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Exercise 41 of 41 · Finance · Advanced · 13 min

Is the Project Worth It? Net Present Value with NPV

Your task: In D2:D4, find the present value of years 1-5, the net present value, and an Accept or Reject decision.

Full instructions, scenario and goal

Scenario

A company is considering buying a machine for 50,000. Over the next five years it is expected to bring in a cash flow each year. Management uses an 8% discount rate and wants to know the present value of the five inflows, the net present value after the investment, and whether to go ahead.

Your task

  1. The discount rate is in B1, the investment made today (year 0, a negative number) in B3, and the cash flows of years 1 to 5 in B4:B8.
  2. In D2, find the present value of the five yearly cash flows (years 1 to 5 only).
  3. In D3, find the net present value: that present value plus the investment made today.
  4. In D4, show Accept when the net present value is above zero, otherwise Reject.
  5. Select Check Answer when you are done.

You are done when

  • Only years 1 to 5 are discounted.
  • The investment is added at its full value, because it happens today.
  • The decision follows the net present value.

What you will practise

Discount future cash flows with NPV, treat the initial investment correctly, and turn the result into a decision.

The idea in 30 seconds

Money received in the future is worth less than money today, so a project's future cash flows are discounted at a rate that reflects the return you could earn elsewhere. NPV(rate, values) discounts each value in the list: the first value by one period, the second by two, and so on. The result is the present value of those future cash flows, in today's money.

Read the full explanation below the sheet

Spreadsheet

D2
A
B
C
D
1
2
3
4
5
6
7
8

Loading spreadsheet…

Keyboard shortcuts
Arrow keys
Move between cells
Shift + Arrow keys, or drag with the mouse
Select a range
Ctrl + Arrow keys
Jump to the edge of a block of data
Type, or F2, or double-click
Edit a cell (F2 switches arrow keys between moving and editing)
Click or arrow keys inside a formula
Insert a cell reference after =, +, (, comma and similar
F4
Cycle a reference through A1, $A$1, A$1, $A1
Enter / Tab while editing
Confirm and move down / right (Shift reverses)
Esc
Cancel the edit
Ctrl + C / X / V
Copy, cut and paste (formulas adjust like in Excel)
Delete
Clear the selected cells
Ctrl + Z / Ctrl + Y
Undo and redo
Ctrl + Enter
Check your answer
Tab when not editing
Leave the spreadsheet

Type your answer in cell D2. Click a cell and type. Enter confirms, Esc cancels, Ctrl+Enter checks your answer.Tap a highlighted cell to type in it, then tap the green tick to confirm. Scroll the sheet sideways if it is wider than your screen.

New here? How an exercise works
  1. Read the task. Highlighted cells are yours to fill in; the rest are locked.
  2. Select (or tap) a highlighted cell and type a formula. It starts with =, like =A1+B1.
  3. Press Check answer. Stuck? Reveal hints one at a time.

The full explanation: the idea behind this exercise

Money received in the future is worth less than money today, so a project's future cash flows are discounted at a rate that reflects the return you could earn elsewhere. NPV(rate, values) discounts each value in the list: the first value by one period, the second by two, and so on. The result is the present value of those future cash flows, in today's money.

Because NPV starts discounting from period 1, the investment you make today (period 0) must not be part of the range you give it. Add it separately, entering it as a negative number: net present value = NPV of the future flows + the initial investment. A positive net present value means the project returns more than the discount rate asks for; a negative one means you would do better elsewhere.

Skills you will practise

  • NPV
  • Discounting
  • Investment
  • IF
  • Finance

Complete first: Savings Goal: Future Value with FV

Common mistakes to avoid

Including the investment in the NPV range
NPV treats the first value as one period away. The investment is made today and must be added outside NPV.
Subtracting a number that is already negative
The investment is entered as -50,000. Subtracting it would add 50,000 instead of removing it.