# NAV discount math

There is a common dialog spoken with value stocks that trade at a discount to net asset value (NAV) when someone it trying to make a retort as to why your idea of buying a stock at a discount to net asset value will not work.  It typically goes something like this: It doesn’t matter that stock XYZ is trading at a discount to NAV because that stock has always traded at a discount and always will, so you won’t make any money on it!  I am sure that if you read enough about value stocks that you will hear something like this very often.  Let’s use some math to see if this statement is true or not.

Let’s suppose there are two stocks: Equal Corp. which trades equal to net asset value and Discount Corp. which trades at a 20% discount to net asset value.  Let’s assume Equal Corp. trades for \$10 and has a NAV of \$10 and Discount Corp. trades at \$8 and has NAV of \$10.  Let’s see what happens to each company after they have compounded their NAV by 10% over a year’s time.  Equal Corp will now have a NAV of \$11 and if the discount stays the same will have a stock price of \$11 for an investment gain of 10%.  For Discount Corp. the NAV will also rise to \$11 and if the 20% discount stays the same will have a stock price of \$8.80 for an investment gain of 10% as well.  So we can see in this example if two stocks have the same net asset value, net asset value gains and the discounts remain the same there is no investment return difference between them.  This is quite disappointing as surely the time we value investors spend to find those stocks that trade at a discount should reward us.  Intuitively the stock with the bigger discount should be better.  Well let’s see what happens when dividends are involved.

Let’s assume the same Equal Corp. and Discount Corp. from before but now let’s look at what happens when they pay a \$0.50 end of year dividend.  For Equal Corp. the year end NAV will be \$10.50 resulting in a stock price of \$10.50 plus the \$0.50 dividend will again result in a 10% investment gain.  For Discount Corp. the year end NAV will be \$10.50 resulting in a stock price of \$8.40 plus a \$0.50 dividend will result in investment gains of 11.25%!  Now that’s the result we want to see!  If you follow the math you will get a similar result if the Corps use cash to buy back shares rather than pay dividends.  The way I think of this is that if a company trades at a discount to net asset value but does not distribute any cash to shareholders that discount is trapped in the company and won’t benefit the shareholders.  However if the company distributes the discounted cash to the shareholders by dividends or buybacks then that discount is being given out to the shareholder and they can get benefit from it.

The final lesson is that investing in a stock that trades at a discount to NAV only adds extra value if that company pays dividends or buys back shares, so be sure to look out for that when choosing a company to invest it.  Also if you get the “discount to NAV won’t work line from anybody in your writing feel free to link this page to them to show them why they are wrong.  Happy investing in 2019!

## One thought on “NAV discount math”

1. Karo says:

Thanks for doing the math and bringing it to my attention! 🙂

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