## Sample Value Path Formula

This is the growth-adjusted value path formula. Putting in some representative values for t, sample points on the value path are as follows:

Month |
1 |
$69.86 |
Month |
60 |
$6,513.86 |

Month |
2 |
140.77 |
Month |
120 |
20,397.25 |

Month |
3 |
212.74 |
Month |
180 |
47,903.39 |

Month |
12 |
910.13 |
Month |
240 |
100,001.90 |

Month |
24 |
1,991.02 |

These are the target values you strive to match each month by buying or perhaps selling shares. At this rate, you make steady progress toward your final goal while smoothing out your investment exposure over time.

### Flexible Variations on the Value Path Formula

What if you are not starting from scratch? Some investors may wish to start value averaging with existing shares that already have value. In that case, the best and most flexible method is probably for you to use a computer spreadsheet, as discussed later in this chapter. But if you are willing to calculate another formula, you can set up a value path that accounts for your investment progress to date, instead of starting from scratch. What you will do is set up a value path that is "in progress," and still has the proper length of time remaining before achieving your goal.

For example, suppose you have 17 years to develop a portfolio of $100,000, and you are happy with the r = 1.0% and g = 0.5% market return and investment growth parameters established in earlier examples. But you also have $6,500 in a fund that you want to bring into the value averaging plan as seed money. We can now figure out a value path that includes: those growth factors; has a value of $6,500 somewhere in the middle; and then, 17 years (204 months) later, has a value of $100,000. You see, by bringing seed money into the program, you effectively put yourself many months away from impoverished month zero. In this case, it works out that you are already effectively 87 months into a 291-month VA strategy that ends in a value of $100,000. The difference between month 87 and month 291 is 204 months, or 17 years, which is the time you have remaining to achieve your goal. The artificial 87 months that came before your starting point are nothing more than a convenient placeholder, in that your accumulated $6,500 corresponds to what you would have now had you started from scratch 87 months ago. You simply "skipped" those 87 months by bringing that amount ($6,500) with you to the starting point.

Now we'll construct the formula you can use to begin value averaging with a head start. We'll let n be the number of periods you have available from the present in which to achieve your investment goal (n = 204 here). The variable t (an unknown) will designate the period number in the value path formula that corresponds to today (where we will have $6,500). The variable T, which we must solve for, designates the period number at the end of the value path formula (where we will have $100,000). Of course, we need to find a t (now) and a T (later) that are n periods apart: t = T - n. Two variables for value, current and future, are required and should be known: vt is our current value ($6,500), and VT is our required future value ($100,000). The factor R remains an average of r and g. You can solve for T, the ending period number to use in establishing your value path, using this formula:

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