# 15.13: Time Value of Money


### Learning Outcomes

• Discuss the time value of money

A dollar today is worth more than a dollar a year from now. If someone handed you a $1000 today, and you invested it or they offered you$1000 a year from now, which would you choose? The obvious answer is to take it now, right? What will happen when you put that money into an investment account? It will grow because you will get interest on it! If you stick the same $1000 in a drawer, it will not gain that value, and the buying power will be less than today. The interest rate is an important component of the time value of money. ### Watch It A YouTube element has been excluded from this version of the text. You can view it online here: http://pb.libretexts.org/afm-2/?p=588 Present value can be calculated using the following equation: $\begin{array}{rcl}PV&=&FV\frac{1}{\left(1+r\right)^n}\\\\FV&=&\text{Future value}\\r&=&\text{rate of return}\\n&=&\text{number of periods}\end{array}$ So if you had the option of taking$1000 today, or $2000 in 10 years, and the interest rate is 8%, which would you take? We can calculate that as follows: $\begin{array}{rcl}PV&=&1000\\r&=&8\%\\n&=&10\text{ years}\end{array}$ So, if you follow the chart to page 2.This chart is the time value of$1, so we will need to multiply by 1000 to find our value!

Find 10 periods at 8% interest. At the end of the first period, your $1000 would be worth$1080 with the 8% interest, right? At the end of the second year it would be worth $1166.40 and so on. So at the conclusion of the 10 year period, your$1,000 at 8% interest would be worth $2,158.90 based on the time value of money. SO, now, would you take the$1,000 now, or wait and get $2,000 in 10 years? From this example, it would be better to take the$1,000 NOW and invest it yourself! How would your answer change if the interest rate was 5%? Take a few options and practice with it!!

When we look at money this way, it is important to look at capital budgeting decisions on the basis of WHEN the cash flow will come back to us on an investment.  If we invest $1000 today in a new piece of equipment that will not return our investment for 10 years. Is this a good decision? What if we have an alternative that costs$10,000, but we will get our money back on this one in 2 years? Which piece of equipment should we purchase?

### Practice Questions

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• Time Value of Money. Authored by: Freedom Learning Group. Provided by: Lumen Learning. License: CC BY: Attribution