A dollar today vs a dollar tomorrow
“Why is a dollar today worth more than a dollar tomorrow?”
The DCF, the most famous valuation method, is just this idea applied to a company. Get it here and the DCF becomes arithmetic.
Money today can be invested to grow, so future money is worth less today. Discounting shrinks a future amount back to what it's worth now.
Growing forward, discounting back
$100 invested at 10% grows to $110 in a year and $121 in two. Run it backwards and you're discounting: $110 a year from now is worth $100 today at a 10% rate. That rate reflects what you could earn elsewhere and how risky the payment is.
The higher the rate, or the further away the payment, the less it's worth today. That's why risky, distant cash flows are worth so little now.
- 1$20 a year forever at an 8% rate: $20 ÷ 8% = $250 (a perpetuity).
- 2If that $20 grows 3% a year: $20 ÷ (8% − 3%) = $400 (a growing perpetuity).
- 3$100 a year for just two years at 10%: $100 ÷ 1.1 + $100 ÷ 1.21 ≈ $174 (an annuity).
Dashed: cash flow that year. Filled: what it's worth today. The further out, the more it shrinks.
Try dragging WACC and watch EV.
The growing-perpetuity formula, payment ÷ (rate − growth), is exactly what a DCF uses for its terminal value. You've just learned it.
Say it like this
Money in hand now beats the same amount later, because today's money can be invested to earn a return, and a future payment carries risk. To compare money across time, we discount future cash flows back to the present at a rate that reflects that return and risk. A higher discount rate, or a payment further in the future, means a lower present value.
Traps to avoid
- ✕Discounting by multiplying by the rate instead of dividing by (1 + rate).
- ✕Forgetting that a payment two years away is discounted twice: ÷ 1.1², not ÷ 1.2.
- ✕Using a growth rate higher than the discount rate in the perpetuity formula: the math breaks.
What they'll ask next
›What happens to present value if interest rates rise?
It falls: you divide by a bigger number.
›What's the difference between an annuity and a perpetuity?
An annuity pays for a fixed number of years; a perpetuity pays forever.
›Where does this show up in banking?
In every DCF, in bond pricing, and in comparing deals that pay out at different times.
Check yourself
What's $110 received one year from now worth today, at a 10% discount rate?