Health Economics Metrics

Topic 2 of 76 · Economic reasoning foundations

Discounting and Time Preference

Discounting converts future costs and benefits into present values, because a benefit today is worth more than the same benefit in five years.

Why it matters

Every health-economics appraisal and every serious public-sector business case discounts multi-year streams. The UK's HM Treasury Green Book mandates a 3.5% annual social time preference rate; NICE's reference case discounts both costs and health effects at 3.5% per year (with a 1.5% non-reference-case rate for near-cure therapies with benefits over 30+ years). If your software business case claims "£5 million savings over 10 years," a finance reviewer will immediately ask for the discounted figure.

The math

Present value of a future amount:

PV = FV / (1 + r)^t

PV = present value
FV = future value in year t
r  = discount rate (NICE/Green Book: 0.035)
t  = years from now

For a constant annual benefit B over n years (an annuity):

PV = B × [1 − (1 + r)^(−n)] / r

Worked example

Your software saves an NHS trust £100,000 per year for 5 years, starting one year after go-live.

Undiscounted total: £500,000.

Discounted at 3.5%:

Year 1: 100,000 / 1.035^1 = £96,618
Year 2: 100,000 / 1.035^2 = £93,351
Year 3: 100,000 / 1.035^3 = £90,194
Year 4: 100,000 / 1.035^4 = £87,144
Year 5: 100,000 / 1.035^5 = £84,197

Total PV ≈ £451,505

The honest headline is about £451,000, roughly 10% less than the naive sum. Now suppose delivery slips by one year: every term shifts one year later, and the PV falls to about £436,000 — the discounting view of cost of delay.

Software engineering connection

  • Tech-debt paydown and platform migrations promise benefit streams years out; discount them before comparing against work that pays back this quarter.
  • Front-loaded costs, back-loaded benefits is the standard shape of a migration. Discounting penalizes that shape, correctly: it prices the risk-free time value of committing capacity now for value later.
  • "Savings in year 5" claims deserve skepticism twice over — they are both heavily discounted and highly uncertain (see sensitivity analysis).

Pitfalls

  • Discounting costs but not benefits (or vice versa) — the reference case discounts both, at the same rate.
  • Using a commercial rate (8–12%) in a public-sector case, or 3.5% in a venture-backed one. Match the rate to the decision-maker.
  • Confusing discounting with inflation. Discounting applies to real (inflation-adjusted) values; don't do both implicitly.

Sources