Time Value of Money Concepts

The time value of money (TVM) is the foundation of all investment analysis. Every valuation, every comparison, and every recommendation starts here.

The Core Principle

  • A dollar received today is worth more than a dollar received in the future
  • Why? Because today's dollar can be invested and earn a return
  • The cost of waiting is called the opportunity cost: the return you give up by not having the money now
  • This principle drives how we value bonds, stocks, projects, and retirement savings

Future Value (FV)

Future value tells you what a current investment will be worth at a specific point in the future, assuming a given rate of return.

  • Demonstrates the power of compounding: earning returns on your returns
  • Two factors increase future value:
    • Higher rates of return: more growth per period
    • Longer time periods: more periods for compounding to work
  • Used to project retirement savings goals and investment growth targets

Think of it this way: If you invest $1,000 at 10% per year, after one year you have $1,100. In year two, you earn 10% on $1,100 (not just the original $1,000), so you get $1,210. That extra $10 is compounding at work, and it snowballs over time.

Exam Tip: Gotchas

  • Doubling the time period does NOT double the future value. Compounding makes it grow faster than a simple doubling. Both rate AND time matter.

Net Present Value (NPV)

Net present value is the difference between the present value of an investment's future cash inflows and the initial cost to make that investment.

  • Formula: NPV = Present Value of Cash Inflows - Initial Investment
  • NPV answers: "Is this investment worth more than it costs?"

Decision Rules:

NPV ResultMeaningDecision
NPV > 0Investment adds value (returns exceed the required rate)Accept
NPV < 0Investment destroys value (returns fall short)Reject
NPV = 0Investment earns exactly the required rate of returnIndifferent
  • NPV is considered the preferred method for evaluating investments when NPV and IRR give conflicting signals (for example, when comparing mutually exclusive projects of different sizes)

Exam Tip: Gotchas

  • NPV is a dollar amount, not a percentage. IRR is the percentage rate. The exam tests whether you can distinguish the two.
  • NPV > 0 does not mean the investment is risk-free. It means expected returns exceed the required rate of return after accounting for the discount rate.

Internal Rate of Return (IRR)

The internal rate of return is the discount rate that makes the net present value (NPV) of all cash flows equal to zero.

Think of it this way: IRR answers "What rate of return is this investment actually earning?" If you need at least 8% to justify the risk and the IRR comes back at 12%, the investment clears your bar.

  • For bonds, IRR equals the yield to maturity (YTM)
  • Used to evaluate and rank competing investment opportunities

Decision Rule:

  • Accept if IRR > required rate of return (hurdle rate)
  • Reject if IRR < required rate of return

NPV vs. IRR: When They Conflict

  • For independent projects (choosing one doesn't block the other), NPV and IRR always agree
  • For mutually exclusive projects (you can only pick one), NPV and IRR can give different rankings
  • When they conflict, follow NPV. It measures the actual dollar value added

Exam Tip: Gotchas

  • IRR and YTM are the same concept applied differently. IRR is the general term for any investment's breakeven discount rate. YTM is IRR applied specifically to a bond's cash flows (coupon payments and par value at maturity).
  • When NPV and IRR conflict on mutually exclusive projects, follow NPV. NPV measures the actual dollar value added; IRR can mislead when comparing projects of different sizes.
  • IRR assumes reinvestment at the IRR itself, which may be unrealistic for very high-IRR projects.