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Question

Difficulty: HardInvestment Companies and Managed Funds

An open-end mutual fund holds total portfolio assets of $185,000,000\$185,000,000 and total liabilities of $10,000,000\$10,000,000 at the start of the valuation period. Prior to the 4:00 PM EST market close, portfolio asset value increases by $4,000,000\$4,000,000 due to market appreciation, and the fund accrues an additional $1,000,000\$1,000,000 in management fee liabilities. If the fund has 8,000,0008,000,000 shares outstanding, what is the Net Asset Value (NAV) per share at the market close?

Answer: 22.25 $

Answer

The Net Asset Value (NAV) per share at market close is $22.25\$22.25.
Net Asset Value (NAV) per share is calculated using the formula: NAV per share=Total Assets−Total LiabilitiesShares Outstanding\text{NAV per share} = \frac{\text{Total Assets} - \text{Total Liabilities}}{\text{Shares Outstanding}}. First, adjust total assets to $189,000,000\$189,000,000 ($185,000,000+$4,000,000\$185,000,000 + \$4,000,000) and total liabilities to $11,000,000\$11,000,000 ($10,000,000+$1,000,000\$10,000,000 + \$1,000,000). The net assets of the fund equal $178,000,000\$178,000,000 ($189,000,000−$11,000,000\$189,000,000 - \$11,000,000). Dividing net assets by 8,000,0008,000,000 shares outstanding results in an NAV per share of $22.25\$22.25.

Step-by-Step Solution

1
Calculate total assets at market close
Ending Total Assets = $189,000,000\$189,000,000
Add portfolio appreciation of $4,000,000\$4,000,000 to the initial total assets of $185,000,000\$185,000,000.
2
Calculate total liabilities at market close
Ending Total Liabilities = $11,000,000\$11,000,000
Add newly accrued liabilities of $1,000,000\$1,000,000 to initial liabilities of $10,000,000\$10,000,000.
3
Calculate total net asset value of the fund
Net Fund Assets = $178,000,000\$178,000,000
Subtract total liabilities from total assets ($189,000,000−$11,000,000\$189,000,000 - \$11,000,000).
4
Calculate NAV per share
NAV per share = $22.25\$22.25
Divide net fund assets ($178,000,000\$178,000,000) by total shares outstanding (8,000,0008,000,000).

Key Concept

Net Asset Value (NAV) Calculation for Mutual Funds
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Topics

Investment Companies and Managed Funds

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