Finance and the Economy · Seminar 7 · Finance for business

Is a €18m payoff in four years worth €10m today?

Discount the future payoff at the rate the money could earn elsewhere. If the present value beats the €10m outlay the net present value is positive and the project is worthwhile. The rate at which NPV is exactly zero is the internal rate of return. Question 1, from Business Economics (Mankiw, Taylor & Ashwin, ch. 19).

Pick a part of the question, or move the sliders. The curve shows NPV at every discount rate; it crosses zero at the IRR.

Discount rate (what the money could earn elsewhere)

0%30%

Payoff in the final year (€m)

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Years until the payoff

110

Investment today (€m)

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Investing elsewhere grows to

Present value of payoff

Net present value

Internal rate of return

Two views of the same decision. Compounding the outlay forward (PV × (1 + r)ⁿ) and discounting the payoff back (FV ÷ (1 + r)ⁿ) always agree. NPV falls as the discount rate rises because a higher rate makes future money worth less today.

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