Time Value of Money

By Zeke Anders on November 29, 2023

The foundation of investing is the time value of money, but it can be tricky to understand. The story of finance is translating money across time. A great example of this is actually plants, The cheapest way to start a garden would be to buy seeds. For slower-growing plants, like trees, it could take a long time to get from a seed to the plant height that you want. Instead of waiting, you could pay more for a plant that has already grown for a few years. You have exchanged money for time, by buying a more mature plant. The time value of money in finance is very similar to this example.

If I offered you $100 today, or $100 in a year, which would you prefer? That’s not a trick question, you’d obviously prefer $100 today. What if I offered you $100 today or $105.24 in one year? Or $95.02 today or $100 in one year? That becomes a more difficult question to answer. I calculated those numbers using the yield on a 1-year Treasury bill (5.24% as of November 28, 2023), which is essentially the risk-free rate for a one-year investment. If you need the $100 today, you might accept that offer. If you don’t, you might wait and collect the interest.

If you select payment in one year, you have essentially loaned me $100. Alternatively, I’ve given you an IOU for $100. If you doubt my ability to pay you in one year, you might want more yield than the risk-free rate, 6% for example. The extra yield above the risk-free rate is a risk premium. That is the return you require for the risk you are taking.

When you purchase a bond, you are making a loan to a government or a business. For example, you pay $1,000 for a bond, with the expectation the bond issuer (the borrower) will pay you back $1,000 at the end of the term and pay interest along the way. The borrower now has $1,000 to use to grow their business, and you receive regular interest payments. The interest rate includes the risk-free rate as well as a risk premium. Borrowers that are more financially stable will pay less interest, and companies that are less stable will pay higher interest rates. There’s a formula to calculate the present value of a stream of payments like a bond. We won’t cover the formula itself, but essentially the present value of the future payments from the bond will be the purchase price.

Stocks can be valued in a similar way. The fundamental way to value stocks is the dividend discount model. Many companies pay a dividend to shareholders. Let’s say, for example, you are looking at a share of stock that pays a $2 annual dividend. How much should you pay for that stock? You wouldn’t pay the exact value of those dividends over time, (let’s say $40 for a 20-year period) because that doesn’t account for the time value of money, that $2 in one year is not worth as much as $2 today. Therefore, you’ll use the present value formula with a discount rate, also called the required rate of return. That discount rate includes the risk-free rate as well as a risk premium, just like the bond we discussed above. The risk premium is somewhat subjective. Different investors will have a different perspective on the riskiness of a given business, and thus may have a higher or lower required rate of return. To illustrate the time value of money, the table below shows the value of each $2 dividend using a 7% discount rate over 20 years. To calculate the value of this stock assuming perpetual dividends, you simply take $2 and divide by 7%, which equals $28.57. That’s the value you would theoretically pay for the stock today, ignoring the net value of assets of the business.

The added challenge with stocks is that, unlike coupon payments on bonds, dividends are not fixed or guaranteed. Companies can increase, decrease, or completely stop their dividend over time. This is why it is necessary to estimate the trajectory of the earnings of the business.

The point of this exercise is not to make you a stock analyst, but rather to demonstrate the concept of time value of money. This same concept applies for expected expenditures too. For example, if you know you’ll need to spend $100 in one year, based on the risk-free rate that expenditure is equivalent to $95.47 today.

One dynamic you may notice, is that as interest rates go up, the present value of expenditures and income streams decreases. For example, our $2 dividend above with a 10% required rate of return is only worth $20 instead of $28.57 ($2 divided by 10% equals $20). If you require a higher rate of return on your investment, you’ll want to pay less for it today. At 10% our $100 expenditure is only $90.91 today. This reflects the fact that you can, in this hypothetical, earn 10% on your assets while you wait to pay this expense.

How is this relevant to individuals? Retirement is a series of expenditures, saving for college is a series of expenditures, and there are many other examples. We can find the present value of these liabilities to determine how much we need to save today, or periodically over time to meet these liabilities. It can also tell us how much life insurance we need, and the lump sum value of Social Security or a pension.

Interest rates rose considerably last year. This hurt bond and stock prices as we discussed in our year-in-review piece. On the other hand, the risk-free rate increased, and yields on bonds rose too. This makes the present value of our future liabilities smaller and allows us to get higher yields from more stable assets.  Understanding the time value of money is an important concept for investing and personal finance, and hopefully this piece helped provide a basic overview.

Zeke Anders – Planning Specialist | zanders@twickenhamadvisors.com

Disclaimer

Securities are offered through Hightower Securities, LLC member FINRA and SIPC. Hightower Advisors, LLC or any of its affiliates do not provide tax or legal advice. This material is not intended or written to provide and should not be relied upon or used as a substitute for tax or legal advice. Information contained herein does not consider an individual’s or entity’s specific circumstances or applicable governing law, which may vary from jurisdiction to jurisdiction and be subject to change. Clients are urged to consult their tax or legal advisor for related questions.