Chapter 5: Intro To Time Valuation of Money Flashcards
One of the basic problems that financial managers face is how to determine today’s ___________ that are expected in the future
value of cash flows
Time value of money
refers to the fact that a dollar in hand today is worth more than a dollar promised at some time in the future
Future value (FV) (AKA compound value)
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.
Example of Future value
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.
Investing for a single period (equation)
(1+r)
Where ‘r’ is your interest rate
100x(1+.10) = $110
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?
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%
This $121 has _______ parts.
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: .
Compounding
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
Interest on interest
Interest earned on the reinvestment of previous interest payments.
Compound interest
Interest earned on both the initial principal and the interest reinvested from prior periods.
Simple interest
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
The future of $1 invested equation
Future value = $1x(1+r)^t
Future Value Interest Factor (FVIF) (AKA future value factor)
(1+r)^t component of the equation
Present value (PV)
The current value of future cash flows discounted at the appropriate discount rate.
Discount
To calculate the present value of some future amount.
Present Value calculation equation
SINGLE YEAR / SINGLE PERIOD
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)
Present Values for Multiple Periods equation
PV = $1 / (1+r)^t
Discount factor
Specifically, (1+r)^t portion of present value calculation
Discount rate (aka interest rate or rate of return)
The rate used to calculate the present value of future cash flows.
In other words, the _______ the risk, the _______ money your investment will earn.
higher
more
Discounted cash flow (DCF) valuation
calculating the present value of a future cash flow to determine its worth today
Quick recap:
Future value factor: (1+r)^t
Present value factor: 1/(1+r)^t
Basic present value equation
PV = FVt / (1+r)^t
Basic present value equation:
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.
Rate of return questions:
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%
Finding the number of periods:
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.
To find T
T =
ln (FV/PV) / ln (1+r)
ln= natural log
To find r
r =
(FV/PV)^1/t - 1
The future value of a single sum will increase less rapidly when the frequency of compounding increases.
False
