Tutorial: Present Values and Debt Pricing

Tutorial: Present Values and Debt Pricing

This material involves a review of topics covered during your FIN 214 course. You may also find more information on it in Chapter 6 of the AC 305/306 textbook (the first half of the book may be accessed through the "Read, Study, & Practice" module of WileyPlus).

When you are considering any type of long-term investment - whether you are making the investment in a project, or making an investment in a long-term asset, or attempting to get long-term financing for your own projects or investments - it is not OK to consider the cash flows in terms of current dollars. The existence of inflation means that a dollar today will buy more than that same dollar next year. The year-to-year effect may be small when inflation is low, as it is now, but when your investment horizon is measured in decades instead of months, that inflation effect can get very large. If you are not sure what I mean by "large" - just ask your parents (or aunts, uncles, friends who are 15-20 years older than you) how much they paid for a gallon of gas when they were in college. For me, I graduated from college in 1996, and in that year, I usually paid about $1.30 for the gallon of gas that now costs me $3.50. I paid about $1.00 per pound for a whole chicken. Now that same chicken costs $1.35 per pound. That's a 30% increase for the chicken, over the last 16 years...and for the gas? It's a 169% increase over the same period.

You can see from this example that inflation is not the only thing that makes prices go up over time, because if it was, then the bread would increase by 30% and so would the gas. This is not the case (30% vs 169%). So there are other factors under consideration. With the gas, the "other factors" have to do with long-term supply of the commodity, as well as the geopolitical situation.

In this course, we're primarily concerned with money - so what kinds of things make the "price" of money increase? By "price" of money, I'm referring to the price that someone who wants to use someone else's money has to pay in exchange for that privilege. The interest that you receive on a savings account is the "price" of money for the bank - they have to pay this to you in order for you to let them use your money. The dividends that a company pays, or its commitment to raising the share price, are the "price" of money for a company that issues stock - they have to pay this to the investors in order to get to use the investor's financial capital. In the business world, we refer to the "price" of money as a "return". A return is what an investor gets in exchange for letting someone else use their money for a while.

Just like everything else, the return is subject to inflation...because you can probably buy more gas with $1 today than you will be able to 10 years from now. The return is also affected by factors like risk. If you, the investor, are less certain of the company's ability to deliver the promised return, you're going to charge them more, or you're going to demand that they deliver the return more quickly, than you would if you were more confident in their ability to pay for your money.

This is why we don't look at long-term investments of any kind in terms of current dollars, but in terms of present values. We want to know how much the investment - after we factor in how long the investment period is and how risky the project or company is - is worth in current dollars.

How exactly you do this is the same, regardless of whether you're looking to sell bonds and need to price them, or you're looking to buy bonds and need to price them, or you're buying a long-lived asset, or making a capital budgeting decision. You should always base these decision on an analysis of present values - not current dollars.

The process of computing present values is also exactly the same. The first thing you need to do is determine what kind of cash flow you're looking at. Are you lending (borrowing) a roll of cash today, and will be getting it back (repaying it) in a lump sum in several years? Or are you lending (borrowing) a lump of cash today and you expect a to receive (to make) a series of payments over the next years, with maybe a lump sum as well at the end?

You need to figure this out, because the time value of money is sensitive to exactly how much time you're talking about.

Example 1

If you put down $10,000 today and expect to get that $10,000, plus another $1,000 in interest, all at the same time, five years from now, there's only a single time-value adjustment you need to make (and it will affect the repayment of the principle, and the payment of interest, equally).

Example 2

But what if you put down $10,000 today, and expect to get that $10,000 in five years, and in the meantime, you're expecting to get 5 annual payments of $200 in interest? That's actually five different time value adjustments...because $1 next year is not worth $1 a year after that, and that's not worth $1 a year after that, etc.

Fortunately, we have some shortcuts. We have present value tables (in the book) or present value functions (on your financial calculator or in Excel or on the web) that will help you do this. But before you use any of these tools, you need to use your brain to identify several piece of information.

First, as discussed above, you need to know the amount and timing of payments to be made or expected to be received. In the first example, you expect $11,000 five years from now. In the second, you expect $200 in year 1, $200 in year 2, $200 in year 3, $200 in year 4, and $10,200 in year 5.