Finance⏱ 5 min read
What Is the Time Value of Money? (And Why It Changes Every Decision)
The time value of money is the single most important concept in finance. It explains why a pound today is worth more than a pound tomorrow — and how to calculate by exactly how much.
The time value of money (TVM) is the foundational principle that money available now is worth more than the same amount in the future. This sounds obvious, but the quantification of exactly how much more changes every financial decision — from mortgages to pensions to business investments.
Why Money Has Time Value
Three reasons make a pound today more valuable than a pound in the future:
- Opportunity cost: Money received now can be invested to earn returns
- Inflation: A pound in the future buys less than today (typically)
- Risk: Future payments are uncertain; present cash is certain
Future Value: What Money Grows To
FV = PV x (1 + r)^n
PV = Present value (money today)
r = Interest/return rate per period
n = Number of periods
Example: £5,000 invested at 7% per year for 10 years
FV = 5,000 x (1.07)^10 = 5,000 x 1.9672 = £9,836
The £5,000 doubles (nearly) in 10 years at 7% — entirely
through the compounding effect of time value.
Present Value: What Future Money Is Worth Today
PV = FV / (1 + r)^n (rearranged from FV formula)
This is called "discounting" — finding the present value
of a future sum.
Example: Someone promises you £20,000 in 5 years.
Assuming 6% discount rate (your opportunity cost):
PV = 20,000 / (1.06)^5 = 20,000 / 1.3382 = £14,942
The promise of £20,000 in 5 years is worth only ~£14,942 today.
You should pay no more than £14,942 for it now.
Net Present Value (NPV) for Decisions
NPV = Sum of all discounted cash flows - Initial investment
Should you invest £10,000 in equipment that saves £3,000/year for 5 years?
Discount rate: 8%
Year 1: 3,000 / (1.08)^1 = £2,778
Year 2: 3,000 / (1.08)^2 = £2,572
Year 3: 3,000 / (1.08)^3 = £2,382
Year 4: 3,000 / (1.08)^4 = £2,205
Year 5: 3,000 / (1.08)^5 = £2,042
Total PV of savings: £11,979
Less investment: £10,000
NPV = +£1,979 — positive, so worth doing
The Discount Rate: Choosing the Right Rate
Common discount rate choices:
Risk-free rate: Current government bond yield (~4-5% in 2025)
Personal opportunity cost: Your savings/investment rate (~6-8%)
Business WACC: Weighted Average Cost of Capital (varies widely)
Inflation rate: For real (inflation-adjusted) analysis
If your discount rate is 7% and an investment returns 7%,
NPV = 0 — you're just breaking even (no value created).
Positive NPV = value created above your opportunity cost.
Negative NPV = better to do nothing and invest at the discount rate.
Annuity: Regular Payments
PV of an annuity (regular equal payments):
PV = PMT x [1 - (1+r)^-n] / r
What is a £500/month annuity for 20 years worth today (5% annual = 0.417%/mo)?
r = 0.05/12 = 0.004167
n = 240 months
PV = 500 x [1 - (1.004167)^-240] / 0.004167
= 500 x [1 - 0.3683] / 0.004167
= 500 x 151.52 = £75,760
A pension or annuity that pays £500/month for 20 years has
a present value of ~£75,760 today (at 5% discount rate).