The Financial SectorModules 22-29

AP MacroNancy K. Ware InstructorGainesville High School

Section 5

Module 24 The Time Valueof Money

Module 24 Essential Questions

1. Why is a dollar today worth more than a dollar a year from now?

2. How can the concept of present value help you make decisions when costs or benefits come in the future?

Start up Which one is more valuable: $1000

today or $1000 dollars one year from now?

Why?

Borrowing, Lending, & Interest Oh My!

• The effect of time on cost benefit analysis

Question: Suppose you could have $1000 today or $1000 next year. Which would you choose?

Why? Reason 1:

Reason 2 Conclusion:

Borrowing, Lending, & Interest Oh My!

Question: Suppose you could have $1000 today or $1000 next year. Which would you choose?

Money today! Why? satisfaction of buying or saving

today, rather than waiting. Reason 1: You need to buy food or

pay rent! You can’t wait a year to get your hands on that money!

Reason 2: If you had the money today, you could put it in the bank and in a year you would have more than $1000.

So for both reasons, $1000 today is worth more than waiting a year to get $1000.

Borrowing, Lending, & Interest Oh My!

You are going to lend your friend $100, and he is going to pay you back in 1 year. Assume no inflation, you agree to a 10% interest rate (the going rate you could receive if you had simply saved the money) 1. Why do you need to receive interest on this loan?

2. What is the opportunity cost of lending your friend $100?

3. What does the interest measure?

4. If you did not save it what could you have done with the money?

5. Repayment received on lending $100 for one year (simple interest is prt)=

Borrowing, Lending, & Interest Oh My!Part 1

You are going to lend your friend $100, and he is going to pay you back in 1 year. Assume no inflation, you agree to a 10% interest rate (the going rate you could receive if you had simply saved the money) 1. Why do you need to receive interest on this loan? To

compensate you!!2. The opportunity cost of lending your friend $100 is the

interest you could have earned, $10, after a year had passed. 3. The interest rate measures the cost to you of forgoing

(giving up) the use of that $100. 4. OR Rather than saving it, you could have spent $100 on

clothing right now that would have provided immediate benefit to you.

 5. Repayment received on lending $100 for one year = $100 + $100*.10 = $110

Borrowing, Lending, & Interest Oh My!Part 1

What if you were going to lend your friend the money for 2 years?1. Repayment in 2 years? =2. Your friend, as a borrower, must pay you $______to compensate you for the fact that he _________________ for a period of____years. 3. What could you have done as a saver? How much more money would you have had? They are equivalent measures of purchasing power, just measured at two different points in time, and it is the interest rate that equates the two.

Borrowing, Lending, & Interest Oh My!Part 2

What if you were going to lend your friend the money for 2 years?1. Repayment in 2 years = $100(1.10)*(1.10) = $1212. Your friend, as a borrower, must pay you $_21_to compensate you for the fact that he __has your money___ for a period of_2_years. 3. What could you have done as a saver? You could put the $100 in the bank today, 2 years from now you would have $121 to spend on goods and services!! They are equivalent measures of purchasing power, just measured at two different points in time, and it is the interest rate that equates the two.

Borrowing, Lending, & Interest Oh My! Part 2http://www.calculator.net/mortgage-calculator.html

Defining Present Value

• Let fv = future value of $pv = present value of $

r = real interest rate n = # of years (also known as t)

• The Simple Interest Formula

fv = ( 1 + r )n * pv

pv = fv / (1 + r)n

Dollars received today & dollars received in the future: there is a difference! To see the relationship between dollars today (present value PV) and dollars 1 year from now (future value FV), use this equation: Future Payment, or FV = PV*(1+r) 1. 1 year into the future, $100 in the present will be worth ?.

2. This is true whether you s_______it or l______ it to your friend.

 To solve for the present value PV: PV = FV/(1+r)3. What is $110 received a year from now worth in today’s dollars?4. PV =5. This tells us that $110 received a year from now is worth $______

today’s dollars. 

Defining Present Value Part 1

Dollars received today & dollars received in the future: there is a difference! To see the relationship between dollars today (present value PV) and dollars 1 year from now (future value FV), use this equation:  Future Payment, or FV = PV*(1+r) FV = $100*(1.10) = $110 So in other words, 1 year into the future, $100 in the present will be

worth $110. This is true whether you saved it or lent it to your friend. To solve for the present value PV: PV = FV/(1+r)1. What is $110 received a year from now worth in today’s dollars?  PV = $110/(1.10) = $100 This tells us that $110 received a year from now is worth $100 in

today’s dollars. 

Defining Present Value Part 1

1. What if you decide to lend the money ($100) for a period of t=2 years:

2. Formula: FV = PV(1+r)(1+r) or FV = PV(1+r)t

3. Repayment in two years?

4. Solve for Present value: PV = FV/(1+r)t

5. BIG IDEA: Money today is m________v_________than the same amount of money in the f____________.

6. Formula: The present value of $1 received one year from now is ___________.

7. Formula: The future value of $1 invested today is ____________. 8. Interest paid on savings and interest charged on borrowing

is designed to equate the value of d________t________ with the value of f__________ dollars.

Defining Present Value Part 2

1. What if you decide to lend the money ($100) for a period of t=2 years?

2. Formula: FV = PV(1+r)(1+r) or FV = PV(1+r)t

3. Repayment in two years = $100(1.10)*(1.10) = $121

Solve for present value: PV = FV/(1+r)t = 121/(1+.10)2 = 100

4. BIG IDEA: Money today is more valuable than the same amount of money in the future.

5. The present value of $1 received one year from now is $1/(1+r).6. The future value of $1 invested today is $1*(1+r). 7. Interest paid on savings and interest charged on borrowing

is designed to equate the value of dollars today with the value of future dollars.

Defining Present Value Part 2

Present & Future Value The present value of $1 received one year from now is $1/(1+r). Calculate using an interest rate of 5%.

The future value of $1 invested today is $1*(1+r). Calculate using an interest rate of 5%.

Which would you rather do? Receive or invest?

Present & Future Value The present value of $1 received one year from now is $1/(1+r). Calculate using an interest rate of 5%.$.95The future value of $1 invested today is $1*(1+r). Calculate using an interest rate of 5%.$1.05Which would you rather do? Receive or invest?

Using Present Value: Why?

Net Present Value: present value of current and future benefits minus the present value of current and future costs.

In other words, do the benefits outweigh the costs?

Calculating Net Present Value

Calculate the net present value of all the 3 hypothetical projects described below. Assume the interest rate is 5%. [PV = FV/(1+r)]a. Project A: You receive an immediate payoff of $1000.Project B: You pay $100 today in order to receive $1200 a year from now.Project C: You received $1200 today but must pay $200 one year from now.

b. Which of the 3 projects would you choose to undertake based in your net present value calculations?

Calculating Net Present Value

Calculate the net present value of all the 3 hypothetical projects described below. Assume the interest rate is 5%. [PV = FV/(1+r)]a. Project A: You receive an immediate payoff of $1000.Project B: You pay $100 today in order to receive $1200 a year from now.Project C: You received $1200 today but must pay $200 one year from now. Project A: NPV $1000 Project B: NPV : 1200/1 + .05 = 1200/1.05 = $1142.86 - $100 = $1042.86 Project C: NPV: 200/1.05 = $190.48. $1200 - $190.48 = $1009.52

b. Which of the 3 projects would you choose to undertake based in your net present value calculations? Project B has the highest NPV

Net Present ValueYou have won the state lottery. There are 2 ways in which you can receive your prize. You can either have 1 million in cash now, or you can have 1.2 million that is paid out as follows: $300,000 now, $300,000 in one year, $300,000 in 2 years, & $300,000 in 3 years. The interest rate is 20%. How do you want to receive your prize?

Net Present ValueThe drug company Pfizer is considering whether to invest in the development of a new cancer drug. Development will require an initial investment od 10 million now, and beginning a year from now, the drug will generate annual profits of 4 million for 3 years. a. If the interest rate is 12% should Pfizer invest in the development of the new drug? Why or why not?b. If the interest rate is 8%, should Pfizer invest in the development of the new drug? Why or why not?

[PV = FV/(1+r)]

Net Present ValueYou have won the state lottery. There are 2 ways in which you can receive your prize. You can either have 1 million in cash now, or you can have 1.2 million that is paid out as follows: $300,000 now, $300,000 in one year, $300,000 in 2 years, & $300,000 in 3 years. The interest rate is 20%. How do you want to receive your prize?

Complete Module 24 Review Questions p. 241-241

Read Module 25 p. 243-251