Time Value of Money and Discounted Cash Flows

Introduction to Time Value of Money (TVM)

  • Core Concept: The Time Value of Money is the principle that a dollar today is worth more than a dollar in the future because of its potential earning capacity (interest, investments) or loss of value (inflation).

  • Foundational Variables:     * Present Value (PVPV)     * Future Value (FVFV)     * Interest rate per period (rr)     * Number of periods (nn)     * Periodic payments (PMTPMT)

  • Real Estate Significance: TVM is essential for long-term decisions such as mortgage calculations (20−3020-30 years), valuing rental income, and property appreciation.

The 6 Key TVM Formulas

  • Future Value of a Lump Sum (FVLS): Determines how much a single amount today grows over time.     * Formula: FV=PV×(1+r)nFV = PV \times (1 + r)^n

  • Present Value of a Lump Sum (PVLS): Determines current worth of a future amount.     * Formula: PV=FV(1+r)nPV = \frac{FV}{(1 + r)^n}

  • Future Value of an Annuity (FVA): Value of regular, equal payments growing over time.     * Formula: FV=PMT×(1+r)n−1rFV = PMT \times \frac{(1 + r)^n - 1}{r}

  • Present Value of an Annuity (PVA): Today's value of a series of future payments (e.g., used by banks for loan affordability).     * Formula: PV=PMT×1−(1+r)−nrPV = PMT \times \frac{1 - (1 + r)^{-n}}{r}

  • Sinking Fund Payment (SFP): Periodic payment needed to reach a future lump sum target.     * Formula: PMT=FV×r(1+r)n−1PMT = FV \times \frac{r}{(1 + r)^n - 1}

  • Capital Recovery Payment (CRP) / Loan Payment: Periodic payment (principal and interest) needed to repay a loan.     * Formula: PMT=PV×r(1+r)n(1+r)n−1PMT = PV \times \frac{r (1 + r)^n}{(1 + r)^n - 1}

Discounted Cash Flows (DCF) and Valuation

  • Definition: A method to estimate investment value by discounting expected future cash flows (rents, sales proceeds) to their present value.

  • Formula Basis: NPV=⨄CFt(1+r)tNPV = \textstyle \biguplus \frac{CF_t}{(1 + r)^t}

  • Components:     * Inflows: Rental income, signage/tower income, and terminal value (property sale).     * Outflows: Repairs, taxes, vacancies, and mortgage payments.

  • Net Present Value (NPV): The sum of the PV of each cash flow. If NPV > 0 (or exceeds the purchase price), the project is considered a good investment.

Profitability Metrics: IRR and MIRR

  • Internal Rate of Return (IRR): The discount rate that makes the NPVNPV of all cash flows equal to zero (00).     * Limitation: It assumes all positive cash flows are reinvested at the same (often high) IRR rate, which is often unrealistic.

  • Modified IRR (MIRR): Fixes IRR's assumptions by using a dedicated finance rate for borrowing and a reinvestment rate for positive cash flows.     * Advantage: Provides a more conservative and realistic return estimate for real estate properties (e.g., reinvesting rents at 8%8\% instead of a theoretical 20%20\%+).

Practical Examples and Assumptions

  • Melbourne Real Estate Scenario: A investment of $400,000\$400,000 in rental property might yield an IRR of approximately 18−22%18-22\%, but the MIRR might be closer to 15−19%15-19\% when using realistic reinvestment rates.

  • Critical Assumptions: Accurate valuations require realistic projections for rent growth (e.g., 3−5%3-5\%), vacancy rates, and the required discount rate (7−10%7-10\%) based on risk.