nothing and has an immediate payoff to you of $100. Project B requires that you pay $10 toady in order to receive $115 a year from now. Project C gives you an immediate payoff of $119 but requires you pay $20 a year from now. Assume the interest rate is 10%. Calculate the net present value to determine which project is most profitable.
Project
Dollars realized today
Dollars realized one year from today
Present value of dollars realized one year from now
Dollars realized today + present value of dollars realized one year from now = net present value A B C

9. Suppose you have to choose one of three projects to undertake
Suppose you have to choose one of three projects to undertake. Project A costs nothing and has an immediate payoff to you of $100. Project B requires that you pay $10 toady in order to receive $115 a year from now. Project C gives you an immediate payoff of $119 but requires you pay $20 a year from now. Assume the interest rate is 10%. Calculate the net present value to determine which project is most profitable.
Project
Dollars realized today
Dollars realized one year from today
Present value of dollars realized one year from now
Dollars realized today + present value of dollars realized one year from now = net present value A
 $100 B
 -$10 C
 $119

10. Suppose you have to choose one of three projects to undertake
Suppose you have to choose one of three projects to undertake. Project A costs nothing and has an immediate payoff to you of $100. Project B requires that you pay $10 toady in order to receive $115 a year from now. Project C gives you an immediate payoff of $119 but requires you pay $20 a year from now. Assume the interest rate is 10%. Calculate the net present value to determine which project is most profitable.
Project
Dollars realized today
Dollars realized one year from today
Present value of dollars realized one year from now
Dollars realized today + present value of dollars realized one year from now = net present value A
 $100  0 B
 -$10
 $115 C
 $119
 -$20

11. Dollars realized today Dollars realized one year from today
Suppose you have to choose one of three projects to undertake. Project A costs nothing and has an immediate payoff to you of $100. Project B requires that you pay $10 toady in order to receive $115 a year from now. Project C gives you an immediate payoff of $119 but requires you pay $20 a year from now. Assume the interest rate is 10%. Calculate the net present value to determine which project is most profitable.
Project
Dollars realized today
Dollars realized one year from today
Present value of dollars realized one year from now
Dollars realized today + present value of dollars realized one year from now = net present value A
 $100  0 B
 -$10
 $115 C
 $119
 -$20
$P = __$F__
(1 + r)

12. Dollars realized today Dollars realized one year from today
Suppose you have to choose one of three projects to undertake. Project A costs nothing and has an immediate payoff to you of $100. Project B requires that you pay $10 toady in order to receive $115 a year from now. Project C gives you an immediate payoff of $119 but requires you pay $20 a year from now. Assume the interest rate is 10%. Calculate the net present value to determine which project is most profitable.
Project
Dollars realized today
Dollars realized one year from today
Present value of dollars realized one year from now
Dollars realized today + present value of dollars realized one year from now = net present value A
 $100  0  _ B
 -$10
 $115
 $104.55 C
 $119
 -$20
 $-18.18
$P = __$F__
(1 + r)

13. Which project should you choose? WHY?
Suppose you have to choose one of three projects to undertake. Project A costs nothing and has an immediate payoff to you of $100. Project B requires that you pay $10 toady in order to receive $115 a year from now. Project C gives you an immediate payoff of $119 but requires you pay $20 a year from now. Assume the interest rate is 10%. Calculate the net present value to determine which project is most profitable.
Project
Dollars realized today
Dollars realized one year from today
Present value of dollars realized one year from now
Dollars realized today + present value of dollars realized one year from now = net present value A
 $100  0  _ B
 -$10
 $115
 $104.55
 $94.55 C
 $119
 -$20
 $-18.18
 $100.82
Which project should you choose? WHY?

14. Consider the three project from the previous page
Consider the three project from the previous page. This time however, suppose that the interest rate is only 2%. Calculate the net present value to determine which project is most profitable.
Project
Dollars realized today
Dollars realized one year from today
Present value of dollars realized one year from now
Dollars realized today + present value of dollars realized one year from now A B C

15. Dollars realized today Dollars realized one year from today
Consider the three project from the previous page. This time however, suppose that the interest rate is only 2%. Calculate the net present value to determine which project is most profitable.
Project
Dollars realized today
Dollars realized one year from today
Present value of dollars realized one year from now
Dollars realized today + present value of dollars realized one year from now = net present value A
 $100  0 B
 -$10
 $115 C
 $119
 -$20
$P = __$F__
(1 + r)

16. Dollars realized today Dollars realized one year from today
Consider the three project from the previous page. This time however, suppose that the interest rate is only 2%. Calculate the net present value to determine which project is most profitable.
Project
Dollars realized today
Dollars realized one year from today
Present value of dollars realized one year from now
Dollars realized today + present value of dollars realized one year from now = net present value A
 $100  0 0  B
 -$10
 $115
 $112.75 C
 $119
 -$20
 $-19.61
$P = __$F__
(1 + r)

17. Consider the three project from the previous page
Consider the three project from the previous page. This time however, suppose that the interest rate is only 2%. Calculate the net present value to determine which project is most profitable.
Project
Dollars realized today
Dollars realized one year from today
Present value of dollars realized one year from now
Dollars realized today + present value of dollars realized one year from now = net present value A
 $100  0 0  B
 -$10
 $115
 $112.75
 $102.75 C
 $119
 -$20
 $-19.61
 $99.39
Which project should be selected now?
Explain why the preferred choice is different with a 2% interest rate than it was with a 10% interest rate.

18. The following Examples all involve time periods of more than 1 year.
What is the present value of $100 realized two years from now if the interest rate is 10%?
  $P = __$F__
(1 + r)N
$P =_$100_
(1 + .1)2
$P = _$100
1.21
$P = $82.64

19. The following Examples all involve time periods of more than 1 year.
What is the amount you will receive in three years if you loan $1,000 at 5% interest?
  $F = $P x (1 + r)N
$F = $1000 x (1 +  .05)3
$F = $1000 x (1.16)
$F = $1,160

20. The following Examples all involve time periods of more than 1 year.
What is the present value of $1,000 received in three years if the interest rate is 5%
$P = $1,000
1.16
$P = $862.07 
$P = __$F__
(1 + r)N
( )3

21. Imagine that General Motors is thinking about building a new factory
Imagine that General Motors is thinking about building a new factory. Suppose that the factory will cost $100 million today and will yield the company $200 million in 10 years. Should General Motors undertake the project? HINT - To make its decision, the company will compare the present value of the $200 million return to the $100 million cost.
If the interest rate is 5% what is the present value of the $200 million?
  $P = __$F__
(1 + r)N
$P = $200
( ) 10
1.63
$P = $122.70

22. Imagine that General Motors is thinking about building a new factory
Imagine that General Motors is thinking about building a new factory. Suppose that the factory will cost $100 million today and will yield the company $200 million in 10 years. Should General Motors undertake the project? HINT - To make its decision, the company will compare the present value of the $200 million return to the $100 million cost.
If the interest rate is 5% what is the present value of the $200 million?
  P = $122.70
Should General Motors make this investment?

23. Imagine that General Motors is thinking about building a new factory
Imagine that General Motors is thinking about building a new factory. Suppose that the factory will cost $100 million today and will yield the company $200 million in 10 years. Should General Motors undertake the project? HINT - To make its decision, the company will compare the present value of the $200 million return to the $100 million cost.
If the interest rate is 8% what is the present value of the $200 million?
  $P = __$F__
(1 + r)N
$P = $200
( ) 10
2.16
$P = $93
Should General Motors make this investment NOW?

24. Imagine that General Motors is thinking about building a new factory
Imagine that General Motors is thinking about building a new factory. Suppose that the factory will cost $100 million today and will yield the company $200 million in 10 years. Should General Motors undertake the project? HINT - To make its decision, the company will compare the present value of the $200 million return to the $100 million cost.
If the interest rate is 8% what is the present value of the $200 million?
$P = $93
 Should General Motors make this investment NOW?