FNCE20005 · Corporate Financial Decision Making
Time Value of Money
The time value of money is the engine under every valuation in FNCE20005: a dollar today is worth more than a dollar tomorrow, so you must discount a future cash flow back to a present value before you can compare or add cash flows. The subject assumes you met this in Principles of Finance and never re-teaches it as a topic — but it powers every later model (leases, WACC, capital budgeting, takeovers, real options), and the relevant formulae sit on the exam formula sheet. Five building blocks carry the whole subject: the single sum PV = FV/(1+r)t, the annuity, the perpetuity, the growing perpetuity, and the growing annuity. From them you assemble bond prices (a coupon annuity plus a face-value single sum), share prices (the dividend discount model and its Gordon-growth special case), and the terminal value inside any DCF. The marks are in matching the rate to the cash flow — same period, same risk, same tax basis — and in using next period's cash flow (D1, not D0) where the formula demands it.
What this chapter covers
- 011.1 Single sums — present and future value
- 021.2 Nominal vs effective rates, and the after-tax rate
- 031.3 Annuities — ordinary, due, and the future value of an annuity
- 041.4 Perpetuities and growing perpetuities (need r > g)
- 051.5 The growing annuity
- 061.6 Bond valuation and yield to maturity
- 071.7 Share valuation — the dividend discount model and Gordon growth
Worked example: Gordon-growth share price and the implied cost of equity
- +1Step the dividend forward: Gordon growth uses next year's dividend, so D1 = D0(1 + g) = 2.00 × 1.04 = $2.08.
- +1Apply Gordon growth: P0 = D1 / (ke − g) = 2.08 / (0.10 − 0.04) = 2.08 / 0.06 = $34.67.
- +1Check via the rearranged form: ke = D1/P0 + g = 2.08/34.67 + 0.04 = 0.06 + 0.04 = 10.0% — consistent.
- +1State the result: the dividend yield is 6% and growth adds 4%, summing to the 10% required return.
Key terms
- Present value (PV)
- The value today of a future cash flow, found by discounting at the per-period rate r over t periods: PV = FV/(1 + r)t. Discounting moves a cash flow back in time; compounding moves it forward.
- Annuity
- A constant cash flow C paid every period for t periods. An ordinary annuity pays at the end of each period; an annuity due pays at the start (e.g. lease rentals 'in advance') and is worth (1 + r) times the ordinary-annuity value.
- Perpetuity
- A cash flow paid forever. A level perpetuity is worth C/r; a growing perpetuity that grows at g forever is worth C1/(r − g), which requires r > g. Both value the stream one period before the first cash flow.
- Yield to maturity (YTM)
- The single discount rate that makes the present value of a bond's coupons and face value equal its market price — an internal rate of return on the bond. It is not the coupon rate, the current yield, or (mechanically) the cost of debt used in WACC.
- Gordon growth model
- The dividend discount model under constant dividend growth: P0 = D1/(ke − g). Rearranged, it gives a DCF cost of equity ke = D1/P0 + g, used as an alternative to CAPM.
Time Value of Money FAQ
Is time value of money examined on its own in FNCE20005?
Rarely. The subject assumes you learned discounting in Principles of Finance, so it is never re-taught as a standalone topic. Instead these formulae are buried inside bigger problems: a capital-budgeting answer is a string of single-sum discountings, a terminal value is a growing perpetuity, a lease is an annuity, and a share price is a growing perpetuity of dividends. Master the five building blocks and you can assemble any valuation in the course.
What does 'match the rate to the cash flow' actually mean?
Three things must line up. (1) Period — monthly cash flows need a monthly rate, not an annual one. (2) Real vs nominal — a real cash flow must be discounted at a real rate. (3) Risk — the discount rate must reflect the cash flow's risk, which is the single most-repeated warning in the whole subject: never discount a risky cash flow at the risk-free rate. There is also a tax dimension: a finance lease is discounted at the after-tax cost of debt, r(1 − tc).
Why does an annuity due pay more than an ordinary annuity?
An annuity due (payable 'in advance', like lease rentals) has every cash flow arriving one period sooner, so each is discounted one period less. The shortcut is to multiply the ordinary-annuity PV by (1 + r). Forgetting this is the single most common annuity error on lease questions.
When can I use the Gordon growth model?
Only when dividends grow at a constant rate g forever and ke > g. You also must use next year's dividend, D1 = D0(1 + g). You cannot apply constant-g Gordon growth to a firm growing faster than its discount rate, and a firm with non-constant growth needs an explicit multi-stage forecast before the perpetuity kicks in.
Exam move
Drill the five building blocks until you can write each from memory, then practise recognising which one a problem wants: a level stream is an annuity, a forever stream is a perpetuity, a growing forever stream is a growing perpetuity, and a bond is a coupon annuity plus a face-value single sum. For every problem, first check the rate matches the cash flow on period, risk and tax basis — this is where most marks are lost. Keep three traps in front of you: an annuity due is the ordinary annuity times (1 + r); a terminal value computed at year T must still be discounted back T years; and Gordon growth uses D1, not D0. Because the formula sheet is provided, the exam rewards clean selection and clean arithmetic, not memorisation.
