Time Value of Money
The time value of money (TVM) is one of the most fundamental concepts in finance: a dollar today is worth more than a dollar in the future because of its earning potential. Investment advisers use TVM concepts daily when analyzing investments and planning for client goals.
Why a Dollar Today Is Worth More
| Reason | Explanation |
|---|---|
| Earning Potential | Money today can be invested to earn returns |
| Inflation | Future dollars buy less due to rising prices |
| Risk | A promise of future money carries uncertainty |
| Opportunity Cost | Can't use future money for today's opportunities |
Core Concepts
Present Value (PV)
Present value is the current worth of a future sum of money, discounted at a given rate.
Question it answers: "What is $10,000 received in 5 years worth today?"
Future Value (FV)
Future value is the value of a current sum of money at a future date, compounded at a given rate.
Question it answers: "What will $10,000 invested today be worth in 5 years?"
Key Formulas
Future Value Formula
FV = PV × (1 + r)^n
| Variable | Meaning |
|---|---|
| FV | Future Value |
| PV | Present Value |
| r | Interest rate per period |
| n | Number of periods |
Example: $10,000 invested at 8% for 5 years:
- FV = $10,000 × (1.08)^5 = $10,000 × 1.469 = $14,693
Present Value Formula
PV = FV / (1 + r)^n
Example: What is $14,693 received in 5 years worth today at 8%?
- PV = $14,693 / (1.08)^5 = $14,693 / 1.469 = $10,000
The Rule of 72
A quick way to estimate how long it takes to double your money:
Years to Double ≈ 72 / Interest Rate
| Interest Rate | Years to Double |
|---|---|
| 4% | 72 / 4 = 18 years |
| 6% | 72 / 6 = 12 years |
| 8% | 72 / 8 = 9 years |
| 10% | 72 / 10 = 7.2 years |
| 12% | 72 / 12 = 6 years |
The Rule of 72 works in reverse too: At what rate do you need to invest to double money in 10 years? 72 / 10 = 7.2%
Compounding Frequency
More frequent compounding results in higher effective returns:
| Compounding | Periods per Year | $10,000 at 8% for 1 Year |
|---|---|---|
| Annual | 1 | $10,800.00 |
| Semi-annual | 2 | $10,816.00 |
| Quarterly | 4 | $10,824.32 |
| Monthly | 12 | $10,830.00 |
| Daily | 365 | $10,832.78 |
Key Point: For the same stated (nominal) rate, more frequent compounding = higher effective annual rate (EAR).
Effective Annual Rate (EAR)
The effective annual rate converts any compounding frequency to an annual equivalent:
EAR = (1 + r/m)^m - 1
Where m = number of compounding periods per year
Example: 8% compounded monthly:
- EAR = (1 + 0.08/12)^12 - 1 = 8.30%
Annuities
An annuity is a series of equal payments at regular intervals. Investment advisers encounter annuities in retirement planning, loan analysis, and income products.
Types of Annuities
| Type | Payment Timing | Example |
|---|---|---|
| Ordinary Annuity | End of each period | Most loans, bonds |
| Annuity Due | Beginning of each period | Rent, insurance premiums |
Key Difference: Annuity due payments occur one period earlier, so an annuity due is worth more than an otherwise identical ordinary annuity.
Annuity Applications
| Application | TVM Concept Used |
|---|---|
| Retirement planning | How much to save (PV of future need) |
| Loan payments | Monthly payment calculation |
| Education funding | Future cost of tuition |
| Income planning | What can be withdrawn annually |
Discount Rate Selection
The discount rate used in TVM calculations significantly affects results:
| Discount Rate Choice | When Used |
|---|---|
| Risk-free rate | Government bonds, guaranteed payments |
| Required return | Investments with specific risk levels |
| Opportunity cost | Alternative investment returns |
| Inflation rate | Real purchasing power calculations |
Important: Higher discount rates result in lower present values. A risky investment's cash flows should be discounted at a higher rate than a safe investment's cash flows.
In Practice: How Investment Advisers Apply This
Client planning applications:
- Calculate how much to save monthly for retirement
- Determine if a lump sum or annuity is more valuable
- Compare investment alternatives with different timing
- Evaluate whether early payment of debt makes sense
Investment analysis:
- Calculate present value of expected cash flows
- Compare bonds with different maturities
- Evaluate NPV of investment opportunities
On the Exam
The Series 65 exam tests your ability to:
- Understand that a dollar today is worth more than a dollar tomorrow
- Apply the Rule of 72 to estimate doubling time
- Recognize that more frequent compounding increases effective returns
- Distinguish between ordinary annuity and annuity due
- Understand how discount rate affects present value
Expect 2-3 questions on TVM. Common formats include Rule of 72 calculations and understanding compounding frequency effects.
Key Takeaways
- Time value of money: A dollar today is worth more than a dollar in the future
- Future value: Grows current money at a given rate
- Present value: Discounts future money back to today
- Rule of 72: Years to double = 72 / interest rate
- More frequent compounding = higher effective annual rate
- Ordinary annuity: Payments at end of period; Annuity due: Payments at beginning
- Higher discount rates result in lower present values
Using the Rule of 72, approximately how many years will it take for an investment to double at a 6% annual return?
Which statement about compounding is TRUE?
An annuity due differs from an ordinary annuity because an annuity due has:
2.6 IRR and NPV
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