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Difficulty: MediumInvestment Companies and Managed Funds

An open-end growth fund reports total portfolio assets of $510,000,000\$510,000,000 and total liabilities of $35,000,000\$35,000,000. The fund has 20,000,00020,000,000 shares outstanding. If Class A shares of the fund carry a front-end sales charge of 5%5\%, what is the Public Offering Price (POP) per share in dollars?

Answer: 25 $

Answer

The Public Offering Price (POP) per share is $25.00.
To find the Public Offering Price (POP), first calculate the fund's Net Asset Value (NAV) per share: NAV=Total Assets−Total LiabilitiesShares Outstanding=$510,000,000−$35,000,00020,000,000=$475,000,00020,000,000=$23.75\text{NAV} = \frac{\text{Total Assets} - \text{Total Liabilities}}{\text{Shares Outstanding}} = \frac{\$510,000,000 - \$35,000,000}{20,000,000} = \frac{\$475,000,000}{20,000,000} = \$23.75. Next, divide the NAV by (1−Sales Load %)(1 - \text{Sales Load \%}) to determine the POP: POP=$23.751−0.05=$23.750.95=$25.00\text{POP} = \frac{\$23.75}{1 - 0.05} = \frac{\$23.75}{0.95} = \$25.00.

Step-by-Step Solution

1
Calculate the Net Asset Value (NAV) per share.
$23.75
NAV is determined by subtracting total liabilities from total assets and dividing by the number of outstanding shares: (510,000,000−510,000,000 - 35,000,000) / 20,000,000 = $23.75.
2
Calculate the Public Offering Price (POP) using the sales load formula.
$25.00
POP is calculated by dividing NAV by (1 - Sales Load %): 23.75/(1−0.05)=23.75 / (1 - 0.05) = 23.75 / 0.95 = $25.00.

Key Concept

Net Asset Value (NAV) and Public Offering Price (POP) Calculation

Alternative Method

You can verify the answer by subtracting the 5% sales charge (25.00∗0.05=25.00 * 0.05 = 1.25) from the POP of 25.00,whichyieldstheNAVof25.00, which yields the NAV of 23.75.
Estimated Time:1m 30s
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Topics

Investment Companies and Managed Funds

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