Net Present Value (NPV)
Present value of future cash flows.
Why This Matters
Net Present Value (NPV) is the central tool of capital budgeting. It answers the most important question for any investment:
"After we account for the time value of money and risk, how much value (in today's dollars) does this project add to the business?"
NPV > 0
Project creates value โ accept
NPV < 0
Project destroys value โ reject
NPV Definition and Formula
NET PRESENT VALUE
NPV = ฮฃ CFโ / (1 + r)แต
OR:
NPV = โCFโ + ฮฃ (CFโ / (1 + r)แต) for t = 1 to N
CFโ = net cash flow in period t
r = discount rate (required return)
N = project life in periods
Decision: NPV > 0 accept ยท NPV < 0 reject ยท NPV = 0 indifferent
Choosing the Discount Rate
The discount rate represents the required rate of return, reflecting time value of money, risk compensation, and cost of capital.
WACC โ base rate for average-risk projects
Risk-adjusted โ higher/lower rates for above/below-average risk
ABC Coffee: r = 10% for small equipment investments
NPV Calculator
Enter initial outlay, cash flows (annual annuity or year-by-year), and discount rate to compute NPV and accept/reject decision. Pre-loaded with ABC's roaster project.
Net Present Value
$-124.76
Decision @ 10%
REJECT
NPV < 0
Sum of Discounted CFs
$-124.76
Present Value Breakdown
| Year | Cash Flow | PV Factor | Present Value |
|---|---|---|---|
| Y0 | โ$43,000 | 1.0000 | $-43,000.00 |
| Y1 | +$10,000 | 0.9091 | $9,090.91 |
| Y2 | +$10,000 | 0.8264 | $8,264.46 |
| Y3 | +$10,000 | 0.7513 | $7,513.15 |
| Y4 | +$10,000 | 0.6830 | $6,830.13 |
| Y5 | +$18,000 | 0.6209 | $11,176.58 |
| NPV (Total PV) | $-124.76 | ||
NPV Formula
NPV = ฮฃ CFโ / (1 + r)แต
NPV > 0 โ accept ยท NPV < 0 โ reject ยท NPV = 0 โ earns exactly r
Example โ NPV of ABC's Roaster Project
STEP 1 โ PV OF OPERATING FLOWS
PV = $10,000 ร [(1 โ 1.10โปโต) / 0.10] = $10,000 ร 3.791 โ $37,910
STEP 2 โ PV OF TERMINAL FLOW
PV = $8,000 / 1.10โต โ $8,000 ร 0.6209 = $4,967
STEP 3 โ NPV
NPV = โ$43,000 + $37,910 + $4,967 = โ$123
At 10%, project barely fails. At 9%, NPV would be slightly positive.
ABC Roaster โ NPV Profile vs. Discount Rate
NPV crosses zero near 9.9% โ that's the IRR. At 10%, NPV โ โ$123 (barely negative).
Including Taxes and Depreciation
AFTER-TAX OPERATING CASH FLOW
CFโ = (Revenue โ Cash Expenses) ร (1 โ Tax Rate) + Depreciation ร Tax Rate
Second term = depreciation tax shield โ real cash savings from reduced taxes
Comparing Projects with NPV
Mutually Exclusive
Choose the project with the higher NPV at the appropriate discount rate.
Independent
Accept all projects with NPV > 0, subject to capital constraints (use Profitability Index to rank).
Capital Budgeting Module Track
NPV is module 3 of 4 (#100โ103):
| Module | Core Concept | # |
|---|---|---|
| Capital Budgeting Basics | Long-term investments; cash flows; time value of money | #100 |
| Payback Period | Time to recover initial investment from cash flows | #101 |
| Net Present Value (NPV) โ You are here | Dollar value added today from discounted cash flows | #102 |
| Internal Rate of Return (IRR) | Discount rate where NPV = 0; compare to hurdle rate | #103 |
Common Mistakes
Mixing nominal and real values
โ Wrong
Using inflation-adjusted cash flows with a nominal discount rate.
โ Right
Match nominal CFs with nominal r, or real CFs with real r.
Ignoring working capital
โ Wrong
Modeling only equipment cost, missing inventory/receivables funding.
โ Right
Include WC outflow at start and recovery at project end.
Double-counting depreciation
โ Wrong
Subtracting depreciation as cash expense AND adding tax shield.
โ Right
Depreciation affects taxes only โ not a cash outflow.
Key Takeaway
Net Present Value (NPV) discounts all expected project cash flows at an appropriate required rate of return and subtracts the initial investment to measure the value created today. A positive NPV means the project increases firm value; a negative NPV means it reduces value. NPV is the primary capital budgeting decision rule because it directly links project choice to value creation, while also respecting the time value of money and risk.
Test Your Understanding
NPV calculation, decision rules, ABC roaster, and project comparison.
Question 1: A project costs $20,000 today and yields $7,000 per year for 4 years. Discount rate 10%. PV factor โ 3.170. Approximate NPV?
Question 2: True or False: If a project's NPV is positive at a discount rate equal to the firm's cost of capital, accepting the project will increase the firm's value.
Question 3: ABC roaster: โ$43,000 Y0; $10,000/yr Y1โ5; +$8,000 terminal Y5. At 10%, NPV is approximately:
Question 4: Two mutually exclusive projects: Project A NPV = $15,000; Project B NPV = $22,000. Which should be chosen?
Ready to Practice?
Build NPV models with annual or year-by-year cash flows, test sensitivity to discount rates, and compare projects in the Practice Lab.
Try the Practice LabWhat's Next?
Internal Rate of Return (IRR) โ The discount rate that makes NPV exactly zero, and how to interpret and compare it to the required rate of return.
Internal Rate of Return (IRR)
Discount rate where NPV = 0
Payback Period
Time to recover investment