Finance: Yield Rates, NPV, and IRR Calculation Methods

r

Required return in the NPV formula.

IRR

Rate that makes NPV equal to zero.

i

Rate at which interest is earned in the reinvestment example.

j

Rate at which interest payments are reinvested in that example.

NPV

NPV = Σ (net CF)ₜ/(1+r)ᵗ

IRR equation

0 = NPV = Σ (net CF)ₜ/(1+IRR)ᵗ

Yield-rate setup

What I have = what I demand.

NPV decision rule

NPV>0 ⇒ do the project; choose the project(s) with the greatest NPV if funds are limited.

IRR decision rule

IRR>r ⇒ do the project; choose the project(s) with the greatest IRR if funds are limited.

What I have

Inflows accumulated at the reinvestment rate.

What I demand

Outflows accumulated at the desired yield rate.

NPV vs IRR

NPV discounts all net cash flows at the required return r; IRR solves for the rate that forces total NPV to zero.

Reinvestment rate

Separate the original earning mechanism from the reinvestment of the interest cash flows.

Yield-rate questions

Place both sides at the same ending time: accumulate what the investor receives and compare it with what the investor requires.

Common trap with IRR

Using IRR in the NPV denominator when the question gives a required return r and asks for NPV.

Common trap with reinvested cash flows

Accumulating reinvested cash flows at the original earning rate when the problem gives a separate reinvestment rate j.

Common trap with memorization

Memorizing the sheet's reinvestment example instead of rebuilding the cash-flow process.

IRR equation definition

NPV = 0.

'What I have' in yield-rate setup

Cash inflows accumulated at the reinvestment rate.

Reinvestment-rate formula instruction

Understand the process rather than memorize the displayed formula.

Calculator worksheets for IRR

CF and IRR.