Finance · level 2
IRR of a lump-sum payoff
For one outlay and one payoff the IRR is just the multiple annualised. Berk & DeMarzo's warning: IRR agrees with NPV only for a conventional, stand-alone project — never rank mutually exclusive projects on it.
Worked example: Invest $7M today and receive a single $10.5M in 2 years. What is the IRR?
Step by step
- 1
Multiple
$10.5M / $7M = 1.5×
- 2
Annualise
1.5^(1/2) − 1 = 22.47%
- 3
Rule of 72 check
A 1.5× in 2 years is less than a doubling; 72 / 2 = 36% would be exactly 2×.
- 4
Decision rule
Accept if IRR > cost of capital — only when cash flows are conventional (one sign change) and projects are not mutually exclusive.
Invest $7M today and receive a single $10.5M in 2 years. What is the IRR? = 22.5
The theory behind it
Intuition
Finance is time and risk applied to cash: move every cash flow to the same date at a rate that reflects its risk, then compare.
Common pitfalls
- ×Discounting a nominal flow at a real rate (or vice versa).
- ×Mixing enterprise-value and equity-value numbers in the same ratio.
In the interview
Valuation, WACC, LBO and accretion rounds — where a wrong bridge is a wrong answer.