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Time Value Of Money Essay

5195 words - 21 pages

Review Fundamentals of Valuation

These class notes review this material and also provide some help for a financial calculator. It also has some self-test questions and problems. Class notes are necessarily brief. See any principles of finance book for a more extensive explanation.

Eugene F. Brigham, Joel F. Houston Fundamentals of financial management HG 4026 B6693 1998
Ross, Stephen A, Westerfield, and Jordan Fundamentals of corporate finance HG 4026 .R677 1995

PART I: Single Sum.

Time Value of Money: Know this terminology and notation

FV Future Value
(1+i)t Future Value Interest Factor [FVIF]

PV Present Value
1/(1+i)t Present Value Interest ...view middle of the document...

The investment earns 8% for four years and then earns 4% for the remaining six years.
FV = $10,000·(1+i)·(1+i)·(1+i)·(1+i)·(1+i)·(1+i)·(1+i)·(1+i)·(1+i)·(1+i)
FV = $10,000·(1.08)·(1.08)·(1.08)·(1.08)·(1.04)·(1.04)·(1.04)·(1.04)·(1.04)·(1.04)
FV = $10,000 x (1.08)4 x (1.04)6
FV = $17,214.53

B. Present Value:
Same idea, but begin at the end. Rearrange the Future value equation to look like this:

PV = FV÷ [(1+i)·(1+i)·(1+i)·(1+i)·(1+i)·(1+i)·(1+i)·(1+i)·(1+i)·(1+i)]
PV = FV ÷ (1+i)t [2]

Example: How much do I need to invest at 8% per year, in order to have $10,000 in__.
a. One year: PV =10,000 ÷ (1.08) = $9,259.26
b. Two years: PV = $10,000 ÷ (1.08) ÷ (1.08)
OR $10,000 ÷ (1.08)2 = $8,573
c. Ten years PV = $10,000 ÷ (1.08)10 = $10,000 ÷ 2.1589 = $4,632

C. Rate of Return

START WITH SAME RELATIONHSIP: FV = PV x (1+i)t
Solve for i.
(1+i)t =FV/PV.
1+i = (FV/PV)1/t
i = (FV/PV)1/t-1.
Question: An investor deposits $10,000. Ten years later it is worth $17,910. What rate of return did the investor earn on the investment?
Solution:
$17,910 = $10,000 x (1+i)10
(1+i)10 = $17,910/10,000 = 1.7910
(1+i) = (1.7910) 1/10 = 1.060
i = .060 = 6.0%

D. Finding the Future Value
Find the value of $10,000 today at the end of 10 periods at 5% per period.

1. Scientific Calculator:
Use [yx] y = (1+i) = 1.05 and x =t= 10.
1. Enter 1.05.
2. Press [yx].
3. Enter the exponent.
4. Enter [=].
5. Multiply result by $10,000.

2. Spreadsheet:

3. Financial calculator. You may need to input something like this.
Specific functions vary. Be sure to consult the calculator’s manual!!!!!!

n [N]
i [I/YR]
PV
PMT
FV

10
5
10,000
0
?
NOTE: The future value will be negative, indicate an opposite direction of cash flow.

1. Set the calculator frequency to once per period.
2. Enter negative numbers using the [+/-] key, not the subtraction key.
3. Be sure the calculator is set in the END mode.

E. Fundamental Idea.
Question: What is the value of any financial asset?
Answer: The present value of its expected cash flows.
F. Finding the Present Value
Find the present value of $10,000 to be received at the end of 10 periods at 8% per period.

a. Scientific Calculator

Scientific Calculator:
Use [yx ] where y = 1.08 and x = -1,-2, or -10.
1. Enter 1.08.
2. Press [yx]
3. Enter the exponent as a negative number
4. Enter [=].
5. Multiply result by $10,000.

b. Spreadsheet

c. Financial calculator. You may need to input something like this.
Specific functions vary. Be sure to consult the calculators’ manual!!!!!!

n [N]
i [I/YR]
PV
PMT
FV
c.
10
8
10,000
0
?

The present value will be negative, to indicate the opposite direction of cash flow.

G. Finding the [geometric average] rate...

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