One exciting aspect of the stock market is that prices fluctuate. There are times when an investor's favorite stocks can appear extremely cheap and other times when they feel expensive.

Still, just because a stock is expensive does not mean it will not do well for investors. It does, however, make it more difficult because the position would be starting at a higher valuation. That being said, there is usually a reason or several that make a stock expensive.

For instance, one of the best causes for an expensive valuation is because the company has excellent business prospects. That's precisely the case for the three stocks discussed below. They sell at lofty valuations, but their excellent opportunities could make the price worthwhile.

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1. Nvidia

Nvidia's (NASDAQ: NVDA) stock has delivered exceptional returns to shareholders over the last several years. That price appreciation has it trading at seemingly excessive valuations. Nvidia is selling at a price-to-sales of 27, price-to-free cash flow of 90, and a price-to-earnings of 77. The aforementioned are near the highest prices in its last five years.

However, the valuations can be justified considering Nvidia's excellent operating performance and opportunities. From 2016 to 2021, it increased its operating profit margin to 27.2% from 17.5%. Meanwhile, it more than tripled revenue from $5 billion to $16.7 billion.

Nvidia is a leading player in high-performance cloud solutions and graphic processing units (GPUs) in gaming. Longer-term, it is poised to benefit from the proliferation of self-driving cars, the metaverse, and artificial intelligence.

2. Apple

The legendary company founded by Steve Jobs has likewise made shareholders wealthier over the years -- so much so that its market cap surpassed $3 trillion in 2022. Apple (NASDAQ: AAPL) is trading at a price-to-sales of 8, a price-to-free cash flow of 31, and a price-to-earnings of 31. Like Nvidia, this is near the highest the stock has sold for in the last five years, according to these metrics.

Sales and profits have surged for Apple since the pandemic onset. Folks are spending more time working and learning from home, and so it has created an increase in demand for Apple's popular electronic devices, from laptops to iPads. Indeed, in 2021, revenue increased from $274 billion to $366 billion over the span of a year. Meanwhile, operating profit expanded from $66 billion to $109 billion for the same period.

Apple's latest iPhone is infused with 5G technology, which could fuel sales growth in the device for several years. Finally, Apple's success in hardware sales has given birth to a robust services business that keeps consumers in Apple's ecosystem long-term.

3. The Trade Desk

The Trade Desk (NASDAQ: TTD) is an online platform that empowers buyers of digital advertising worldwide. Its role in the shift of advertising to digital channels is undoubtedly one cause of its rapid price appreciation. The Trade Desk is selling at a price-to-sales of 33, a price-to-cash flow of 112, and a price-to-earnings of 125.

The global advertising industry is a massive one. One estimate suggests the sector generated $763 billion in revenue in 2021. Interestingly for The Trade Desk, a growing share of that spending is moving to digital. Between 2019 and 2021, the ad spending allocated to digital channels increased from 52.1% to 64.4%.

That helped The Trade Desk gain a more significant piece of the market. In the nine months ended Sept. 30, it grew revenue by 55% from the year before, while global ad spending is estimated to have increased by 22.5%.

While all of the stocks discussed above are selling at lofty valuations, investors can point to valid reasons for paying a premium price. Nevertheless, investors should proceed with caution when buying expensive stocks.

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Parkev Tatevosian owns Apple and The Trade Desk. The Motley Fool owns and recommends Apple, Nvidia, and The Trade Desk. The Motley Fool recommends the following options: long March 2023 $120 calls on Apple and short March 2023 $130 calls on Apple. The Motley Fool has a disclosure policy.