Two sponsors each promise you $1,000,000. One pays after race 2, the other after race 6. Same check, but one is worth more to you, and not only because of interest. This week you find out how much more.
Learning objectives. After this week you can (1) discount a future cash flow to today; (2) value a stream of equal payments as an annuity; and (3) use net present value (NPV) to judge a spending decision.
Remember this: early cash beats late cash. Count the weeks you wait, then discount.
1) Discounting, one period at a time
PV = FV ÷ (1 + r)n
Here r is the rate per period and n is the number of periods you wait. For a racing team the natural period is the race week; the examples use 1% per race week. Standing at race 1, a check after race 2 is one week away and a check after race 6 is five weeks away:
| Payment | Weeks away | Arithmetic | Present value |
|---|---|---|---|
| $1,000,000 after race 2 | 1 | 1,000,000 ÷ 1.01 | $990,099 |
| $1,000,000 after race 6 | 5 | 1,000,000 ÷ 1.015 | $951,466 |
That is $38,633 of difference from discounting alone. There is a second reason early money wins: reinvestment. Cash that lands at race 2 can fund budgets for races 3 to 6. Cash that lands after the last race funds nothing that season.
2) A stream of equal payments: the annuity
PVannuity = PMT × [1 − (1 + r)−n] ÷ r
You expect $1,500,000 of Winnings in each of the next 4 races. At 1% per week: 1,500,000 × [1 − 1.01−4] ÷ 0.01 = 1,500,000 × 3.90197 ≈ $5,852,948. The plain total is $6,000,000; waiting costs about $147,000.
3) NPV: is it worth the money?
NPV = PV of expected inflows − cost today
A $3,000,000 R&D budget is expected to bring in $3,500,000 two race weeks from now. PV = 3,500,000 ÷ 1.012 = $3,431,036, so NPV = 3,431,036 − 3,000,000 = +$431,036. A positive NPV means the inflow is worth more today than it costs.
4) Picking the rate
A discount rate is an opportunity cost: what the same cash could earn in its next-best use. If your cash has good uses right now, or the inflow is uncertain, use a higher rate. Whatever rate you pick, use the same one for every option you compare.
Quick self-check
(a) $1,000,000 arriving in one race week at 1% per week is worth? (b) $1,100,000 in one year at 10%? (c) $3,900,000 now or $4,000,000 five weeks away at 1% per week? (Answers: $990,099; $1,000,000; take $3,900,000, since the later offer is worth about $3,805,863 today.)
Common mistakes
- Counting labels, not gaps. From race 1, "after race 6" is five weeks away, not six.
- Adding future sums as if they were cash today. That overstates every stream.
- Mixing rates. Use a per-week rate with weeks and a yearly rate with years.
This week in the arena
Value your next three races. Use your average Winnings so far as the forecast for each race, discount each one at 1% per race week, and add them up. Compare that with the plain total. Then look at this week's biggest budget line: what would it have to bring back, and how soon, to have a positive NPV?