Chapter 4: Time Value of Money Flashcards
WACC
Weighted average cost of capital - average rate of return required by all of the firm’s investors (equity and debt)
Intrinsic value of a company
Value of all expected free cash flows discounted at the weighted average cost of capital
aka PRESENT VALUE of expected future cash flows
Discounted cash flow analysis
Basically time value of money. method of determining today’s value of a cash flow to be received in the future
can be used to estimate a financial asset’s value by discounting the asset’s expected cash flows at a rate that reflects the asset’s risk
Compounding
Process of finding the future value of a single payment or series of payments based generally based on a periodic interest rate (unless continuous compounding)
Notes on compounding interest
Interest earned is based on balance at beginning of each year (and assumed to be paid at the end of the year)
FV[N]
= PV (1+I)^N
where I= interest rate and N = number of periods
Time value equation as built into financial caluclator
PV(1+I)^N + PMT(((1+I)^N-1)/I)+FV = 0
EITHER PV OR FV MUST BE ENTERED AS 0 (assuming I is less than 100%)
Entering the interest rate on a calculator
Entered as I/Y (interest/year)
automatically converts a whole number percentage into the appropriate decimal
When to use positive or negative sign for outflows on calculator
There are three cash flows in the time value of money equation. At least one must be negative and one positive when you enter information. Two possibilities:
- one negative cash flow out and two positive cash flows in (receiving back interest and principal)
- two negative cash flows out and one positive cash flow in (paying out interest and principal)
Time value of money in excel
=FV (I, N, PMT, PV, 0 or 1)
or
= PV(I, N, PMT, FV, 0 or 1)
I = interest rate (as decimal, unless using a reference cell formatted as a percentage)
N = number of periods
PMT = regular cash flows
PV= present value
FV = Future value
0 = end of period payment
1 = beginning of period payment
same rules for negative and positive values as a financial calcuator
Compound interest
interest that is earned or charged on interest from prior periods as well as principal
simple interest
aka regular interest
interest earned or charged only on the principal
FV of principal with simple interest
= PV + (PVIN)
opportunity costs (for the sake of investing)
A cash flow a firm must forgo in order to accept a project.
rate of return that would be earned on an alternative investment
Present value
the amount that, if it were on hand today, would grow to equal the given future amount in the given number of years
discounting
the process of finding the present value of a single payment or series of payments
reverse of compounding
PV formula
= FV[N] / (1+I)^N
= future value at n periods / (1+ interest rate) to the power of N
Change in present value of a sum to be received as periods extend into the future
PV decreases with more periods
Change in present value of a sum to be received as interest rate rises
higher the interest rate the faster the present value falls
Finding I if PV, FV, and N are known
= (FV/PV)^(1/N) - 1
Finding the interest rate in excel
=Rate(N, PMT, PV, FV, 0 or 1)
0 for end of period payments
1 for beginning of period payments
perpetuity
series of payments of a fixed amount that continue indefinitely
Present value of a perpetuity
PMT / I
PMT = payment received each period
I= rate
relationship of present value to interest rate
inverse. If one rises the other falls
Annuity
equal payments made at fixed intervals
Ordinary annuity
also deferred annuity
payments at the END of each period
assumed unless otherwise stated
Annuity due
Payments at the BEGINNING of each period
Future value of an ordinary annuity
= PMT x (((1+I)^N -1)/I)
Future Value of an annuity Due
= (PMT x (((1+I)^N -1)/I))*(1+I)
payments earn interest for one additional period over an ordinary annuity
Present value of ordinary annuity
= PMT x ((1/I) - (1/(I(1+I)^N)))
Present value of annuity due
= (PMT x ((1/I) - (1/(I(1+I)^N)))) * (1+I)
payments discounted for one less period than an ordinary annuity
Difference between an ordinary annuity payment and annuity due payment
ordinary annuity payment / (1+ rate) = annuity due payment
Excel function to find payments
= PMT(rate, nper, pv, fv, 0 or 1)
0= end of period
1= beginning of the period
Excel function to find number of periods required to save given amount
= NPER (rate, pmt, pv, fv, 0 or 1)
0= ordinary annuity
1 = annuity due
types of uneven cash flows
1) stream of annuity payments + additional lump sum in year N (bonds)
2) other uneven streams (stocks and capital investments)
PV of annuity + final payment on financial calculator
N = number of periods
I/Y = interest rate
PMT = annuity
FV = lump sum
PV = solved for
PV of irregular cash flow on financial calculator
CF button
enter after each value to lock in
down to enter next value
quit out
NPV button
I/Y enter
will show NPV
hit compute to get result
begin with Time 0 cash flow
using excel to get present value of uneven cash flows
Use =NPV function
make sure outflows are negative and inflows are positive
begin with Time 1 cash flow
Net future value of an uneven cash flow
= NPV * (1+I)^N
(unless NFV key is available)
Time period 0
starting point, present time
periods
number of time interest compounts
Rule of 72
Product of the interest rate and number of years it will take to double your money is 72
if FV = 2PV
iN = 72
