Year 1 · Foundations · Corporate Finance & Valuation
Time Value of Money
Learn why a dollar today is worth more than a dollar later, how compounding and discounting work, and how present value, annuities, perpetuities and NPV become the mathematical foundation of valuation.
LEARNING OBJECTIVES
What you should be able to explain after this lesson
01
Explain economically why timing changes the value of cash.
02
Calculate future value and present value for single cash flows.
03
Distinguish simple interest from compound interest and compare compounding frequencies.
04
Value ordinary annuities, annuities due and simple perpetuities.
05
Calculate and interpret net present value.
06
Connect discount rates to opportunity cost, inflation and risk.
CONCEPT MAPThe valuation chain
A dollar today and a dollar tomorrow are not economically identical
CORE FACTS · SAME IN EVERY MODE
Cash received today can be invested, consumed or used to avoid borrowing, so it has an opportunity value.
Inflation can reduce future purchasing power, while uncertainty and credit risk can make future cash flows less certain.
Finance therefore compares cash flows at different dates by moving them to a common point in time.
Compounding moves value forward through time; discounting moves value backward to the present.
BeginnerTeaching style changes, knowledge does not.
If I offer you $1,000 today or $1,000 in one year, the money today is generally more useful because you can invest it immediately. At 5%, $1,000 today could become $1,050 in one year. So receiving only $1,000 next year means giving up that potential return.
COMPARISON
Compounding vs discounting
| Process | Direction | Question answered |
|---|---|---|
| Compounding | Present → future | What will today's money become? |
| Discounting | Future → present | What is future money worth today? |
PROFESSIONAL VOCABULARYOpportunity cost / coût d’opportunité / opportunity cost Discount factor / facteur d’actualisation / discount factor
The value of the best alternative use or return forgone.
The multiplier used to convert a future cash flow into present value.