公司理财第七版Chap005课件
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(applications)
The PV formula has many applications. Given any variables in the equation, you can solve for the remaining variable.
PVFV(11r)t
公司理财第七版Chap005
公司理财第七版Chap005
Present Value
What is it? Why is it useful?
公司理财第七版Chap005
Present Value
Discount Rate:
r
Discount Factor:
DF
1 (1r)t
Present Value:
Recall: t = number of years
Interest Earned 7 7 7 7 7
Value
100 107 114 121 128 135
Value at the end of Year 5: $135
公司理财第七版Chap005
Compound Interest: Example
Interest earned at a rate of 7% for five years on the previous year’s balance.
D enote: C 1T hecashflowinyear1 C 2T hecashflowinyear2 C t T hecashflowinyeart(w ithanynum berofcashflow sinbetw een)
P V(1 C 1 r)1(1 C r2)2....(1 C rt)t
received today.
公司理财第七版Chap005
Future Values
Future Value: Amount to which an investment will grow after earning interest.
Let r = annual interest rate Let t = # of years
PVFV(11r)t
公司理财第七版Chap005
Present Value: Example
Always ahead of the game, Tommy, at 8 years old, believes he will need $100,000 to pay for college. If he can invest at a rate of 7% per year, how much money should he ask his rich Uncle GQ to give him?
公司理财第七版Chap005
Time Value of Money
Money has a time value. It can be expressed in multiple ways:
A dollar today held in savings will grow. A dollar received in a year is not worth as much as a dollar
公司理财第七版Chap005
The Power of Compounding
Interest earned at a rate of 7% for the first forty years on the $100 invested using simple and compound interest.
Simple Interest: Example
Interest earned at a rate of 7% for five years on a principal balance of $100.
Example - Simple Interest
Today
Future Years
1 2345
Example - Compound Interest
Today
Future Years
Interest Earned
71 7.492 8.031 8.458 95.18
107 114.49 122.50 131.08 140.26
Value
100Baidu Nhomakorabea
Value at the end of Year 5 = $140.26
Simple Interest
Compound Interest
F V S im p le= I n itia lin v e s tm e n t ( 1 r t) F V C o m p o u n d= I n itia lin v e s tm e n t ( 1 r ) t
公司理财第七版Chap005
Present Values: Changing Discount Rates
The present value of $100 to be received in 1 to 20 years at varying discount rates:
120
Discount Rates
100 0%
80
5%
Recall: r = the discount rate
公司理财第七版Chap005
Multiple Cash Flows: Example
Your auto dealer gives you the choice to pay $15,500 cash now or make three payments: $8,000 now and $4,000 at the end of the following two years. If your cost of money (discount rate) is 8%, which do you prefer?
10%
60
15%
PV of $100
40
20
0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 公司N理u财m第七b版erChoapf0Y05ears
PV of Multiple Cash Flows
The present value of multiple cash flows can be calculated:
F V $ 1 0 0 , 0 0 0 t 1 0 y r sr 7 %
P V F V (1 1 r)t $ 1 0 0 ,0 0 0 (1 .0 1 7 )1 0 $ 5 0 ,8 3 5
Note: Ignore inflation/taxes
公司理财第七版Chap005
Time Value of Money
The PV formula has many applications. Given any variables in the equation, you can solve for the remaining variable.
PVFV(11r)t
公司理财第七版Chap005
公司理财第七版Chap005
Present Value
What is it? Why is it useful?
公司理财第七版Chap005
Present Value
Discount Rate:
r
Discount Factor:
DF
1 (1r)t
Present Value:
Recall: t = number of years
Interest Earned 7 7 7 7 7
Value
100 107 114 121 128 135
Value at the end of Year 5: $135
公司理财第七版Chap005
Compound Interest: Example
Interest earned at a rate of 7% for five years on the previous year’s balance.
D enote: C 1T hecashflowinyear1 C 2T hecashflowinyear2 C t T hecashflowinyeart(w ithanynum berofcashflow sinbetw een)
P V(1 C 1 r)1(1 C r2)2....(1 C rt)t
received today.
公司理财第七版Chap005
Future Values
Future Value: Amount to which an investment will grow after earning interest.
Let r = annual interest rate Let t = # of years
PVFV(11r)t
公司理财第七版Chap005
Present Value: Example
Always ahead of the game, Tommy, at 8 years old, believes he will need $100,000 to pay for college. If he can invest at a rate of 7% per year, how much money should he ask his rich Uncle GQ to give him?
公司理财第七版Chap005
Time Value of Money
Money has a time value. It can be expressed in multiple ways:
A dollar today held in savings will grow. A dollar received in a year is not worth as much as a dollar
公司理财第七版Chap005
The Power of Compounding
Interest earned at a rate of 7% for the first forty years on the $100 invested using simple and compound interest.
Simple Interest: Example
Interest earned at a rate of 7% for five years on a principal balance of $100.
Example - Simple Interest
Today
Future Years
1 2345
Example - Compound Interest
Today
Future Years
Interest Earned
71 7.492 8.031 8.458 95.18
107 114.49 122.50 131.08 140.26
Value
100Baidu Nhomakorabea
Value at the end of Year 5 = $140.26
Simple Interest
Compound Interest
F V S im p le= I n itia lin v e s tm e n t ( 1 r t) F V C o m p o u n d= I n itia lin v e s tm e n t ( 1 r ) t
公司理财第七版Chap005
Present Values: Changing Discount Rates
The present value of $100 to be received in 1 to 20 years at varying discount rates:
120
Discount Rates
100 0%
80
5%
Recall: r = the discount rate
公司理财第七版Chap005
Multiple Cash Flows: Example
Your auto dealer gives you the choice to pay $15,500 cash now or make three payments: $8,000 now and $4,000 at the end of the following two years. If your cost of money (discount rate) is 8%, which do you prefer?
10%
60
15%
PV of $100
40
20
0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 公司N理u财m第七b版erChoapf0Y05ears
PV of Multiple Cash Flows
The present value of multiple cash flows can be calculated:
F V $ 1 0 0 , 0 0 0 t 1 0 y r sr 7 %
P V F V (1 1 r)t $ 1 0 0 ,0 0 0 (1 .0 1 7 )1 0 $ 5 0 ,8 3 5
Note: Ignore inflation/taxes
公司理财第七版Chap005
Time Value of Money