Mere months ago, investors witnessed shares of Tesla Motors (NASDAQ:TSLA) fall -51% to $141.05/share from all-time highs of $286.65/share. Since then, market sentiment has reversed dramatically, and the stock price has recovered nicely. With Model 3 Fever sweeping the financial world, Tesla shares closed at $237.59 on Friday, less than 15% off all-time highs.

Tesla Motors is a battleground stock here on Seeking Alpha, with investors actively monitoring and vigorously defending their long or short positions. Through all the emotion, we can sometimes forget that Tesla Motors is just a company, and as investors, our No. 1 priority should be how much money we can make in the long run by investing our hard-earned dollars. This begs the question, what about us passive investors who have no interest in short-term volatility and investor emotion? What about those of us who want to plunk down a healthy sum of cash on an attractively priced equity, fall asleep behind the wheel and hope when we awake in 30 years our acorn has grown into a massive oak tree? In this article, I would like to explore the long-term investor's case for Tesla Motors.

*The Parameters*

We must first set parameters for our investment.

- As a 29-year-old millennial, I require an investment horizon of 30 years.
- Individual stocks are always riskier than broad market indices. Historically, the S&P 500's (NYSEARCA:SPY) 30-year return has left investors with at least an 8% CAGR, so I must demand at least a 10% CAGR as a risk premium for an individual company.
- At the current market price of $237.59/share, a 10% CAGR for the next 30 years will require Tesla's market price to reach $4,145.80/share - a long-term gain of 1,745%. This assumes no splits, no buybacks and no distributions - if Tesla Motors simply keeps growing at a 10% rate each year, in 30 years, that will be the share price. If splits, buybacks and distributions occur, the value returned to shareholders will be the same in the end. For this exercise, we will assume Tesla prefers not to split or offer a dividend just to keep the math straightforward.
- While the market can be completely irrational in the short term, it is logical in the long term. In 30 years, Tesla Motors will be a mature company and must be valued accordingly. According to Morningstar.com, industry average P/E ratios and P/S ratios are:
P/E Ratio: 9.2x

P/S Ratio: 0.5xFor example, these ratios for General Motors (NYSE:GM) are:

P/E Ratio: 5.3x

P/S Ratio: 0.3xWhile these ratios for Ford Motor Company (NYSE:F) are:

P/E Ratio: 7.1x

P/S Ratio: 0.4xI will assume that after 30 years, Tesla retains a premium valuation at double the industry average and will apply a P/E ratio of 18.4x and P/S ratio of 1.0x. This is because Tesla is not valued solely as a car company but as a hybrid automobile-technology company.

We can then analyze the likelihood of long-term investor success by working backwards from a required endpoint.

*A Long-Term Analysis of EPS*

Calculating the required earnings of Tesla Motors by Year 30 is fairly straightforward.

Current EPS (diluted): $-6.93

Required Year-30 EPS (diluted): ($4,145.80/share)/(18.4) = $225.32

Tesla Motors must increase their diluted EPS from current (Year-0) -$6.93/share to (Year-30) $225.32/share.

Calculating a CAGR yields an undefined result because we are beginning with a negative number, but if we assume that Tesla is correct and will become profitable by the end of 2016, we will take Yahoo Finance's metrics to calculate our result:

Forward P/E: 71.13x

Analyst Annual EPS Est (Dec-16): $1.31

When charting our course over the next 29 years, we will require an EPS compounded at 19.42% annually to satisfy our goals. *(To calculate this longhand, simply multiply the forward EPS of 1.31 by 1.1942 twenty-nine times.)* This can be confirmed using an exponential growth formula:

x(t) = x0 * (1 + r)^t

Where,

x(t) = value at time t.

x0 = initial value at time t=0.

r = growth rate when r>0, in percent.

t = time in discrete intervals and selected time units.

Our values are:

x0 = 1.31

r = 19.42%

t = 29

We can use Excel to generate an EPS curve using that very formula within pennies of our estimated required Year-30 EPS:

Year | EPS (diluted) |

1 | $ 1.31 |

2 | $ 1.56 |

3 | $ 1.87 |

4 | $ 2.23 |

5 | $ 2.66 |

6 | $ 3.18 |

7 | $ 3.80 |

8 | $ 4.54 |

9 | $ 5.42 |

10 | $ 6.47 |

11 | $ 7.73 |

12 | $ 9.23 |

13 | $ 11.02 |

14 | $ 13.16 |

15 | $ 15.72 |

16 | $ 18.77 |

17 | $ 22.41 |

18 | $ 26.77 |

19 | $ 31.96 |

20 | $ 38.17 |

21 | $ 45.58 |

22 | $ 54.44 |

23 | $ 65.01 |

24 | $ 77.63 |

25 | $ 92.71 |

26 | $ 110.71 |

27 | $ 132.21 |

28 | $ 157.89 |

29 | $ 188.55 |

30 | $ 225.17 |

This will yield the following growth curve:

While we cannot fully expect real-world results to be this neat and clean, Tesla Motors must "knock it out of the park" with their early YoY growth rates as we can expect growth to slow as the company matures. In reality, Tesla must exceed earnings growth goals early to increase our chances of long-term success, but the general best-fit growth curve itself must hold true even if YoY EPS is a bit more "scattered."

*A Long-Term Analysis of Revenues*

Using a mathematical proportional relationship, we can determine that if Tesla Motors has a total market capitalization of $31.38B at a market price of $237.59/share, we can expect Tesla Motors to have a total market capitalization of $547B at a market price of $4,145.80/share. This will yield the following:

(Year-0, current) P/S Ratio: 7.76x

(Year-0, current) TTM Revenues: $4.046B

(Year-30) P/S Ratio: 1.0x

(Year-30) Revenues: $547B

In order for Tesla Motors to hold our assumed valuation, it must increase revenues YoY at a CAGR of 17.77% for the 30-year period. *(To calculate this long-hand, simply multiply the current revenue of $4.046B by 1.1777 thirty times.)*

Calculating for exponential growth, we arrive at the following:

x(t) = x0 * (1 + r)^t

Where,

x0 = 4.046

r = 17.77%

t = 30

Revenues must increase along the following best-fit curve to reach our goals:

Year | Revenues [B] |

0 | $ 4.046 |

1 | $ 4.765 |

2 | $ 5.612 |

3 | $ 6.609 |

4 | $ 7.783 |

5 | $ 9.166 |

6 | $ 10.795 |

7 | $ 12.714 |

8 | $ 14.973 |

9 | $ 17.633 |

10 | $ 20.767 |

11 | $ 24.457 |

12 | $ 28.803 |

13 | $ 33.922 |

14 | $ 39.949 |

15 | $ 47.049 |

16 | $ 55.409 |

17 | $ 65.255 |

18 | $ 76.851 |

19 | $ 90.508 |

20 | $ 106.591 |

21 | $ 125.532 |

22 | $ 147.839 |

23 | $ 174.110 |

24 | $ 205.049 |

25 | $ 241.486 |

26 | $ 284.399 |

27 | $ 334.936 |

28 | $ 394.454 |

29 | $ 464.549 |

30 | $ 547.099 |

We also can solve for the rate of decay of Tesla's P/S Ratio over time. As the company matures, we can expect the multiple that investors are willing to pay for their revenues to decline. In my assumptions, I anticipate that ratio to decline from a current rate of 7.76x to a rate of 1.0x over a 30-period. We can reevaluate our initial equation to solve for "r." Reevaluating yields the following:

Where,

t = 30

x(t) = 1.0

x0 = 7.76

Solving this equation yields a rate of -6.60%. Therefore, we can expect Tesla's P/S ratio to decrease by -6.60% annually as the company ages from start-up to maturity.

*Conclusions*

I would like to preface this conclusion by stating that any forward-looking analysis is flawed. The future is unpredictable, but a forward-looking analysis should be made in any purchase an investor makes, and any of these analyses will use assumptions. It is all we can do to protect ourselves, and only purchases with appropriate margins of safety should be made.

There is always the chance that Tesla Motors will command a premium valuation beyond my assumptions during the 30-year timeframe, which will improve the investor's chance for adequate returns at current prices. However, I feel the assumed 30-year P/E and P/S ratios I assigned to Tesla Motors are rational, and I prefer to be conservative in my outlook. Working backwards, Tesla Motors must ultimately perform along these best-fit curves to reach my 30-year investment goals. The question is, how likely is this scenario?

For Tesla Motors to compound at 10% for the next three decades, its market capitalization must grow to a shareholder-equivalent $547B, either on pure growth or with total shareholder distributions if the company decides to begin paying a dividend. Given we can expect $1.00 to be worth about $0.41 after 30 years (assuming 3% inflation), that would make Tesla Motors' market capitalization worth $225B in today's money. That would require Tesla Motors in 30 years to grow to be the size of Procter & Gamble (NYSE:PG) today. If this analysis were to be even more conservative and we expect Tesla Motors to one day trade at industry average P/E and P/S metrics, or if better rates of compounded annual growth were required, satisfactory returns would become even more difficult.

Just to be clear, these are not my projections for Tesla Motors over 30 years. If you are reading this and you feel the 30-year EPS requirement of $225.32/share and 30-year market cap of $547B seem impossibly high and unrealistic, I agree with you. It may sound crazy, but that is what today's investors who buy Tesla stock are expecting, whether they know it or not.

While the above scenario could be met or exceeded, I believe it is extremely unlikely and investors purchasing Tesla Motors at today's prices will be destined to underperform the market in the long term. Tesla Motors is currently priced beyond perfection - the valuation is so sky-high that any miss can easily send share prices rocketing to the ground. In order to generate market-beating returns for the long-term investor, its record must be nothing short of perfection.

As we have heard before, 99% of car companies go bust. The deck is certainly stacked against Tesla Motors for its ability to survive in a difficult industry, let alone thrive and grow like wildfire for 30 years. Regardless of what you think ethically of Tesla Motors as a company, simply based on valuation, it is a very expensive and risky stock for the long-term investor to purchase. Proceed with extreme caution.

**Disclosure:** I am/we are long SPY.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

**Additional disclosure: **All information found herein, including any ideas, opinions, views, predictions, commentaries, forecasts, suggestions or stock picks, expressed or implied, are for informational, entertainment or educational purposes only and should not be construed as personal investment advice. I am not a licensed investment adviser.