The purpose of our article to use valuation techniques to value Apple (NASDAQ:AAPL). Apple is an unique valuation case because Apple's P/E ratio, 11.69, is well below the S&P 500's P/E, 22.67. In addition, Apple's dividend yield is around 2% which is greater than the rate from a ten year Treasury note. From this analysis alone it appears as if Apple is a great investment. We assume an investor would rather invest in Apple and earn 2% over the next 10 years rather than the US government at a similar rate. However, we need to get deeper to understand whether the current valuation of $109 per share is grossly undervalued or appropriate.

We start with our assumptions that go into both the DCF and comparables model. Our main assumptions for the discounted cash flow are in regard to the projected financials. We assume that the operating expense to revenue ratio is 10% which is the historical average. We project the balance sheet out by assuming that the asset to revenue and liability to revenue ratio for the projected years is the same as the 2015 year.

*Table 1: Assumptions*

In regard to the comparables use Google (NASDAQ:GOOG) (NASDAQ:GOOGL), Microsoft (NASDAQ:MSFT), IBM (NYSE:IBM) and Sony (NYSE:SNE) as comparable companies.

The cost of capital is determined using a CAPM model with a size and firm-specific risk premium to calculate the cost of equity and a proprietary credit model to calculate the cost of debt. Our credit rating for Apple is AA+. The levered beta is 0.96. Putting this together we arrive at a cost of capital of 15.52%.

One of the most important assumptions is the revenue growth rate. Over the past four years Apple's growth rate has been variable, reaching a high of 44.58% in 2012 and a low of 6.95% in 2014.

Figure 1: Apple's Revenue Growth Rate

For the DCF, let's assume the revenue growth rate for the projection period, 2016-2020, is an average of the last three years. This results in an average revenue growth of 15% per year. Then assume in perpetuity, revenue will grow at the 2014 rate, 6.95%. In the comparables model we back out an implied expected ten year growth rate from the comparable company's stock price and financials. The growth rate calculated is 7.85%. We use the 7.85% number in our comparables analysis.

Table 2: Apple's Fair Value Stock Price

The stock price calculated, $115.34, is very similar to the actual stock price trading on April 12, 2016, of $109. In addition, we find that both methods result in a similar value. Therefore, our results indicate that the market is currently valuing Apple around its fair value.

Next we look at different growth rate scenarios. We keep everything the same for both the DCF and comparables but change our growth rate assumption. Table 4 displays the different revenue growth rate scenarios. These growth rates are for the projection period and terminal value calculation.

Table 3: Revenue Growth Scenarios

We can see that when revenue growth hits 10% or more the valuation of Apple can increase dramatically. Is it possible for Apple to increase revenue further?

We believe it is. Since the iPhone has been launched in 2007 revenue growth has averaged slightly over 30%. If we assume Apple's long-term growth rate will be 10%, one third of its growth rate since 2007, Apple's stock price is 30% under-valued.

Let us go over some DCF scenarios.

Table 4: DCF Revenue Growth Scenarios

Let us assume Apple earns a 30% revenue growth rate for the next five years and then in perpetuity earns a modest 5% growth rate. In this scenario we obtain a $145 per share stock price.

If we assume Apple earns a 15% revenue growth rate for five years and then 8% in perpetuity we obtain a $138 per share stock price.

The tax rate is important. We do not really know what their actual tax rate is. If the tax rate is as low as 10%, a 10% long-term revenue growth rate yields a $177 per share stock price. Also, a 10% revenue growth for next five years and a 2% perpetuity growth rate, the inflation rate, yields an $80 per share stock price. That is 60% upside versus 27% downside. We are willing to bet that Apple's revenue growth rate will be greater than 2% in perpetuity.

Apple has the ecosystem and following to create additional revenue through services. In addition, there is a lot of room to grow globally. Countries such as India and Russia are untapped markets.

Now assume, as many critics do, that Apple will become mature to the point where it has not real growth. Many dominant companies, such as Microsoft, reach a point where no more growth is possible. If this occurs sooner rather than later, then we need to look at different perpetuity growth rates. Let us assume that Apple's revenue growth starts at 30% for 2016 and declines by 5% per year until 2020 and then Apple grows at the 2% expected inflation rate. Therefore, Apple grows for five more years and then becomes a no real growth company. The stock price in this scenario, with a 10% tax rate, is $106.39. Essentially the stock price at which Apple is trading at as of April 2016. Assuming a more realistic tax rate, the market is expecting Apple to become a no-growth company in the next five years. If we use the same growth rates but the stated 25% effective tax rate, the stock price value we calculate is $80.

The bad case scenario yields a 30% negative return. We believe the probability of a bad case scenario is small. As of today, Apple's stock price is trading at very modest growth expectations. The market does not believe Apple will create amazing growth for the future. If Apple can slightly exceed modest growth expectations, we believe the stock price can increase 50% in the following year from beating those expectations. The probability of modest growth or slightly beating expectations is much greater than any other scenario. Therefore, we agree that Apple stock is a good buy at the current price.

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

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.