Which machine should we choose?

A positive NPV says a project creates value. It does not say which of two projects is better when they last a different number of years, or when money to invest is limited. This lab builds NPV, the equivalent annual annuity (EAA) and the profitability index (PI) from your own figures, and shows when each one should decide.

The recipe

From cash flows to a decision

1 · Discount factorDF = 1 ÷ (1 + r)ᵗWhat R1 received in year t is worth today

2 · NPVNPV = Σ CFₜ × DFₜValue created after paying for capital

3 · Annuity factorAF = DF₁ + … + DFₙToday's value of R1 a year for n years

4 · EAAEAA = NPV ÷ AFNPV spread into equal yearly amounts

5 · PIPI = (NPV + I) ÷ IPV of inflows per R1 invested

6 · Decidelives? rationing?The situation picks the method

Your figures

Enter the two projects

Each project can be repeated when it reaches the end of its life Capital is rationed (not enough money for every positive-NPV project)

Change trackerChange a figure, then press Enter or click away. This line shows what moved in NPV, EAA and PI.

Steps 1 – 2 · Net present value

Bring every cash flow back to today

Steps 3 – 4 · Equivalent annual annuity

Unequal lives: turn each NPV into a yearly amount

A project that runs longer has more years in which to build up NPV, so a bigger NPV may just mean a longer life. The EAA asks: what equal amount every year, over the project's own life, has the same present value as its NPV? Comparing those yearly amounts puts both projects on the same footing.

Step 5 · Profitability index

How much present value does each R1 invested buy?

The present value of the future inflows equals the investment plus the NPV. The PI divides that total by the investment. So whenever NPV is positive, PI must be greater than 1. The bars below show this: each bar is the PV of inflows, the grey part is the investment, and the tick marks count how many times the investment fits into it.

Step 6 · The decision

The situation decides which method to trust

Nora Ltd · reading the model answer

Checking the model answer's figures

EAA: correct

The EAA table in the model answer matches this lab exactly: R388 157 for the existing machine and R502 071 for the new one. On a financial calculator: N = 5, I/Y = 16, PV = −1 270 939, FV = 0, then compute PMT. Repeat with N = 6 and PV = −1 850 000.

PI: the method needs correcting

The answer finds "PV" by subtracting the investment from the NPV. The NPV already has the investment deducted, so the PV of the inflows is NPV plus the investment. PIs of 0.61 and 0.76 cannot be right: a PI below 1 would mean a negative NPV, yet both NPVs are positive.

	Existing machine	New machine
NPV	1 270 939	1 850 000
Investment used in the answer	790 000	1 050 000
Answer: "PV" = NPV − I	480 939	800 000
Correct: PV of inflows = NPV + I	2 060 939	2 900 000
Answer: PI	0.61	0.76
Correct: PI = PV ÷ I	2.61	2.76
If the R150 000 working capital is included in I	2.35 (on 940 000)	not given

The ranking does not change: the new machine still has the higher PI, so the recommendation stands. The answer also shows (1 100 000) in one line where the purchase price is 1 050 000. Its figure of 0.61 is really NPV ÷ I − 1, which is not a recognised measure.

Experiments to try

See what moves, and why

Raise the WACC from 16% to 20%. Every NPV falls, and the later cash flows lose the most, so the longer project suffers more.
Load "Longer life, bigger NPV". The six-year project has the higher NPV but the lower EAA. Untick "can be repeated" and watch the verdict switch back to NPV.
Load "Small vs big under rationing" and tick "Capital is rationed". NPV prefers the big project, while PI prefers the one that earns more per rand invested.
Make a year-0 outflow larger until NPV reaches zero. PI lands exactly on 1.00, because both measures cross their hurdle at the same point.