Unit 11 asks: how do organizations decide which long-term investments are worth making? Capital budgeting is the set of tools that answer this question — evaluating projects, programs, and enterprises by their financial returns. The five methods covered here (NPV, IRR, MIRR, Payback, Profitability Index) each offer a different lens. But the curriculum's central message is unambiguous: NPV is the gold standard — the only method that directly measures wealth creation in dollars and always gives the correct accept/reject decision. For BBYM, these tools determine which community programs are financially self-sustaining, which need grant support, and how to rank competing investments when resources are limited.
Part 1 — Core Topics Explained
Every major concept tested on the Unit 11 assessment
📋 Learning Objectives
- Calculate NPV and use the NPV rule to accept or reject a project
- Explain why NPV is the superior capital budgeting method
- Calculate and interpret IRR; explain the multiple IRR problem
- Calculate MIRR and explain how it fixes IRR's reinvestment rate assumption
- Calculate payback period and discounted payback period
- Calculate the Profitability Index and use it to rank projects under capital rationing
- Correctly rank mutually exclusive projects using NPV (not IRR)
- Apply capital budgeting methods to BBYM community enterprise investment decisions
1. What Is Capital Budgeting?
Capital budgeting is the process of evaluating and selecting long-term investments — projects, programs, equipment, or enterprises — that generate cash flows over multiple years. These are strategic decisions with lasting consequences: building a community center, launching a job-training program, purchasing equipment for a youth enterprise.
Capital Budgeting in the BBYM Context:
Every major investment decision at BBYM is a capital budgeting decision:
• Should we invest $80,000 in a Youth Culinary Arts Kitchen that generates program fees and catering revenue?
• Should we spend $50,000 on a Digital Literacy Lab that generates tuition income and grant eligibility?
• If we can only fund one this year, which creates more value for the community?
Capital budgeting provides the financial rigor to answer these questions objectively — separating emotional appeal from financial sustainability.
Every major investment decision at BBYM is a capital budgeting decision:
• Should we invest $80,000 in a Youth Culinary Arts Kitchen that generates program fees and catering revenue?
• Should we spend $50,000 on a Digital Literacy Lab that generates tuition income and grant eligibility?
• If we can only fund one this year, which creates more value for the community?
Capital budgeting provides the financial rigor to answer these questions objectively — separating emotional appeal from financial sustainability.
2. The Five Capital Budgeting Methods — Overview
NPV ★
Accept if NPV > 0
✓ Measures $ value created
✓ Always correct decision
✕ Needs accurate WACC
IRR
Accept if IRR ≥ WACC
✓ Intuitive % return
✕ Multiple IRR problem
✕ Wrong for mutually exclusive
MIRR
Accept if MIRR ≥ WACC
✓ Fixes IRR reinvestment flaw
✓ Single unique answer
✕ Less familiar than IRR
Payback
Accept if Payback ≤ target
✓ Simple & quick
✓ Liquidity gauge
✕ Ignores TVM & post-payback
PI
Accept if PI ≥ 1.0
✓ Best for ranking under rationing
✕ Can conflict with NPV on scale
Assessment Q11 Answer — NPV is the BEST Method:
NPV is the gold standard of capital budgeting because it is the only method that:
(1) Directly measures the dollar value of wealth created for investors/stakeholders
(2) Accounts for the time value of money (all cash flows discounted at WACC)
(3) Always gives the correct accept/reject decision for independent projects
(4) Always correctly ranks mutually exclusive projects (choose highest NPV)
All other methods have limitations that can lead to incorrect decisions. NPV never does, as long as the discount rate (WACC) is correct.
NPV is the gold standard of capital budgeting because it is the only method that:
(1) Directly measures the dollar value of wealth created for investors/stakeholders
(2) Accounts for the time value of money (all cash flows discounted at WACC)
(3) Always gives the correct accept/reject decision for independent projects
(4) Always correctly ranks mutually exclusive projects (choose highest NPV)
All other methods have limitations that can lead to incorrect decisions. NPV never does, as long as the discount rate (WACC) is correct.
3. The NPV Formula — Core of Capital Budgeting
Net Present Value (NPV)
NPV = CF₀ + CF₁/(1+r) + CF₂/(1+r)² + … + CFₙ/(1+r)ₙ
NPV = ∑ [CFₜ ÷ (1+r)ₜ] (where CF₀ = −Initial Investment)
CFₜ = cash flow in period t | r = discount rate (WACC) | CF₀ is negative (cash outflow at t=0)
Accept if NPV > 0 (project adds value) | Reject if NPV < 0 (project destroys value)
Accept if NPV > 0 (project adds value) | Reject if NPV < 0 (project destroys value)
NPV Worked Example — BBYM Youth Culinary Kitchen:
Initial Investment: −$80,000 at t=0 | WACC = 10%
Year 1 cash flow: $25,000 | Year 2: $32,000 | Year 3: $38,000 | Year 4: $30,000
PV Year 1 = $25,000 ÷ 1.10 = $22,727
PV Year 2 = $32,000 ÷ 1.10² = $32,000 ÷ 1.21 = $26,446
PV Year 3 = $38,000 ÷ 1.10³ = $38,000 ÷ 1.331 = $28,551
PV Year 4 = $30,000 ÷ 1.10⁴ = $30,000 ÷ 1.4641 = $20,490
Total PV of inflows = $22,727 + $26,446 + $28,551 + $20,490 = $98,214
NPV = $98,214 − $80,000 = +$18,214 → Accept ✓
The kitchen creates $18,214 of value above its cost — it earns more than the 10% WACC requires.
Initial Investment: −$80,000 at t=0 | WACC = 10%
Year 1 cash flow: $25,000 | Year 2: $32,000 | Year 3: $38,000 | Year 4: $30,000
Year 0
−$80,000
= −$80,000
Year 1
+$25,000
PV = $22,727
Year 2
+$32,000
PV = $26,446
Year 3
+$38,000
PV = $28,551
Year 4
+$30,000
PV = $20,490
PV Year 1 = $25,000 ÷ 1.10 = $22,727
PV Year 2 = $32,000 ÷ 1.10² = $32,000 ÷ 1.21 = $26,446
PV Year 3 = $38,000 ÷ 1.10³ = $38,000 ÷ 1.331 = $28,551
PV Year 4 = $30,000 ÷ 1.10⁴ = $30,000 ÷ 1.4641 = $20,490
Total PV of inflows = $22,727 + $26,446 + $28,551 + $20,490 = $98,214
NPV = $98,214 − $80,000 = +$18,214 → Accept ✓
The kitchen creates $18,214 of value above its cost — it earns more than the 10% WACC requires.
Part 2 — All Five Methods: Formulas & Complete Examples
Every method applied to the same BBYM project for direct comparison
Base Project (Used for All Methods)
BBYM Digital Literacy Lab:
Initial Investment (CF₀): −$60,000 | WACC = 10%
Year 1: $20,000 | Year 2: $25,000 | Year 3: $30,000
Total undiscounted inflows: $75,000 (gross profit: $15,000 before TVM)
Initial Investment (CF₀): −$60,000 | WACC = 10%
Year 1: $20,000 | Year 2: $25,000 | Year 3: $30,000
Total undiscounted inflows: $75,000 (gross profit: $15,000 before TVM)
Method 1 — Net Present Value (NPV)
NPV
NPV = −$60,000 + $20,000/1.10 + $25,000/1.10² + $30,000/1.10³
= −$60,000 + $18,182 + $20,661 + $22,539 = +$1,382
NPV > 0 → Accept. The project creates $1,382 of value above its cost of capital. Decision: ✓ Accept
Method 2 — Internal Rate of Return (IRR)
The IRR is the discount rate that makes NPV = 0. It is the project's own internal return rate. Accept if IRR ≥ WACC.
IRR Definition
0 = −$60,000 + $20,000/(1+IRR) + $25,000/(1+IRR)² + $30,000/(1+IRR)³
Solved by trial-and-error, financial calculator, or spreadsheet: IRR ≈ 10.68%
IRR (10.68%) ≥ WACC (10%) → Accept ✓ — consistent with NPV decision here
IRR (10.68%) ≥ WACC (10%) → Accept ✓ — consistent with NPV decision here
The Multiple IRR Problem — When IRR Breaks:
IRR can produce multiple answers when a project has more than one sign change in its cash flows (e.g., large positive, then negative, then positive again). Example:
Year 0: −$1,000 | Year 1: +$3,200 | Year 2: −$2,400
Sign changes: negative→positive→negative = 2 sign changes = 2 possible IRRs
This project has IRRs at approximately 20% AND 80%. Which do you use? Neither reliably — the project has conflicting answers. NPV gives a single, unambiguous result at any discount rate. This is the most important reason IRR is considered inferior to NPV despite being commonly used in practice.
IRR can produce multiple answers when a project has more than one sign change in its cash flows (e.g., large positive, then negative, then positive again). Example:
Year 0: −$1,000 | Year 1: +$3,200 | Year 2: −$2,400
Sign changes: negative→positive→negative = 2 sign changes = 2 possible IRRs
This project has IRRs at approximately 20% AND 80%. Which do you use? Neither reliably — the project has conflicting answers. NPV gives a single, unambiguous result at any discount rate. This is the most important reason IRR is considered inferior to NPV despite being commonly used in practice.
The Reinvestment Rate Assumption — IRR's Hidden Flaw:
IRR implicitly assumes that all interim cash flows are reinvested at the IRR itself. If a project has IRR = 25%, IRR assumes your Year 1 and Year 2 cash flows will be reinvested at 25% for the remaining years. This is almost always unrealistic — most firms earn closer to their WACC (9–12%) on reinvested cash, not the project's exceptional IRR.
Result: IRR systematically overstates the true return for projects with high IRRs. NPV uses WACC as the reinvestment rate — a realistic assumption. MIRR corrects this flaw.
IRR implicitly assumes that all interim cash flows are reinvested at the IRR itself. If a project has IRR = 25%, IRR assumes your Year 1 and Year 2 cash flows will be reinvested at 25% for the remaining years. This is almost always unrealistic — most firms earn closer to their WACC (9–12%) on reinvested cash, not the project's exceptional IRR.
Result: IRR systematically overstates the true return for projects with high IRRs. NPV uses WACC as the reinvestment rate — a realistic assumption. MIRR corrects this flaw.
Method 3 — Modified IRR (MIRR)
MIRR fixes IRR by explicitly assuming all positive cash flows are reinvested at WACC (not at IRR). It produces a single, realistic rate of return.
MIRR Formula
MIRR = [TV of Positive CFs / PV of Costs]^(1/n) − 1
TV (Terminal Value) = future value of all positive CFs compounded at WACC to the end of the project
PV of Costs = PV of all negative CFs discounted at WACC
Accept if MIRR ≥ WACC
PV of Costs = PV of all negative CFs discounted at WACC
Accept if MIRR ≥ WACC
MIRR Worked Example — Digital Literacy Lab:
Step 1 — Terminal Value (compound all inflows to Year 3 at WACC = 10%):
Year 1 CF: $20,000 × (1.10)² = $20,000 × 1.21 = $24,200
Year 2 CF: $25,000 × (1.10)¹ = $25,000 × 1.10 = $27,500
Year 3 CF: $30,000 × (1.10)⁰ = $30,000 × 1.00 = $30,000
TV = $24,200 + $27,500 + $30,000 = $81,700
Step 2 — PV of Costs = $60,000 (already at t=0)
Step 3 — MIRR:
MIRR = ($81,700 / $60,000)^(1/3) − 1 = (1.3617)^(0.333) − 1 = 1.1060 − 1 = 10.60%
MIRR (10.60%) ≥ WACC (10%) → Accept ✓
MIRR is slightly lower than IRR (10.68%) because it uses the realistic 10% reinvestment rate instead of the overstated 10.68%.
Step 1 — Terminal Value (compound all inflows to Year 3 at WACC = 10%):
Year 1 CF: $20,000 × (1.10)² = $20,000 × 1.21 = $24,200
Year 2 CF: $25,000 × (1.10)¹ = $25,000 × 1.10 = $27,500
Year 3 CF: $30,000 × (1.10)⁰ = $30,000 × 1.00 = $30,000
TV = $24,200 + $27,500 + $30,000 = $81,700
Step 2 — PV of Costs = $60,000 (already at t=0)
Step 3 — MIRR:
MIRR = ($81,700 / $60,000)^(1/3) − 1 = (1.3617)^(0.333) − 1 = 1.1060 − 1 = 10.60%
MIRR (10.60%) ≥ WACC (10%) → Accept ✓
MIRR is slightly lower than IRR (10.68%) because it uses the realistic 10% reinvestment rate instead of the overstated 10.68%.
Method 4 — Payback Period & Discounted Payback
Payback Period
Payback = Year before full recovery + (Remaining cost / Next year CF)
Simple payback ignores TVM. Discounted payback uses PV of cash flows instead of nominal amounts.
Payback and Discounted Payback — Digital Literacy Lab:
Simple Payback:
After Year 1: $60,000 − $20,000 = $40,000 remaining
After Year 2: $40,000 − $25,000 = $15,000 remaining
During Year 3: $15,000 ÷ $30,000 = 0.50 years
Payback = 2.50 years
Discounted Payback (using PV of CFs at 10%):
PV Year 1 = $18,182 | Remaining: $60,000 − $18,182 = $41,818
PV Year 2 = $20,661 | Remaining: $41,818 − $20,661 = $21,157
PV Year 3 = $22,539 | Remaining: $21,157 ÷ $22,539 = 0.939 years
Discounted Payback = 2.94 years
Discounted payback is always longer than simple payback because discounted CFs are smaller. If the target payback is 3 years, both pass. If target is 2.5 years, simple payback passes but discounted payback fails — showing how ignoring TVM can lead to false comfort.
Simple Payback:
After Year 1: $60,000 − $20,000 = $40,000 remaining
After Year 2: $40,000 − $25,000 = $15,000 remaining
During Year 3: $15,000 ÷ $30,000 = 0.50 years
Payback = 2.50 years
Discounted Payback (using PV of CFs at 10%):
PV Year 1 = $18,182 | Remaining: $60,000 − $18,182 = $41,818
PV Year 2 = $20,661 | Remaining: $41,818 − $20,661 = $21,157
PV Year 3 = $22,539 | Remaining: $21,157 ÷ $22,539 = 0.939 years
Discounted Payback = 2.94 years
Discounted payback is always longer than simple payback because discounted CFs are smaller. If the target payback is 3 years, both pass. If target is 2.5 years, simple payback passes but discounted payback fails — showing how ignoring TVM can lead to false comfort.
Payback's Two Fatal Flaws:
(1) Ignores cash flows after payback: A project recovering its cost in Year 2 then generating $500,000 in Years 3–10 looks the same as one generating $0 after payback. Payback can't see long-term value creation.
(2) Ignores time value of money (simple version): $20,000 received in Year 1 is treated the same as $20,000 in Year 3, even though Year 3 money is worth less today. Discounted payback fixes flaw #2 but not flaw #1.
Payback is best used as a quick liquidity screen — "how fast do we get our money back?" — not as a primary decision tool.
(1) Ignores cash flows after payback: A project recovering its cost in Year 2 then generating $500,000 in Years 3–10 looks the same as one generating $0 after payback. Payback can't see long-term value creation.
(2) Ignores time value of money (simple version): $20,000 received in Year 1 is treated the same as $20,000 in Year 3, even though Year 3 money is worth less today. Discounted payback fixes flaw #2 but not flaw #1.
Payback is best used as a quick liquidity screen — "how fast do we get our money back?" — not as a primary decision tool.
Method 5 — Profitability Index (PI)
Profitability Index (PI)
PI = PV of Future Cash Flows ÷ Initial Investment
Accept if PI ≥ 1.0 (equivalent to NPV ≥ 0)
PI > 1.0 means each dollar invested generates more than $1 in present value
PI > 1.0 means each dollar invested generates more than $1 in present value
PI Calculation — Digital Literacy Lab:
PV of inflows = $18,182 + $20,661 + $22,539 = $61,382
PI = $61,382 ÷ $60,000 = 1.023
PI ≥ 1.0 → Accept ✓
Interpretation: Every $1 invested generates $1.023 in present value — a 2.3-cent surplus per dollar. PI is especially useful for capital rationing: when a BBYM has limited capital (say, $100,000) and multiple projects exceeding that budget, PI ranks projects by "bang per buck," maximizing total NPV within the constraint.
PV of inflows = $18,182 + $20,661 + $22,539 = $61,382
PI = $61,382 ÷ $60,000 = 1.023
PI ≥ 1.0 → Accept ✓
Interpretation: Every $1 invested generates $1.023 in present value — a 2.3-cent surplus per dollar. PI is especially useful for capital rationing: when a BBYM has limited capital (say, $100,000) and multiple projects exceeding that budget, PI ranks projects by "bang per buck," maximizing total NPV within the constraint.
Part 3 — Project Ranking, Conflicts & BBYM Application
Mutually exclusive vs. independent projects, when methods conflict, and capital rationing
Independent vs. Mutually Exclusive Projects
| Type | Definition | Decision Rule | Example |
|---|---|---|---|
| Independent Projects | Accepting one does not affect the decision on another — each stands on its own | Accept ALL projects with NPV > 0 (or IRR ≥ WACC) if capital is unlimited | Launching both a culinary program AND a digital literacy lab — one doesn't prevent the other |
| Mutually Exclusive Projects | Only one can be chosen — they compete for the same resources or serve the same purpose | Choose the project with the highest NPV (never use IRR to rank) | Two different designs for a community center — you build one or the other, not both |
The Critical Warning — Never Use IRR to Rank Mutually Exclusive Projects:
IRR ranks by percentage return; NPV ranks by dollar value. These can conflict — and when they do, NPV is always correct.
Example — BBYM Must Choose Between Two Programs:
IRR says choose Program A (35% > 18%). But Program A only creates $3,500 of value. Program B creates $28,000 — eight times more. If these are mutually exclusive (only one can be funded), always choose the higher NPV: Program B. IRR is misleading here because it doesn't account for scale — 35% of $10,000 is less than 18% of $100,000.
IRR ranks by percentage return; NPV ranks by dollar value. These can conflict — and when they do, NPV is always correct.
Example — BBYM Must Choose Between Two Programs:
| Project | Investment | NPV | IRR | IRR Rank | NPV Rank |
|---|---|---|---|---|---|
| Program A (Small) | $10,000 | $3,500 | 35% | #1 | #2 |
| Program B (Large) | $100,000 | $28,000 | 18% | #2 | #1 |
IRR says choose Program A (35% > 18%). But Program A only creates $3,500 of value. Program B creates $28,000 — eight times more. If these are mutually exclusive (only one can be funded), always choose the higher NPV: Program B. IRR is misleading here because it doesn't account for scale — 35% of $10,000 is less than 18% of $100,000.
Capital Rationing — When Budget Is Limited
When a firm has more positive-NPV projects than available capital, it must choose which to fund. This is capital rationing. The Profitability Index ranks projects by value-per-dollar to maximize total NPV within the budget.
BBYM Capital Rationing Example — $150,000 Budget, 4 Projects:
Optimal selection: Culinary Kitchen ($80K) + Digital Literacy Lab ($60K) = $140K total ↔ $150K budget
Total NPV = $18,214 + $1,382 = $19,596
The Youth Workforce Center has higher NPV ($22K) but costs $120K — pairing it with anything else exceeds the $150K budget. PI-based selection (Kitchen + Lab) yields more total NPV within the constraint.
| Project | Cost | NPV | PI = (Cost+NPV)/Cost | PI Rank | Select? |
|---|---|---|---|---|---|
| Culinary Kitchen | $80,000 | $18,214 | 1.228 | #1 | ✓ Yes |
| Digital Literacy Lab | $60,000 | $1,382 | 1.023 | #3 | ✓ Yes ($10K left) |
| Youth Workforce Ctr | $120,000 | $22,000 | 1.183 | #2 | ✗ Over budget |
| Heritage Arts Space | $40,000 | $800 | 1.020 | #4 | ✗ Budget exhausted |
Optimal selection: Culinary Kitchen ($80K) + Digital Literacy Lab ($60K) = $140K total ↔ $150K budget
Total NPV = $18,214 + $1,382 = $19,596
The Youth Workforce Center has higher NPV ($22K) but costs $120K — pairing it with anything else exceeds the $150K budget. PI-based selection (Kitchen + Lab) yields more total NPV within the constraint.
Method Comparison — When They Agree and When They Conflict
| Situation | NPV | IRR | MIRR | Payback | PI | Best Method |
|---|---|---|---|---|---|---|
| Single independent project, normal CFs | ✓ Agree | ✓ Agree | ✓ Agree | May disagree | ✓ Agree | Any (NPV preferred) |
| Mutually exclusive — different sizes | ✓ Correct | ✗ Wrong | Usually OK | ✗ Wrong | May conflict | NPV only |
| Multiple sign changes in CFs | ✓ Correct | ✗ Multiple IRRs | ✓ Correct | — | ✓ Correct | NPV or MIRR |
| Capital rationing — rank projects | By total NPV | ✗ Misleading | ✗ Misleading | ✗ Ignores TVM | ✓ Best for ranking | PI for ranking, NPV for value |
| Liquidity / quick screening | Too complex | Useful | Useful | ✓ Best | OK | Payback as screen |
Non-Profit & Social Enterprise Capital Budgeting — BBYM Adaptations
Adapting NPV for Mission-Driven Organizations:
Pure NPV measures only financial cash flows. BBYM's programs often generate social value — youth employment outcomes, educational attainment, community cohesion — that doesn't appear in a cash flow statement. Two adaptations:
1. Social Return on Investment (SROI): Assign dollar values to social outcomes (e.g., each youth employed saves $5,000 in social services costs) and add them to financial cash flows before calculating NPV. A program returning −$5,000 financially but generating $30,000 in social value has a positive social NPV of +$25,000.
2. Blended Value Hurdle Rate: Apply a lower WACC to programs with strong social impact, reflecting the fact that mission-aligned funders (CDFIs, foundations, PRIs) accept lower financial returns in exchange for social impact. A program meeting a 4% blended hurdle rate may be fundable even if its pure financial return is below the market WACC of 9%.
The key insight: capital budgeting frameworks work for nonprofits — you just need to be explicit about what "return" includes. BBYM can apply NPV to every major program decision, using blended social + financial cash flows and mission-adjusted discount rates.
Pure NPV measures only financial cash flows. BBYM's programs often generate social value — youth employment outcomes, educational attainment, community cohesion — that doesn't appear in a cash flow statement. Two adaptations:
1. Social Return on Investment (SROI): Assign dollar values to social outcomes (e.g., each youth employed saves $5,000 in social services costs) and add them to financial cash flows before calculating NPV. A program returning −$5,000 financially but generating $30,000 in social value has a positive social NPV of +$25,000.
2. Blended Value Hurdle Rate: Apply a lower WACC to programs with strong social impact, reflecting the fact that mission-aligned funders (CDFIs, foundations, PRIs) accept lower financial returns in exchange for social impact. A program meeting a 4% blended hurdle rate may be fundable even if its pure financial return is below the market WACC of 9%.
The key insight: capital budgeting frameworks work for nonprofits — you just need to be explicit about what "return" includes. BBYM can apply NPV to every major program decision, using blended social + financial cash flows and mission-adjusted discount rates.
Part 4 — Key Terms Defined
Master these 14 terms for the Unit 11 assessment
Capital Budgeting
The process of evaluating and selecting long-term investments (projects, programs, equipment, enterprises) that generate cash flows over multiple years. Requires applying time value of money principles to compare initial costs against future cash flow benefits. The central activity of corporate finance — determining which investments to undertake with scarce capital.
Net Present Value (NPV)
The sum of all project cash flows discounted at the WACC, including the initial investment: NPV = Σ[CFₜ/(1+r)ₜ]. The gold standard of capital budgeting — the only method that directly measures the dollar value of wealth created. Accept if NPV > 0; reject if NPV < 0. Always gives the correct decision. The Assessment Q11 answer.
Internal Rate of Return (IRR)
The discount rate that makes NPV = 0 — the project's own internal return rate. Accept if IRR ≥ WACC (the hurdle rate). Intuitive and widely used in practice, but has two flaws: (1) assumes reinvestment at IRR (usually unrealistic), and (2) can produce multiple answers when cash flows change sign more than once. Never use to rank mutually exclusive projects.
Modified IRR (MIRR)
A corrected version of IRR that assumes positive cash flows are reinvested at WACC (not at IRR). Formula: MIRR = (TV of positive CFs / PV of costs)^(1/n) − 1. Always produces a single answer; more realistic than IRR. Accept if MIRR ≥ WACC. Preferred over IRR when reinvestment rate matters — especially for high-IRR projects where the reinvestment assumption is most unrealistic.
Payback Period
The time required to recover the initial investment from the project's cash flows, without discounting. Simple to calculate and intuitive — provides a quick liquidity gauge. Fatal flaws: ignores the time value of money and ignores all cash flows after the payback point. Best used as a quick screening tool, not a primary decision method. A project with a short payback but small long-term returns may have a negative NPV.
Discounted Payback Period
A modified payback calculation using discounted (present value) cash flows instead of nominal amounts. Fixes the TVM flaw of simple payback but still ignores cash flows after the payback point. Always longer than simple payback because PV of cash flows is less than nominal. Gives a more conservative and accurate picture of how long recovery actually takes in real dollars.
Profitability Index (PI)
The ratio of the PV of future cash flows to the initial investment: PI = PV of CFs / Initial Investment. Accept if PI ≥ 1.0 (equivalent to NPV ≥ 0). Primary use: ranking projects under capital rationing by value created per dollar invested — maximizing total NPV within a budget constraint. PI = 1.05 means each dollar invested generates $1.05 in present value.
Hurdle Rate
The minimum acceptable rate of return on an investment — typically set equal to the firm's WACC for average-risk projects. Projects must clear the hurdle rate to be accepted. IRR and MIRR are compared against the hurdle rate (WACC) to determine acceptability. Higher-risk projects should use a higher hurdle rate; lower-risk projects a lower one.
Independent Projects
Projects whose acceptance or rejection does not affect the decision on other projects. When facing independent projects with unlimited capital, accept all with NPV > 0. With capital rationing, rank by PI and accept until the budget is exhausted. The simplest capital budgeting scenario — each project stands alone on its merits.
Mutually Exclusive Projects
Projects that compete for the same resources or serve the same purpose — only one can be chosen. When ranking mutually exclusive projects, always use NPV (choose the highest NPV). Never use IRR to rank mutually exclusive projects — IRR can give incorrect rankings because it ignores scale (the size of the investment).
Capital Rationing
A situation in which a firm has more positive-NPV projects than available capital to fund them all. Forces prioritization among projects. Under capital rationing, use the Profitability Index (PI) to rank projects from highest to lowest PI, then select the highest-PI projects until the budget is exhausted — this maximizes total NPV within the capital constraint.
Terminal Value (TV) in MIRR
The future value of all positive cash flows compounded to the end of the project at the WACC (reinvestment rate). The numerator in the MIRR formula. Calculated by taking each positive cash flow and compounding it forward to the final year of the project at WACC. The terminal value is then compared to the PV of costs to calculate MIRR.
Reinvestment Rate Assumption
The assumed rate at which interim cash flows are reinvested during the project's life. IRR assumes reinvestment at the IRR itself — an optimistic assumption that overstates returns for high-IRR projects. MIRR uses WACC as the reinvestment rate — a more realistic assumption reflecting what the firm can actually earn on reinvested cash. NPV implicitly uses WACC as the reinvestment rate, which is another reason it is the superior method.
Social Return on Investment (SROI)
A capital budgeting adaptation for mission-driven organizations that adds monetized social value to financial cash flows before calculating NPV. Allows nonprofits to evaluate programs that generate community benefit beyond financial profit. Example: a BBYM job-training program generating $20,000 in program fees plus $40,000 in estimated social value (reduced incarceration costs, tax base expansion) has a blended cash flow of $60,000 per year.
Part 5 — Practice Questions
Show all work — these mirror the Unit 11 assessment format exactly
Conceptual Questions
Q1Which capital budgeting method directly measures wealth creation in dollars and is considered the BEST decision tool? A) Payback Period B) IRR C) NPV D) Accounting Rate of Return. (Unit 11 curriculum assessment question.)▼
Answer: C — Net Present Value (NPV)
NPV is the gold standard for three reasons:
(1) It is the only method that directly measures the dollar amount of value created — an NPV of $18,214 means $18,214 of real wealth is added above and beyond the cost of capital.
(2) It accounts for the time value of money by discounting all cash flows at WACC.
(3) It always gives the correct accept/reject decision and correctly ranks mutually exclusive projects.
Payback ignores TVM and ignores post-payback cash flows. IRR assumes reinvestment at IRR (unrealistic) and can give multiple answers. Accounting Rate of Return uses accounting income rather than cash flows and ignores TVM. Only NPV avoids all these flaws.
NPV is the gold standard for three reasons:
(1) It is the only method that directly measures the dollar amount of value created — an NPV of $18,214 means $18,214 of real wealth is added above and beyond the cost of capital.
(2) It accounts for the time value of money by discounting all cash flows at WACC.
(3) It always gives the correct accept/reject decision and correctly ranks mutually exclusive projects.
Payback ignores TVM and ignores post-payback cash flows. IRR assumes reinvestment at IRR (unrealistic) and can give multiple answers. Accounting Rate of Return uses accounting income rather than cash flows and ignores TVM. Only NPV avoids all these flaws.
Q2Explain the "multiple IRR problem." When does it occur, and why does it make IRR unreliable in those situations?▼
The multiple IRR problem occurs when a project's cash flows change sign more than once — for example, negative, then positive, then negative again.
By Descartes' Rule of Signs, a polynomial equation can have as many real roots (solutions) as sign changes. Since IRR is found by solving NPV = 0 (a polynomial), a project with 2 sign changes can have 2 IRRs, and one with 3 sign changes can have 3 IRRs.
Real-world example: A mining project: initial investment (−$1M), then revenue years (+$3M), then environmental cleanup required (−$2M). Cash flows: −, +, − = 2 sign changes = 2 possible IRRs (perhaps 20% and 80%). Which one do you compare to WACC? Neither can be trusted uniquely.
This is why MIRR is preferred when cash flows have multiple sign changes — MIRR always produces exactly one answer by explicitly specifying the reinvestment rate. NPV also has no multiple-value problem because it produces a single number at any given discount rate.
By Descartes' Rule of Signs, a polynomial equation can have as many real roots (solutions) as sign changes. Since IRR is found by solving NPV = 0 (a polynomial), a project with 2 sign changes can have 2 IRRs, and one with 3 sign changes can have 3 IRRs.
Real-world example: A mining project: initial investment (−$1M), then revenue years (+$3M), then environmental cleanup required (−$2M). Cash flows: −, +, − = 2 sign changes = 2 possible IRRs (perhaps 20% and 80%). Which one do you compare to WACC? Neither can be trusted uniquely.
This is why MIRR is preferred when cash flows have multiple sign changes — MIRR always produces exactly one answer by explicitly specifying the reinvestment rate. NPV also has no multiple-value problem because it produces a single number at any given discount rate.
Q3BBYM must choose between two mutually exclusive programs. Program X: NPV = $12,000, IRR = 28%. Program Y: NPV = $35,000, IRR = 19%. Which should BBYM choose, and why?▼
Choose Program Y — the higher NPV project.
IRR says choose X (28% > 19%), but this is incorrect for mutually exclusive projects.
NPV says choose Y ($35,000 > $12,000). This is always the correct answer.
Why NPV wins: IRR measures the percentage return but ignores scale. Program X might invest $10,000 at 28% to generate $12,000 of value. Program Y might invest $100,000 at 19% to generate $35,000 of value. The extra $23,000 of NPV from Y represents real wealth that benefits the community — no matter what percentage return it took to generate it.
The universal rule: for mutually exclusive projects, always choose the highest NPV. IRR should never be used to rank mutually exclusive projects because it ignores the scale of the investment.
IRR says choose X (28% > 19%), but this is incorrect for mutually exclusive projects.
NPV says choose Y ($35,000 > $12,000). This is always the correct answer.
Why NPV wins: IRR measures the percentage return but ignores scale. Program X might invest $10,000 at 28% to generate $12,000 of value. Program Y might invest $100,000 at 19% to generate $35,000 of value. The extra $23,000 of NPV from Y represents real wealth that benefits the community — no matter what percentage return it took to generate it.
The universal rule: for mutually exclusive projects, always choose the highest NPV. IRR should never be used to rank mutually exclusive projects because it ignores the scale of the investment.
Q4What are the two fatal flaws of the simple payback period, and how does discounted payback fix one of them (but not both)?▼
Flaw 1 — Ignores the time value of money: Simple payback treats $1,000 received in Year 1 the same as $1,000 received in Year 5 — even though Year 5 money is worth significantly less today. This can lead to accepting projects that look fast-payback but have poor discounted returns.
Flaw 2 — Ignores all cash flows after the payback point: A project that recovers its investment in Year 2 then generates zero cash flow forever looks identical to a project recovering in Year 2 then generating $1,000,000 over the next 10 years. Payback is blind to everything after recovery.
What discounted payback fixes: By using PV of cash flows, discounted payback addresses Flaw 1 — it accounts for the time value of money. The recovery period is calculated using discounted cash flows, giving a more accurate (longer, more conservative) estimate of true recovery time.
What discounted payback still doesn't fix: Flaw 2 — it still ignores all cash flows after the payback point. A project with a 3.5-year discounted payback but massive cash flows in Years 4–15 still looks worse than a project with a 2-year payback and nothing afterward. For long-lived value-creating projects, payback in any form is an incomplete measure.
Flaw 2 — Ignores all cash flows after the payback point: A project that recovers its investment in Year 2 then generates zero cash flow forever looks identical to a project recovering in Year 2 then generating $1,000,000 over the next 10 years. Payback is blind to everything after recovery.
What discounted payback fixes: By using PV of cash flows, discounted payback addresses Flaw 1 — it accounts for the time value of money. The recovery period is calculated using discounted cash flows, giving a more accurate (longer, more conservative) estimate of true recovery time.
What discounted payback still doesn't fix: Flaw 2 — it still ignores all cash flows after the payback point. A project with a 3.5-year discounted payback but massive cash flows in Years 4–15 still looks worse than a project with a 2-year payback and nothing afterward. For long-lived value-creating projects, payback in any form is an incomplete measure.
Calculation Questions
Q5Calculate NPV for a BBYM Youth Enterprise: Initial investment $50,000, WACC = 9%. Cash flows: Year 1: $15,000, Year 2: $20,000, Year 3: $22,000, Year 4: $18,000. Should BBYM invest?▼
PV Year 1 = $15,000 ÷ 1.09 = $13,761
PV Year 2 = $20,000 ÷ 1.09² = $20,000 ÷ 1.1881 = $16,833
PV Year 3 = $22,000 ÷ 1.09³ = $22,000 ÷ 1.2950 = $16,988
PV Year 4 = $18,000 ÷ 1.09⁴ = $18,000 ÷ 1.4116 = $12,751
Total PV of inflows = $13,761 + $16,833 + $16,988 + $12,751 = $60,333
NPV = $60,333 − $50,000 = +$10,333
NPV > 0 → Accept ✓. The enterprise creates $10,333 of value above its 9% cost of capital. BBYM should invest.
PV Year 2 = $20,000 ÷ 1.09² = $20,000 ÷ 1.1881 = $16,833
PV Year 3 = $22,000 ÷ 1.09³ = $22,000 ÷ 1.2950 = $16,988
PV Year 4 = $18,000 ÷ 1.09⁴ = $18,000 ÷ 1.4116 = $12,751
Total PV of inflows = $13,761 + $16,833 + $16,988 + $12,751 = $60,333
NPV = $60,333 − $50,000 = +$10,333
NPV > 0 → Accept ✓. The enterprise creates $10,333 of value above its 9% cost of capital. BBYM should invest.
Q6Calculate the simple payback and discounted payback (WACC = 9%) for the Q5 project. If BBYM's target payback is 3 years, what does each method say?▼
Simple Payback:
After Year 1: $50,000 − $15,000 = $35,000 remaining
After Year 2: $35,000 − $20,000 = $15,000 remaining
During Year 3: $15,000 ÷ $22,000 = 0.682 years
Simple Payback = 2.68 years → Passes 3-year target ✓
Discounted Payback (using PV of each year's CF):
PV Year 1 = $13,761 | Remaining: $50,000 − $13,761 = $36,239
PV Year 2 = $16,833 | Remaining: $36,239 − $16,833 = $19,406
PV Year 3 = $16,988 | Remaining: $19,406 ÷ $16,988 = 1.142 years
Discounted Payback = 3.14 years → Fails 3-year target ✗
Conflict: Simple payback passes (2.68 yrs) but discounted payback fails (3.14 yrs). This illustrates why ignoring TVM creates false confidence. The project has a positive NPV (+$10,333) and should be accepted — the payback methods are supplemental screens, not the primary decision tool. NPV is the correct basis for the accept decision.
After Year 1: $50,000 − $15,000 = $35,000 remaining
After Year 2: $35,000 − $20,000 = $15,000 remaining
During Year 3: $15,000 ÷ $22,000 = 0.682 years
Simple Payback = 2.68 years → Passes 3-year target ✓
Discounted Payback (using PV of each year's CF):
PV Year 1 = $13,761 | Remaining: $50,000 − $13,761 = $36,239
PV Year 2 = $16,833 | Remaining: $36,239 − $16,833 = $19,406
PV Year 3 = $16,988 | Remaining: $19,406 ÷ $16,988 = 1.142 years
Discounted Payback = 3.14 years → Fails 3-year target ✗
Conflict: Simple payback passes (2.68 yrs) but discounted payback fails (3.14 yrs). This illustrates why ignoring TVM creates false confidence. The project has a positive NPV (+$10,333) and should be accepted — the payback methods are supplemental screens, not the primary decision tool. NPV is the correct basis for the accept decision.
Q7Calculate MIRR for a 3-year project: Investment $40,000, WACC = 8%. Year 1: $12,000, Year 2: $18,000, Year 3: $20,000. Should the project be accepted?▼
Step 1 — Terminal Value (compound all inflows to Year 3 at 8%):
Year 1: $12,000 × (1.08)² = $12,000 × 1.1664 = $13,997
Year 2: $18,000 × (1.08)¹ = $18,000 × 1.08 = $19,440
Year 3: $20,000 × (1.08)⁰ = $20,000 × 1.00 = $20,000
TV = $13,997 + $19,440 + $20,000 = $53,437
Step 2 — PV of Costs = $40,000 (at t=0)
Step 3 — MIRR:
MIRR = ($53,437 / $40,000)^(1/3) − 1 = (1.3359)^(0.333) − 1 = 1.1013 − 1 = 10.13%
MIRR (10.13%) ≥ WACC (8%) → Accept ✓
Verify with NPV: PV of CFs = $12,000/1.08 + $18,000/1.08² + $20,000/1.08³ = $11,111 + $15,432 + $15,877 = $42,420
NPV = $42,420 − $40,000 = +$2,420 → Also Accept ✓ (consistent)
Year 1: $12,000 × (1.08)² = $12,000 × 1.1664 = $13,997
Year 2: $18,000 × (1.08)¹ = $18,000 × 1.08 = $19,440
Year 3: $20,000 × (1.08)⁰ = $20,000 × 1.00 = $20,000
TV = $13,997 + $19,440 + $20,000 = $53,437
Step 2 — PV of Costs = $40,000 (at t=0)
Step 3 — MIRR:
MIRR = ($53,437 / $40,000)^(1/3) − 1 = (1.3359)^(0.333) − 1 = 1.1013 − 1 = 10.13%
MIRR (10.13%) ≥ WACC (8%) → Accept ✓
Verify with NPV: PV of CFs = $12,000/1.08 + $18,000/1.08² + $20,000/1.08³ = $11,111 + $15,432 + $15,877 = $42,420
NPV = $42,420 − $40,000 = +$2,420 → Also Accept ✓ (consistent)
Q8Calculate the Profitability Index for these three BBYM projects. Then rank them under capital rationing with a $120,000 budget:
• Workforce Training: Cost $100,000, PV of CFs = $118,000
• Arts Program: Cost $40,000, PV of CFs = $49,200
• Tech Lab: Cost $60,000, PV of CFs = $68,400▼
• Workforce Training: Cost $100,000, PV of CFs = $118,000
• Arts Program: Cost $40,000, PV of CFs = $49,200
• Tech Lab: Cost $60,000, PV of CFs = $68,400▼
PI Calculations:
Workforce Training: PI = $118,000 ÷ $100,000 = 1.180 | NPV = $18,000
Arts Program: PI = $49,200 ÷ $40,000 = 1.230 | NPV = $9,200
Tech Lab: PI = $68,400 ÷ $60,000 = 1.140 | NPV = $8,400
PI Ranking: Arts (1.230) > Workforce (1.180) > Tech Lab (1.140)
Capital Rationing ($120,000 budget):
#1 Arts Program: $40,000 → Budget remaining: $80,000 → Cumulative NPV: $9,200
#2 Workforce Training: $100,000 → EXCEEDS remaining $80,000 → Skip
#3 Tech Lab: $60,000 → Budget remaining: $80,000 → Cumulative NPV: $9,200 + $8,400 = $17,600
Remaining budget: $20,000 → No other projects
Optimal selection: Arts + Tech Lab = $100,000 total, Total NPV = $17,600
Compare: Arts + Workforce = $140,000 (exceeds budget). Tech + Workforce = $160,000 (exceeds budget).
PI-based ranking correctly identifies Arts + Tech Lab as the value-maximizing combination within the $120,000 constraint.
Workforce Training: PI = $118,000 ÷ $100,000 = 1.180 | NPV = $18,000
Arts Program: PI = $49,200 ÷ $40,000 = 1.230 | NPV = $9,200
Tech Lab: PI = $68,400 ÷ $60,000 = 1.140 | NPV = $8,400
PI Ranking: Arts (1.230) > Workforce (1.180) > Tech Lab (1.140)
Capital Rationing ($120,000 budget):
#1 Arts Program: $40,000 → Budget remaining: $80,000 → Cumulative NPV: $9,200
#2 Workforce Training: $100,000 → EXCEEDS remaining $80,000 → Skip
#3 Tech Lab: $60,000 → Budget remaining: $80,000 → Cumulative NPV: $9,200 + $8,400 = $17,600
Remaining budget: $20,000 → No other projects
Optimal selection: Arts + Tech Lab = $100,000 total, Total NPV = $17,600
Compare: Arts + Workforce = $140,000 (exceeds budget). Tech + Workforce = $160,000 (exceeds budget).
PI-based ranking correctly identifies Arts + Tech Lab as the value-maximizing combination within the $120,000 constraint.
Q9The Swanson Initiative is evaluating two mutually exclusive endowment projects. Project A: 5-year project, costs $200,000, NPV = $45,000, IRR = 22%. Project B: 5-year project, costs $500,000, NPV = $80,000, IRR = 16%. Which should be selected, and why is IRR misleading here?▼
Select Project B — NPV = $80,000 > Project A's $45,000.
IRR incorrectly recommends Project A (22% > 16%). This is the mutually exclusive ranking error.
Why IRR is misleading: Project A invests $200,000 and earns 22% — generating $45,000 of NPV. Project B invests $500,000 and earns 16% — generating $80,000 of NPV. The question is not "which percentage is higher?" but "which creates more value for the Swanson Initiative?"
Project B creates $35,000 more in actual dollar value ($80K vs $45K). That's $35,000 more in real wealth for BBYM community programs — a material difference in what the endowment can accomplish. The lower percentage (16% vs 22%) is irrelevant when the dollar outcome is what matters.
The intuition: Would you rather earn 22% on $10 (= $2.20) or 16% on $100 (= $16.00)? The absolute dollar amount always wins for wealth creation. Project B wins.
IRR incorrectly recommends Project A (22% > 16%). This is the mutually exclusive ranking error.
Why IRR is misleading: Project A invests $200,000 and earns 22% — generating $45,000 of NPV. Project B invests $500,000 and earns 16% — generating $80,000 of NPV. The question is not "which percentage is higher?" but "which creates more value for the Swanson Initiative?"
Project B creates $35,000 more in actual dollar value ($80K vs $45K). That's $35,000 more in real wealth for BBYM community programs — a material difference in what the endowment can accomplish. The lower percentage (16% vs 22%) is irrelevant when the dollar outcome is what matters.
The intuition: Would you rather earn 22% on $10 (= $2.20) or 16% on $100 (= $16.00)? The absolute dollar amount always wins for wealth creation. Project B wins.
Q10A BBYM community kitchen program has these cash flows: Year 0: −$30,000, Year 1: +$50,000, Year 2: −$25,000 (major equipment replacement). Why does this project have a multiple IRR problem? How would you properly evaluate it?▼
This project has two sign changes: negative → positive → negative (−, +, −). By Descartes' Rule, there can be up to 2 IRRs.
Setting NPV = 0: −$30,000 + $50,000/(1+r) − $25,000/(1+r)² = 0
This quadratic equation has two solutions — approximately IRR ≈ 17% and IRR ≈ 117%. Which do you compare against WACC (say 10%)? Both are mathematically valid. The IRR rule gives contradictory guidance.
Proper evaluation methods:
(1) NPV (preferred): At WACC = 10%:
NPV = −$30,000 + $50,000/1.10 − $25,000/1.21 = −$30,000 + $45,455 − $20,661 = −$5,206
NPV < 0 → Reject. Clear, unambiguous answer.
(2) MIRR: TV = $50,000 × 1.10 + (−$25,000 discounted: PV = −$20,661)
PV of all negative CFs = $30,000 + $20,661 = $50,661 | TV of positive CFs = $55,000
MIRR = ($55,000/$50,661)^(1/2) − 1 = (1.0857)^(0.5) − 1 ≈ 4.2% < WACC 10% → Reject ✓ (consistent with NPV)
NPV and MIRR both correctly recommend rejection. IRR alone fails.
Setting NPV = 0: −$30,000 + $50,000/(1+r) − $25,000/(1+r)² = 0
This quadratic equation has two solutions — approximately IRR ≈ 17% and IRR ≈ 117%. Which do you compare against WACC (say 10%)? Both are mathematically valid. The IRR rule gives contradictory guidance.
Proper evaluation methods:
(1) NPV (preferred): At WACC = 10%:
NPV = −$30,000 + $50,000/1.10 − $25,000/1.21 = −$30,000 + $45,455 − $20,661 = −$5,206
NPV < 0 → Reject. Clear, unambiguous answer.
(2) MIRR: TV = $50,000 × 1.10 + (−$25,000 discounted: PV = −$20,661)
PV of all negative CFs = $30,000 + $20,661 = $50,661 | TV of positive CFs = $55,000
MIRR = ($55,000/$50,661)^(1/2) − 1 = (1.0857)^(0.5) − 1 ≈ 4.2% < WACC 10% → Reject ✓ (consistent with NPV)
NPV and MIRR both correctly recommend rejection. IRR alone fails.
Q11BBYM's Job Training Program generates $8,000/year in program fees but $22,000/year in measurable social value (reduced public assistance costs, increased tax contributions). Initial cost: $60,000. WACC = 9%, Program life: 5 years. Should BBYM invest using (a) financial NPV only, (b) social NPV including social returns?▼
(a) Financial NPV only (using $8,000/year annuity):
PV annuity factor for 9%, 5 years = [1 − 1/(1.09)⁵] ÷ 0.09 = [1 − 0.6499] ÷ 0.09 = 0.3501 ÷ 0.09 = 3.8897
PV of financial CFs = $8,000 × 3.8897 = $31,118
Financial NPV = $31,118 − $60,000 = −$28,882 → Reject on financial grounds alone
(b) Social NPV (using $8,000 + $22,000 = $30,000/year total returns):
PV of blended CFs = $30,000 × 3.8897 = $116,691
Social NPV = $116,691 − $60,000 = +$56,691 → Accept on blended social + financial grounds
Recommendation: The program should be funded — but using a mix of program fees AND mission-aligned grant funding to bridge the $28,882 financial gap. BBYM needs at least $28,882 in grants or subsidized capital to make the program financially sustainable. Alternatively, if philanthropic funders accept a 0% financial return in exchange for the $22,000 in social returns they value, the program becomes fully fundable at zero financial cost.
This is why social impact measurement is financially strategic for BBYM — it unlocks access to capital (grants, PRIs, impact investors) that turns a financial rejection into an investment that creates $56,691 in community value.
PV annuity factor for 9%, 5 years = [1 − 1/(1.09)⁵] ÷ 0.09 = [1 − 0.6499] ÷ 0.09 = 0.3501 ÷ 0.09 = 3.8897
PV of financial CFs = $8,000 × 3.8897 = $31,118
Financial NPV = $31,118 − $60,000 = −$28,882 → Reject on financial grounds alone
(b) Social NPV (using $8,000 + $22,000 = $30,000/year total returns):
PV of blended CFs = $30,000 × 3.8897 = $116,691
Social NPV = $116,691 − $60,000 = +$56,691 → Accept on blended social + financial grounds
Recommendation: The program should be funded — but using a mix of program fees AND mission-aligned grant funding to bridge the $28,882 financial gap. BBYM needs at least $28,882 in grants or subsidized capital to make the program financially sustainable. Alternatively, if philanthropic funders accept a 0% financial return in exchange for the $22,000 in social returns they value, the program becomes fully fundable at zero financial cost.
This is why social impact measurement is financially strategic for BBYM — it unlocks access to capital (grants, PRIs, impact investors) that turns a financial rejection into an investment that creates $56,691 in community value.
Part 6 — Quick Reference Summary
Read this the night before the assessment
Unit 11 in 5 Essential Sentences
Sentence 1
NPV = Σ[CFₜ/(1+r)ₜ] is the gold standard capital budgeting tool because it directly measures wealth created in dollars, accounts for TVM at WACC, and always gives the correct decision — the Assessment Q11 answer.
Sentence 2
IRR is the discount rate making NPV = 0; accept if IRR ≥ WACC, but never use IRR to rank mutually exclusive projects (it ignores scale) and it fails when cash flows have multiple sign changes (multiple IRR problem).
Sentence 3
MIRR fixes IRR by reinvesting positive CFs at WACC (not IRR): MIRR = (TV/PV of costs)^(1/n) − 1; always produces one answer and is more realistic for high-return projects.
Sentence 4
Payback = time to recover investment (ignores TVM and post-payback CFs); discounted payback uses PV of CFs (fixes TVM but still ignores post-payback); PI = PV of CFs / Cost, best for ranking under capital rationing.
Sentence 5
For mutually exclusive projects: always choose highest NPV; for capital rationing: rank by PI and select until budget is exhausted; for BBYM nonprofits: add social value to financial CFs to get the true blended NPV that unlocks mission-aligned capital.
Must-Know Facts for the Assessment
| Concept / Formula | Answer |
|---|---|
| NPV formula | ∑ [CFₜ ÷ (1+r)ₜ] | CF₀ = −Initial Investment |
| NPV decision rule | Accept if NPV > 0; Reject if NPV < 0 |
| Assessment Q11 answer | NPV — the only method measuring $ wealth created directly |
| IRR definition | Discount rate that makes NPV = 0; accept if IRR ≥ WACC |
| IRR flaw #1 | Multiple IRR problem: 2+ sign changes in CFs can produce 2+ IRRs |
| IRR flaw #2 | Assumes reinvestment at IRR (unrealistic); overstates returns for high-IRR projects |
| MIRR formula | (TV of positive CFs / PV of costs)^(1/n) − 1; uses WACC as reinvestment rate |
| Payback formula | |
| Payback flaws | Ignores TVM (simple version) AND ignores all cash flows after recovery point |
| PI formula | PV of Future CFs ÷ Initial Investment; accept if PI ≥ 1.0 |
| PI best use | Capital rationing — rank projects by value per dollar to maximize total NPV |
| Mutually exclusive ranking | ALWAYS use NPV (highest NPV wins); NEVER use IRR (ignores scale) |
| Independent projects rule | Accept ALL with NPV > 0 (if unlimited capital); use PI ranking if capital-constrained |
| BBYM social NPV | Financial CFs + monetized social value = blended cash flows for mission-driven NPV |