Time Value of Money: Concepts, Calculations & Applications

Core Concepts: Why Money’s Value Changes

1. The Time Value of Money (TVM) Principle

Money today is worth more than the same amount in the future because:

• Inflation: Prices rise over time (e.g., ₹100 today buys less than ₹100 in 5 years).
• Opportunity Cost: Money can earn returns if invested (e.g., ₹100 in a bank earns interest).
• Risk: Future cash flows are uncertain (e.g., a loan repayment may default).

In the real world:

• eSewa: When you pay a bill via eSewa, the platform charges a small fee (e.g., 2% of the transaction). This fee reflects the time value of money—eSewa earns a return for processing payments immediately, even if the utility company receives the money later.
• Daraz’s "Buy Now, Pay Later": Daraz offers schemes like "Pay in 3 installments" with 0% interest. The store uses TVM to calculate how much to charge upfront to cover the risk of delayed payments (e.g., if a customer defaults, Daraz loses the time value of that money).
• Nepal Rastra Bank (NRB): When NRB sets benchmark interest rates (e.g., 7% for deposits), it accounts for TVM to ensure banks and customers are fairly compensated for the time their money is tied up.

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Key TVM Calculations

2. Future Value (FV) and Present Value (PV)

• Future Value (FV): How much ₹X today will grow to in n periods at rate r. Formula: $$FV=PV\times (1+r{)}^n$$
• Present Value (PV): How much ₹X in the future is worth today at rate r. Formula: $$PV=\frac{FV}{(1+r{)}^n}$$

Worked Example: Kathmandu Retail Shop’s Savings Scenario: A shop owner deposits ₹50,000 in a bank at 6% annual interest. How much will it be worth in 3 years?

Comparison Table: PV vs. FV

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3. Annuities: Regular Cash Flows

An annuity is a series of equal payments over time. Two types:

1. Ordinary Annuity: Payments at the end of each period (e.g., monthly rent).
2. Annuity Due: Payments at the beginning of each period (e.g., lease payments).

Formulas:

• FV of Annuity: $$F{V}_{annuity}=PMT\times \frac{(1+r{)}^n-1}{r}$$
• PV of Annuity: $$P{V}_{annuity}=PMT\times \frac{1-(1+r{)}^{-n}}{r}$$

Worked Example: Pathao Driver’s Savings Plan Scenario: A Pathao driver saves ₹2,000/month for 5 years at 5% annual interest. How much will he have?

Mermaid Diagram: Annuity Types

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4. Loan Amortization: Breaking Down Payments

Loans (e.g., car loans, home loans) are repaid in equal installments, where each payment covers:

• Interest (calculated on the remaining balance).
• Principal (reduces the loan balance).

Example: Ncell’s Phone Loan Scenario: A customer takes a ₹20,000 loan at 12% annual interest for 2 years (compounded monthly). Monthly payment = ₹917.25. Key Insight: Early payments are mostly interest; later payments reduce principal faster.

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5. Perpetuities: Infinite Cash Flows

A perpetuity is an annuity with infinite payments (e.g., some government bonds). Formula: $$P{V}_{perpetuity}=\frac{PMT}{r}$$

Example: NEPSE Dividend Stocks Scenario: A stock pays ₹500/year in dividends forever. If the discount rate is 8%, its PV is: $$PV=\frac{500}{0.08}=₹6,250$$

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Advanced Applications

6. Net Present Value (NPV) and Decision Making

NPV compares the PV of cash inflows to the PV of cash outflows. If NPV > 0, the investment is profitable. Formula: $$NPV=\sum \frac{C{F}_t}{(1+r{)}^t}-InitialInvestment$$

Example: Daraz’s New Warehouse Scenario: Daraz spends ₹50 million on a warehouse. It expects ₹20 million/year for 5 years. At 10% discount rate:

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7. Internal Rate of Return (IRR)

IRR is the discount rate that makes NPV = 0. It shows the effective return of an investment. Example: If IRR = 15% for a project, it’s better than a 10% bank deposit.

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In the Real World

1. eSewa’s Fee Structure:

   • When you pay a ₹1,000 bill via eSewa, it charges a 2% fee (₹20). This fee compensates eSewa for the time value of money—it processes the payment instantly but may take days for the utility to receive funds. The fee also covers the opportunity cost of tying up capital.

2. Khalti’s "Khalti Loan":

   • Khalti offers instant loans (e.g., ₹50,000 for 30 days at 1.5% interest). The interest is calculated using simple interest (not compounded daily), but the TVM principle ensures Khalti earns a return for the risk of non-repayment.

3. NTC’s Tariff Hikes:

   • When NTC increases electricity tariffs by 10%, it’s partly due to inflation (money’s purchasing power decreases over time). NTC uses TVM to ensure its long-term projects (e.g., hydropower dams) remain financially viable despite rising costs.

4. Bank Fixed Deposits:

   • If you deposit ₹100,000 in a bank for 3 years at 7% interest, the bank uses compound interest to calculate your FV. The bank itself borrows this money at a lower rate (e.g., 5% from NRB) and earns the spread (2%) as profit—this spread is a direct application of TVM.

5. Tourism Business: Hotel Room Reservations:

   • A hotel in Pokhara may offer a discount for advance bookings (e.g., 20% off if paid 6 months early). This discount reflects the time value of money—the hotel prefers guaranteed cash now rather than uncertain future bookings.

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Exam Tip

1. Memorize the 4 Core Formulas:

   • PV, FV, PV of annuity, FV of annuity. Always label axes in graphs (e.g., "Years" vs. "₹ Value").
   • Common Mistake: Forgetting to adjust for compounding periods (e.g., monthly vs. annual). If r is annual but payments are monthly, divide r by 12 and multiply n by 12.

2. Worked Examples Are Key:

   • Exams often give real-world scenarios (e.g., "A tourism business invests ₹2M in a new resort..."). Always show your steps like this:

     Year 0: -₹2,000,000 (outflow)
     Year 1: +₹800,000 / (1.10)^1
     Year 2: +₹1,000,000 / (1.10)^2
     NPV = Sum of above
     

3. Annuity vs. Perpetuity:

   • Annuity: Finite payments (e.g., loan EMIs). Use the annuity formula.
   • Perpetuity: Infinite payments (e.g., dividend stocks). Use $PV=PMT/r$.
   • Exam Trap: If the question says "forever," it’s a perpetuity!

4. Loan Amortization Tables:

   • Must-know: Early payments = mostly interest; later payments = mostly principal.
   • Shortcut: For quick checks, use the rule of 78s (sum of digits method) to estimate interest allocation.

5. NPV vs. IRR:

   • NPV tells you whether to invest (if >0).
   • IRR tells you how good the investment is (compare to your required return).
   • Example Question: "A tourism project has NPV = ₹5M at 12% and IRR = 15%. Should you invest if your cost of capital is 10%?" Answer: Yes, because IRR (15%) > cost of capital (10%) and NPV is positive.

6. Real-World Applications:

   • Banks: Use TVM to price loans and deposits.
   • eCommerce (Daraz/Khalti): Use TVM to design "Buy Now, Pay Later" schemes.
   • Tourism: Hotels use TVM to decide between renovating now or later.
   • Government (NRB/NTC): Use TVM to set interest rates and tariffs.

7. Graphs in Exams:

   • If asked to plot PV vs. FV, always:
     • Label axes (e.g., "Time (years)" and "₹ Value").
     • Show a downward-sloping curve for PV (money loses value over time).
     • Show an upward-sloping curve for FV (money grows with interest).

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Final Visual Summary