chapter 4 - discounted cash flow valuation

Question 1

breakdown the compound interest rate calculation for 2 years (compounded annual)

Answer 1

= P * (1 + r)^2

assume P = $1

so, above is = 1 * (1 + r)^2 = (1 + r)^2

= 1 + 2r + r^2

the 1 is the principle
the 2r is the simple interest (2 years * the interest rate, r)
and the r^2 is the compound interest

Question 2

should wealthy families bequeath money to their children?

Answer 2

no, to their grandchildren because of the time value of money (they should make their grand kids very rich instead of making their kids just moderately rich)

Question 3

effective annual rate

Answer 3

aka effective annual yield

this is the rate that takes into account the effects of compounding

example:

assume you have stated annual rate of interest of 20% and monthly compounding

the annual rate is 20% but after taking into account the monthly compounding, the EAR will be > 20%

effective annual rate = (1 + r/m)^m - 1

where r is the quoted rate, m is the number of compounding periods (12)

Question 4

perpetuity

Answer 4

constant stream of cash flows without end

present value of a perpetuity is a geometric series:

PV = C/(1 + r) + C/(1 + r)^2 + C/(1 + r)^3 + …

PV = C/r

according to this, it’s easy to see that the PV of a perpetuity rises when interest rates fall

Question 5

growing perpetuity

Answer 5

an instrument that provides cash flows that grow over time

PV = [C / (1 + r)] + [C * (1 + g)^2] / (1 + r)^2 + [C * (1 + g)] / (1 + r)^3 + …

PV = C / (r - g)

C is the cash flow
r is the discount rate (interest rate)
g is the rate of growth per period

Question 6

annuity

Answer 6

An annuity is a level stream of regular payments that lasts for a fixed number of periods. Not
surprisingly, annuities are among the most common kinds of financial instruments. The pensions that
people receive when they retire are often in the form of an annuity. Leases and mortgages are also often
annuities.

PV = C/(1 + r) + C/(1 + r)^2 + C/(1 + r)^3 + … + C/(1 + r)^T

obviously, PV of annuities has to be less than PV of perpetuities because they don’t go on forever

a derivation leads to this conclusion:

PV of an annuity = C * [ (1/r) - 1 / (r * (1 + r)^T) ]

also can be written PV = C/r * { (1 - [1 / (1 + r)^T ] }

Question 7

annuity factor

Answer 7

term we use to compute the present value of the stream of level payments, C, for T years is
called an annuity factor.

Question 8

ordinary annuity/annuity in arears vs. annuity in advance/annuity due

Answer 8

ordinary annuity and annuity in arrears are the same thing = they are fixed payment streams that start one period hence for the specified number of periods

an annuity due (aka annuity in advance) is one that start starts at time zero

Question 9

infrequent annuity

Answer 9

payments occur less frequently than every year

Question 10

growing annuity

Answer 10

Cash flows in business are likely to grow over time, due either to real growth or to inflation. The
growing perpetuity, which assumes an infinite number of cash flows, provides one formula to handle this
growth. We now consider a growing annuity, which is a finite number of growing cash flo