Chapter 10: Capital Budgeting

NPV • IRR • Payback Period • Mutually Exclusive vs. Independent Projects
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Chapter 10
Resources & Tools Key Concepts (Fast Review) In-Class Exercises Homework (Due with Final) Disclaimer
Tip: For mutually exclusive projects, default to the higher NPV at the required return (unless capital rationing is specified and analyzed formally).

Resources & Tools

Slides (PPT)
Use the class PPT for definitions, decision rules, and examples.
Self-produced video
Exploring Capital Budgeting Key Concepts and Strategies.
Interactive Game
Open the capital budgeting game
Quiz
Quiz on NPV, IRR, and Payback Period (in class / LMS).
NPV, IRR, Payback Calculator
Open calculator
Excel Template
Open NPV/IRR/Payback template

Key Concepts (Fast Review)

  • Payback period: time needed to recover the initial outlay from undiscounted cash flows. Useful for liquidity/simplicity; ignores time value of money and cash flows after payback.
  • NPV: present value of benefits minus present value of costs at the required return (WACC / hurdle rate). NPV > 0 creates value; NPV < 0 destroys value.
  • IRR: discount rate that makes NPV = 0. Accept if IRR > required return (with caveats: multiple IRRs, non-normal cash flows, and mutually exclusive ranking conflicts).
  • Mutually exclusive: choose only one project → typically rank by NPV at the required return; IRR can conflict due to scale/timing differences.
  • Crossover rate: discount rate where two projects have equal NPVs. Above vs. below that rate can flip the NPV ranking.

In-Class Exercises

Question 1: $20,000 outlay; 5 years of FCFs (Payback, NPV @10%, IRR)
YearFree Cash Flow
0–20,000
18,000
24,000
33,000
45,000
510,000
Solution / Key Takeaways 
Payback (undiscounted):
Year 1 cum = 8,000
Year 2 cum = 12,000
Year 3 cum = 15,000
Year 4 cum = 20,000  → Payback = 4.00 years

Does payback consider time value of money?
No (standard payback does not discount).

NPV at 10%:
NPV ≈ +2,456.74

Interpretation:
NPV > 0 → accept (value-creating at 10% hurdle rate).
Does NPV consider time value of money?
Yes.

IRR:
IRR ≈ 14.55%

Interpretation:
IRR > 10% → accept (subject to usual IRR caveats).
Does IRR consider time value of money?
Yes (implicitly via discounting).
Question 2: $60,000 outlay; 5 years of FCFs (Payback, NPV @15%, IRR)
YearFree Cash Flow
0–60,000
125,000
224,000
313,000
412,000
511,000
Solution / Key Takeaways 
Required return = 15%

Payback (undiscounted):
After Year 2 cum = 49,000
Need 11,000 more; Year 3 CF = 13,000
Payback = 2 + (11,000 / 13,000) = 2.8462 years

NPV at 15%:
NPV ≈ +764.27  → accept

IRR:
IRR ≈ 15.64%
IRR > 15% → accept (barely above hurdle rate)
Question 3: Mutually Exclusive vs. Independent Projects (Ranking conflicts + crossover)
(1) One-year projects A vs. B (required return 10%) 
Initial Outlay: A = 200; B = 1,500
Inflow (Year 1): A = 300; B = 1,900
r = 10%

NPV(A) = -200 + 300/1.10 ≈ +72.73
NPV(B) = -1500 + 1900/1.10 ≈ +227.27

Decision (mutually exclusive, choose one):
Choose B (higher NPV).

Note:
IRR(A) = 50%; IRR(B) ≈ 26.67%
This is a classic scale problem: IRR ranks A higher, but NPV ranks B higher.
(2) Projects A vs. B over 3 years (required return 10%) + crossover rate 
Initial outlay for both: 1,000
r = 10%

Cash flows:
A: Year1=100, Year2=200, Year3=2,000
B: Year1=650, Year2=650, Year3=650

NPV(A) @10% ≈ +758.83
NPV(B) @10% ≈ +616.45
→ Mutually exclusive: choose A at 10%
→ Independent: accept both (both NPVs > 0)

IRR(A) ≈ 34.84%
IRR(B) ≈ 42.57%

Crossover rate (rate where NPV(A) = NPV(B)):
≈ 21.01%
Below ~21.01% → A has higher NPV
Above ~21.01% → B has higher NPV
Question 4: Crossover rate example (answer: 11.8%)
PeriodProject AProject B
0-500-400
1325325
2325200
Solution / Key Takeaways 
At required return = 10%:

NPV(A) @10% ≈ +64.05
NPV(B) @10% ≈ +60.74
→ Mutually exclusive: choose A at 10%
→ Independent: accept both (both NPVs > 0)

IRR(A) ≈ 19.43%
IRR(B) ≈ 22.17%

Crossover rate:
≈ 11.80% (given; computed from incremental cash flows)

If required return = 13%:
NPV(A) @13% ≈ +42.13
NPV(B) @13% ≈ +44.24
→ Mutually exclusive: choose B at 13%
→ Independent: accept both

Chapter 10 Homework (Due with Final)

Use the calculator and/or Excel template above to verify your numbers. Show clean work and state the decision (accept/reject; choose A vs. B; both if independent).
1) Two projects (NPV @ 15%): mutually exclusive vs. independent
ProjectYear 0Year 1Year 2Year 3Year 4Discount Rate
A-100404040N/A0.15
B-73303030300.15
Answer (given) 
NPV(A) ≈ -8.67
NPV(B) ≈ +12.65

Mutually exclusive: choose B
Independent: accept B (reject A)
2) IRR decision rule (required return 15.5%)
Cash flows image:
Answer (given) 
IRR ≈ 17.53%
Since IRR > 15.5%, accept (based solely on IRR rule).
3) Ice cream cart payback period 
Cost = 6,000
Annual cash flow = 3,600 for 3 years
Salvage = 0
Answer (given) 
Payback = 6,000 / 3,600 = 1.67 years
4) Payback period: $1,190 for 10 years, initial cost $8,000
Answer (given) 
Payback = 8,000 / 1,190 = 6.72 years
5) NPV decision rule at 14% (image prompt)
Cash flows image:
Answer (given) 
NPV ≈ 7,264.95
Decision: accept
6) Two mutually exclusive projects (NPV & IRR @ 10%) + crossover rate
YearCash Flow (A)Cash Flow (B)
0(10,110)(10,110)
15,3734,443
23,3733,543
34,4735,343
Answer (given) 
NPV(A) ≈ 922.78 ; IRR(A) ≈ 15.33%
NPV(B) ≈ 871.47 ; IRR(B) ≈ 14.68%
Crossover rate ≈ 6.29%
7) IRR (nearest whole %) for 4,000,000 outlay and 1,546,170 for 4 years
Answer (given) 
IRR ≈ 20.03% (≈ 20% to nearest whole percent)
Welltran Corp. machine NPV @ 13.5% (5 years, salvage in year 5) 
Cost = 1,875,000
Annual net cash flow = 650,000 for 5 years
After-tax salvage value at end of year 5 = 120,000
Required return = 13.5%
Hint: Year 5 cash flow = 650,000 + 120,000 = 770,000
Answer (given) 
NPV ≈ 447,291.91

Disclaimer

Educational content for jufinance.com. Figures and answers are provided for learning and practice. Students are responsible for showing work and explaining decisions using the correct capital budgeting rule(s) for the setting (independent vs. mutually exclusive; required return).