Question

we can project what future value of investment will be if we make assumptions about growth and contribution rates. Also, we need to make assumptions about inflation and taxes. Even with all those assumptions which may turn out to be inaccurate, why is this planning exercise still useful with clients?

Answer 1

When making a business case to invest money into a new business project such as a possible acquisition, or an equipment purchase with a long holding period, it's important to have a way to calculate the potential return or profit you'll gain in the future. This part of the decision-making process can be handled with the future value formula and a few inputs.

You can use any of three different ways to work the formula and get your answer. Each method uses a different means of calculation, but the underlying formula is the same in all three instances. A business case might be complex, but the formula's use can be demonstrated with a very simple example. Say you have $100 to invest all at once, and you can get an interest rate of 5 percent. What will the value of your investment be at the end of the first year? The formula for the future value of this lump sum investment is as follows:

FV1 = (PV + INT) or PV(1 + I)ⁿ

The first part of this equation, (FV₁ = PV + INT) reads, "the future value (FV) at the end of one year, represented by the subscript letter ᵢ, equals the present value plus the added value of the interest at the specified interest rate.

The next formula presents this in a form that is easier to calculate the value added by the accrued interest ( PV(1 + I)ⁿ) which reads, "the present value (PV) times (1 + I)ⁿ, where l represents the interest rate and the superscript ⁿ is the number of compounding periods.

Now let's use the example from above. In one year, your $100 lump sum investment earning 5 percent interest per year will equal:

FV = $100(1 + 0.05) = $105

In this instance, you do not see a superscript (n) for compounding periods because at this point you're solving for the first year only. To determine the value of your investment at the end of two years, you would change your calculation to include an exponent representing the two periods:

FV = $100(1 + 0.05)² = $110.25

You can solve this, which is a compound interest problem, in a different way if your calculator can't handle exponents, by calculating the value at the end of the first year, then multiplying the outcome by the same 5 percent rate for the second year:

FV = [$100(1+0.05)] + [$105(1+0.05)] = $110.25

You can continue this process to find the future value of the investment for any number of compounding periods. Spelling out this process way, manually performing each year's added value from interest, then using that value to make similar calculations for each following year, makes it clear how we're arriving at the result, but it's time-consuming.

Solving for a future value 20 years in the future means repeating the math 20 times. There are faster and better ways of accomplishing this, one of them being the use of a financial calculator.

The formula for finding the future value of an investment on a financial calculator is:

FVN = PV(1 + I)ⁿ

Although it doesn't quite look like it, this is the same formula we used when we did the calculations manually. Incidentally, you can use this formula with any calculator that has an exponential function key; many do. However, using a financial calculator is better because it has dedicated keys corresponding to each of the four variables we'll be using, speeding up the process and minimizing the possibility of error. Here are the keys you will punch:

Punch N and 2 (for 2 years' holding period)

Punch I/YR and 5 (for the interest rate of 5 percent)

Punch PV and -105 (for the amount of money we are calculating interest on in year 2)

Take note that you need to set the investment's present value as a negative number so that you can correctly calculate positive future cash flows. If you forget to add the "minus" sign, your future value will show as a negative number.

Punch PMT and PMT (there are no payments beyond the first one)

Punch FV, which returns the answer of $110.25

No one truly knows what inflation will be or exactly how long they need their money to last. And, if you did, then, retirement planning would be easy. As every situation is unique, it requires using historical comparisons and rules of thumb.

Run Best and Worst Case Examples Using Assumptions About Inflation, Rates of Return, and Life Expectancy in Retirement

Variables like your rate of return on investments, life expectancy, inflation and your willingness to spend principal will all have a giant impact on the amount of money you calculate that you will need to retire.

Best Case Example

Let's assume you need $50,000 per year to spend above and beyond your guaranteed sources of income. Below are the remaining best-case assumptions:

2% inflation rate

25-year life expectancy

7% return on investments

Okay to spend principal down to nothing

The software tells us that you will need almost exactly $700,000 to provide this $50,000 per year of inflation-adjusted income for 25 years.

Worst Case Example

Again, let's assume you need $50,000 per year above and beyond your guaranteed sources of income. Below are the remaining worst-case assumptions:

4% inflation rate

35-year life expectancy

5% return on investments

You want to retain $700k of principal to pass along to your heirs

Now the software says you will need $1.8 million to provide that same $50,000 per year of inflation-adjusted income for 35 years.

The answer in the example above is likely somewhere between $700k and $1.8 million. If real life throws a set of circumstances at you that are worse than the worst case scenario, maybe even more.

Since you don't know what inflation will be in retirement, what your rate of return will be, or how long you will live, you can't come up with an exact answer. The next best thing is to come up with a reasonable set of assumptions and make sure you re-evaluate every few years.

To help you determine the right assumptions to use, and to accurately factor in tax consequences, you may want to seek the assistance of a qualified retirement planner, and/or take the time to read several books on retirement planning.

The idea of present and future value is valuable in settling on venture choices. It is used to settle on a choice on the amount of cash to contribute. It is utilized to speak to the sum that one need to contribute today at a given interest rate over a predetermined time period to collect the future sum.