Exponential Discounting – Traditional Time Preference Model
Time Value of Money
Traditional finance treats time preference using exponential discounting: Money today is worth more than money tomorrow at a constant discount rate.
Formula: PV = FV / (1 + r)^t
Where:
- PV = Present Value
- FV = Future Value
- r = discount rate (time preference)
- t = time periods
The Exponential Curve
Discounting future cash flows exponentially:
| Time | Value of ₹100 (at 10% discount rate) |
|---|---|
| Today | ₹100.00 |
| Year One | ₹90.91 |
| Year Two | ₹82.64 |
| Year Five | ₹62.09 |
| Year Ten | ₹38.55 |
Shape: Smooth, consistent exponential decay.
Key Properties
Time-Consistency
Same trade-off valued equally regardless of when it occurs:
Today: ₹100 now vs ₹110 in 1 year → Choose ₹110 (10% gain worth waiting)
Future: ₹100 in year 5 vs ₹110 in year 6 → Also choose ₹110 (same 10% gain, same preference)
Consistency: Preferences don't reverse based on timing.
Mathematical Elegance
Exponential discounting is foundation of:
- DCF Valuation: Discount future cash flows to present
- NPV: Net Present Value for project evaluation
- Bond Pricing: Discount coupons and principal
- Retirement Planning: PV of future needs
Investment Applications
Stock Valuation (DCF):
Value = Σ [Dividend_t / (1+r)^t]
Discount each future dividend back to present.
Capital Budgeting:
NPV = Σ [CashFlow_t / (1+r)^t] - Initial Investment
If NPV > 0, invest. If NPV < 0, reject.
Bond Pricing:
Price = Σ [Coupon / (1+r)^t] + [Face Value / (1+r)^n]
Assumptions
Traditional exponential model assumes:
- Constant discount rate across all horizons
- Time-consistent preferences
- Rational patience level
- No present bias—today isn't psychologically special
Limitations
While mathematically elegant, exponential discounting fails to describe actual human behavior:
Can't Explain:
- Why people undersave for retirement
- Credit card debt at 24% APR while having savings at 4%
- Procrastination in financial planning
- Preference reversals ("I'll start SIP next month"... next month never comes)
Reality: People exhibit hyperbolic discounting (covered in other chapter), not exponential!
Exponential vs Actual Behavior
| Exponential Prediction | Actual Behavior |
|---|---|
| Smooth consistent discounting | Steep discount near-term, flat long-term |
| ₹100 today = ₹110 tomorrow (indifferent at 10% rate) | Strongly prefer ₹100 today! |
| Patience consistent over time | Impatient now, patient for future trade-offs |
| Should save 15-20% for retirement | Actually save less than 5% (present bias) |
Why Taught?
Despite limitations for describing behavior:
- Still used for prescriptive analysis (how you should decide)
- Mathematically tractable
- Foundation for valuation models
- Benchmark for measuring biases
Modern Approach: Use exponential for normative models, hyperbolic for descriptive reality.
Key Takeaways
- Exponential discounting: Constant rate, smooth decay, time-consistent
- Applications: DCF, NPV, bond pricing, all traditional finance
- Assumptions: Rationality, consistency, no present bias
- Limitation: Can't explain actual behavior (undersaving, debt, procrastination)
- Reality: Humans use hyperbolic discounting, not exponential
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