BFF2140 Chap.1 Time Value of Money
Time Value of Money
Time Value of Money turns cash flows at different dates into comparable values. The chapter uses timelines to separate present value from future value, distinguishes single sums from annuities and perpetuities, and keeps compounding frequency consistent with the interest rate. These habits support every later valuation, project and financing decision in the unit.
A sound set-up begins with a valuation date and labels each payment before selecting an equation. Compounding moves present money forward, while discounting moves future money back, and both require a rate expressed for the same period as the cash flows. Ordinary annuities pay at period ends, annuities due begin immediately, and perpetuity formulas locate value one period before the first payment.
Uneven streams must be valued line by line. Nominal quotations also need conversion when interest compounds within the year, so effective annual rates provide a common comparison basis. Directional reasoning is an important control: higher positive discount rates lower present value, earlier receipts are worth more today, and an annuity due exceeds an otherwise identical ordinary annuity.
The timeline therefore does more than organise arithmetic. It exposes off-by-one errors, mismatched clocks and signs that would otherwise remain hidden inside calculator inputs.
What this chapter covers
- 01
Cash-flow timelines and time 0
- 02
Future value and compounding
- 03
Present value and discounting
- 04
Ordinary annuities and annuities due
- 05
Perpetuities and growing cash flows
- 06
Nominal and effective annual rates
- 07
Reasonableness controls for payment timing, rate periodicity, cash-flow signs and calculator modes before a valuation answer is accepted
Worked example · free
Value a future sum and an annuity today
- 3Future value is $12,500 multiplied by 1.06^4, which equals $15,780.96.
- 3The ordinary-annuity present value is $4,200 multiplied by [1 - 1/1.07^5] / 0.07, which equals $17,220.83.
Key terms
- Compounding
- Moving a cash flow forward by earning returns on principal and accumulated returns.
- Discounting
- Moving a future cash flow backward by removing the required return.
- Annuity due
- A fixed series whose first payment occurs immediately.
Time Value of Money FAQ
Why is a dollar today worth more?
A dollar today can be invested to earn a return, while a promised future dollar carries timing and risk. The relevant comparison is therefore not nominal amounts alone but their values at the same date using an appropriate rate.
How do I choose between PV and FV?
Identify the date requested by the question. Move earlier cash flows forward with compounding and later cash flows backward with discounting until every amount sits on that requested date.
What causes most annuity errors?
The usual error is timing. An ordinary annuity pays at each period end, while an annuity due begins immediately. Draw the first and last payment dates before selecting the annuity factor.
Exam move
Treat time-value work as a sequence of decisions rather than a formula hunt. Begin each problem by drawing time 0, the payment dates and the requested valuation date. Write the cash-flow sign from one consistent perspective, then label the rate per payment period and the total number of periods.
Only after those choices are visible should you decide whether the cash flow is a single sum, an ordinary annuity, an annuity due, a perpetuity or an uneven stream. Drill pairs of nearly identical questions in which only the first payment date changes; this makes the extra period in an annuity due and the one-period-before rule for a perpetuity easy to recognise.
Build rate fluency by converting nominal monthly or quarterly quotations to an effective annual rate and by reversing the conversion when the payment period is shorter than a year. Check every answer directionally: positive compounding should increase a present amount, positive discounting should reduce a future receipt, and moving a payment earlier should raise its present value.
For calculator practice, clear stored registers, enter the timeline on paper before touching the keys, and reproduce one result with direct arithmetic so you know the mode and sign convention are correct. Mixed streams deserve individual discounting rather than an annuity shortcut. When a stream is deferred, value it at the formula date first and then move that lump sum to today.
Keep full precision through intermediate steps and round only the displayed answer. During revision, maintain an error log organised by cause: wrong valuation date, rate-period mismatch, payment mode, sign, formula-date error or premature rounding. Rework each error with new numbers until the correction is automatic.
Finish every solution with one sentence interpreting what the value represents and at which date it is measured. That final sentence prevents two valid numbers from being added merely because they appear in the same question and prepares the valuation discipline used in bonds, projects and WACC later in the unit.
Working through Time Value of Money in BFF2140? Sia is AskSia’s AI Finance tutor — ask any BFF2140 Time Value of Money question and get a clear, step-by-step explanation grounded in how BFF2140 is taught and assessed. Read this chapter free, then take your hardest questions to Sia.
