✏️ Net Asset Value

$$\text{Net Asset Value} = \frac{\text{MarketValueOfAssets - Liabilities}}{\text{SharesOutstanding}}$$

The best way to understand this formula is via balance sheets and examples.

✏️ Suppose a real estate professional is marketing a new real estate investment fund. Consider the following balance sheet:

Assets	Liabilities
$1B Real Estate Holdings (market value)	$300M of Debt
	$ Shares Outstanding: 10M shares

What is the NAV?

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Short answer:

$$\begin{aligned} \text{Net Asset Value} &= \frac{\text{MarketValueOfAssets - Liabilities}}{\text{SharesOutstanding}} \\ &= \frac{\$1\text{B}-\$300\text{M}}{10\text{M Shares}} \\ &= \$70 \end{aligned}$$

Intuition:

You prospective investors will want to know what they are purchasing. In particular, they will want to know about the assets that their shares gain them ownership of.

Each of the 10M shares purchases 1/10Millionth of the $1B of Real Estate Holdings. So the value of 1 share would be

$$\frac{\$1\text{B}}{10\text{M}} = \$100$$

It’s true that 1 share represents $100 worth of the real estate assets. BUT WHAT ABOUT THE LIABILITIES?!?!?! 1 share also represents about $30 worth of debt. The way to correct this is to subtract off (or “net out” the debt). This will give us the “Net Asset Value.” Specifically, net of the debt, the assets are worth $1B-$300M=$700M. Once you divide it into 10M shares, then your portion is worth ($1B-$300M)/10M = $70. The true Net Asset Value of a share is $70.

✏️ SPY, the SPDR S&P 500 ETF Trust, is one of the largest investment companies in the world. Coincidentally, it’s managed in Boston. Suppose Spy has .900 billion shares outstanding.

Spy’s assets are worth $421.05B and its liabilities are worth .05B.

What is it’s NAV?

Assets	Liabilities
$421.05B of stocks	.05B of debt
	900 million ownership shares

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$$\begin{aligned} \text{Net Asset Value (NAV)} &= \frac{\text{(Market Value of Assets - Liabilities)}}{\text{Shares Outstanding}} \\ &= \frac{421}{.9} \\ &=\$467.78 \end{aligned}$$

Bottom line: any share in a mutual fund represents a basket of stocks. The NAV is the value one ownership share in the basket of stocks.

✏️ Suppose that you are buying a regular mutual fund (not an ETF). The NAV today is $467. In one month, you sell it for $477. Along the way, you received income of $2 from the investment and it also distributed $2 of capital gains. What is your return on this investment?

$$\text{R} = \frac{\text{NAV}_1 - \text{NAV}_0 + \text{Income} + \text{Capital Gain}}{\text{Nav}_0}$$

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$$\text{R} = \frac{(\$10 + \$2 + \$2)}{467} = 3\%$$