To encourage you to invest by the closing date, discounts or warrants are sometimes included to sweeten the deal. “If granted, it is almost always one or the other, but not both,” asserts Dan Rosen, chair of the Seattle Alliance of Angels. 
“It is, of course, cleaner to just lower the price per share, but often there are reasons (e.g., a higher-priced friends and family round) not to do so,” he adds.
If the price per share in the friends and family round is high, issuing a lower price per share in the Series A round may significantly dilute the value and holdings of friends and family investors. Seasoned angels usually try their best, within reason, to keep entrepreneurs happy. No entrepreneur wants to tell his or her friends and family that their holdings have been diluted substantially.
Receiving a discount means you get to purchase shares at a lower price than the price per share for that round.
Warrants give you the right to purchase additional Series A shares within a specified time frame.
Purchasing additional shares allows you to increase ownership and enjoy the upside if the company does well.
In cases where the company issues new shares and dilution is inevitable, exercising your warrants would help protect your percentage of ownership up to a certain amount, which would help reduce the impact of dilution. 
Here’s the beauty of warrants: They provide you with potential upside and dilution protection (albeit limited), but you don’t have to pay up-front. You have a choice – you can exercise them within the agreed time period, or not.
For the company, issuing warrants allows it to sweeten the deal without reducing the company’s valuation, or price per share.
Even so, warrant does come with its own set of issues. (What doesn’t?) We’ll discuss those some other time.
The “exercise price” is the price you pay to purchase the warrants. The exercise price is usually set at Series A price.
The warrant coverage is expressed as a percentage. Twenty-five percent coverage for a $750,000 Series A investment would give you the right to purchase $750,000 x 25% = $187,500 worth of additional Series A shares.
Most warrants can be exercised from a couple of years to 10 years after closing.
In the event of an acquisition or IPO, however, warrants typically expire immediately. 
“Acquirors do not want to assume warrants and generally demand that warrants be exercised prior to closing,” explains Yokum Taku, corporate and securities partner at Wilson Sonsini Goodrich & Rosati (WSGR).
And “many companies prefer to have warrants expire on an IPO to eliminate the share overhang associated with the warrants.”
Seasoned angel investors always make sure the clause that gives them the option to exercise their warrants immediately before these liquidity events (e.g. M&A and IPO) is included in the agreements.
* For series, references are published in the last installment of the series.