Time Value of Money - Why $1 Today Is Worth More Than $1 Tomorrow

📉 Inflation, Opportunity Cost, and Daily Life

Inflation and Purchasing Power

What Inflation Does:

Inflation is the general increase in prices over time. As prices rise, each dollar purchases less - your purchasing power declines.

NZ Inflation Context:

• Reserve Bank target: 1-3% annually
• Long-term average: ~2-2.5%
• Recent years: Varied (COVID impacts)
• Silently erodes money's value

Inflation Example:

$100 at 3% annual inflation:

• Today: Buys $100 of goods
• 1 year: Same $100 buys what cost $97.09 today (3% less)
• 5 years: $100 buys what cost $86.26 today (14% less)
• 10 years: $100 buys what cost $74.41 today (26% less)
• 20 years: $100 buys what cost $55.37 today (45% less)

Your $100 note is still $100, but it purchases dramatically less. This is why $100 today is worth more than $100 in 10 years.

Real Life Inflation Impact:

Scenario: House rent in Auckland

• 2010: Average $350/week
• 2020: Average $520/week (49% increase)
• 2024: Average $600+/week

Money saved in 2010 without growth can't afford 2024 rent.

Opportunity Cost

What Opportunity Cost Means:

The benefit you could have received by taking an alternative action. In time value context: money received today can be invested to grow, but money received tomorrow has missed that growth opportunity.

Opportunity Cost Example:

Choice: $5,000 now vs $5,500 in 2 years

Option A - Take $5,000 now:

• Invest at 6% annually for 2 years
• Year 1: $5,000 × 1.06 = $5,300
• Year 2: $5,300 × 1.06 = $5,618
• End result: $5,618

Option B - Wait for $5,500:

• Receive $5,500 in 2 years
• No growth during wait
• End result: $5,500

Better choice: Option A - get $5,000 now, invest it, end up with $5,618 vs $5,500. The $118 difference is the opportunity cost of waiting.

Opportunity Cost in Reverse:

When evaluating future payment, must discount by what you could have earned:

$5,500 in 2 years, discounted at 6% = $5,500 ÷ (1.06)^2 = $4,896 in today's dollars

So $5,500 in 2 years is actually worth less than $5,000 today (in present value terms).

Present vs Future Value in Daily Life

Real-World Applications:

1. Early Payment Discounts:

• Supplier offers: Pay now for 5% discount, or full price in 30 days
• Invoice: $1,000
• With discount: $950 now
• Without: $1,000 in 30 days
• Saving $50 over 30 days = ~60% annualized return
• Almost always worth taking discount

2. Lump Sum vs Installments:

• Buy couch: $2,000 cash or $180/month for 12 months ($2,160 total)
• Installments cost $160 extra
• Effective interest rate: ~8%
• If you have cash, paying upfront saves money
• If must finance, compare to other options (credit card, personal loan)

3. Rental Bond Return:

• Pay $1,600 bond at move-in
• Get back $1,600 when move out 2 years later
• Looks like "even" but actually lost opportunity cost
• $1,600 invested at 5% for 2 years = $1,766
• Opportunity cost: $166
• This is cost of renting (beyond rent itself)

4. Lottery Winnings (Annuity vs Lump):

• Win $1 million - two options:
• Option A: $50,000/year for 20 years (total $1M)
• Option B: $600,000 lump sum today
• Which is better? Depends on discount rate
• If can earn 7%+ on lump sum, lump sum better
• Annuity spreads risk but limits investment opportunity

5. Job Offers with Deferred Compensation:

• Job A: $80,000 salary now
• Job B: $75,000 salary + $10,000 bonus in 2 years
• Which is better over 2 years?
• Job A: $80k + $80k = $160k (can invest extra $5k annually)
• Job B: $75k + $75k + $10k = $160k (but bonus delayed)
• Job A slightly better due to earlier access to extra $5k annually

💳 Loan and Investment Decisions

Loan Decisions and Time Value

Why Early Repayment Matters:

Time value of money means that paying off debt sooner saves money due to compound interest working against you. Every extra payment saves future interest.

Mortgage Extra Payment Example:

Scenario:

• Mortgage: $400,000
• Interest rate: 6%
• Term: 30 years
• Regular payment: $2,398/month

Option A - Regular payments:

• Total paid over 30 years: $863,352
• Interest paid: $463,352

Option B - Pay extra $200/month:

• Repayment: ~25 years (5 years sooner)
• Total paid: $750,000
• Interest paid: $350,000
• Saving: $113,352

The $200/month extra ($60,000 over 25 years) saves $113,352 in interest. Time value working in your favour.

Should You Pay Off Debt or Invest?

Rule of thumb: Compare interest rates.

Example:

• Have $10,000 spare
• Mortgage rate: 6%
• Investment return potential: 8%

Option A - Pay mortgage:

• Save 6% interest on $10,000
• Guaranteed $600/year saving

Option B - Invest:

• Earn 8% on $10,000
• Expected $800/year return
• But not guaranteed, subject to risk

Decision: If confident in achieving 8%, invest. If want certainty, pay mortgage. Gap must be worthwhile to justify investment risk.

Credit Card Debt - Time Value Nightmare:

Why credit card debt is so expensive:

• Interest rates: 15-25% in NZ
• Compounds daily
• Minimum payments barely cover interest

Example:

• Balance: $5,000
• Interest: 20%
• Minimum payments only
• Time to pay off: 15+ years
• Total paid: $10,000+

Time value working massively against you. Every day carrying balance costs money.

Investment Decisions and Time Value

Compound Returns Magnify Time Value:

Investment returns compound - you earn returns on returns. Time amplifies this effect dramatically.

Power of Starting Early:

Scenario: Retirement savings

Person A - Starts at 25:

• Invests $5,000/year
• Stops at 35 (10 years, $50,000 invested)
• Leaves to grow until 65 (30 more years)
• Returns: 8% annually
• At 65: $787,000

Person B - Starts at 35:

• Invests $5,000/year
• Continues until 65 (30 years, $150,000 invested)
• Returns: 8% annually
• At 65: $612,000

Result: Person A invested $100,000 LESS but has $175,000 MORE. Starting 10 years earlier was worth more than tripling contributions. This is time value of money in action.

$1 Invested at Different Ages:

$1,000 invested at 8% annual return:

• Age 25, withdrawn at 65 (40 years): $21,725
• Age 35, withdrawn at 65 (30 years): $10,063
• Age 45, withdrawn at 65 (20 years): $4,661
• Age 55, withdrawn at 65 (10 years): $2,159

Same $1,000 investment, dramatically different outcomes based solely on TIME.

Investment vs Savings Example:

$10,000 over 20 years in NZ:

Option A - Savings account (1.5% interest):

• Future Value: $13,469
• Real value after 3% inflation: $7,449
• Lost purchasing power despite growth

Option B - Diversified investment (7% average):

• Future Value: $38,697
• Real value after 3% inflation: $21,406
• Grew purchasing power significantly

Time value of money + compound returns = enormous difference over 20 years.

When Time Value Matters Less:

Time value diminishes in importance for:

• Very short periods: Days or weeks - opportunity cost minimal
• Small amounts: $10 today vs $10 tomorrow - difference trivial
• Negative interest rates: Rare, but cash today could lose value (storage costs, bank fees)

👤 NZ Scenario and Decision Checklist

NZ Scenario: Sarah's Car Sale Dilemma

Background:

• Sarah: 28, selling her car in Wellington
• Buyer offers two payment options
• Sarah unsure which is better

The Two Options:

Option A: $10,000 cash today

• Immediate payment
• No waiting
• No risk

Option B: $11,000 in 2 years

• $1,000 premium for waiting
• Buyer needs time to save
• Written agreement

Sarah's Analysis:

Initial reaction: "Option B is $1,000 more - obviously better!"

But consider time value...

Factor 1 - Opportunity Cost:

• Sarah can invest $10,000 in term deposit at 5.5%
• Year 1: $10,000 × 1.055 = $10,550
• Year 2: $10,550 × 1.055 = $11,130
• Option A grown: $11,130
• Option B: $11,000
• Option A actually $130 better

Factor 2 - Inflation:

• Inflation at 3% annually
• $11,000 in 2 years buys what $10,357 buys today
• Real purchasing power of Option B = $10,357
• Option A = $10,000 today (but can grow to overcome inflation)

Factor 3 - Risk:

• Buyer might not pay in 2 years (circumstances change)
• Enforcement would require legal action (costly, time-consuming)
• Option A has zero payment risk

Sarah's Decision Framework:

Present Value Calculation:

• Discount $11,000 at 5.5% for 2 years
• PV = $11,000 ÷ (1.055)^2
• PV = $11,000 ÷ 1.113 = $9,883

In today's dollars:

• Option A: Worth $10,000 today
• Option B: Worth $9,883 today
• Option A is $117 better

Sarah's Decision:

Sarah chose Option A - $10,000 today. Reasoning:

• Present value analysis shows it's actually worth more
• Can invest at 5.5% and have $11,130 in 2 years (more than Option B)
• Zero payment risk - money in hand immediately
• No ongoing relationship or enforcement concerns
• Can use money sooner if needed (flexibility)

Alternative Scenario - Different Numbers:

What if buyer offered $12,000 in 2 years instead?

• Present Value: $12,000 ÷ (1.055)^2 = $10,779
• Higher than $10,000 today
• Extra $1,221 premium might justify waiting and risk
• Would consider Option B

The "break-even" future payment (where options equal) is ~$11,130. Anything above that, and waiting starts to make sense if willing to accept risk.

Lessons from Sarah's Experience:

• Nominal amounts ($11k vs $10k) deceive - must calculate present values
• Opportunity cost is real - money today can be invested to grow
• Risk premium required for future payments (buyer needed to offer significantly more than $11k)
• Simple formula helps make complex decisions
• Time value applies to everyday transactions, not just finance theory

Time Value Decision-Making Checklist

When Comparing Payment Options:

• ☐ Identify all options with amounts and timing
• ☐ Note which payments are today vs future
• ☐ Determine relevant discount rate (what you could earn)
• ☐ Calculate present value of all future payments
• ☐ Compare all options in today's dollars
• ☐ Consider risk of future payments not materializing
• ☐ Factor in your need for liquidity (access to money)
• ☐ Choose option with highest present value

Key Questions to Ask:

• ☐ What could I earn if I had the money today?
• ☐ What is current inflation rate eroding purchasing power?
• ☐ How certain is the future payment?
• ☐ Do I need money sooner rather than later?
• ☐ What is the real difference in today's dollars?

For Loan Decisions:

• ☐ Understand total interest paid over life of loan
• ☐ Calculate how extra payments reduce future interest
• ☐ Compare debt interest rate to investment return potential
• ☐ Consider paying high-interest debt first (credit cards)
• ☐ Remember: debt interest compounds against you

For Investment Decisions:

• ☐ Start as early as possible (time is most valuable asset)
• ☐ Understand compound returns amplify time value
• ☐ Account for inflation when evaluating returns
• ☐ Compare returns after fees and taxes (real returns)
• ☐ Don't let "safe" low-return options erode purchasing power

Red Flags:

• ☐ Someone downplays time value ("it's only 2 years")
• ☐ Payment plans without interest rate disclosure
• ☐ "No interest" offers that are really deferred payment
• ☐ Comparing nominal amounts across different time periods
• ☐ Ignoring inflation in long-term projections

Final insight: Time value of money: $1 today worth more than $1 tomorrow due to inflation (purchasing power erosion), opportunity cost (can invest and grow), and risk (future uncertain). Present value discounts future amounts to today's worth. Future value grows today's amounts forward. Formula: FV = PV × (1 + rate)^years. Inflation example: $100 today buys more than $100 in 10 years - at 3% inflation, purchasing power declines 26% over decade. Opportunity cost: $5,000 today invested at 6% for 2 years = $5,618 vs $5,500 received in 2 years - taking today better by $118. Daily life applications: early payment discounts almost always worthwhile (~60% annualized), lump sum vs installments comparison, rental bond opportunity cost, deferred compensation evaluation. Loan decisions: extra mortgage payments save compounding interest (e.g., $200/month extra saves $113k over life of $400k mortgage), debt vs invest comparison uses interest rate differential, credit card debt nightmare due to 15-25% rates. Investment decisions: starting early amplifies time value dramatically - $1k at age 25 becomes $21,725 at 65 vs only $2,159 if starting at 55, compound returns magnify over time. Sarah scenario: $10k today vs $11k in 2 years - present value analysis shows $10k better ($11k PV = $9,883), can invest at 5.5% to reach $11,130, zero risk. Decision checklist: calculate present values, consider opportunity cost and inflation, assess risk, choose highest present value option.