Chapter 5: Intro To Time Valuation of Money

Question 1

One of the basic problems that financial managers face is how to determine today’s ___________ that are expected in the future

Answer 1

value of cash flows

Question 2

Time value of money

Answer 2

refers to the fact that a dollar in hand today is worth more than a dollar promised at some time in the future

Question 3

Future value (FV) (AKA compound value)

Answer 3

The amount an investment is worth after one or more periods. Also compound value.

refers to the amount of money to which an investment would grow over some length of time at some given interest rate.

Question 4

Example of Future value

Answer 4

Suppose you were to invest $100 in a savings account that pays 10% interest per year.

You would have $110.

This $110 is equal to your original principal of $100 plus $10 in interest that you earn.

We say that $110 is the FV of $100 invested for one year at 10%, and we simply mean that $100 today is worth $110 in one year, given that 10% is the interest rate.

Question 5

Investing for a single period (equation)

Answer 5

(1+r)

Where ‘r’ is your interest rate

100x(1+.10) = $110

Question 6

Investing for more than 1 period:

Say now the $100 you invested is going to be held for 2 years. How much money is yours after 2 years and 10% interest rate?

Answer 6

If you leave the entire $110 in the bank, you will earn $110x.10= $11 in interest during the second year, so you will have a total of $110 + $11 = $121 . This $121 is the future value of $100 in two years at 10%

Question 7

This $121 has _______ parts.

Answer 7

four

1) The first part is the $100 original principal.
2) The second part is the $10 in interest you earned in the first year along with another $10 (the third part) you earn in the second year, for a total of $120.
4) The last $1 you end up with (the fourth part) is interest you earn in the second year on the interest paid in the first year: .

Question 8

Compounding

Answer 8

The process of accumulating interest in an investment over time to earn more interest.

This process of leaving your money and any accumulated interest in an investment for more than one period

Question 9

Interest on interest

Answer 9

Interest earned on the reinvestment of previous interest payments.

Question 10

Compound interest

Answer 10

Interest earned on both the initial principal and the interest reinvested from prior periods.

Question 11

Simple interest

Answer 11

Interest earned only on the original principal amount invested.

Simply: the interest is not reinvested

How to calculate simple interest:

500 x 1.06 = 530
-Now, remove that $30 to bring it back to $500.
-Now, multiply the $30 (or whatever the interest is) by how many years it would have compounded for.
If compounded annually: 500x.106^30 = 2,871.75
With simple interest: $30x30+500 = 1400
$2,871.75 - 1,400 = $1,471.75

When:
t=30
r= 6%
Investment = $500

Question 12

The future of $1 invested equation

Answer 12

Future value = $1x(1+r)^t

Question 13

Future Value Interest Factor (FVIF) (AKA future value factor)

Answer 13

(1+r)^t component of the equation

Question 14

Present value (PV)

Answer 14

The current value of future cash flows discounted at the appropriate discount rate.

Question 15

Discount

Answer 15

To calculate the present value of some future amount.

Question 16

Present Value calculation equation

SINGLE YEAR / SINGLE PERIOD

Answer 16

Suppose you need $400 to buy textbooks next year. You can earn 4% on your money. How much do you have to invest today?

=400/1.04 = $384.62

or

PV = $1 / (1+r)

Question 17

Present Values for Multiple Periods equation

Answer 17

PV = $1 / (1+r)^t

Question 18

Discount factor

Answer 18

Specifically, (1+r)^t portion of present value calculation

Question 19

Discount rate (aka interest rate or rate of return)

Answer 19

The rate used to calculate the present value of future cash flows.

Question 20

In other words, the _______ the risk, the _______ money your investment will earn.

Answer 20

higher

more

Question 21

Discounted cash flow (DCF) valuation

Answer 21

calculating the present value of a future cash flow to determine its worth today

Question 22

Quick recap:

Answer 22

Future value factor: (1+r)^t

Present value factor: 1/(1+r)^t

Question 23

Basic present value equation

Answer 23

PV = FVt / (1+r)^t

Question 24

Basic present value equation:

Answer 24

There are only four parts to this equation:

1) the present value (PV),
2) the future value (FVt),
3) the discount rate (r),
4) and the life of the investment (t).

Given any three of these, we can always find the fourth part.

Question 25

Rate of return questions:

Answer 25

Will provide you with PV, FT, and a time frame (years usually)

Now you must find ‘r’

Example: 100 = 200 / (1+r)^8
Simplified: (1+r)^8 = 200 / 100
Simplified: (1+r)^8 = 2

Now, solve for r.

Can be done by taking the eighth root of 2 and seeing the percentage includes
This = 9.05%

Question 26

Finding the number of periods:

Answer 26

Provides you PV, FT, and interest rate

Now you must find ‘t’

Example: Suppose we were interested in purchasing an asset that costs $50,000. We currently have $25,000. If we can earn 12% on this $25,000, how long until we have the $50,000?

1) 25,000 = 50,000 / (1.12)^t
2) Simplify: (1.12)^t = 2

We thus have a future value factor of 2 for a 12% rate.

Question 27

To find T

T =

Answer 27

ln (FV/PV) / ln (1+r)

ln= natural log

Question 28

To find r

r =

Answer 28

(FV/PV)^1/t - 1

Question 29

The future value of a single sum will increase less rapidly when the frequency of compounding increases.

Answer 29

False