Risk in Capital Budgeting: Types, Techniques & NPV Adjustments

Key Concepts and Definitions

What is Risk in Capital Budgeting?

Risk in capital budgeting refers to the uncertainty surrounding the future cash flows of a project. Unlike accounting risk (which focuses on financial statements), capital budgeting risk assesses:

• Variability in returns (how much actual returns may differ from expected returns).
• Probability of loss (chance that a project fails to meet its financial targets).
• Market and operational uncertainties (e.g., changes in interest rates, demand fluctuations, or regulatory risks).

Why does risk matter? Investors demand higher returns for taking on more risk. If a project is riskier, its discount rate (cost of capital) must increase to reflect that risk, which can make even profitable projects appear unviable.

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Types of Risk in Capital Budgeting

Risk in capital budgeting can be classified into three broad categories:

Visualizing Stand-alone vs. Market Risk

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Measuring Risk: Quantitative Techniques

1. Standard Deviation (σ)

Measures the dispersion of possible outcomes around the expected value.

• Higher σ = More risk (wider range of possible returns).
• Lower σ = Less risk (returns cluster closely around the mean).

Formula: $$\sigma =\sqrt{\frac{\sum (X_i-\mu {)}^2}{N}}$$ Where:

• $X_i$ = Possible cash flow outcomes
• $\mu$ = Expected value (mean)
• $N$ = Number of outcomes

Example: Risk of a Kathmandu Tea Shop’s Investment Suppose a tea shop is considering buying a new espresso machine. The possible net present values (NPVs) over 5 years are:

• Optimistic: Rs. 500,000 (probability 20%)
• Most Likely: Rs. 300,000 (probability 50%)
• Pessimistic: Rs. 100,000 (probability 30%)

Step 1: Calculate Expected NPV ($\mu$) $$\mu =(0.20\times 500,000)+(0.50\times 300,000)+(0.30\times 100,000)=Rs.290,000$$

Step 2: Calculate Variance and Standard Deviation $${\sigma }^2=[(500,000-290,000{)}^2\times 0.20]+[(300,000-290,000{)}^2\times 0.50]+[(100,000-290,000{)}^2\times 0.30]$$ $${\sigma }^2=12,100,000,000+500,000+54,900,000,000=67,000,500,000$$ $$\sigma =\sqrt{67,000,500,000}\approx Rs.258,850$$

Interpretation: The standard deviation of Rs. 258,850 indicates high risk. The shop’s actual NPV could range from Rs. 100,000 to Rs. 500,000, meaning the investment is volatile.

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2. Coefficient of Variation (CV)

Compares risk to return by standardizing standard deviation. $$CV=\frac{\sigma }{\mu }$$

• Lower CV = Better risk-return tradeoff.
• Used when comparing projects with different expected returns.

Example: Comparing Two Projects

Decision: The solar panel project has a lower CV (0.25 vs. 0.33), meaning it offers a better risk-adjusted return despite having a lower expected NPV.

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3. Beta (β)

Measures market risk (how a project’s returns move with the market).

• β > 1: More volatile than the market (higher risk).
• β = 1: Moves with the market.
• β < 1: Less volatile (safer).

Example: Ncell’s 5G Investment Suppose Ncell is considering a Rs. 2 billion 5G expansion. Historical data shows:

• Market return (${\mu }_M$) = 10%
• Risk-free rate ($R_f$) = 5%
• Project’s expected return (${\mu }_P$) = 15%

Using the Capital Asset Pricing Model (CAPM): $$\beta =\frac{{\mu }_P-R_f}{{\mu }_M-R_f}=\frac{15\%-5\%}{10\%-5\%}=2$$ Interpretation: Ncell’s 5G project has a beta of 2, meaning it is twice as volatile as the market. Investors would demand a higher discount rate to compensate for this risk.

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Adjusting for Risk: Discount Rate Approaches

1. Risk-Adjusted Discount Rate (RADR)

Increases the discount rate to reflect risk.

• Formula: $$RADR=R_f+\beta ({\mu }_M-R_f)+\text{Risk Premium}$$
• Example: If the risk-free rate is 5%, market return is 10%, and the project’s beta is 1.5, with an additional risk premium of 3%: $$RADR=5\%+1.5(10\%-5\%)+3\%=15.5\%$$

Visual: How RADR Affects NPV

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2. Sensitivity Analysis

Tests how changes in key variables affect NPV.

• Key variables: Sales volume, price, costs, discount rate.
• Example: Daraz’s Delivery Time Impact Suppose Daraz is evaluating a new warehouse. The base-case NPV is Rs. 5 million, but:

  Variable	Base Case	+10% Change	-10% Change	NPV Impact
  Delivery Time (days)	3	2.7	3.3	+Rs. 800K
  Shipping Cost (per order)	Rs. 200	Rs. 220	Rs. 180	-Rs. 1M

Interpretation:

• A 10% increase in shipping cost reduces NPV by Rs. 1 million.
• Faster delivery (10% reduction in time) increases NPV by Rs. 800,000.

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3. Scenario Analysis

Evaluates best-case, worst-case, and most-likely scenarios.

• Example: NEPSE Stock Investment Suppose an investor is considering buying shares in a Nepali company. Three scenarios:

Expected Return: $$(0.20\times 25\%)+(0.50\times 12\%)+(0.30\times -5\%)=10.5\%$$

Decision: If the investor’s required return is 12%, this stock may not be worth the risk.

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4. Monte Carlo Simulation

Uses random sampling to model thousands of possible outcomes.

• Steps:
  1. Define probability distributions for key variables (e.g., sales, costs).
  2. Run simulations (e.g., 10,000 trials).
  3. Generate a probability distribution of NPV.

Example: Kathmandu Traffic Management System A city is evaluating a smart traffic light system with:

• Cost: Rs. 50 million
• Annual Savings: Rs. 8–12 million (due to reduced congestion)
• Lifespan: 10 years

Using Monte Carlo simulation, the output might look like:

Interpretation:

• 60% chance the project is profitable.
• 15% chance it loses money.
• Expected NPV ≈ Rs. 20 million.

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In the Real World

1. Ncell’s Network Expansion

   • Idea Used: Beta (β) and RADR
   • How? Ncell uses CAPM to adjust its discount rate for high-risk 5G projects. If a project has a beta of 1.8, the required return might be 18%, making only high-growth projects viable.

2. Daraz’s Warehouse Location

   • Idea Used: Sensitivity Analysis
   • How? Daraz tests how changes in delivery time, shipping costs, and order volume affect NPV before opening new warehouses in Pokhara or Biratnagar.

3. Nepal Rastra Bank’s Loan Approvals

   • Idea Used: Scenario Analysis
   • How? Banks evaluate loans under best-case (low inflation), worst-case (high inflation), and base-case scenarios to ensure borrowers can repay even if economic conditions worsen.

4. Khalti’s Digital Payment Growth

   • Idea Used: Monte Carlo Simulation
   • How? Khalti models user adoption rates, fraud risks, and regulatory changes to predict long-term profitability before scaling new features.

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Worked Example: Evaluating a Retail Shop’s Expansion

Business: Kathmandu Corner Store (a small retail shop in Thapathali) Project: Expanding to a larger space (cost: Rs. 3 million). Expected Cash Flows (5 years):

Step 1: Calculate Expected NPV (without risk adjustment)

• Discount rate = 10% (current cost of capital).
• Expected cash flows: $$\mu =(0.30\times 800,000)+(0.50\times 1,000,000)+(0.70\times 1,200,000)+(0.40\times 900,000)+(0.20\times 700,000)=Rs.990,000\text{ (per year)}$$
• NPV calculation (simplified for brevity): $$NPV=-3,000,000+\frac{990,000}{(1.10{)}^1}+\frac{990,000}{(1.10{)}^2}+\cdots +\frac{990,000}{(1.10{)}^5}\approx Rs.1,200,000$$

Step 2: Adjust for Risk (Standard Deviation)

• Calculate σ for each year’s cash flow (as shown earlier).
• Suppose σ = Rs. 200,000 per year.
• Risk Premium: Add 3% to the discount rate (new RADR = 13%).
• Recalculate NPV with 13%: $$NP{V}_{adjusted}=-3,000,000+\frac{990,000}{(1.13{)}^1}+\cdots +\frac{990,000}{(1.13{)}^5}\approx Rs.800,000$$

Step 3: Sensitivity Analysis

Decision:

• Base-case NPV (Rs. 800,000) is positive, but sensitive to sales volume.
• If sales drop by 10%, NPV falls to Rs. 400,000 (still acceptable).
• Recommendation: Proceed with the expansion but monitor sales closely.

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Comparison Table: Risk Assessment Techniques

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Advantages and Disadvantages of Risk Adjustment Methods

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Exam Tip

1. Always adjust for risk – If a question gives expected cash flows but no discount rate, assume you must calculate a risk-adjusted rate (e.g., using CAPM or adding a premium).
2. Show calculations – Even if a question is theoretical, write down formulas (e.g., NPV with RADR, beta calculation).
3. Compare techniques – If asked which method to use, discuss pros/cons (e.g., "Monte Carlo is best for complex projects, but sensitivity analysis is quicker for small businesses").
4. Real-world tie-ins – Examiners love Nepali examples (e.g., "How would Ncell use beta to evaluate a new tower?").
5. Graphs and tables – Always draw a sensitivity table or scenario analysis if the question involves multiple variables.

Common Mistakes to Avoid:

• Forgetting to discount cash flows when calculating NPV.
• Using the wrong discount rate (e.g., risk-free rate instead of RADR).
• Ignoring probabilities in scenario analysis.
• Misinterpreting beta (e.g., thinking β=1.5 means 150% risk instead of 50% more volatile than the market).

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