# Valuation With a Gumball Machine

Updated: Mar 7, 2021

On your 15th birthday, your uncle makes you an offer. H's willing to give you an annuity or a gumball machine. The choice is yours.

You want to know which is more valuable so you gather the following information.

So, you have a choice between a riskier \$15 and a safer \$10. How do you choose?

You decide that in order to make your choice you're going to have to value each asset. How do you do that? The key concept when valuing cash flows is the time value of money. Here's how it works.

Would you rather 100 dollars now or 100 dollars a year from now? Any sane person would of course choose \$100 now.

Let's make it more complicated, I'll give you \$100 now or \$110 a year from now. Now it's harder to make a decision. Clearly, you prefer money sooner rather than later, but you are also willing to wait to get more money.

Let's imagine that at your local bank you can get 15% interest on your money with no risk. If that's true you would take the \$100 dollars now and invest it at15% to have \$115 in a year, more than the \$110 offered. In other words, the future value of \$100 is \$115.

We can also look at the situation from the opposite standpoint, what is the value of \$110 a year from now today if the risk-free rate is 15%. To find this value we will use discounting, in the case would divide \$110/ (1+15)%. The present value is \$95.65. (the value of a future payment today)

Perfect, now we know how to move money through time. In that case, if we want to figure how much our bubble gum machine and annuity are worth all we have to do is move all of the payments we'll receive back to today's date.

We call our local banker and ask what the interest rates are on Low risk and Medium risk investments. He tells us that low risk offers 5% and medium risk offers 7%. With that info, we can find the PV of the cash flow for each option, because both have one payment forever they are both valued as perpetuities.

You decide that you would like to choose the Gumball machine because it appears to have a higher present value, meaning it appears to compensate you more generously for the risk you have taken.