Question

Here’s an example of how breakpoint discounts on sales commissions for mutual fund investors work:

Sales charge

Less than $25,000, 5.75%

$25,000 to $49,999, 5.5%

$50,000 to 99,999, 4.75%

$100,000 to $249,999, 3.75%

Nancy Dolan is interested in the T Rowe Price Mid Cap Fund. Assume the NAV is 19.15.

a. What minimum amount of shares must Nancy purchase to have a sales charge of 5.5%? (Round up to the nearest share even if it is less than 5.)

Minimum amount of shares            

b. What minimum amount of shares must Nancy purchase to have a sales charge of 4.75%? (Round up to the nearest share even if it is less than 5.)

Minimum amount of shares            

c. What minimum amount of shares must Nancy purchase to have a sales charge of 3.75%? (Round up to the nearest share even if it is less than 5.)

Minimum amount of shares            

d. What would be the total purchase price for (a), (b), or (c)? (Round your answers to the nearest cent.)

	Total purchase price
(a)	$
(b)	$
(c)	$

Answer 1

a. Minimum shares that Nancy must purchase to have sales charge of 5.5% is computed as:

For sales charge of 5.5%,minimum sales is $25,000

Minimum amount of shares=Minimum sales/NAV

Minimum amount of shares=$25,000/19.15

Minimum amount of shares=1,305.48

Minimum amount of shares=1,306 shares

b.Minimum shares that Nancy must purchase to have sales charge of 4.75% is computed as:

For sales charge of 4.75%,minimum sales is $50,000

Minimum amount of shares=Minimum sales/NAV

Minimum amount of shares=$50,000/19.15

Minimum amount of shares=2610.96

Minimum amount of shares=2,611 shares

c.Minimum shares that Nancy must purchase to have sales charge of 3.75% is computed as:

For sales charge of 3.75%,minimum sales is $100,000.

Minimum amount of shares=Minimum sales/NAV

Minimum amount of shares=$100,000/19.15

Minimum amount of shares=5,221.93

Minimum amount of shares=5,222 shares

d.Total purchase price for(a), (b), (c) can be computed as:

Thus,total purchase price is ($26,375+$52,375+$103,750)=$182,500