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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

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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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