Question

Your firm has $45.0 million invested in accounts receivable, which is 90 days of net revenues. If this value could be reduced to 50 days, what annual increase in income would your firm realize if the increase in cash could be invested at 7.5 percent

Answer 1

Solution :

Number of days = 90 days

Amount invested = $45 million

So the current earnings is $\ 45 \text{ million } \times 1.075 \text{ in}\ \ 90 \text{ days}$

The number of days is reduced to 50 days. So we can now make the same amount in just 50 days.

So the net increase is what we will make in the remaining $40$ days.

If in 50 days, we earn 0.075 return, then we can consider 50 days as $t=1.$

Then the $50$ days = $45 \times 0.075^1$  return, and

$40$ days = $45 \times (0.075)^{40/50}$

             $=45 \times (0.075)^{4/5}$

              = $\ 5.66580371$ million increase

              = $ 5.7 million