Difficulty: Intermediate | Prerequisites: Introductory financial accounting; familiarity with basic algebra and the concept of interest rates.
Present value sits at the heart of how accountants measure bonds, leases, pensions, and any other obligation or asset that involves future cash flows. The core idea is that a pound (or dollar) received today is worth more than one received later, because today's pound can be invested and grow. This chapter gives you the mechanical toolkit, PV tables, formulas, and the logic behind them, that the rest of ACCTG 472 will lean on heavily. If you are comfortable with basic interest calculations and can rearrange a simple equation, you have what you need to start.
Present value is what a future cash flow is worth right now, after discounting it by an interest rate over a number of periods. For a single lump sum you multiply by a PV factor from the table; for equal recurring payments (an ordinary annuity) you use the PVA table instead. Higher discount rates and longer time horizons both shrink the present value.
Present value (PV)
The current worth of a future amount of money, given a specified rate of return. Think of it as the answer to "how much would I need to invest today to end up with that future amount?"
Future value (FV)
The amount a present sum will grow to over a given period at a given interest rate. In simple terms, this is what your money becomes after earning interest.
Discount rate (i)
The interest rate used to convert a future amount back to its present value. Sometimes called the market rate of interest or the required rate of return. The higher the discount rate, the lower the present value.
Number of periods (n)
The count of compounding intervals between now and when the cash is received. Periods can be years, quarters, months, or any regular interval, and must match the rate used.
PV factor
The decimal multiplier found in the PV of $1 table at the intersection of a given n and i. You multiply this factor by the future amount to get its present value.
Ordinary annuity
A series of equal payments received (or paid) at the end of each period for a set number of periods. Think of it as a repeating cash flow that always arrives at the close of each interval, not the start.
PVA factor (present value of an annuity factor)
The multiplier from the PVA table at a given n and i. Multiply it by the per-period payment to get the total present value of the entire annuity stream.
Discounting
The process of translating a future cash flow into present-day terms. In simple terms, it is the reverse of compounding: instead of growing money forward, you shrink it back.
Cash in hand can be invested immediately, so it grows over time.
A future payment is therefore worth less than the same number today, because you miss out on the return you could have earned in the interim.
To compare amounts that arrive at different times, we restate them all in present-day terms by discounting.
Locate the row for n (number of periods) and the column for i (discount rate per period) in the PV of $1 table.
Read off the PV factor at that intersection.
Multiply: PV = Future Amount x PV Factor.
Example: $5,000 to be received in 4 years, discounted at 3% per year.
PV factor (n = 4, i = 3%) = 0.88849
PV = $5,000 x 0.88849 = $4,442 (rounded)
Intuition check: if you invested $4,442 today at 3% compounded annually, after four years you would have approximately $5,000.
A higher required return means you would pay less today for the same future cash.
Example: an investment guaranteed to pay $2,000 in one year.
At 5%: PV = $2,000 / 1.05 = $1,905
At 7%: PV = $2,000 / 1.07 = $1,869
The jump from 5% to 7% lowered the price you would accept by $36.
An ordinary annuity is a stream of equal payments, each arriving at the end of its period.
Use the PVA table instead of the single-amount table: find the row for n (total number of payments) and the column for i (discount rate per period).
Multiply: PV = Payment per Period x PVA Factor.
Example: $5,000 received quarterly for 2 years (8 periods), beginning one period from now, at 3% per quarter (12% annual).
PVA factor (n = 8, i = 3%) = 7.01969
PV = $5,000 x 7.01969 = $35,098
The discount rate and the number of periods must use the same interval. If payments are quarterly, use the quarterly rate and count quarters, not years.
A common source of error is using the annual rate with quarterly periods, or vice versa.
PV tables round factors to five decimal places, so table-based answers may differ slightly from calculator or spreadsheet results.
Small rounding differences are expected and acceptable on exams that specify table use.
PV of a single amount
PV = FV \times \frac{1}{(1 + i)^n}where FV is the future value, i is the discount rate per period, and n is the number of periods.
The fraction 1 / (1 + i)^n is the PV factor you look up in the table.
PV of an ordinary annuity
PVA = PMT \times \frac{1 - \frac{1}{(1 + i)^n}}{i}where PMT is the equal payment each period. The entire fraction is the PVA factor from the annuity table.
Present value is how bond prices are set: the market discounts the bond's future coupon payments and face value back to today at the prevailing market interest rate. It is also the basis for valuing leases, pension obligations, and any contract that promises cash flows over time. Outside accounting, the same logic drives mortgage pricing, capital budgeting decisions ("is this project worth the upfront cost?"), and personal finance calculations like how much you need to save today to fund a future goal.
Students often confuse the discount rate per period with the annual rate. If cash flows are quarterly, you need the quarterly rate (annual rate / 4) and the number of quarters, not years.
A higher discount rate does not mean a higher present value. It means the opposite: a higher rate shrinks the PV, because you are demanding more return and therefore willing to pay less today.
Students sometimes use the PVA (annuity) table for a single lump-sum payment. The annuity table is only for a series of equal payments; a one-off future amount uses the PV of $1 table.
Rounding differences between table-based and calculator-based answers are not errors. Small discrepancies are expected and examiners are aware of them.
Present value mechanics reappear in nearly every major topic in ACCTG 472: bond pricing, bond amortisation, lease accounting, pension obligations, and asset impairment.
Expect exam questions that give you a future cash flow, a rate, and a number of periods, then ask you to compute PV using the table factor. Know which table to use (single amount vs. annuity).
Watch for questions that state an annual rate but describe quarterly or semi-annual payments. Converting the rate and adjusting n is a frequent exam trap.
You may be asked to explain why a bond sells at a premium or discount; the answer traces directly back to the relationship between the coupon rate and the market discount rate through PV.
True or false: a dollar received five years from now is worth less than a dollar received today. (True)
If the discount rate increases, the present value of a future cash flow ______ (increases / decreases). (Decreases)
True or false: the PVA table is used when you have a single lump-sum payment. (False, use the PV of $1 table)
Fill in the blank: PV = Future Amount x ______. (PV factor)
True or false: when payments are quarterly, n should be the number of quarters, not years. (True)
Q: An investment will pay you $10,000 in 5 years. If your required rate of return is 6%, what is the most you should pay for it today? (PV factor at n = 5, i = 6% is 0.74726.)
A: PV = $10,000 x 0.74726 = $7,473. You should pay no more than $7,473.
Q: You will receive $3,000 at the end of each year for 4 years. The discount rate is 8%. What is the present value of this annuity? (PVA factor at n = 4, i = 8% is 3.31213.)
A: PV = $3,000 x 3.31213 = $9,936.
Q: A bond pays $2,500 semi-annually for 3 years, and the annual market rate is 10%. What values of n and i should you use when looking up the PVA factor?
A: n = 6 (3 years x 2 periods per year) and i = 5% (10% / 2). You must match the period length of the payments.
Q: Explain in one sentence why the present value of $1,000 due in 10 years is lower at 9% than at 4%.
A: A higher discount rate means each year of waiting "costs" more in foregone return, so the amount you need to invest today to reach $1,000 is smaller.
Q: Your PV table gives $4,442 for a problem, but your calculator gives $4,444. Is this an error?
A: No. The small difference is a rounding artefact caused by the table's five-decimal-place factors. Both answers would be accepted on an exam that permits either method.
This material connects directly to bond valuation (Chapter 14 in most intermediate texts), where the bond price is the PV of its coupon annuity plus the PV of its face value at maturity. It also underpins lease accounting (IFRS 16 / ASC 842), where the lessee records a right-of-use asset at the PV of future lease payments. Later in the course, pension obligations and asset impairment tests rely on the same discounting mechanics introduced here.
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