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  1. 099Project A costs Rs 100 crore and returns Rs 130 crore after one year. Project B costs Rs 100 crore and returns Rs 20 crore a year for ten years. You can do only one. Which ranks higher on IRR, which on NPV at a 10% cost of capital, and which would you take?Private and real asset mathsHardPIMCOMunich · 2024

    Try it first

    At a 10% cost of capital, which project creates more value?

    Show the worked solution

    A wins on IRR, 30% against about 15%; B wins on NPV at 10%, Rs 22.9 crore against Rs 18.2 crore. Take B. IRR measures a rate, NPV measures rupees of value at your actual cost of capital. The two disagree because A returns its money in one year and B keeps earning for ten. Above about 11%, the ranking flips.

    How can one project have the higher return and the other create more value?

    Would you rather earn 30% on Rs 100 for a day, or 15% on Rs 100 for ten years? The first is a better rate; the second makes you more money. IRR is a rate per year and says nothing about how long the money earns it, while NPV counts the rupees created at your cost of capital, so when projects differ in timing the two can rank them in opposite order.

    IRR ranks A first; at a 10% cost of capital, NPV ranks B first5%10%15%20%25%30%35%-40501000cost of capital 10%B: NPV 22.9 at 10%A: NPV 18.2 at 10%lines cross at 11.2%IRR B15.1%IRR A 30%B: 20 a year, 10 yearsA: 130 in one yearDiscount rateRs croreIRRA 30.0 / B 15.1NPV at 10%A 18.2 / B 22.9NPV measuresvalue created
    Project B's NPV falls steeply with the discount rate from Rs 100 crore at 0% and crosses zero at its 15.1% IRR, while A's starts at Rs 30 crore and crosses at 30%; the lines meet at about 11.2%, so at a 10% cost of capital B is worth Rs 22.9 crore to A's Rs 18.2 crore.
    The relationship
    NPVA=1301.10−100=18.2,NPVB=20×1−1.10−100.10−100=22.9NPV_A = \frac{130}{1.10} - 100 = 18.2, \qquad NPV_B = 20 \times \frac{1 - 1.10^{-10}}{0.10} - 100 = 22.9
    130A's single payout after one year, Rs crore
    20B's yearly payout for ten years, Rs crore
    10%the cost of capital
    What it says in wordsDiscount each project's cash at the cost of capital and subtract what it costs.

    When would A be the right choice after all?

    Two cases. If the cost of capital is above about 11.2%, the crossover rate, A's NPV is the higher one; and if A's Rs 130 crore could be put straight into another project earning well above 10%, the pair of projects might beat B. Both are really statements about the reinvestment rate. IRR implicitly assumes A's proceeds are reinvested at 30%; NPV assumes the cost of capital, which is usually the more honest assumption.

    In real estate and private markets this is the everyday tension between a quick flip and a long hold. Give both numbers, name the crossover, and say that for mutually exclusive projects NPV decides.

    Where candidates lose it

    The common slip is picking A because 30% beats 15%. With mutually exclusive projects of different lengths, IRR ranks rates, not value, and the interviewer asks this to see if you know the difference.

    The second loss is stopping at take B without saying when that changes. Name the crossover rate and the reinvestment assumption; that is the part that sounds like an investor.

    What the interviewer asks next

    • At what cost of capital are you indifferent between the two?
    • What if B's cash flows ran for twenty years instead of ten?
    • Why might a fund manager paid on IRR prefer A anyway?

    Asked at PIMCO, Real Estate, Munich, 2024 (Wall Street Oasis): just asked a bunch of questions on recent real estate news, as well as a couple of technicals including IRR, NPV