Mod. 2 Time Value of Money & Valuing Cash Flow Streams

prefer 5,000 today instead of 5,100 in 2 years

• you win a cash prize of $5,000

• option A: 5,000 today

• option B: 5,100 in 2 years

Choose option A because

• consumption: want the money now to spend

• inflation: cash doesn’t move with inflation so a dollar today is worth more than a dollar tomorrow

• investment opportunity: if i have the cash today, i can invest it

money has time a value

“A dollar today is worth more than a dollar tomorrow.”

• compare the $5,000 today to $5,100 in 2 years by finding

• present value of 5,100

• future value of 5,000

interest rate

• an exchange rate across time

• the rate at which we can exchange money today for money in the future

interest rate factor

1 + r =

discount factor

1 / (1 +r) =

present value

when we express the value in terms of dollars today

future value

if we express dollars in the future

timeline

• a linear representation of the timing of potential cash flows

steps

1) identify periods

2) identify cash flow amounts

3) determine if its a cash inflow + or cash outflow -

3 rules of time value

1. can only compare money at the same point in time

2. to use cash flows forward in time, it must compound (have an interest factor- future value)

3. to use cash flows backward in time, it must be discounted (present value)

net present value (NPV)

PV benefits - PV costs

• the difference between the present value of the project or investments benefits and the present value of its costs

• compares the present value of cash inflows (benefits) to the present value of cash outflows (costs)

approach 1 of valuing a stream of cash flows

• finding the PV (rule 3)

• move the stream of cash flows backward to the same point in time

• find a pv for each cash flow

• add them up

approach 2 of valuing a stream of cash flows

• finding the FV (rule 2)

• move the stream of cash flows forward to the same time point

• finding an FV for each cash flow

• add them up

Perpetuity

a constant cash flow that occurs at regular intervals forever

• C / r = constant

• C / (r-g) = growing

• C = cash flows

• r = rate of return or the interest rate

• can have a constant or growing

Annuity

when a constant cash flow occurs at regular intervals for a finite number of periods (N)

• can use a formula or calculator

• N = number of payments

  • depends on if its at the beginning of the year = n-1

  • end of year = amount of yrs given

growing annuity

• a cash flow stream occurring at regular intervals for a finite number of periods (N)

• The initial cash flow is C, it grows at a rate of g