A dollar later is not a dollar now
Calder Coffee's bean supplier owes it a $100 credit and offers two ways to settle: $100 today, or $121 in two years. The owner reaches for the bigger number. Which one is bigger depends on a rate.
Money today is worth more than the same money later. You can invest it now, and a promise two years out is less certain than cash in hand. Present value divides future cash by (1 + rate) once for every period: PV = future cash ÷ (1 + rate)^periods. At 10% a year, $121 in two years is worth 121 ÷ 1.1² = 121 ÷ 1.21 = $100 today. The two offers are equal at exactly 10%. At a lower rate the wait is worth it; at a higher rate, take the cash.
The discount rate is a required return, not a penalty. It is what the holder of the claim could earn elsewhere for the same risk, so it depends on the risk of the cash and on whose money is waiting. A government bond and a two-person startup do not share a rate, and neither do a lender and an owner of the same business. Valuation runs on the cash clock: this unit reads the Cash Ledger (cash flow statement) and asks the claim question, whose claim is this cash, and what return does that claimant require?
Net present value is the present value of inflows minus the present value of outflows. A roaster costing $100 now and returning $121 in two years has NPV = 100 − 100 = 0 at 10%. A bigger payoff, or a lower required rate, makes it positive. Zero NPV means the project exactly earns its required return, no more.
IRR is the rate that makes NPV zero, 10% for the roaster. It is a percentage, so people like it, and it misleads in two ways. When cash flows change sign more than once, there can be several IRRs or none. And IRR cannot rank projects of different size or timing: a 50% return on $10 adds less value than a 20% return on $1,000. NPV at the right hurdle measures value added directly, in dollars, and ranks correctly.
- Dollars of value added at the hurdle
- Ranks projects of any size and timing
- Needs a stated discount rate
- The rate at which NPV is zero
- Can be multiple, or missing, when flows change sign twice
- Ignores scale, so it cannot rank
Nominal cash flows take nominal rates; real cash flows take real rates. Do not discount annual cash at a monthly rate without converting one of them. Time, currency and risk have to match on both sides of the division before the arithmetic means anything.
At a 20% annual discount rate, what is $144 received at the end of year two worth today?