Present Value

Overview

Present Value calculations are a calculation that takes a series of cash flows that occur at different times in the future and produces a single number , which represents the value of those cash flows today. Future value is similar to present value, but it calculates what the value of a series of cash flows would be at a future date instead of today.

A simple way to think about present value/future value calculations is to assume that there exists a bank that will freely grant risk free loans/deposits at the current interest rate. When such a bank is available, any series of cash flows can be exchanged with the bank for a series of cash flows occuring at other times.

Example

As an example, suppose you have a contract that will pay you 100 dollars in a year. However, you want the money today. You can get the money today by taking out a loan from the bank such that it matures in a year at the point in time when you receive the 100 dollars and you can pay off the loan.

Because of the interest you have to pay, you will not be able to borrow the full 100 dolars, rather, you will borrow a lesser amount such that the principal plus the accrued interest in one year is equal to 100 dollars. The amount of money that you can receive today in the form of loan would be the present value of the 100 dollars 1 year in the future.

Suppose the annual interest rate today is 10%, then the amount of money that I can borrow is or We call the loan value, the present value of the $100 cash flow I expect to receive in 1 year.

Topics

• Future Value - the flip side of prevent value, the future value is the value of a financial contract at some point in the future.
• Calculations - demonstrates basic present value calculations
• Quotation Conventions
• Continuous Time Value - the most robust way to do present value calculations is to work with continuous compounding.
• Present Value of a Portfolio - shows how present value applies to a portfolio of instruments.
• Discount Curve

Additional Topics

• Spread Analysis - analyzes the spread (difference) between the rate that an instrument receives and the disount curve.
• Weighted Discount - when a portfolio consists of instruments with different rates, a weighted discount rate of the individual weights replicates the present value of the portfolio.
• Stochastic Cash Flow - when the cash flows are risky (random) the choice of discount rate has to be adjusted to account for the risk.