A mutual fund has a load of 4 percent and a net asset value (NAV) of $20 per share. What must an investor pay to purchase 250 shares? A) $5,200. B) $4,800. C) $5,208. D) $5,013. Does anyone understand why the solution is $20/.96 * 250? I don’t understand the intuition, and feel that $20*1.04*250 would be appropriate.

It is because you have to pay 4% of a front load. Thus, 96% will go to the NAV and the other 4% to the front end load. If you simply multiply by 1.04, then 96% of that will be less than the requires NAV of $20. If you divide by .96, then when you remultiply by .96, you will be right back at the NAV of $20. Does this help?

good question!

C. good question.

Thanks. After thinking about this some more, I think that it makes more sense.

0.96 M = $250 * $50 Solve for M.

My issue with questions like this is that they dont indicate whether its a front end load or a back end load. Or am i supposed to assume that its a front end load

Well front load is when you buy. Back-end load is when you sell. In this case, the question is asking for the price to buy 250 shares.

If I said A mutual fund has a backend load of 4 percent and a frontend of 7% and a net asset value (NAV) of $20 per share. What must an investor pay to purchase 250 shares? or A mutual fund has a backend load of 4 percent and a net asset value (NAV) of $20 per share. What must an investor pay to purchase 250 shares? Arent these two questions fundamentally different?

Yes.

So when you sell … for instance at $50 per share… and the back load is … say 5 % what would be the net receipts for 250 shares ?

Am I thinking about this wrong? You want to have 250 shares, each worth $20. So you want to have $5000 worth of shares. For each $20 share, you pay a 4% load, so you originally pay $20.80 for each share. $20.80 x 250 = 5200? So is the answer 5200, or 5208?

Is there any formula for this? C comes as follows: As explained above: 96 % of the total amount to be paid for buyong 250 shares @ 20. (if there is no load then we need 250 * 20 = $5000) Assuming “M” is the total amount paid, then M * .96 = 250 * 20 so, M = 5208.33 (Matches with “C”) What is wrong with the following though? 4% of 20 for 1 share = $0.80 So for 250 shares = 250 * 0.80 = 200 => represents only load. Now, 250 shares cost 250 * 20 = 5000 and if we add load as calculated above we get $5200 and that matches with “A” above. I am confused now as I am not able to see what I am missing as I expect both calculation to come up with one answer.

I think the “4%” is not a percent of the actual share price, i.e. 20.00 in this case. 4% means that of whatever money you pay toward buying the share, 4% will be held as a fee, and will not buy you any shares. So, if you wanted to buy one share, by your calculation, you'd want to pay 104% of 20.00 = 20.80 BUT, 20.80 * 0.96 = 19.96…which means you have managed to pay only 19.96 toward the share as opposed to the 20.00 you thought you were paying… The difference is subtle, but think a little more over it and it gets obvious.

Shreya, Great explanation, makes sense thanks.

Just as shreya pointed, loads on funds are always applied to the actual cash amount and not the unit price. Thus, when a fund is quoted with let’s say 3.5% front-end load (upfront charge) you are paying 3.5% of the money invested, and not 3.5% of the units/share price. Same goes for back-end loads.