One-time versus annual, over the lease term

Two offices, one horizon

Prairie Sky Software Inc., a Saskatoon firm of ninety people, must sign a five-year lease and has two options.

Downtown: rent 240,000 a year; no transit subsidy needed (staff walk or take the bus); staff-turnover cost — recruiting and training replacements — estimated at 20,000 a year; a one-time fit-out of 120,000.

Suburban: rent 150,000 a year; a transit subsidy of 30,000 a year to get staff there; turnover cost 45,000 a year, because the location is harder to recruit for; a one-time fit-out of 200,000.

Two more facts arrive with the file. The current office has an unamortised fit-out of 40,000 on the balance sheet. And the CEO prefers a downtown address.

Strike, then separate by kind

The 40,000 fails the future test — it was spent on an office Prairie Sky is leaving whichever option it picks — so it is sunk, and it will be written off under both alternatives. Strike it. The CEO’s preference is real but not a number: it goes on the qualitative side, not in the worksheet.

What survives is of two kinds, and the trap in this lesson is mixing them. Annual costs recur every year of the lease; one-time costs are paid once. Put them on the same horizon before comparing — the horizon is the five-year lease term the prompt states.

                              Downtown     Suburban
Rent (annual)                  240,000      150,000
Transit subsidy (annual)             0       30,000
Turnover cost (annual)          20,000       45,000
Annual total                   260,000      225,000

Fit-out (one-time)             120,000      200,000
Unamortised old fit-out          sunk         sunk

Five-year total   5 × annual + one-time
                             1,420,000    1,325,000
Advantage of Suburban                        95,000

Suburban costs 35,000 a year less but 80,000 more to fit out; over five years the annual saving (175,000) outruns the extra one-time cost by 95,000. In a spreadsheet the five-year line is =5*B5+B6 — annual total in row 5, fit-out in row 6.

The horizon changes the answer

The two kinds of cost trade off differently at different horizons, which is why the prompt always states one. On a three-year lease: Downtown 3 × 260,000 + 120,000 = 900,000; Suburban 3 × 225,000 + 200,000 = 875,000; Suburban by only 25,000. Short the horizon further and Downtown wins, because the extra 80,000 of fit-out has fewer years of rent saving to pay for it. A learner who adds the fit-out to every year’s cost, or who compares annual totals alone and ignores the fit-out, gets a number that is wrong in a way the marker recognises at once.

The estimate is still relevant

The turnover cost is an estimate — nobody knows exactly how many developers will leave a suburban office. It is tempting to drop it as “too uncertain”. Wrong: it is future and it differs by 25,000 a year, which over five years is 125,000 — larger than the whole Suburban advantage. A relevant estimate is estimated, stated as an assumption, and tested: at what turnover cost would the answer flip? If Suburban’s turnover cost were 64,000 instead of 45,000, the five-year advantage would be gone. That sensitivity is the useful thing to tell the CEO, alongside the fact that her preference for downtown would cost the firm about 95,000 over the lease — a price she may decide is worth paying.

One honesty about method: a five-year comparison of costs paid at different times really wants discounting. Module 13 does it; this lesson, like the e-text’s, compares undiscounted totals over the stated horizon.