The Ultimate CPA Guide to Capital Budgeting & NPV
The Ultimate CPA Guide to Capital Budgeting & NPV
BAR exam review: time value of money, payback period, NPV, IRR, ARR, and the Black-Scholes model
Last updated: March 2026 • Reviewed by Kyle Lee Ashcraft, CPA
Capital budgeting is one of the highest-weighted topic areas on BAR. Companies invest real money in long-term assets every day, and your job on the exam is to evaluate whether those investments make financial sense.
This guide walks through the full toolkit: time value of money, payback period, discounted payback, accounting rate of return, net present value, internal rate of return, and the Black-Scholes model — from core concepts all the way to a harder simulation-style problem.
Who this guide is for:
- BAR students who need a full capital budgeting review
- Students who want to clearly separate NPV, IRR, ARR, and payback period
- Anyone struggling with depreciation tax shields, salvage value, or present value logic
- Students preparing for multi-step BAR simulations
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Get My Free CPA 101 CourseHow Does the BAR Exam Test Capital Budgeting? BAR
Capital budgeting appears in Area I: Business Analysis, under prospective analysis. It is one of the more calculation-heavy areas on BAR and is tested at both application and analysis levels.
| Representative Task | Skill Level |
|---|---|
| Calculate present value of future cash flows or the NPV of an investment | Application |
| Determine how changes in assumptions affect value, including Black-Scholes logic | Analysis |
| Compare investment alternatives using payback, NPV, IRR, or related metrics | Analysis |
What this means for your exam prep
- NPV and present value calculations are tested at the application level
- Black-Scholes and sensitivity-style questions are tested at the analysis level
- Comparing methods is also an analysis skill — you need to know decision rules, pros, and limitations
Video Overview
Prefer to watch first? This video covers the core capital budgeting concepts before you move into the full written breakdown.
Time Value of Money BAR High-Yield
Capital budgeting asks whether future cash inflows are worth enough today to justify the investment. To answer that, you discount future cash flows back to present value using a discount rate.
Four key present/future value concepts
| Concept | What It Means | Example (5%, 5 years) |
|---|---|---|
| PV of a Lump Sum | One future payment brought back to today | $100,000 in 5 years ≈ $78,300 today |
| PV of an Ordinary Annuity | Equal payments at the end of each period | $20,000/year for 5 years ≈ $86,000 today |
| PV of an Annuity Due | Equal payments at the beginning of each period | Beginning-of-period rent stream has a higher PV |
| Future Value | An amount today grown forward to the future | $5,000 invested today at 5% for 30 years ≈ $21,600 |
Discount rate, hurdle rate, and actual rate of return
| Term | Definition |
|---|---|
| Discount Rate | Any rate used to convert future cash flows to present value |
| Hurdle Rate | The minimum acceptable return management requires |
| Actual Rate of Return (IRR) | The return the investment actually generates |
Study Tip: The BAR exam usually gives you the PV factors. Focus on identifying whether the cash flow pattern is a lump sum, ordinary annuity, or annuity due.
Common Trap: Students often use the annuity factor when the cash flow is actually a one-time salvage value or lump-sum receipt. Always match the factor to the cash flow pattern.
Payback Period BAR
The payback method asks a simple question: how many years until we get our money back? It does not use the time value of money and ignores cash flows after the payback point.
Discounted Payback Period
The discounted payback period uses the same recovery concept, but discounts annual cash flows first. Because discounted inflows are smaller than nominal inflows, discounted payback is always longer than basic payback.
| Method | Uses TVM? | Pro | Con |
|---|---|---|---|
| Payback Period | No | Easy to calculate | Ignores TVM and post-payback cash flows |
| Discounted Payback | Yes | More realistic than basic payback | Still ignores post-payback cash flows |
Accounting Rate of Return (ARR) BAR
ARR goes beyond payback by using accounting income, which means depreciation matters. It expresses a return as a percentage, but still ignores time value of money.
Example
| Annual Cash Inflows | $25,000 |
| Less: Depreciation ($100,000 / 10 years) | ($10,000) |
| Accounting Income | $15,000 |
Study Tip: ARR uses one year of accounting income, not total lifetime cash flows. It is income-based, not cash-based.
Net Present Value (NPV) BAR High-Yield
Unlike payback and ARR, NPV fully uses time value of money. Future cash flows are discounted at the hurdle rate and compared to the up-front cost.
Basic Example: Even Cash Flows
Suppose we invest $100,000 and receive $25,000 per year for 10 years. The hurdle rate is 10%, and the ordinary annuity factor is 6.144.
| PV of cash inflows: $25,000 × 6.144 | $153,600 |
| Less: Initial investment | ($100,000) |
| Net Present Value | $53,600 |
Because NPV is positive, we accept the project.
NPV with Uneven Cash Flows
If annual cash flows are uneven, you cannot use the annuity factor. Discount each year individually using the PV of $1 factor for that year, then add the present values together.
Depreciation Tax Shield
Depreciation is non-cash, but it reduces taxable income. That tax savings is a real cash benefit called the depreciation tax shield.
Example: $10,000 depreciation × 20% tax rate = $2,000 annual tax shield.
Important: Only add the depreciation tax shield if the problem says cash flows are pre-tax. If the problem says cash flows are already after-tax, the tax shield is already included.
Salvage Value
Salvage value is a one-time final-year cash inflow, so it is discounted using the PV of $1 lump-sum factor, not the annuity factor.
Study Tip: NPV is expressed in dollars, uses the hurdle rate as the discount rate, and considers all relevant cash flows across the asset’s life.
Kyle’s 90+ Score Insight: The most common NPV mistake is adding the depreciation tax shield when cash flows are already after-tax. The second most common mistake is treating salvage value like part of the annuity instead of a lump sum.
Capital budgeting simulations are among the most complex TBS questions on BAR.
My Free CPA 101 Course shows you how I approach multi-step BAR simulations so you do not panic when you see a 6-step NPV question on exam day. Check it out here.
Internal Rate of Return (IRR) BAR High-Yield
NPV and IRR evaluate the same investment from two angles. NPV expresses the answer in dollars. IRR expresses the answer as a percentage.
IRR decision rule
| Comparison | Decision | NPV Equivalent |
|---|---|---|
| IRR > Hurdle Rate | Accept | Positive NPV |
| IRR < Hurdle Rate | Reject | Negative NPV |
If the hurdle rate is 10% and IRR is 21.4%, the project is accepted because it exceeds the minimum required return.
Study Tip: The BAR exam usually will not ask you to calculate IRR from scratch. You will more often compare a given IRR to the hurdle rate.
Decision-Making Methods: Side-by-Side Comparison BAR
| Method | Measured By | Uses TVM? | Formula | Pro | Con |
|---|---|---|---|---|---|
| Payback Period | Time (years) | No | Investment / Undiscounted Cash Flows | Easy to calculate | Ignores TVM and later cash flows |
| Discounted Payback | Time (years) | Yes | Investment / Discounted Cash Flows | Uses TVM | Still ignores later cash flows |
| Accounting Rate of Return | % (per year) | No | Accounting Income / Investment | Uses income and depreciation | Ignores TVM |
| Net Present Value | $ (total) | Yes | PV of Cash Inflows − Investment | Uses TVM and all cash flows | More complex |
| Internal Rate of Return | % (total) | Yes | Rate that causes NPV = $0 | Uses TVM and is intuitive as a % | More complex |
Kyle’s 90+ Score Insight: A lot of comparison questions can be answered with no math at all. Know these cold: which methods ignore TVM, which one uses accounting income, which one gives a dollar answer, and which one gives a percentage answer.
Black-Scholes Option Pricing Model BAR
The model applies only to European-style options, which can only be exercised at expiration.
The six inputs and their directional effect on call option value
| Input | What It Represents | Effect on Call Value if Input Rises |
|---|---|---|
| Current Stock Price | Price of the underlying stock today | Increases |
| Strike Price | Exercise price of the option | Decreases |
| Risk-Free Interest Rate | Rate on a risk-free investment | Increases |
| Time to Maturity | Time remaining until expiration | Increases |
| Volatility | How much the stock price fluctuates | Increases |
| Option Premium | The fair value output of the model | N/A |
Study Tip: For a call option, only the strike price has an inverse relationship with value. The rest of the main inputs generally push value upward when they rise.
Practice Simulation: ClearWater Nonprofit (Difficult Level) BAR Simulation
This problem mirrors the complexity of a real BAR task-based simulation. It combines a depreciation tax shield, an annuity, and a salvage value lump sum into one NPV calculation.
The Question
ClearWater is considering purchasing a water treatment system for $250,000 that produces uniform pre-tax cash inflows of $90,000 for five years. Residual value is $25,000. Useful life is five years. Straight-line depreciation. Tax rate is 30%. Cost of capital is 12%.
Given factors: PV of $1 for 5 years at 12% = 0.567 | PV of $1 ordinary annuity for 5 years at 12% = 3.605
What is the NPV?
Step-by-step solution
Calculate annual depreciation
($250,000 − $25,000) / 5 = $45,000 per year
Calculate the depreciation tax shield
$45,000 × 30% = $13,500 per year
Calculate total annual cash inflows
$90,000 + $13,500 = $103,500 per year
Present value the annual inflows
$103,500 × 3.605 = $373,117.50
Present value the residual value
$25,000 × 0.567 = $14,175
Calculate NPV
$373,117.50 + $14,175 − $250,000 = $137,292.50
| Component | Amount |
|---|---|
| PV of annual cash inflows | $373,117.50 |
| PV of residual value | $14,175.00 |
| Less: Initial investment | ($250,000.00) |
| Net Present Value | $137,292.50 |
Because NPV is positive, ClearWater should accept the investment.
Kyle’s 90+ Score Insight: Two simulation mistakes show up constantly: forgetting to subtract salvage value from the depreciable base before calculating depreciation, and discounting salvage value with the annuity factor instead of the lump-sum factor.
Quick Reference Glossary
Use this table for fast final review.
| Term | One-Line Definition |
|---|---|
| Time Value of Money | A dollar today is worth more than a dollar in the future |
| Discount Rate | Any rate used to convert future cash flows to present value |
| Hurdle Rate | The minimum required return used in capital budgeting |
| Lump Sum | A one-time future payment |
| Ordinary Annuity | Equal payments at the end of each period |
| Annuity Due | Equal payments at the beginning of each period |
| Payback Period | Years to recover the investment from undiscounted cash flows |
| Discounted Payback Period | Payback period using discounted cash flows |
| Accounting Rate of Return | Accounting income divided by investment |
| Net Present Value | PV of cash inflows minus initial investment |
| Internal Rate of Return | The rate that makes NPV equal zero |
| Depreciation Tax Shield | Depreciation expense × tax rate |
| Salvage Value | Expected end-of-life proceeds from selling the asset |
| Black-Scholes Model | Option pricing model for European-style options |
| European-Style Option | Can only be exercised at expiration |
| American-Style Option | Can be exercised before or at expiration |
FAQ
Which capital budgeting methods use the time value of money?
NPV, IRR, discounted payback period, and present value methods use the time value of money. Basic payback period and ARR do not.
What is the difference between NPV and IRR?
NPV expresses value in dollars. IRR expresses the investment’s actual return as a percentage.
When do I add the depreciation tax shield?
Add it when the problem gives pre-tax cash flows. Do not add it if the problem says the cash flows are already after-tax.
How is salvage value treated in NPV problems?
Salvage value is a one-time final-year lump sum, so it is discounted using the PV of $1 factor for the final year.
Will I calculate Black-Scholes from scratch on BAR?
No. You mainly need to know the inputs and how changes in those inputs affect call option value.
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Kyle Ashcraft is a CPA who scored a 90+ on all four CPA exams. Kyle founded Maxwell CPA Review, which is an exam-prep company that offers a comprehensive CPA exam review course and private tutoring.
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