Unit 2 Flashcards
The goal of finance
Maximize the decider’s wealth
An investment is worth undertaking if it is expected that our wealth will increase as a result of the investment
True
To determine if an investment contributes to the increase of wealth, we compare which 2 figures?
The price of investment
The value of the investment
The price of the investment
The amount of money we need to pay upfront to undertake the investment
The value of the investment is …
the exact worth of the investment
Price
What you need to collect
What you actually paid for the investment
Value
What you think would be a fair price for the investment
What you think the investment is actually worth
The maximum amount of money an investor is willing to pay for an asset at a given moment in time
If we know the price and value of an investment, it will be easy to make the right decision
True
If price > value, the investment is:
a. good
b. bad
Bad because you pay more than you receive.
You lose money.
If price = value, the investment is:
a. good
b. bad
c. the same
C. The same
You pay the same amount that you receive.
If price < value, the investment is:
a. good
b. bad
c. the same
A. Good
You receive more than you pay so you gain money.
We are looking for opportunities where we …
pay less than the value of the company.
We find out the price by …
looking at the market or asking the seller of the asset.
We find out the value by …
calculating the future cash flows.
The value of money …
changes over time.
15 euros now is worth __________ than 15 euros in the future.
more
Why does the value of money change over time?
- Opportunity cost
2. Risk
What is opportunity cost?
To receive money in the future is to lose an opportunity to buy/invest and increase your wealth now
If you receive 1000 euros today, you can deposit it in the bank at an interest rate of 1% and get back 1,010 euros in a year. But, if you receive that same 1000 euros in a year, you will receive ______ euros.
Therefore, you have _______ the opportunity of ______ 10 euros.
This is an example of __________.
If you receive 1000 euros today, you can deposit it in the bank at an interest rate of 1% and get back 1,010 euros in a year. But, if you receive that same 1000 euros in a year, you will receive 1000 euros.
Therefore, you have lost the opportunity of gaining 10 euros.
This is an example of opportunity cost .
In finance, people are seen as _________
risk averse
Risk averse means
that you prefer certain outcomes to uncertain outcomes.
Since people are risk-averse, even if the opportunity cost is 0, it would be preferable to ___________ instead of ________ because ________.
get the money right now
in the future
if you get the money now, you have money, but if you get the money in the future, you only have the promise of money and the risk of that promise being broken.
What risks justify the time value of money?
- Solvency
- Inflation
- Interest
What is solvency risk?
When the person who must make the payment can’t pay because they don’t have any money
What is inflation risk?
When you can buy less things now with the same amount of money as before because the price of goods and services went up.
What is interest risk?
When you have undertaken an investment and you find another investment that would have been better to undertake, but you can’t undertake the second investment because you have already undertaken the first
Since the value of money changes overtime, any value we estimate must be associated with a specific amount
True
Capital
the sum of money in a given moment in time
Ct
the moment at which a sum is collected/paid
Timeline
the tool used to identify the timing of a capital
Future value
how much a sum of money is worth in the future
Ct > C0 means that the value of money …
increases with time through accumulation
You can’t simply add, subtract or multiply capital because ….
the time value of money is always there.
I(t) is
the interest in $$$$
I(t) =
Ct - C0
future value - present value
Accumulating means
calculating the future value of a given capital
move from beginning to end
Value in the future > value today means that we have
inflation
Present value of capital
the current value of a future sum
Discounting
calculating the present value of a given capital
move from end to the beginning
i
rate of interest
i =
i = I1/C0 i = interest generated/initial capital
i =
i = (C1 - C0)/C0
d
rate of discount
d =
d = I1/C1 d = interest generated/final capital
d =
d = (C1 - C0)/C1
Simple interest
C0*i
C0 = 1000 euros i = 2% t = 3 yrs
The simple interest after 3 years is ______
The final value of the capital after 3 years is _________
C0 * i * t = I
C3 = C0 + I
Compound Interest
The interests at the end of each month are added to the capital and the interest is calculated on the new capital
I = 20 euros C0 = 1000 compounded yearly t = 3 yrs
C1 = C3 =
C1 = I+C0 C3 = (C1 * i) + C1 + (C2*i) C3 = C2 + I3
Ct (compounded) =
Ct = C0(1+i)^t
Ct (simple interest) =
Ct = C0(1+it)
Simple interest produces higher values when t < 1
True
Compound interest produces higher values when t > 1
True
Simple and compound interest produce different values if t = 1
False
The produce the same values at t = 1
Compound interest is used for short term operations because it produces more money if t < 1
False
This is simple interest
Compound interest is used for long-term operations because it produces more money if t > 1
True
i(k)
the interest rate in period k
i
the annual interest rate
i(2)
the 1/2 yearly rate
i(3)
the cuatrimestral rate
i(4)
the quarterly rate
i(12)
the monthly rate
i(360)
the daily rate
i(365)
the daily rate
i(1/2)
the two year rate
i(1/3)
the 3 year rate
i(1/4)
the 4 year rate
Convert the annual rate to the monthly rate (i -> i(12))
i/12 = monthly rate
i -> 1(360)
1/360 = daily rate
When estimating the value of capital …
the time and interest must be compatible (in same units)
What do you do if the time and interest rates are not in the same units?
- Convert the units of time to match the rate
2. Convert the units for the rate to match the time
Two rates are equivalent if …
for the same initial investment and period of time, the final value is the same for both interest rates
C1 @ i(k) = C2 @ i(t) = Cn
d is the _______ discount
commercial
With commercial discounts, C0 =
C0 = Ct(1-dt)
A bill of exchange is
Like a cheque, but the bank writes it; the person with the paper collects the money from the bank, and if the bank has the paper, the bank collects from the person who wrote the cheque
The value on a BOE is the face value
true
Discount rate is the commercial discount rate
true
A discount at a certain interest rate is just called a discount
true
i = i(k)*k
true
non-annual rate = annual rate/period of time
true
discounting with a simple interest rate is the reverse of accumulating with simple interest
true
In many short-term financial operations, the ______ capital is not calculated using a __________ but a _________.
initial
simple interest rate
simple discount rate
Pressing F4 on the keyboard results in B5 transforming to ….
$B$5
The difference between an interest rate and a discount rate is ….
the interest rate is applied to the initial capital
discount rate is applied to the final capital
d = (C1-C0)/C1
true
Discounting is applied to BOEs, Treasury Bills, IOUs, loans, invoice cash, etc …
true
A bill of exchange is written as an unconditional order of payment of a sum of money at a fixed or determined period of time in the future
true
The person who writes the BOE is called the drawer
true
The person is who ordered to pay is called the drawer
false
the person ordered to pay is called the drawee
If a drawer of a BOE does not want to wait until the due date of the bill, he may …
sell his bill to a bank at a certain rate of discount
If the bank buys a BOE, they are now …
the holder AND owner of the bill
After getting the bill, the bank will …
pay cash to the payee equal to the face value of the bill minus the interest or discount rate for the remaining time left on the bill
The cost of discounting is also known as …
the interest paid by the drawer
Given that the discount rate is applied to the final capital and the interest rate is applied to the initial capital, for a same rate, the discount is more expensive than the interest.
True
We can calculate the rate of interest that is equivalent to a given discount rate. To so, we calculate the interests of a period.
True
Interest rate: I = C0i
Discount Rate: I = C1d
In both cases I = C1 - C0
Interest rate: I = C0i
Discount Rate: I = C1d
In both cases I = C1 - C0
True
d = i/1 + i*t
True
i = d/1 - d*t
True
In the compound interest method, the non-paid interests are periodically added to the initial capital (also called the principal) to generate future interests.
True
In the compound interest method, the sum of the initial capital (or principal) and the interests generated to the date is called compound amount or accumulated value,
True
In the compound interest method, the time between two successive interest computations is the interest period, compound period or conversion period.
True
If we start from an initial capital of C0 and an interest rate of i per annum compounded annually, we can compute the value of that initial capital at any moment t as: Ct = C0(1+i)^t
True
If we know the final capital and we want to calculate the initial capital, we can isolate C0.
True
C0 = Ct/(1+i)^t
The interests generated between the moment 0 and the moment t would be C1 - C0
True
I = C0[(1+i)^t -1]
True
If you know the initial and the final capitals, as well as the time between them, you can find the interest rate with the following formula:
Ct=C0·(1+i)^t
If you know the initial and the final capitals, as well as the interest rate, the time between the two capitals can be estimated with the following formula:
t=Ln(Ct/C0)/Ln(1+i)
Like with simple interest, we can consider that two compound interest rates referred to different periods are equivalent if, for the same initial investment and over the same time interval, the final value of the investment, calculated with the two interest rates, is equal.
True
We can calculate the annual rate i equivalent to a period rate ik.
True
ik = (1+i)^1/k - 1
i = (1+ik)^k -1
True
“Effective rates” are called so because they are directly applied to the initial capital to calculate the generated interests.
True
It is common for financial contracts present a “nominal annual rate compounded on a given frequency” rather than the effective rate.
True
Nominal annual rates are denoted as jk, k being the number of times that rate compounds per year.
True
The equivalence between a nominal and an effective rate is the following: jk = ik *k
True
The APR is an indicator of the effective cost or output of a financial operation.
True
The APR includes …
all expenses and commissions of the financial operation.
The APR is very useful to compare financial products
True
Financial institutions are obligated to report the APR in the advertising of their financial products.
True
