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### Chapter

Time Value of Money Concepts

Time Value of Money

- The dollar amount cash flows difference between the present value of an amount and its future value. The difference is also referred to as the interest.
- Example:
- The time value of $100 for one year at i = 10%.
- Present value=$100
- Future value=$100 x (1+10%)=$110
- The time value of one year for this $100
- =$110-$100=$10

Time Value of Money Concepts

$10,000 x (1+i)2 = $12,100

A.Future Value of A Single Amount- FV= I x ( 1 + i)n
- Where:FV = Future value of the invested amount;
- i = Amount invested at the beginning of the
- period;
- n = the number of compounding periods.
- Example: The future value of $10,000 invested on
- 1/1/x1, at the end of year 2 (i.e.;12/31/x2)
- with i=10%.

Time Value of Money Concepts

$12,100 / (1+10%)2 = $10,000

B.Present Value of A Single Amount- FV = I x (1 + i)n
- I = FV / (1 + i)n
- Where: I = Present value of a single amount.
- Example: The present value of $12,100 to be
- received two years from now with i =10%

Time Value of Money Concepts

End of Year 3

End of Year 1

0

First payment

$10,000

2nd payment

$10,000

3rd payment

$10,000

C. Annuity- The cash flows of a constant amount to be received or paid each period.
- Case 1: Future value of an ordinary annuity
- FVA: Annuity amount x future value annuity factor
- Example:The future value of paying $10,000 every year
- for the following three years at i= 10%. The first
- $10,000 is to be paid one year from today (n=0).
- Diagram of these payments

Time Value of Money Concepts

The future value annuity factor

The future value

C.Annuity (contd.) Case 1 (contd.)- The future value of these payments (an ordinary annuity) is:

Time Value of Money Concepts

the future value annuity factor

(Table 6A-3 under 10%, n=3)

C.Annuity (contd.) Case 1 (contd.)- A short cut:
- FVA = $10,000 x 3.31

a=(1+10%)2=1.21

b=(1+10%)1=1.10

Time Value of Money Concepts

End of Year 2

End of Year 1

0

future value

First payment

$10,000

2nd payment

$10,000

3rd payment

$10,000

C.Annuity (contd.) Case 2: Future Value of An Annuity Due- Diagram of this annuity

- Note:
- This annuity is similar to that of Case 1 except that the first payment was made at the beginning of year 1.

Time Value of Money Concepts

(Table 6A-3, the factor under 10%, 4 period minus one.

or Table 6A-5, under 10%, n=3)

C.Annuity (contd.) Case 2: (contd.)- Future value of these payments:

- A short cut: $10,000x3.641=36,410

Time Value of Money Concepts

End of Year 2

End of Year 1

0

First payment

$10,000

2nd

payment

$10,000

3rd payment

$10,000

Present

Value

?

C.Annuity (contd.) Case 3:Pre. Val. of An Ordinary Annuity- PVA=annuity amount x present value annuity factor
- Example: The present value of paying $10,000
- every year for the following three years at
- i=10%. The first $10,000 is to be paid
- one year from today (n=0).
- Diagram of these payments

Time Value of Money Concepts

The present value annuity factor(Table 6A-4,under 10%, n=3)

C.Annuity (Contd.) Case 3: (contd.)- The Present value of these payments (an ordinary annuity) is:

- a=1/(1+10%)=0.90909
- b=1/(1+10%)2=0.82645
- A short cut: $10,000 x 2.48685=24,868

Time Value of Money Concepts

End of Year 2

End of Year 1

Present Value ?

0

First

payment

$10,000

3rd payment

$10,000

2nd

payment

$10,000

C.Annuity (contd.) Case 4: Pre. Value of An Annuity Due- Diagram of this annuity

- Note:
- This annuity is similar to that of Case 3 except that the first payment was made at the beginning of year 1.

Time Value of Money Concepts

(Table 6A-4, the factor under i=10%, n=2 plus one.

Or Table 6A-6, factor under i= 10%, n=3)

C.Annuity (contd.) Case 4 : (contd.)- The present value of these payments:

- A short cut: $10,000 x 2.73554=$27,355

Time Value of Money Concepts

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