Inflation, Interest Rates & Financial Planning: Theory, Math & Real-World Impact

Core Concepts

1. Inflation: Definition and Types

Inflation is the sustained increase in the general price level of goods and services over time, eroding purchasing power. It is measured by indices like the Consumer Price Index (CPI) or Wholesale Price Index (WPI).

Types of Inflation

Real-World Example: Nepal’s Inflation (2020–2023)

• 2020: Deflationary pressure due to COVID-19 (-0.2% CPI).
• 2021–2022: Demand-pull inflation (5.2% average) from post-pandemic recovery.
• 2023: Cost-push inflation (7.8%) due to global oil shocks and supply chain disruptions.

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2. Measuring Inflation: CPI vs. WPI

Example Calculation (Nepal 2022):

• Base Year (2015): CPI = 100
• 2022: Household expenditure = NPR 25,000 (vs. NPR 20,000 in 2015)
• CPI 2022 = $\frac{25,000}{20,000}\times 100=125$ → 25% inflation

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3. Nominal vs. Real Interest Rates: The Fisher Equation

The Fisher Equation links nominal interest rates ($r_n$), real interest rates ($r_r$), and expected inflation ($\pi$): $$1+r_n=(1+r_r)\times (1+\pi )$$ For small inflation rates: $r_n\approx r_r+\pi$.

Worked Example: Ncell Loan Pricing

• Real risk-free rate ($r_r$): 3% (NRB’s policy rate).
• Expected inflation ($\pi$): 6% (NRB’s 2023 forecast).
• Nominal loan rate ($r_n$): $$r_n=3\%+6\%+1\%\text{ (risk premium)}=10\%$$ Ncell charges 10% on personal loans to cover inflation and default risk.

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4. Time Value of Money (TVM) Calculations

Simple vs. Compound Interest

Annuities (Regular Payments)

• Future Value of Annuity (FVA): $$FVA=PMT\times \frac{(1+r{)}^t-1}{r}$$
• Present Value of Annuity (PVA): $$PVA=PMT\times \frac{1-(1+r{)}^{-t}}{r}$$

Example: Daraz’s Supplier Financing

• Loan: NPR 500,000 for 2 years at 12% annual compounding.
• Monthly PMT: $$PMT=\frac{500,000\times 0.12}{1-(1+0.12/12{)}^{-24}}=\text{NPR }23,865/\text{month}$$

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5. Financial Planning for Inflation

Tools to Mitigate Inflation Risk

1. Gap Ratio Analysis (for banks): $$\text{Gap Ratio}=\frac{\text{Rate-Sensitive Assets}-\text{Rate-Sensitive Liabilities}}{\text{Total Assets}}$$

   • Higher gap ratio = More sensitive to interest rate changes.
   • Example: Bank A (25%) vs. Bank B (30%) → Bank B is riskier if rates rise.

2. Duration Analysis: Measures a bond’s sensitivity to interest rate changes. $$\text{Modified Duration}=\frac{\text{Macauley Duration}}{1+y}$$

   • Example: A 5-year bond with 3-year duration → Less sensitive than a 10-year bond.

3. Hedging Strategies:

   • Treasury Inflation-Protected Securities (TIPS): Adjust principal with CPI.
   • Commodity-Backed Loans: NTC uses oil price-linked bonds to hedge fuel cost inflation.

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In the Real World

1. eSewa and Khalti (Digital Payments)

   • Idea Used: Inflation-adjusted transaction fees.
   • How: Both apps dynamically adjust merchant fees (e.g., 2–3% of transaction value) to account for inflation and operational costs. During high inflation (2022–23), fees rose by ~1% annually to maintain profitability.

2. Nepal Rastra Bank (NRB) Policy Rates

   • Idea Used: Real vs. nominal interest rate targeting.
   • How: NRB sets the policy rate (currently 8.5%) by adding a real rate (3%) + expected inflation (6%) + risk premium (0.5%). This guides commercial banks’ lending rates (e.g., Ncell’s 10% loans).

3. Daraz’s Inventory Financing

   • Idea Used: Time-value-of-money for supplier loans.
   • How: Daraz offers suppliers compound-interest loans (12–15% p.a.) with monthly repayments. Suppliers use PVA calculations to decide whether to borrow or use cash flow. During inflation spikes (2022), Daraz tightened loan terms to offset higher financing costs.

4. Nepal Stock Exchange (NEPSE) Index

   • Idea Used: Inflation-adjusted returns.
   • How: Investors compare nominal returns (e.g., +15% in 2021) vs. real returns (15% – 5% inflation = +10%). High inflation reduces the attractiveness of fixed-income securities (e.g., NABIL bonds).

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6. Inflation and Financial Planning: A Kathmandu Retailer’s Case

Scenario: Shree Ram Store (a Kathmandu-based retail shop) wants to plan for inflation over 5 years.

Given:

• Current inventory cost: NPR 2,000,000
• Expected inflation: 6% annually
• Desired real return: 4% annually

Step 1: Calculate Future Inventory Cost (Inflation Impact)

$$F{V}_{\text{inventory}}=2,000,000\times (1+0.06{)}^5=\text{NPR }2,676,500$$

Step 2: Determine Required Nominal Savings

Using the Fisher equation: $$1+r_n=(1+0.04)\times (1+0.06)⟹r_n=10.24\%$$ Future Value Needed (FV) = NPR 2,676,500 Present Value (PV) = ? $$PV=\frac{2,676,500}{(1.1024{)}^5}=\text{NPR }1,750,000$$ Shree Ram Store must save NPR 1,750,000 today to cover future inventory costs at a 4% real return.

Step 3: Annuity Savings Plan

If saving monthly for 5 years: $$PMT=\frac{1,750,000\times 0.1024}{1-(1+0.1024/12{)}^{-60}}=\text{NPR }29,500/\text{month}$$

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Exam Tip

1. Inflation Questions:

   • Always distinguish between nominal and real rates. Use the Fisher equation: $$r_n=r_r+\pi +\text{risk premium}$$
   • For past exam questions, if given inflation expectations (e.g., 5% in 2022, 6% in 2023), calculate multi-year nominal rates by compounding: $$r_n=(1+r_r)(1+{\pi }_1)(1+{\pi }_2)-1$$

2. Gap Ratio and Interest Rate Sensitivity:

   • Higher gap ratio = More sensitive to rate changes.
   • Example: If Bank A has a 20% gap and Bank B has 25%, Bank B is riskier if rates rise (assets earn more, but liabilities cost more).
   • Exam Trap: Some questions ask which bank is less sensitive—lower gap ratio wins.

3. TVM Calculations:

   • Memorize formulas for FV, PV, annuities, and perpetuities.
   • Always label units (e.g., "NPR 50,000 at 8% for 3 years").
   • Use a calculator for complex problems (e.g., annuities with monthly compounding).

4. Real-World Applications:

   • NRB’s policy rate is always based on $r_r+\pi$. Relate it to bank lending rates (e.g., Ncell’s 10% loans).
   • NEPSE/Nabil bonds: Explain how inflation erodes real returns.
   • eSewa/Khalti fees: Link to inflation-adjusted pricing.

5. Common Mistakes to Avoid:

   • Ignoring compounding: Simple interest = $P\times r\times t$; compound = $P\times (1+r{)}^t$.
   • Mixing CPI and WPI: CPI affects households; WPI affects producers.
   • Forgetting risk premiums: Nominal rate = real rate + inflation + risk.

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Final Mermaid Summary: The Accounting Cycle of Inflation Impact