PRESENT VALUE

                          PRESENT VALUE 

What Is Present Value – PV?

Present value (PV) is the current value of a future sum of money or stream of cash flows given a specified rate of return. Future cash flows are discounted at the discount rate, and the higher the discount rate, the lower the present value of the future cash flows. Determining the appropriate discount rate is the key to properly valuing future cash flows, whether they be earnings or obligations

Problem

Suppose you are depositing an amount today in an account that earns 5% interest, compounded annually. If your goal is to have $5,000 in the account at the end of six years, how much must you deposit in the account today?

Solution

The following information is given:

• future value = $5,000
• interest rate = 5%
• number of periods = 6

We want to solve for the present value.

present value = future value / (1 + interest rate)^{number of periods}

or, using notation

PV = FV/ (1 + r)^t

Inserting the known information,

PV = $5,000 / (1 + 0.05)⁶

PV = $5,000 / (1.3401)

PV = $3,731

We can use the present value table (or table of discount factors) to solve for the present value.

PV = FV (discount factor for r and t)

The discount factor, from the table, is 0.7462. Therefore,

PV = $5,000 (0.7462)

PV = $3,731

PV Formula and Calculation

$\begin{aligned} &\text{Present Value} = \dfrac{\text{FV}}{(1+r)^n}\\ &\textbf{where:}\\ &\text{FV} = \text{Future Value}\\ &r = \text{Rate of return}\\ &n = \text{Number of periods}\\ \end{aligned}$