Suppose that 12 months ago, an investor purchased a given number of shares of a

ID: 2799098 • Letter: S

Question

Suppose that 12 months ago, an investor purchased a given number of shares of a Mutual fund at the then fund’s Net Asset Value of $4.00. Assume that today (12 months later) this investor sells those shares at today’s NAV and that the yield on this individual’s investment is - 4.5%, yes, negative 4.5%. Suppose, furthermore, that the Fund’s Balance Sheet as of today shows the following information, in no particular order:

Cash…$24,790

Accrued fees and other liabilities… $87,458

Current market value of holdings of stocks…$5,749,612

Current market value of holdings of bonds... $2,579,536

Please calculate the number of this fund’s shares outstanding as of today. Please show your work clearly.

Explanation / Answer

Calculation of NAV per share

Yield= -4.5%, NAV 12 month ago = $ 4.00, since Yield= (Sale Price-Purchase price)/Purchase Price*t

So, -0.045= (x - 4)/4

x= $ 3.82, we get current NAV per share = $ 3.82

NAV of mutual fund

Cash

24,790

Current market value of holdings of stocks

57,49,612

Current market value of holdings of bonds

25,79,536

(-) Accrued fees and other liabilities

87,458

NAV

82,66,480

NAV Per share= NAV/No. of share outstanding

We know current NAV of fund as above i.e. $ 3.82

So no. of Share outstanding = NAV/NAV per share

= 8266480/3.82

= 2,164,000 Shares outstanding