1. Time Value of Money

2. The Present Value Relationship
Where
PV = present value
CFt = the cash flow occurring at time t
r = the discount rate
N = the number of periods

3. The Present Value Relationship and the discount rate, r
What determines r?
The real rate compensates investors for deferring consumption when they lend their money.
A premium for expected inflation keeps investors from losing expected purchasing power of their money.
A premium for risk, induces investors to invest in risky projects that might otherwise not attract investment dollars.

4. The Present Value Relationship and the discount rate, r
What is the present value of $1 received one year from now if the appropriate discount rate is 5% versus 10%?
PV = $1/(1.05) = $.952
PV = $1/(1.10) = $.909
Why does the term “discount” make sense in this context? Suppose the discount rate were zero. What would that mean?

5. The Present Value Relationship and the timing of cash flows
Timing refers to the time at which cash flows arrive. A time line is useful in forming a picture of the arrival process. 1 2 3
What is the present value of $1 received one year from now versus two years from now if the appropriate discount rate is 10%?
PV = $1/(1.10)1 = $.909
PV = $1/(1.10)2 = $.826

6. The Present Value Relationship and Cash Flow Patterns
A Lump Sum
An annuity
An annuity and a lump sum
$10 $1 $1 $1 $1 $1 $1 $1
$1 + $10

7. The Present Value Relationship A Practice Problem
Assume you want to buy a home that costs $150,000. You will pay regular monthly payments for 10 years, and then pay a balloon payment of $50,000. The current interest rate is 8%. Create an amortization schedule. If interest payments are tax deductible and you are in the 35% tax bracket, what is the present value of the tax savings? What the present value of the cost to you for purchasing the home?

8. The Present Value Relationship A Practice Problem
PV = -$150,000
FV =
N =
I%/Yr =
FV =
PMT =
Describe the cash flow stream on this mortgage.

9. The Present Value Relationship A Practice Problem
See Excel Worksheet for the rest of the story