Suppose the fund pays off its liabilities while at the same time the value of its assets doubles. How many shares will an investor who invests $50,000 receive?

What will be an ideal response?

The proportion of ownership for our investor is given by $50,000 (investor's initial investment) divided by the value of the assets at that ($510 million) minus the liabilities at that time ($10 million). Thus, the investor's proportion of ownership is $50,000 / ($510,000,000 – $10,000,000) = 0.0001 or 1.00%. One percent of 50 million shares is 5,000 shares. This assumes that the investor does not sell or redeem shares over time as can be the case for an open-end investment company. It is shown below that this is the same number of shares owned when the liabilities are paid off if the number of shares do not change.

Given that the market value of the portfolio assets has doubled, the liabilities are now zero, and assuming the number of shares outstanding have remained at 50 million, we use our NAV equation to get:

First, let us note that the NAV has increased by ($20.40 – $10) / $10 = 1.0400 or 104.00%. The increase of $20.40 – $10.00 = $10.40 means that investor has more than doubled their initial investment of $10 per share and now has an investment valued at$50,000(20.4/10) = $50,000(2.04) = $102,000 . Given the total value is now $1,020,000,000, this means the investor's proportion of ownership is $102,000 / $1,020,000,000 or 1.00%. Thus, the investor still owns 1.00% of the company and 1.00% of shares outstanding. Assuming 50 million shares are still outstanding, this means that the investor still owns 0.0001(50 million shares) =5,000 shares.