BFB1001 Chap.2 Value, Price and Time Value of Money
Value, Price and Time Value of Money
Value, Price and Time Value of Money distinguishes a transaction price from a conditional estimate of economic value. Price records what is paid, while value depends on expected cash flow, timing and the return required for its risk. A cash-flow timeline places today at time zero and reveals whether an amount must move forward by compounding or backward by discounting.
The chapter develops single-sum present and future value, explains why rates and periods must use the same unit, and shows the inverse relation between required return and present value. Distant cash is more sensitive to the discount rate because the rate operates repeatedly. Every decision compares alternatives at one common valuation date and ends by interpreting whether estimated value supports the quoted price.
What this chapter covers
- 01
Value versus market price
- 02
Cash-flow timelines
- 03
Present value of a single sum
- 04
Future value through compounding
- 05
Rate and period alignment
- 06
Discount-rate sensitivity
Worked example · free
Move one amount forward and reverse it
- 1Place $6,400 at time zero and count four annual intervals.
- 2Apply $FV=6,400(1.06)^4$.
- 1Calculate future value of $8,079.85.
- 2Discount $8,079.85 back four periods to recover $6,400.
Key terms
- Price
- The amount exchanged in a transaction.
- Value
- An estimate of economic worth under stated cash-flow and required-return assumptions.
- Compounding
- Moving a present amount forward as returns earn further returns.
- Discounting
- Moving a future amount backward using the opportunity cost of funds.
Value, Price and Time Value of Money FAQ
Why is a dollar today worth more?
It can be used immediately and can earn a return before the future date. Waiting also exposes the recipient to inflation and uncertainty, so economic equivalence requires a return that compensates for those features.
What date should cash flows be compared at?
Any common date can work, but every cash flow must be moved to that same date before addition or comparison. Time zero is often convenient because price is usually quoted today, but a later decision date can also be valid.
What happens when the discount rate rises?
Present value falls because the same future cash flow must compete with a more rewarding alternative use of current funds. The effect is usually larger for a cash flow that is further away because discounting operates over more periods.
How do I choose between present value and future value?
Look at the requested valuation date. Move cash right on the timeline to find future value and left to find present value. The direction determines whether to multiply or divide by the compounding factor.
Why must the rate and number of periods match?
The rate operates once per period, so an annual rate pairs with years and a monthly rate pairs with months. Changing only the rate or only the count applies the compounding process an inconsistent number of times.
How can I check a time-value calculation?
Predict the direction, inspect the scale and reverse the operation when possible. With a positive rate, future value exceeds present value. Discounting the calculated future amount by the same rate and periods should recover the starting amount.
Why can value differ between two investors?
Investors may require different returns because they face different opportunities, risks, liquidity needs or borrowing costs. The expected cash flow can be identical while the discount rate differs, producing different values. Market price is one observed transaction amount, not proof that every investor assigns the same worth.
What does compounding on compounding mean?
Return earned in an early period becomes part of the balance that earns return later. This is why future value grows by a power rather than by adding the same dollar amount each period. The effect becomes larger with a higher periodic rate or more periods.
How should rounding be handled in time-value problems?
Keep several decimal places in factors and intermediate values, then round the final monetary answer sensibly. Early rounding can accumulate across periods and create avoidable differences. A small final discrepancy may reflect rounding, but a reversed direction or large gap indicates a method or input error.
Assessment move
Draw time zero, each cash-flow date and the periodic rate before selecting an equation. Write the target date explicitly and decide whether the cash moves right by compounding or left by discounting. Convert percentages to decimals and keep the rate unit aligned with the period count.
After calculating, perform three checks: the direction must make economic sense, the scale should be plausible, and the inverse operation should recover the starting amount when rounding permits. Practise comparisons by valuing the same receipt at two required returns and two maturities, predicting the direction before using a calculator.
For price decisions, calculate value at time zero, subtract price at time zero and state whether the expected cash flow compensates for the required return. Record errors as timing, rate, period, operation or interpretation. That classification turns one correction into a reusable method rather than an isolated answer.
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