Chapter 4 (come back to 4.6) Flashcards
Excl. 4.7 - 4.10
What does a stream of cash flow mean?
Its when we refer to and value a series of cash flows lasting several periods.
How can we show how a stream of cash flows look like graphically?
On a timeline
What is a timeline?
Its a linear representation of the ‘timing’ of the expected cash flows
Timelines are an important first step in organizing and solving a financial problem.
Its useful in tracking cash flows if you interpret each point on the timeline as a specific date.
Example:
Suppose a friend owes you money (today) and he has agreed to repay the loan by making two payments of $10,000 at the end of each of the next two years. We represent this information on a timeline how?
There are three places
Date 0 (refer to as today)
Date 1 (1 yrs from today) - You will recieve payment 1 at the end of the first year.
Date 2 (2 yrs from today) - You will recieve payment 2 at the end of the second year
Example:
Suppose a friend owes you money (today) and he has agreed to repay the loan by making two payments of $10,000 at the end of each of the next two years.
What does date 0 / date 1 / date 2 mean?
Date 0 is the beginning of the first year
Date 1 is the end of the first year and also the beginning of the second year.
Date 2 - Is the end of the second year
In many financial decisions we often see what two things about cash flow?
Cash inflow
Cash outflow
What sign do we assign a cash inflow?
A positive symbol to represent a cash inflow
What sign do we assign a cash outflow
A negative symbol to represent a cash outflow
Example:
To illustrate, suppose you’re still feeling generous and have agreed to lend your brother $10,000 today. Your brother has agreed to repay this loan in two instalments of $6000 at the end of each of the next two years. The timeline is what?
Date 0 - -10,000
Date 1 - +6,000
Date 2 - +6,000
So far you have learnt and seen on timelines that cash flows occur at the end of the year. Is that true in all cases and give me an example.
No,
we can use timelines to represent cash flows that take place at the end of any time period
For example, if you pay rent each month, you could use a timeline like the one in our first example to represent two rental payments, but you would replace the “year” label with “month.”
What do they recommend to do for every problem?
Draw a timeline!
example: Suppose you must pay tuition and residence fees of $10,000 per year for the next two years. Assume your tuition and residence fees must be paid in equal instalments at the start of each semester (assume July 1 and January 1 as the semester-payment due dates). What is the timeline of your tuition and residence fee payments
Go to the end of 4.1 : Chapter 4
What do we have to do a lot for financial decisions?
It requires us often to compare or combine cash flows that occur at different points in time.
What are the three important rules that central financial decisions that allow us to compare on combine values (cash flows)?
Rule 1: Only Cash Flow Values at the Same Point in Time Can Be Compared or Combined
Rule 2: To Move a Cash Flow Forward in Time, You Must Compound It
Rule 3: To Move a Cash Flow Backward in Time, You Must Discount It.
Explain the first rule of comparing or combing cash flows that occur at different points in time?
The first rule states that its only possible to compare or ‘combine cash flows’ or values at the same point in time.
Meaning only cash flows in the same units (either PV or Fv both) can be compared or combined.
To compare or combine cash flows that occur at different points in time, you first need to convert the cash flows into the same units (either PV or FV) or move them to the same point in time.
What does the second rule of financial decisions when we want to compare or combine cash flows mean what?
To move a cash flow forward in time, you must compound it.
How do we move the cash flow forward in time? (Calculation wise)
We multiply the interest rate factor (1+ r) to the cash flow to move the cash flow.
What is compounding?
Its the process of moving a value or cash flow forward time.
To move a cash flow forward in time, we must compound it
Example: Suppose we have $1000 today, and we wish to determine the equivalent amount in one year’s time. If the current market interest rate is 10%, we can use that rate as an exchange rate to move the cash flow forward in time. That is,
1000*(1.10) = 1100
Example:
Example: Suppose we have $1000 today, and we wish to determine the equivalent amount in one year’s time. If the current market interest rate is 10%, we can use that rate as an exchange rate to move the cash flow forward in time.
how can we show this on a timeline (for two years)
date 0 - present would have 1000
Date 1 - would have 1100
Date 2- would have1210
Due to the 10% interest rate they are all equivalent in terms of value but expressed in different units (different points in time)
What does the future value mean?
its the value of a cash flow that is moved forward in time.
Ex: 1210 is the FV of 1000 (10% interest rate)
What happens when we move the cash flow further into the future?
the value grows as we move the cash flow further into the future
What is the time value of money
its the ability to show two equivalent cash flows at different points in time.
two different units basically mean they are equivalent however they are at expressed at different points in time
What is simple interest?
Its when an investment only earns interest on principle payment you made and no interest on accrued interest
What does compound interest mean?
Its when the investment earns interest on the original principal amount and also earn interest on the accrued interest (interest that accumulates over time)
How to calculate the future value in ‘n’ periods of a cash flow today?
FV = Cash flow * (1+r) ^ n
What does rule three tell us when making financial decisions if we want to move it forward or backward in time?
It describes how to move cash flows backward in time.
To move a cash flow backwards in time, we must discount it
Example: Suppose you would like to compute the value today of $1000, you anticipate receiving in one year. If the current market interest rate is 10%, you can compute this value by converting units as we did in Chapter 3
1000/1.10 = 909.09
How can we move a cash flow backwards in time? (Calculation wise)
have to divide by the interest rate factor (1+r) or multiplying by 1/(1+r)
What is discounting?
Its the process of moving a value or cash flow backward in time to help find the equivalentvalue today of a potential future cash flow
Example:
To illustrate, suppose that you anticipate receiving the $1000 two years from today rather than in one year. If the interest rate for both years is 10%, we can prepare the following timeline:
Date 0:
826.45
Date 1:
909.09
Date 2: 1000
These are all equivalent but expressed as different units (different points in time)
What happens when when we continue to discount a cash flow?
The value decreases as we move the cash flow further back.
How can we calculate the present value today of a cash flow that occurs ‘n’ periods in the future?
PV = Cash flow divided by (1+R) ^n
What does the rule of time travel allow us to do?
It allows us to ‘compare or combine cash flows’ that occur at different points in time.
Example:
Suppose we plan to save $1000 today, and $1000 at the end of each of the next two years. If we earn a fixed 10% interest rate on our savings, how much will we have three years from today?
Look in 4.2 (end)
What are the three rules of time travel?
Rule 1: only cash flows at the same point in time can be compared or combined
Rule 2: To move a cash flow forward in time you must compound it (fv = cf ^(1+r)^ n)
Rule 3: To move a cash flow backward in time, you must discount it
Pv = CF / (1+r)^n
what do we know about most investment opportuntiies?
They have multiple cash flows that occur at different points in time
How can we compute the present value a cash flow stream (multiple cash flows)
PV = C0 + C1/ (1+r) + C2/(1+r)^2 ….
How to calculate the NPV of future cash flows?
NPV = PV(benefits) - PV (costs)
What is the NPV of an investment opportunity?
Its the present value of the stream of cash flows of the opportunity
What is a regular perpetuity?
Its a stream of ‘equal’ cash flows that:
- Occur at a consistent time interval and last forever
What do we refer to a regular perpetuity as?
Perpetuity
What is an example of a regular perpetutity?
Its a government bond called a consol
What is a consol bond?
Its a government bond that promises the owner equal fixed cash flow every year forever
What do we have to note about the first cash flow of a perpetuity bond?
It does not arrive at the beginning of the first period but it arrives at the end of the first period (date 1 instead of date 0).
t time 0, nothing is paid.
At time 1, the first cash flow
𝐶
C is received.
At time 2, the second cash flow
𝐶
C is received.
This pattern continues indefinitely (at time 3, time 4, etc.).
What is it called when a payment occurs at the end of the period rather than the beginning?
Payment in arrears
How can we calculate the present value of a perpetuity?
- We have to calculate the value of a perpetuity by creating our own perpetuity.
- Then we can calculate the PV of the perpetuity by the Law of One Price, the value of the perpetuity must be the same as the cost we incurred to create our own perpetuity.
[This principle states that if two assets provide the same cash flows in every situation, they must have the same price. In other words, something that offers the same benefits (in this case, a stream of payments) should cost the same, no matter how it is created or where it’s purchased.]
How do we calculate (using the short cut to calculate the perpetuity)
PV = C/ R
This helps us calculate the present value of a perpetuity with a discount rate and constant cash flow starting in date 1
What is a regular annuity?
Its a stream of ‘n’ equal cash flows paid over constant time intervals
What do we often refer to regular annuities as?
Annutities
What is the difference between an annuity and a perpetuity?
Its that an annuity does recieve an equal ‘nth’ amount of equal cash flows however the cash flows end after some fixed number of payments.
What are examples of annuities?
Car loans
Mortgages
Bonds
What do we have note about the payment cycle of cash flows for an annutiy?
the first payment takes place at date 1 (at the end of the period)
What is a common mistake that people make using the perpetuity formula?
The perpetuity formula assumes that the first payment occurs at the end of the first period (at date 1). Sometimes perpetuities have cash flows that start later in the future.
The common mistake in this type of problem, where the first payment starts in a future period (in this case, at the end of year 2), is discounting the cash flows too many times.
This happens when people double discount—meaning they discount the amount once when applying the perpetuity formula and then discount it again unnecessarily.
We only need to discount it up until date 1 (cash flows come at the end of the period)
How can we calculate the future value of n years? (annuity)
FV = C* 1/r *((1+r)^n -1)
How can we compute the PV of an anuity?
PV(annuity of c for n periods) = c * 1/ r * (1- 1/(1+r) ^n-1)
What is a growing perpetuity?
Its a stream of cash flows that occur at regular intervals and grow at a constant rate forever.
The first payment occurs at date 1 (end of the year
How to calculate the present value today (date 0) of a growing perpetuity rate?
PV = C/R-G
What is a growing annuity?
its a stream of nth growing cash flows paid at regular intervals that eventually comes to an end
The first payment occurs at date 1 (end of the year)
How to calculate the pv of a growing annuity?
Look at paper
How to calculate the fv of a growing annuity?
Write it out and check textbook
How to calculate the FV of a regular annuity?
Write it out and check textbook
