Chapter 4

Question 1

define a stream of cash flows

Answer 1

a series of cash flows lasting several periods

Question 2

how can a stream of cash flows be represented?

Answer 2

on a timeline - linear representation of timing of expected cash flows

Question 3

what’s the first rule of comparing cash flows?

Answer 3

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.

Question 4

what’s the 2nd rule in how to move a cash flow forward?

Answer 4

To Move a Cash Flow Forward in Time, You Must Compound It

Question 5

define simple interest

Answer 5

If an investment only earns interest on principal and no interest on accrued interest

Question 6

define compound interest

Answer 6

investments earn interest on the original principal amount invested and earn interest on the accrued interest

Question 7

define the rule of 72

Answer 7

how many years it would take to double your money with different interest rates

years to double = 72/ interest rate in percent

Question 8

what’s the 3rd rule of how to move cash flows backwards in time

Answer 8

To Move a Cash Flow Backward in Time, You Must Discount It

Question 9

define discounting

Answer 9

finding the equivalent value today of a future cash flow

Question 10

what’s the present value of the cash flow stream

Answer 10

sum of the present values of each cash flow

Question 11

what’s the NPV of an investment opportunity

Answer 11

present value of the stream of cash flows of the opportunity

Question 12

what’s a pitfall of he NPV function in excel?

Answer 12

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.

Question 13

define a regular perpetuity

Answer 13

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

Question 14

what’s the consol bond

Answer 14

biritish government bond

Question 15

how can you find the value of a perpetuity cash flow

Answer 15

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

Question 16

what’s the cashflow and principal and discount rate formula

Answer 16

C = r x P

PVo = C/r

Question 17

what’s the present value of the perpetuity

Answer 17

C/r
r in decimals

Question 18

define regular annuity

Answer 18

stream of n equal cash flows paid over constant time intervals

Question 19

annuity vs perpetuity

Answer 19

n annuity is a stream of periodic cash flows that ends after some fixed number of payments.

Question 20

how to avoid the common mistake of discount one too many times for perpetuities annuities and special cases

Answer 20

Remember—the present value formula for the perpetuity already discounts the cash flows to one period prior to the first cash flow.

Question 21

what’s the present value of an annuity? and what’s the formula?

Answer 21

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]}

Question 22

define a growing perpetuity

Answer 22

a stream of cash flows that occur at regular intervals and grow at a constant rate forever.

Question 23

what’s the formula for PV with growing perpetuity

Answer 23

check textbook

Question 24

what happens if the growth rate is greater or less than the discount rate in a growing perpetuity?

Answer 24

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!

Question 25

What does an infinite present value mean?

Answer 25

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).

Question 25

define a growing annuity

Answer 25

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.

Question 25

how to derive the formula for the present value of a growing perpetuity

Answer 25

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.

Question 26

what’s a viable growing perpetuities

Answer 26

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.

Question 27

what’s the formula for PV of growing annuity

Answer 27

check textbook

Question 28

what’s the formula for a growing annuity when n = infinite

Answer 28

PVo = C1/(r-g)

Question 29

what’s the future value of a growing annuity

Answer 29

check textbook

Question 30

what are the excel functions to help compute finance calculations

Answer 30

NPER, RATE, PV, PMT, and FV.