German College

13. A mutual fund owns 300 shares of General Electric, currently trading at $30, and 400 shares of Microsoft Inc., currently trading at $54. The fund has 1,000 shares outstanding. a. What is the net asset value (NAV) of the fund? b. If investors expect the price of General Electric shares to increase to $34 and the price of Microsoft shares to decrease to $46 by the end of the year, what is the expected NAV at the end of the year? c. Assume that the expected price of the General Electric shares is realized at $34. What is the maximum price decrease that can occur to the Microsoft shares to realize an end-of-year NAV equal to the NAV estimated in part (a)?

Answers

Answer 1

a. The net asset value (NAV) of the fund is calculated by dividing the total value of the assets by the number of shares outstanding:

Total value of General Electric shares = 300 shares X $30/share = $9,000

Total value of Microsoft shares = 400 shares X $54/share = $21,600

Total value of assets = $9,000 + $21,600 = $30,600

Net asset value (NAV) of the fund = Total value of assets / Number of shares outstanding = $30,600 / 1,000 shares = $30.60/share.

Therefore, the NAV of the fund is $30.60/share.

b. To calculate the expected NAV at the end of the year, we need to calculate the total value of the assets at the end of the year using the expected prices of the shares:

Expected total value of General Electric shares = 300 shares X $34/share = $10,200

Expected total value of Microsoft shares = 400 shares X $46/share = $18,400

Expected total value of assets = $10,200 + $18,400 = $28,600

Expected NAV of the fund = Expected total value of assets / Number of shares outstanding = $28,600 / 1,000 shares = $28.60/share.

Therefore, the expected NAV at the end of the year is $28.60/share.

c. We can use the formula for the NAV to calculate the maximum price decrease of Microsoft shares that would still result in an NAV equal to the NAV estimated in part (a):

$30.60/share = (300 shares X $34/share + 400 shares X $54/share - 400 shares x P)/1,000 shares

where P is the price of Microsoft shares at the end of the year.

Solving for P, we get:

P = ($30.60/share X 1,000 shares - 300 shares X $34/share - 400 shares x $54/share)/-400 shares

P = $42.15/share

Therefore, the maximum price decrease that can occur to the Microsoft shares to realize an end-of-year NAV equal to the NAV estimated in part (a) is $54/share - $42.15/share = $11.85/share.

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