Chapter 4: Time Value of Money

Question 1

WACC

Answer 1

Weighted average cost of capital - average rate of return required by all of the firm’s investors (equity and debt)

Question 2

Intrinsic value of a company

Answer 2

Value of all expected free cash flows discounted at the weighted average cost of capital

aka PRESENT VALUE of expected future cash flows

Question 3

Discounted cash flow analysis

Answer 3

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

Question 4

Compounding

Answer 4

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)

Question 5

Notes on compounding interest

Answer 5

Interest earned is based on balance at beginning of each year (and assumed to be paid at the end of the year)

Question 6

FV[N]

Answer 6

= PV (1+I)^N

where I= interest rate and N = number of periods

Question 7

Time value equation as built into financial caluclator

Answer 7

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%)

Question 8

Entering the interest rate on a calculator

Answer 8

Entered as I/Y (interest/year)

automatically converts a whole number percentage into the appropriate decimal

Question 9

When to use positive or negative sign for outflows on calculator

Answer 9

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)

Question 10

Time value of money in excel

Answer 10

=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

Question 11

Compound interest

Answer 11

interest that is earned or charged on interest from prior periods as well as principal

Question 12

simple interest

Answer 12

aka regular interest

interest earned or charged only on the principal

Question 13

FV of principal with simple interest

Answer 13

= PV + (PVIN)

Question 14

opportunity costs (for the sake of investing)

Answer 14

A cash flow a firm must forgo in order to accept a project.

rate of return that would be earned on an alternative investment

Question 15

Present value

Answer 15

the amount that, if it were on hand today, would grow to equal the given future amount in the given number of years

Question 16

discounting

Answer 16

the process of finding the present value of a single payment or series of payments

reverse of compounding

Question 17

PV formula

Answer 17

= FV[N] / (1+I)^N

= future value at n periods / (1+ interest rate) to the power of N

Question 18

Change in present value of a sum to be received as periods extend into the future

Answer 18

PV decreases with more periods

Question 19

Change in present value of a sum to be received as interest rate rises

Answer 19

higher the interest rate the faster the present value falls

Question 20

Finding I if PV, FV, and N are known

Answer 20

= (FV/PV)^(1/N) - 1

Question 21

Finding the interest rate in excel

Answer 21

=Rate(N, PMT, PV, FV, 0 or 1)

0 for end of period payments
1 for beginning of period payments

Question 22

perpetuity

Answer 22

series of payments of a fixed amount that continue indefinitely

Question 23

Present value of a perpetuity

Answer 23

PMT / I

PMT = payment received each period
I= rate

Question 24

relationship of present value to interest rate

Answer 24

inverse. If one rises the other falls

Question 25

Annuity

Answer 25

equal payments made at fixed intervals

Question 26

Ordinary annuity

Answer 26

also deferred annuity payments at the END of each period assumed unless otherwise stated

Question 27

Annuity due

Answer 27

Payments at the BEGINNING of each period

Question 28

Future value of an ordinary annuity

Answer 28

= PMT x (((1+I)^N -1)/I)

Question 29

Future Value of an annuity Due

Answer 29

= (PMT x (((1+I)^N -1)/I))*(1+I) payments earn interest for one additional period over an ordinary annuity

Question 30

Present value of ordinary annuity

Answer 30

= PMT x ((1/I) - (1/(I(1+I)^N)))

Question 31

Present value of annuity due

Answer 31

= (PMT x ((1/I) - (1/(I(1+I)^N)))) * (1+I) payments discounted for one less period than an ordinary annuity

Question 32

Difference between an ordinary annuity payment and annuity due payment

Answer 32

ordinary annuity payment / (1+ rate) = annuity due payment

Question 33

Excel function to find payments

Answer 33

= PMT(rate, nper, pv, fv, 0 or 1) 0= end of period 1= beginning of the period

Question 34

Excel function to find number of periods required to save given amount

Answer 34

= NPER (rate, pmt, pv, fv, 0 or 1) 0= ordinary annuity 1 = annuity due

Question 35

types of uneven cash flows

Answer 35

1) stream of annuity payments + additional lump sum in year N (bonds) 2) other uneven streams (stocks and capital investments)

Question 36

PV of annuity + final payment on financial calculator

Answer 36

N = number of periods I/Y = interest rate PMT = annuity FV = lump sum PV = solved for

Question 37

PV of irregular cash flow on financial calculator

Answer 37

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

Question 38

using excel to get present value of uneven cash flows

Answer 38

Use =NPV function make sure outflows are negative and inflows are positive begin with Time 1 cash flow

Question 39

Net future value of an uneven cash flow

Answer 39

= NPV * (1+I)^N (unless NFV key is available)

Question 40

Time period 0

Answer 40

starting point, present time

Question 41

periods

Answer 41

number of time interest compounts

Question 42

Rule of 72

Answer 42

Product of the interest rate and number of years it will take to double your money is 72 if FV = 2*PV i*N = 72