Unit 11 Assessment — Capital Budgeting

💰 NPV Method

📐 IRR & MIRR

⏱️ Payback & Discounted Payback

📊 Profitability Index & Rankings

Net Present Value (NPV)

NPV FormulaNPV = Σ[CF_t ÷ (1+r)^t] − Initial Cost

Accept RuleAccept if NPV > 0 → adds value to firm

Reject RuleReject if NPV < 0 → destroys value

NPV & Value CreationNPV = exact dollar value added to the firm

Mutually Exclusive ProjectsChoose highest NPV (not highest IRR)

IRR & MIRR

IRR DefinitionDiscount rate where NPV = 0

IRR Accept RuleAccept if IRR > WACC (hurdle rate)

IRR LimitationMultiple IRRs possible with non-normal CFs; reinvestment assumption unrealistic

MIRRModified IRR — assumes CFs reinvested at WACC; solves IRR reinvestment flaw

NPV vs. IRR ConflictWhen rankings conflict, trust NPV for value creation

Payback & Discounted Payback

Payback PeriodYears until cumulative CFs recover initial cost · ignores TVM

Discounted PaybackUses PV of CFs — accounts for TVM · still ignores post-payback CFs

Payback UseQuick liquidity screen · NOT a value measure

LimitationIgnores all cash flows after payback cutoff

Accept RuleAccept if payback ≤ firm's target cutoff period

Profitability Index & Rankings

Profitability Index (PI)PI = PV of future CFs ÷ Initial Investment

PI Accept RuleAccept if PI > 1.0 (equivalent to NPV > 0)

Capital RationingUnder budget constraints, rank by PI to maximize NPV per dollar

Independent ProjectsAll methods agree: NPV>0 ↔ IRR>WACC ↔ PI>1

Non-Normal CFsCash outflow mid-project can produce multiple IRRs

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out of 100 points

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Section 1

—/40

Multiple Choice

Section 2

—/20

True / False

Section 3

—/20

Short Answer

Section 4

—/20

Extended Response

⚠ Sections 3 & 4 are teacher-graded. Use the rubric selectors below to finalize the score.

Multiple Choice

Select the best answer · Includes NPV, payback, IRR & PI calculations

2 pts each · 40 pts

Click the best answer. Use the formula reference panel and decision rules strip above. Each question is worth 2 points.

True or False

Click TRUE or FALSE for each statement

2 pts each · 20 pts

Select TRUE or FALSE for each statement. Each is worth 2 points.

Short Answer

Show all calculations + explain in 2–4 sentences · Teacher-graded

5 pts each · 20 pts

Answer in 2–4 complete sentences. Show every calculation step clearly. Rubric selectors appear after grading.

Extended Response — BBYM Capital Investment Decision

Full capital budgeting analysis · NPV · IRR · Payback · Recommendation · Teacher-graded

20 pts

Read the scenario carefully. Write a well-organized analytical memo of at least 8 sentences. Show all calculations with labeled steps. Use and underline at least four unit vocabulary terms.

📋 Scenario — BBYM Workforce Development Center: Two Competing Capital Projects

BBYM is evaluating two mutually exclusive capital investments for its new workforce development center. Both projects require the same initial investment. The board has asked you, as student financial analyst, to run a full capital budgeting analysis and recommend which project to fund. The firm's WACC (hurdle rate) is 10% and the board's maximum payback cutoff is 3 years.

Project Alpha — Digital Skills Lab

Initial Cost: −$120,000
CF Year 1: $50,000
CF Year 2: $50,000
CF Year 3: $50,000
CF Year 4: $20,000

Project Beta — Trades Training Center

Initial Cost: −$120,000
CF Year 1: $20,000
CF Year 2: $40,000
CF Year 3: $60,000
CF Year 4: $80,000

PV Factors @ 10%

Year 1: 0.9091
Year 2: 0.8264
Year 3: 0.7513
Year 4: 0.6830

Hurdle Rate & Cutoff

WACC = 10%
Payback cutoff: 3 years
Projects are MUTUALLY EXCLUSIVE

35 Write your full capital budgeting memo covering all four parts: (a) Calculate the NPV of both Project Alpha and Project Beta using the PV factors provided — show every discounted cash flow step; (b) Calculate the payback period for both projects — show the cumulative cash flow table — and state which project(s) meet the 3-year cutoff; (c) The IRR of Project Alpha is approximately 21.9% and the IRR of Project Beta is approximately 17.8%. Using both NPV and IRR, determine whether there is a ranking conflict between the two projects and explain which method should be trusted for the final decision and why; (d) Write a 2–3 sentence recommendation to the BBYM board stating which project to fund, using NPV as the primary criterion, and acknowledge any tradeoffs between the two projects. Use at least four underlined vocabulary terms.

📋 Teacher Scoring Rubric

Criterion	Excellent (Full)	Proficient (Partial)	Developing (Minimal)	Score
Part (a) — NPV Calculations Alpha: 50K×(.9091+.8264+.7513)+20K×.6830 − 120K = 50K×2.4868+13,660−120K = 124,340+13,660−120K = $18,000 · Beta: 20K×.9091+40K×.8264+60K×.7513+80K×.6830−120K = 18,182+33,056+45,078+54,640−120K = $30,956	Both NPVs correctly calculated with each discounted CF shown; Alpha ≈ $18,000 and Beta ≈ $30,956	Correct method; one NPV slightly off due to rounding; all CFs discounted	One or both NPVs missing; formula not applied to all cash flows	/6
Part (b) — Payback Period Alpha cumulative: Y1=$50K, Y2=$100K, Y3=$150K → payback = 2.4 years (120K recovered in Year 3) · Beta: Y1=$20K, Y2=$60K, Y3=$120K → payback exactly 3.0 years · Both meet 3-yr cutoff; Alpha is faster	Cumulative CF table shown for both; Alpha ≈ 2.4 yrs and Beta = 3.0 yrs; both pass cutoff; Alpha faster payback noted	Both periods calculated; table missing or cutoff comparison incomplete	Only one payback calculated or cumulative method not shown	/5
Part (c) — NPV vs. IRR Conflict IRR ranks: Alpha 21.9% > Beta 17.8% → IRR prefers Alpha · NPV ranks: Beta $30,956 > Alpha $18,000 → NPV prefers Beta · CONFLICT exists · Trust NPV for mutually exclusive projects	Conflict correctly identified; explains WHY NPV is superior (measures dollar value created; IRR assumes reinvestment at its own high rate which is unrealistic)	Conflict identified; explanation of why NPV wins is thin or incomplete	No conflict identified or methods confused	/5
Part (d) — Board Recommendation	Recommends Beta based on higher NPV ($30,956 vs. $18,000); acknowledges Alpha's faster payback and higher IRR as tradeoffs; clear and professional memo language with ≥4 underlined vocabulary terms	Correct recommendation; limited tradeoff discussion; some vocabulary terms used	Wrong recommendation or no reference to NPV; no tradeoff discussion	/4

Extended Response Total: — / 20

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