Investment Analysis: Time Value of Money

Investment Analysis

Time Value of Money

• Present Value (PV): The current value of a future cash flow.
• Future Value (FV): The value of a current cash flow at a future date.
• Net Present Value (NPV): The difference between the PV of future cash inflows and the PV of future cash outflows.

Calculating PV and FV

• Formulae:
  • PV = FV / (1 + r)^n
  • FV = PV x (1 + r)^n
  • NPV = Σ (CFt / (1 + r)^t) where: - r = discount rate - n = number of periods - CFt = cash flow at time t - t = time period

Discounted Cash Flow (DCF) Analysis

• Discount Rate: The rate used to discount future cash flows to their present value.
• DCF Formula:
  • NPV = Σ (CFt / (1 + r)^t)
• Interpretation:
  • NPV > 0: Investment is profitable
  • NPV < 0: Investment is not profitable
  • NPV = 0: Investment breaks even

Payback Period

• Definition: The time it takes for an investment to generate cash flows equal to its initial cost.
• Formula:
  • Payback Period = Initial Investment / Annual Cash Flow
• Interpretation:
  • Shorter payback period indicates faster return on investment

Internal Rate of Return (IRR)

• Definition: The discount rate at which the NPV of an investment is zero.
• Formula:
  • IRR = r when NPV = 0
• Interpretation:
  • IRR > Cost of Capital: Investment is profitable
  • IRR < Cost of Capital: Investment is not profitable
  • IRR = Cost of Capital: Investment breaks even

Investment Analysis

Time Value of Money

• Present value (PV) is the current value of a future cash flow, taking into account the time value of money.
• Future value (FV) is the value of a current cash flow at a future date, also considering the time value of money.
• Net present value (NPV) is the difference between the PV of future cash inflows and the PV of future cash outflows, measuring the profitability of an investment.

Calculating PV and FV

• The formula to calculate PV is: PV = FV / (1 + r)^n, where r is the discount rate and n is the number of periods.
• The formula to calculate FV is: FV = PV x (1 + r)^n, using the same variables.
• The formula to calculate NPV is: NPV = Σ (CFt / (1 + r)^t), where CFt is the cash flow at time t and t is the time period.

Discounted Cash Flow (DCF) Analysis

• The discount rate is the rate used to discount future cash flows to their present value.
• The DCF formula is: NPV = Σ (CFt / (1 + r)^t), where r is the discount rate.
• If NPV is greater than 0, the investment is profitable; if NPV is less than 0, the investment is not profitable; and if NPV is equal to 0, the investment breaks even.

Payback Period

• The payback period is the time it takes for an investment to generate cash flows equal to its initial cost.
• The formula to calculate the payback period is: Payback Period = Initial Investment / Annual Cash Flow.
• A shorter payback period indicates a faster return on investment.

Internal Rate of Return (IRR)

• The internal rate of return (IRR) is the discount rate at which the NPV of an investment is zero.
• The formula to calculate IRR is: IRR = r when NPV = 0.
• If IRR is greater than the cost of capital, the investment is profitable; if IRR is less than the cost of capital, the investment is not profitable; and if IRR is equal to the cost of capital, the investment breaks even.