Lesson1A_Review time value of money

Page 1: Lesson Overview

  • Title: Review Time Value of Money RE 3095: Real Estate Finance

  • Focus on understanding the importance and implications of time value of money in financial calculations related to real estate.

Page 2: Basics of Financial Calculations

Future Value with Simple Interest

  • Principal (P): The initial amount of money.

  • Real Interest Rate (r): The percentage of the principal earned or paid in interest over a specific period.

  • Interest Payment for a One-Year Bond:

    • Formula: INT = rP

  • Future Value (FV): Total value after 1 year.

    • Formula: FV = P + (n * rP)

    • Reiteration of the accumulated value with interest over time.

Page 3: Future Value with Simple Interest (Extended)

  • If there are n periods, the calculation expands:

    • Formula: FV = P(1 + nr)

    • Illustrates future value considering multiple periods at simple interest.

Page 4: Future Value with Compound Interest

One Period Ahead

  • Formula for FV one period ahead:

    • FV1 = P + rP = P(1 + r)

    • Identical to simple interest for single periods.

Two Periods Ahead

  • Formula for FV two periods ahead:

    • FV2 = FV1 + rFV1 = P(1 + r)²

  • Generalizing to n periods ahead:

    • Formula: FVN = P(1 + r)ⁿ

Page 5: Discounting Future Cash Flows

Finding Present Value

  • Present Value (PV) of future cash flows is calculated using:

    • PV = FVN / (1 + r)ⁿ

    • Example:

      • Cost: $10,000 today

      • Benefits: $5,000 & $6,000 in years 1 & 2

      • Discount rate (r): 10%

  • Net Present Value (NPV): Essential to assess value over time.

Page 6: Understanding Inflation in Financial Calculations

Impact of Inflation on Interest Rate

  • Nominal Interest Rate (i) compared to Real Interest Rate (r):

    • Formula: 1 + i = (1 + r)(1 + p)

    • Simplification when rates are small:

    • Approximation: i ≈ r + p

  • Highlights the importance of including inflation in financial analysis.

Page 7: Present Value of an Annuity

NPV Representation

  • Net Present Value and its formula involving three components:

    • Payment (either inflow or outflow)

    • Time horizon

    • Discount rate

  • When calculated using nominal terms, maintains accuracy unless disparity in inflation rates exists for costs/benefits.

Page 8: Internal Rate of Return (IRR)

Concept of IRR

  • IRR: The rate of return that yields a NPV of zero, crucial for investment decisions.

  • Decision Rule: Invest if IRR exceeds the next best alternative investment return.

Page 9: Considerations with IRR

Situations of Use

  • Effective when payments (PMT) remain constant.

  • Caution with projects featuring uneven cash flows or significant environmental costs; validate with NPV to avoid misleading results.

Page 10: Key Takeaways on IRR

  • IRR: Dominant metric in real estate finance.

  • The necessity to understand IRR's foundational basis in Present Value.

Page 11: Van Pool Example Introduction

Case Study: Van Service for Senior Citizens

  • Scenario of evaluating ownership (purchase) vs leasing of vans.

  • Utilize Excel for modeling cost comparisons between options.

Page 12: Purchase Option Details

Cost Structure

  • Purchase cost per van: $200,000 with a 10% down payment.

  • Loan interest rate: 4%

  • Depreciation: 25% value loss immediately, followed by 10% annual depreciation.

  • Ownership culminates after three years, allowing for sale of depreciated value.

Page 13: Lease Option Details

Lease Specifications

  • Lease duration: 3 years with 5% down payment, forfeiting buyout option.

  • Annual lease payment: $34,000

  • Conditions: 15,000-mile annual limit; overage incurs penalties ($0.25/mile).

Page 14: Additional Assumptions

  • Insurance, maintenance, and operational costs are disregarded in calculations.

  • Agency’s investment strategy focuses on a money market account with a 5% compound interest rate.

  • All figures represent “real” values, adjusting for inflation.