RE5003 Chap.6 NPV, IRR and the Profitability Index
NPV, IRR and the Profitability Index
Three measures of one question
Once the cash flow row exists, the course applies three investment measures. Net present value discounts each future cash flow at the required rate and subtracts the initial investment. The profitability index divides the present value of inflows by the present value of outflows. The internal rate of return is the rate that makes net present value zero.
On a simple decision to invest or not, the rules are invest if NPV is above zero, if PI is above one, and if IRR is above the required rate.
What the required rate means
The lecture defines the discount rate as the minimum return the investor requires given the riskiness of the investment, an opportunity cost.
A positive NPV means the investment is worth more than the equity put in at that standard; a negative NPV means the same capital could earn more elsewhere at the same risk. The IRR cannot be solved by formula and is found by trial or by a spreadsheet; the lecture notes the computation is the same as an effective yield.
Timing of the outlay
The standard formula assumes the whole investment is paid at the start.
If part is paid later, that part is discounted too, so the present value of the outlay falls. The lecture writes the formula with a second outlay one period later for exactly this case.
Zero NPV is not zero profit
The lecture poses a discussion question: would you invest if NPV were zero? Its corollary is that such deals are acceptable.
They still earn the required return and miss only the profit above it, so they are a problem only when they take the place of a positive-NPV opportunity. At market value, a fair price produces exactly zero NPV. The lecture's own illustrations include a leased property held for five years and then sold, and an office acquisition that fails the test because its IRR falls short of a 15% requirement.
What this chapter covers
- 01
The four steps from cash flows to net present value
- 02
The NPV, PI and IRR decision rules
- 03
The discount rate as an opportunity cost
- 04
Solving for the internal rate of return
- 05
Outlays spread over more than one period
- 06
Why zero-NPV deals are acceptable
Worked example · free
A three-year hold at 5%
- 1Write the cash flow row.
- 2Discount each flow at 5%.
- 1Compute NPV and PI.
- 2State the IRR and the decision.
Key terms
- Net Present Value
- Discounted future cash flows less the initial investment; positive means the investment beats the required return.
- Internal Rate of Return
- The rate at which the present value of future cash flows equals the cost of the investment.
- Profitability Index
- The present value of inflows divided by the present value of outflows.
- Hurdle Rate
- The minimum return an investor requires before accepting an investment.
- Opportunity Cost
- The return given up on the best alternative investment of similar risk.
- NPV Profile
- A curve of net present value against the discount rate, crossing zero at the IRR.
- Super-Normal Profit
- Return above the required rate, the part that a zero-NPV deal lacks.
NPV, IRR and the Profitability Index FAQ
Do NPV, PI and IRR ever disagree?
On a single conventional cash flow row with an outlay first and inflows after, they always agree on whether to invest: a positive NPV, a PI above one and an IRR above the required rate are the same condition seen three ways.
Why would anyone accept a zero-NPV investment?
Because it still earns exactly the required return. The lecture's corollary treats it as acceptable: it pays the full required return and misses only the excess above it, which matters only if it crowds out a better deal.
How is the IRR calculated in practice?
There is no closed formula. The rate is found by trial, narrowing in on the value that makes NPV zero, or by a spreadsheet function. The lecture notes it is the same calculation as an effective yield.
What happens to NPV if part of the price is paid a year later?
The later payment is discounted by one period, so the present value of the outlay falls and NPV rises. Payment timing alone can turn a marginal deal from negative to positive.
Why does the NPV fall as the discount rate rises?
Every future cash flow is divided by a larger factor, so it is worth less today. The steeper the fall, the more of the value arrives late in the hold, which is typical when the sale proceeds dominate.
Assessment move
Work one cash flow row through all three measures, then plot NPV at five rates to see the curve cross zero at the IRR. Once you have seen the three rules as one curve, you will not need to memorise them separately.
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