Time Value Of Money

Section: Time Value of Money Estimated study time: 45 minutes Content: The time value of money (TVM) is the foundational concept underpinning nearly all of finance: a dollar available today is worth more than a dollar available in the future, because today's dollar can be invested to earn a return. The core TVM variables are: present value (PV), future value (FV), interest rate per period (I/Y or r), number of periods (N), and periodic payment (PMT). Mastery of TVM calculations is essential for CFA Level 1 — it underpins bond valuation, equity valuation, capital budgeting, and retirement planning problems throughout the curriculum. The basic future value formula is: FV = PV × (1 + r)^N. The present value formula reverses this: PV = FV / (1 + r)^N. These formulas assume a single lump sum; annuity problems add a PMT component. An annuity is a series of equal payments made at regular intervals. An ordinary annuity (annuity-immediate) makes payments at the end of each period, while an annuity due makes payments at the beginning. The present value of an ordinary annuity is: PV = PMT × [1 – (1 + r)^(–N)] / r. The future value is: FV = PMT × [(1 + r)^N – 1] / r. An annuity due is worth more than an ordinary annuity by a factor of (1 + r) because each payment compounds for one additional period. A perpetuity is an annuity that pays forever; its present value is simply: PV = PMT / r. For example, a preferred stock paying $2 per year with a required return of 8% is worth $2 / 0.08 = $25. Recognizing whether a problem involves a…