# Investment Banking: How to Determine a Bond’s Present Value

Valuing bonds for investment banking relies on the basic principle of *present value* (a dollar to be received today is worth more than a dollar to be received tomorrow or at some point in the future). The rationale is that a dollar received today can be invested to earn interest and will be worth more at a later date.

It may seem like a great deal of math is required to value bonds — and it is — but the mathematical proficiency needed is around a junior-high level, so don’t be intimidated by it!

The present value of an amount to be received one year (or one period) in the future is

Where *r* is the appropriate interest rate or discount rate (more about that in a bit).

So, the present value of a dollar to be received a year from today if the appropriate interest rate is 6 percent is:

In other words, a rational investor shouldn’t care whether she receives $0.9434 today or $1.00 a year from now. The difference between the two amounts — $0.0566 — represents the interest she could earn on the $0.9434 at the rate of 6 percent. This simple idea is the basis for all discounted cash-flow models in finance and investments.

Extending this idea beyond a year, the present value of a dollar to be received in *two* years is

The subscript 2 after Future Value indicates that the amount is to be received two periods (or two years) from today, and the superscript 2 after (1 + *r*) indicates that interest on that amount could be earned for two periods (or two years) if it was received today instead of in two years.

So, the present value of a dollar to be received in two years if the appropriate interest rate is 6 percent is

In other words, a rational investor shouldn’t care whether he receives $0.8900 today or $1.00 two years from now. The difference between the two amounts — $0.1100 — represents the interest he could earn on the $0.8900 at the rate of 6 percent compounded for two years.

Compounding refers to the ability to reinvest the interest earned in year 1 and earn interest in year 2 on both the original amount and the year 1 interest.

So, the present value of a dollar to be received in ten years if the appropriate interest rate is 6 percent is

Again, a rational investor shouldn’t care whether she receives $0.5584 today or $1.00 in ten years. The difference between the two amounts — $0.4416 — represents the interest she could earn on the $0.5584 at the rate of 6 percent compounded annually.

By the way, this is an illustration of compound interest, a concept that none other than Albert Einstein called the eighth wonder of the world.