Consider two options to buy equipment for your emergency department. You are given the choice to pay $15,000 in cash now, or pay zero upfront, but make four payments of $5,000. If the cost of capital is 2.5%, which is the best based on NPV?

  • 2
    What frequency are the payments to be made? Annually? Quarterly? Daily?
    – quid
    Commented Jun 26, 2019 at 19:13
  • My professor didn't provide me with that information but let's say it's annually.
    – user87482
    Commented Jun 26, 2019 at 19:15
  • 5
    What answer did you get when you* plugged these numbers into the NPV formula? Please show your work!
    – RonJohn
    Commented Jun 26, 2019 at 20:16

1 Answer 1


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This might help illustrate the solution. I look at NPV of each cash flow. i.e. take each payment and calculate the PV of that future amount. $5000/1.025 means that $5000 in a year is worth $4878 if discounted by the 2.5%. The effect compounds, (1.025)^2 for year 2 etc.

At a glance, a total $20K would require a far higher cost of capital to make those payments preferable to the $15K lump sum.

  • 1
    Looks like the interest rate would need to be 12.59% or so in order for the two to be comparable.
    – Peter K.
    Commented Jun 27, 2019 at 2:39

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