Chapter 3: Capital Budgeting Decisions
Capital budgeting is the process of evaluating and selecting long-term investments that are consistent with the goal of wealth maximization. These decisions involve large outlays, are irreversible, and have long-term consequences. This chapter covers capital budgeting techniques including Payback Period, ARR, NPV, IRR, and Profitability Index.
3.1 Capital Budgeting Techniques
| Method | Formula | Decision Rule | TVM? |
|---|---|---|---|
| Payback Period | Years to recover initial investment | Accept if PBP < target period | No |
| Discounted Payback | Years to recover using discounted cash flows | Accept if DPBP < target | Yes |
| ARR | Average Profit / Average Investment × 100 | Accept if ARR > required rate | No |
| NPV | Σ [CF/(1+r)^t] - Initial Investment | Accept if NPV > 0 | Yes |
| IRR | Rate where NPV = 0 | Accept if IRR > cost of capital | Yes |
| Profitability Index | PV of inflows / Initial investment | Accept if PI > 1 | Yes |
3.2 Comprehensive Worked Example
Project Data: Initial investment = NPR 10,00,000. Cost of capital = 12%. Life = 5 years. No salvage value.
| Year | Cash Flow | Cumulative CF | PV Factor @12% | PV of CF | Cumulative PV |
|---|---|---|---|---|---|
| 0 | (10,00,000) | (10,00,000) | 1.000 | (10,00,000) | (10,00,000) |
| 1 | 3,00,000 | (7,00,000) | 0.893 | 2,67,857 | (7,32,143) |
| 2 | 3,50,000 | (3,50,000) | 0.797 | 2,79,018 | (4,53,125) |
| 3 | 4,00,000 | 50,000 | 0.712 | 2,84,712 | (1,68,413) |
| 4 | 3,00,000 | 3,50,000 | 0.636 | 1,90,695 | 22,282 |
| 5 | 2,50,000 | 6,00,000 | 0.567 | 1,41,857 | 1,64,139 |
Payback Period: 2 + (3,50,000/4,00,000) = 2.875 years
Discounted Payback: 3 + (1,68,413/1,90,695) = 3.88 years
NPV: Sum of PV of inflows - Investment = 11,64,139 - 10,00,000 = NPR 1,64,139 (Positive → Accept)
PI: 11,64,139 / 10,00,000 = 1.164 (> 1 → Accept)
ARR: Average profit = (Total CF - Depreciation)/5. Depreciation = 10,00,000/5 = 2,00,000/yr. Avg profit = [(3,00,000+3,50,000+4,00,000+3,00,000+2,50,000)/5] - 2,00,000 = 3,20,000 - 2,00,000 = 1,20,000. Avg investment = 10,00,000/2 = 5,00,000. ARR = 1,20,000/5,00,000 = 24%
3.3 NPV vs IRR
| Basis | NPV | IRR |
|---|---|---|
| Definition | Dollar value added to firm | Rate of return on investment |
| Reinvestment Assumption | Cash flows reinvested at cost of capital (realistic) | Cash flows reinvested at IRR (may be unrealistic) |
| Mutually Exclusive Projects | Always gives correct ranking | May conflict with NPV due to scale/timing |
| Multiple IRRs | No issue | Can have multiple IRRs with non-conventional cash flows |
| Recommendation | Preferred method (theoretically superior) | Popular in practice (intuitive %) |
3.4 IRR Calculation (Interpolation)
IRR by Interpolation:
At 15%: NPV = +NPR 50,000
At 20%: NPV = -NPR 30,000
IRR = 15% + [50,000/(50,000+30,000)] × (20%-15%) = 15% + 0.625 × 5% = 18.125%
3.5 Mutually Exclusive Projects — NPV vs IRR Conflict
Example: Two projects, cost of capital 10%
| Year | Project A | Project B |
|---|---|---|
| 0 | (10,00,000) | (10,00,000) |
| 1 | 6,00,000 | 1,00,000 |
| 2 | 4,00,000 | 3,00,000 |
| 3 | 2,00,000 | 5,00,000 |
| 4 | 1,00,000 | 7,00,000 |
Project A: NPV@10% = 6,00,000/1.1 + 4,00,000/1.21 + 2,00,000/1.331 + 1,00,000/1.4641 - 10,00,000
= 5,45,455 + 3,30,579 + 1,50,263 + 68,301 - 10,00,000 = NPR -5,402 (Negative!)
Project B: NPV@10% = 1,00,000/1.1 + 3,00,000/1.21 + 5,00,000/1.331 + 7,00,000/1.4641 - 10,00,000
= 90,909 + 2,47,934 + 3,75,657 + 4,78,109 - 10,00,000 = NPR 92,609 (Positive)
IRR (approximate): Project A ≈ 9.8% | Project B ≈ 13.2%
Decision: Both NPV and IRR agree — choose Project B. But in cases where they conflict (different scales or timing), ALWAYS prefer NPV because it directly measures value addition.
3.6 Unequal Life Projects — Equivalent Annual Annuity
When comparing projects with different lifespans, comparing NPVs directly is misleading. The Equivalent Annual Annuity (EAA) converts NPV into an annual equivalent for fair comparison.
EAA = NPV / PVIFA(r, n)
Example: Machine X: Cost NPR 5L, life 3 years, NPV = NPR 1,20,000
Machine Y: Cost NPR 8L, life 5 years, NPV = NPR 1,80,000
At 10%: PVIFA(10%,3) = 2.4869, PVIFA(10%,5) = 3.7908
EAA(X) = 1,20,000/2.4869 = NPR 48,233/year
EAA(Y) = 1,80,000/3.7908 = NPR 47,484/year
Despite Y having higher NPV, X has higher EAA → Choose X (gives more value per year)
3.7 Capital Budgeting Under Risk
| Method | Approach | When to Use |
|---|---|---|
| Risk-Adjusted Discount Rate | Use higher discount rate for riskier projects | When project risk differs from company average |
| Certainty Equivalent | Convert risky cash flows to certain equivalents, then discount at risk-free rate | When risk varies across time periods |
| Sensitivity Analysis | Change one variable at a time; see impact on NPV | Identify which variables matter most |
| Scenario Analysis | Best case, worst case, most likely case NPVs | Understand range of possible outcomes |
| Decision Tree | Map sequential decisions and their probabilities | Multi-stage investment decisions |
Scenario Analysis Example
Hydropower project in Nepal — NPR 50 crore investment:
| Scenario | Probability | Annual CF (crore) | NPV @ 12% |
|---|---|---|---|
| Optimistic (high demand + good monsoon) | 0.25 | 15 | +34.7 crore |
| Most Likely (normal conditions) | 0.50 | 10 | +6.5 crore |
| Pessimistic (drought + low demand) | 0.25 | 6 | -16.1 crore |
Expected NPV = 0.25(34.7) + 0.50(6.5) + 0.25(-16.1) = 8.675 + 3.25 - 4.025 = NPR 7.9 crore (Positive → Accept)
But note: 25% probability of NPR 16 crore loss — management must assess risk tolerance.
3.8 Capital Rationing
When a firm has limited funds and cannot invest in all positive-NPV projects, it must rank and select projects to maximize total NPV. Use the Profitability Index (PI) for ranking under capital rationing.
Example: Budget = NPR 50,00,000
| Project | Investment | NPV | PI | Rank |
|---|---|---|---|---|
| A | 20,00,000 | 6,00,000 | 1.30 | 2 |
| B | 15,00,000 | 5,25,000 | 1.35 | 1 |
| C | 25,00,000 | 5,00,000 | 1.20 | 4 |
| D | 10,00,000 | 2,50,000 | 1.25 | 3 |
Optimal selection (by PI rank within budget):
B (NPR 15L) + A (NPR 20L) + D (NPR 10L) = NPR 45L ≤ 50L budget
Total NPV = 5,25,000 + 6,00,000 + 2,50,000 = NPR 13,75,000
Practice Questions
Short Answer:
1. What is capital budgeting? Why is it important?
2. Compare NPV and IRR methods.
3. What are the limitations of payback period?
4. Define profitability index. When is it useful?
5. How is IRR calculated using interpolation?
Long Answer:
6. Investment NPR 15,00,000. Cash flows: Y1=4,00,000, Y2=5,00,000, Y3=6,00,000, Y4=4,00,000, Y5=3,00,000. Cost of capital 10%. Calculate: Payback, Discounted Payback, NPV, PI. Should the project be accepted? (15 marks)
7. Two mutually exclusive projects: A costs NPR 5,00,000 with NPV of 80,000. B costs NPR 8,00,000 with NPV of 1,00,000. Which should be selected and why? Discuss using NPV and PI. (15 marks)
8. Compare all capital budgeting techniques (PBP, ARR, NPV, IRR, PI). Which is theoretically best and why? (15 marks)
9. A hydropower company in Nepal is evaluating a NPR 50 crore project. Cash flows: NPR 12 crore/year for 8 years. Cost of capital 14%. Calculate NPV and advise the company. (15 marks)
10. "NPV is superior to IRR for capital budgeting decisions." Discuss with examples showing conflict between NPV and IRR. (15 marks)
Exam Tips: ✓ NPV calculation is ALWAYS asked — show complete PV table ✓ Know IRR interpolation method ✓ NPV vs IRR comparison is very frequently tested ✓ Always state decision clearly: Accept/Reject with reason ✓ Payback is simplest but know its limitations