Question

All else constant, an increase in the days inventory held period will have what effect on the net present value (NPV) of working capital

a. it depends

b. decrease in NPV

c. increase in NPV

d. no change in NPV

Answer 1

This has various interpretations. At the outset, let us first agree on the term "days inventory held period". I assume your books teach this to be the average number of days the company holds the inventory before selling it.

Let us understand how it can increase:

1. When the company buys excess inventory, but sales did not increase along with inventory. [Here, value of inventory increases - which causes an increase in "days inventory held period"]
2. When the sales significantly drop. [Here, value of inventory does not change - but the drop in sales is what that causes an increase in "days inventory held period"]

Now, let us see how can the NPV of working capital change in relation to change in inventory:

1. If inventory increases: then there is no change in working capital because the increase in inventory is offset by an outflow of cash (or increase in current liability).
2. If inventory decreases: then it generally means that there was some extra sales, causing an increase in working capital because of the profit element.
   
   The question deals with "increase in days inventory held period" which does not arise when inventory decreases. So this point 2 is beyond the scope of your question. So, let's stick with point (1).

But when inventory increases [which could cause an increase in days inventory held period], there is no change in working capital, and hence no change in NPV.

So in normal cases, the answer is "d. No change in NPV". But there are some interpretations where the answer can be different. It depends upon the assumptions taken. But that does not negate the logical assumptions I have taken, but the answer would be "a. It depends" in such case - for example, if it is assumed in this way:
Year 1: Sales = 100,000; Average Inventory = 10,000. So, Days inventory held period = 365 x 10,000/100,000 = 36.5.
Year 2: Sales = 90,000; Average Inventory = 15,000. So, Days inventory held period = 365 x 15,000/90,000 = 60.83; and because of this lower level of sales, the total working capital could be lower, hence a lower NPV for working capital, in which case, there is change in NPV, but in Year 1, there is no change in working capital, making our answer as "a. It depends".

So, normally you have 2 acceptable answers, (a) and (d); where (d) covers more scenarios, with (a) covering major part of them. You can choose whichever assumption you want to go forth with.

I explained in detail in your academic and career interest. Hope it helps.