💰Corporate Finance Analysis Unit 6 – Time Value of Money & Cash Flow Analysis

Key Concepts

• Time value of money (TVM) principle states that money available now is worth more than an identical sum in the future due to its potential earning capacity
• Present value (PV) represents the current worth of a future sum of money or stream of cash flows given a specified rate of return
• Future value (FV) calculates the value of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today
• Annuity is a series of equal payments or receipts that occur at evenly spaced intervals over a fixed period of time
  • Ordinary annuity has payments occurring at the end of each period
  • Annuity due has payments occurring at the beginning of each period
• Perpetuity is a constant stream of identical cash flows with no end
• Discount rate is the rate of return used to discount future cash flows back to their present value
• Compounding frequency refers to how often interest is calculated and added to the principal (annually, semiannually, quarterly, monthly, daily)

Time Value Basics

• Money has a time value because of the opportunity to earn interest or a return on investment over time
• A dollar today is worth more than a dollar in the future because of its potential to grow and earn a return if invested
• The relationship between the value of money today and the value of money in the future is determined by the discount rate
  • A higher discount rate decreases the present value of future cash flows
  • A lower discount rate increases the present value of future cash flows
• Simple interest is calculated on the principal only, while compound interest is calculated on the principal and the accumulated interest from previous periods
• The rule of 72 is a quick way to estimate how long it will take to double your money at a given interest rate (divide 72 by the annual rate of return)
• Inflation erodes the purchasing power of money over time, so it's important to consider inflation when making long-term financial decisions
• The real rate of return adjusts the nominal rate of return for inflation to determine the actual purchasing power of the return

Present Value Calculations

• Present value (PV) is the current value of a future sum of money or stream of cash flows given a specified rate of return
• The basic formula for calculating present value is: $PV = \frac{FV}{(1+r)^n}$
  • PV = Present Value
  • FV = Future Value
  • r = discount rate (or interest rate)
  • n = number of periods
• Net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time
  • A positive NPV indicates that the projected earnings generated by a project or investment exceed the anticipated costs
  • NPV is used to analyze the profitability of a projected investment or project
• Present value of an annuity (PVA) is the present value of a series of equal payments or receipts that occur at evenly spaced intervals over a fixed period of time
  • The formula for PVA is: $PVA = PMT \times \frac{1 - (1 + r)^{-n}}{r}$
    • PMT = periodic payment
    • r = discount rate (or interest rate)
    • n = number of periods
• Present value of a perpetuity is a constant stream of identical cash flows with no end
  • The formula for the present value of a perpetuity is: $PV = \frac{C}{r}$
    • C = periodic payment
    • r = discount rate (or interest rate)

Future Value Calculations

• Future value (FV) calculates the value of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today
• The basic formula for calculating future value is: $FV = PV \times (1+r)^n$
  • FV = Future Value
  • PV = Present Value
  • r = interest rate (or rate of return)
  • n = number of periods
• Future value of an annuity (FVA) calculates the future value of a series of equal payments or receipts that occur at evenly spaced intervals over a fixed period of time
  • The formula for FVA is: $FVA = PMT \times \frac{(1 + r)^n - 1}{r}$
    • PMT = periodic payment
    • r = interest rate (or rate of return)
    • n = number of periods
• Future value of a growing annuity calculates the future value of a series of payments or receipts that grow at a constant rate over time
  • The formula for the future value of a growing annuity is: $FVGA = PMT \times \frac{(1 + g)}{(r - g)} \times [(1 + r)^n - (1 + g)^n]$
    • PMT = initial payment
    • r = interest rate (or rate of return)
    • g = growth rate
    • n = number of periods
• Rule of 72 estimates the number of years required to double the invested money at a given annual rate of return (divide 72 by the annual rate of return)

Annuities and Perpetuities

• An annuity is a series of equal payments or receipts that occur at evenly spaced intervals over a fixed period of time
  • Ordinary annuity has payments occurring at the end of each period
  • Annuity due has payments occurring at the beginning of each period
• Present value of an annuity (PVA) is the present value of a series of equal payments or receipts that occur at evenly spaced intervals over a fixed period of time
  • The formula for PVA is: $PVA = PMT \times \frac{1 - (1 + r)^{-n}}{r}$
    • PMT = periodic payment
    • r = discount rate (or interest rate)
    • n = number of periods
• Future value of an annuity (FVA) calculates the future value of a series of equal payments or receipts that occur at evenly spaced intervals over a fixed period of time
  • The formula for FVA is: $FVA = PMT \times \frac{(1 + r)^n - 1}{r}$
    • PMT = periodic payment
    • r = interest rate (or rate of return)
    • n = number of periods
• A perpetuity is a constant stream of identical cash flows with no end
  • The formula for the present value of a perpetuity is: $PV = \frac{C}{r}$
    • C = periodic payment
    • r = discount rate (or interest rate)
• Annuities and perpetuities are commonly used in financial planning, such as retirement planning, loans, and leases

Cash Flow Analysis Techniques

• Cash flow analysis is the study of the movement of cash into and out of a business, project, or financial product
• Net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time
  • A positive NPV indicates that the projected earnings generated by a project or investment exceed the anticipated costs
  • NPV is used to analyze the profitability of a projected investment or project
• Internal rate of return (IRR) is the discount rate that makes the net present value (NPV) of all cash flows equal to zero in a discounted cash flow analysis
  • IRR is used to evaluate the attractiveness of a project or investment
  • If the IRR of a project exceeds its cost of capital, the project is considered desirable
• Payback period is the length of time required to recover the cost of an investment
  • The payback period is calculated by dividing the initial investment by the annual cash inflow
  • A shorter payback period is generally considered more desirable
• Discounted payback period is the length of time required to recover the cost of an investment while accounting for the time value of money
  • The discounted payback period is calculated by discounting the future cash flows to their present value and then determining the payback period
• Profitability index (PI) is a measure of a project's or investment's attractiveness
  • PI is calculated by dividing the present value of future cash flows by the initial investment
  • A PI greater than 1 indicates that the project is profitable, while a PI less than 1 indicates that the project is not profitable

Real-World Applications

• Capital budgeting decisions involve evaluating long-term investments, such as new equipment, facilities, or product lines, using cash flow analysis techniques like NPV and IRR
• Loan and lease analysis involves determining the present value of a series of payments over time, such as in mortgages, car loans, or equipment leases
• Retirement planning uses the concepts of annuities and perpetuities to estimate the present value of future cash flows needed to support a desired lifestyle in retirement
• Bond valuation employs present value calculations to determine the fair value of a bond based on its future cash flows (coupon payments and face value) and the investor's required rate of return
• Stock valuation methods, such as the dividend discount model (DDM), use present value calculations to estimate the intrinsic value of a stock based on its expected future dividends
• Mergers and acquisitions (M&A) rely on cash flow analysis techniques to determine the value of a target company and the potential synergies and benefits of the transaction
• Insurance companies use present value calculations to determine the premiums needed to cover future claims and expenses while still generating a profit

Common Pitfalls and Tips

• Remember to use the appropriate discount rate or interest rate for the specific situation, considering factors such as risk, inflation, and opportunity cost
• Be consistent with the compounding frequency (annually, semiannually, quarterly, monthly, daily) when performing calculations
• Double-check the inputs and assumptions used in the calculations, as small errors can lead to significant differences in the results
• Consider the limitations of each cash flow analysis technique and use multiple methods to gain a more comprehensive understanding of the investment or project
• Be aware of the impact of taxes on cash flows and incorporate them into the analysis when appropriate
• Understand the sensitivity of the results to changes in key assumptions, such as the discount rate or growth rate, and perform sensitivity analysis to assess the potential impact of these changes
• When comparing investments or projects, ensure that the cash flows are measured over the same time period and using the same assumptions for a fair comparison
• Consider non-financial factors, such as strategic fit, risk, and sustainability, in addition to the financial analysis when making investment or project decisions