Chapter 4 Flashcards
define a stream of cash flows
a series of cash flows lasting several periods
how can a stream of cash flows be represented?
on a timeline - linear representation of timing of expected cash flows
what’s the first rule of comparing cash flows?
Only Cash Flow Values at the Same Point in Time 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 or move them to the same point in time.
what’s the 2nd rule in how to move a cash flow forward?
To Move a Cash Flow Forward in Time, You Must Compound It
define simple interest
If an investment only earns interest on principal and no interest on accrued interest
define compound interest
investments earn interest on the original principal amount invested and earn interest on the accrued interest
define the rule of 72
how many years it would take to double your money with different interest rates
years to double = 72/ interest rate in percent
what’s the 3rd rule of how to move cash flows backwards in time
To Move a Cash Flow Backward in Time, You Must Discount It
define discounting
finding the equivalent value today of a future cash flow
what’s the present value of the cash flow stream
sum of the present values of each cash flow
what’s the NPV of an investment opportunity
present value of the stream of cash flows of the opportunity
what’s a pitfall of he NPV function in excel?
Another pitfall with the NPV function is that cash flows that are left blank are treated differently from cash flows that are equal to zero
Unfortunately, however, the NPV function computes the present value of the cash flows assuming the first cash flow occurs at date 1. Therefore, if a project’s first cash flow occurs at date 0, we must add it separately.
define a regular perpetuity
stream of equal cash flows that occur at constant time intervals and last forever
first cash flow arrives at the end fo the first period - payment in arrears
what’s the consol bond
biritish government bond
how can you find the value of a perpetuity cash flow
how, even with a shortcut, the sum of an infinite number of positive terms could be finite. The answer is that the cash flows in the future are discounted for an ever increasing number of periods, so their contribution to the sum eventually becomes negligible.
we create our own perpetuity - using the law of 1 price, the value of the perpetuity must be the same as the cost we incurred to create our own perpetuity.
thus, we take the same amount in perpetuity that would result in the same end value each year
what’s the cashflow and principal and discount rate formula
C = r x P
PVo = C/r
what’s the present value of the perpetuity
C/r
r in decimals
define regular annuity
stream of n equal cash flows paid over constant time intervals
annuity vs perpetuity
n annuity is a stream of periodic cash flows that ends after some fixed number of payments.
how to avoid the common mistake of discount one too many times for perpetuities annuities and special cases
Remember—the present value formula for the perpetuity already discounts the cash flows to one period prior to the first cash flow.
what’s the present value of an annuity? and what’s the formula?
initial investment in the bank account minus the present value of the principal that will be left in the account after n years.
PV (annuity of C for n periods) = P - PV(P in period n) = P - {P/[(1+r)^n]} = P*{ 1- [1/(1+r)^n]}
define a growing perpetuity
a stream of cash flows that occur at regular intervals and grow at a constant rate forever.
what’s the formula for PV with growing perpetuity
check textbook
what happens if the growth rate is greater or less than the discount rate in a growing perpetuity?
Suppose g > r. Then, the cash flows grow even faster than they are discounted; each term in the sum gets larger, rather than smaller. If g < r, then each term in the sum is constant, and we would have to sum an infinite number of constant terms. In both of these cases, the sum is infinite!
What does an infinite present value mean?
An infinite present value means that no matter how much money you start with, it is impossible to reproduce those cash flows on your own. Growing perpetuities of this sort cannot exist in practice because no one would be willing to offer one at any finite price. A promise to pay an amount that forever grew as fast as or faster than the interest rate is also unlikely to be kept (or believed by any savvy buyer).
define a growing annuity
a stream of n growing cash flows, paid at regular intervals. It is a growing perpetuity that eventually comes to an end.
only n-1 periods of growth between these payments.
how to derive the formula for the present value of a growing perpetuity
P = C1/ (r-g)
we follow the same logic used for a regular perpetuity: Compute the amount you would need to deposit today to create the perpetuity yourself. In the case of a regular perpetuity, we created a constant payment forever by withdrawing the interest earned each year and reinvesting the principal. To increase the amount we can withdraw each year, the principal that we reinvest each year must grow. We can accomplish this by withdrawing less than the full amount of interest earned each period, using the remaining interest to increase our principal.
suppose you want to create a perpetuity with cash flows that grow by 2% per year, so you invest $100 in a bank account that pays 5% interest. At the end of one year, you will have $105 in the bank—your original $100 plus $5 in interest. If you withdraw only $3, you will have $102 to reinvest—2% more than the amount you had initially.
what’s a viable growing perpetuities
The only viable growing perpetuities are those where the growth rate is less than the interest rate, so that each successive present value term in the sum is less than the previous term and the overall sum is finite. Consequently, we assume that g<r for a growing perpetuity.
what’s the formula for PV of growing annuity
check textbook
what’s the formula for a growing annuity when n = infinite
PVo = C1/(r-g)
what’s the future value of a growing annuity
check textbook
what are the excel functions to help compute finance calculations
NPER, RATE, PV, PMT, and FV.
