FINC2011 Chap.2 Time Value of Money
Time Value of Money
Time value of money gives FINC2011 its common valuation language. The chapter moves single cash flows forward and backward, values level and growing streams, separates ordinary annuities from annuities due, handles delayed payments, and uses net present value to connect mathematics with an investment decision.
The central control is a timeline that fixes the valuation date and number of compounding intervals before any formula is chosen.
What this chapter covers
- 01
Present value and future value of one cash flow
- 02
Cash-flow timelines and valuation dates
- 03
Ordinary annuities and annuities due
- 04
Level and growing perpetuities
- 05
Delayed and uneven payment streams
- 06
Net present value and project choice
- 07
Direction checks for discount rates and timing
Worked example · free
Value a deferred level payment stream
- 1Draw payments at Years 3, 4, 5, and 6 and locate the ordinary-annuity value at Year 2.
- 2Compute PV2 = $6,400 times the four-period annuity factor at 7.5%, giving $21,180.53.
- 1Discount that local value two years: PV0 = $21,180.53 divided by 1.075 squared.
- 1Report $18,325.77 and confirm it is below the undiscounted $25,600 total.
Key terms
- Present Value
- The value today of a future cash flow after discounting at the required periodic return.
- Future Value
- The amount a present sum grows to after earning a periodic return for a stated number of periods.
- Annuity Due
- A finite equal-payment stream whose payments occur at the beginning of each period.
- Growing Perpetuity
- An indefinite cash-flow stream growing at a constant rate below the required return.
Time Value of Money FAQ
Why is the timeline so important?
The timeline fixes the valuation date, payment dates, and interval count. It exposes whether a payment is at the beginning or end of a period and whether an annuity is delayed. Most exponent errors are timing errors that a labelled line would reveal immediately.
How do annuities and perpetuities differ?
An annuity has a finite number of equal payments, so its formula includes the payment count. A perpetuity continues indefinitely and divides the next payment by the periodic discount rate. A growing perpetuity also subtracts growth from required return, with required return above growth.
What does a negative net present value mean?
A negative NPV says the forecast cash flows are worth less than the initial cost at the stated required return. It supports rejection under those assumptions. It does not prove the asset is always unattractive, because different cash-flow estimates or risk could change the valuation.
Exam move
Draw every dated cash flow before choosing a formula. Mark the valuation date with a box and count intervals rather than reading year labels casually. Keep a pattern sheet containing single sums, ordinary annuities, annuities due, perpetuities, growing perpetuities, and irregular streams. For each pattern, write where the formula locates value.
Practise translating a delayed stream into a local annuity value followed by a second discount. Use three direction checks: a higher positive rate lowers present value, a later receipt is worth less today, and a positive-rate present value of positive future cash flows should normally sit below their undiscounted total.
Build every practice solution in four lines: cash-flow pattern, local valuation date, rate and period units, and movement to the requested date. This structure makes timing visible before arithmetic begins. For a delayed annuity, verify the compact formula once by discounting each payment separately; the two routes should agree apart from rounding.
For an annuity due, compare it with the otherwise identical ordinary annuity and explain why receiving every amount one period earlier raises value. When a stream changes shape, partition it into genuine blocks rather than averaging payments. Value each block where its formula naturally places it, label that date, and move the block only afterward.
Practise equivalent-value problems by choosing a focal date other than time zero, then repeat at time zero to prove the result is unchanged. Keep full precision in factors and round only the final currency amount. If using a financial calculator, write the payment mode and sign convention beside the answer so the device cannot hide an incorrect timeline.
Finish each solution with a sentence interpreting dollars and date: present value today, accumulated value at a future date, or NPV relative to the initial cost. This final label catches answers that are numerically tidy but attached to the wrong time. Build a short error log with the timeline mistake, its numerical symptom, and the correction. Rework those questions after changing the first-payment date or compounding period.
If the method still works when the wording changes, you are reasoning from dates rather than recalling a surface pattern.
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