A firm makes only cash sales. It estimates that allowing trade credit
on terms of net 30 would increase monthly sales from 200 to 220 units
per month. The price per unit is $101 and the cost (in present value
terms) is $80. The interest rate is 1%/month. What is the PV of
revenue per unit & the PV of profits? What is the PV of profits if 5%
of all customers fail to pay?

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Clarification of Question by wombat319-ga on 12 May 2005 06:10 PDT

ASSUMPTIONS:
Price per unit           $101
Cost per unit            $80
Current profits          $4,200 based on 200 units sold
Interest rate            1% per month
Current sales            200/month
Projected sales          220/month

Hi wombat319!
I will assume here that if the firm allows credit sales at the same
price ($101), then all customers will take advantage of this policy,
as there is no incentive to pay $101 today if there exists the
possibility of paying $101 in 1 month.

In order to find the PV of the revenue per unit, since the price
receives for each unit is $101, we must find the present value of $101
in 1 month. Since the 1-month interest rate is 1%, then the PV of $101
in a month is:

$101/1.01 = $100

So the PV of revenue per unit is $100.

The PV of profits is calculated in the following way:

PV of profits = PV of revenue    minus   PV of costs

We know that the PV of the cost per unit is $80. Since the firm will
sell 220 units, then the PV of total costs is 80*220 = $17,600. Also,
using the fact that the PV of revenue per unit is $100, we get that
the PV of total revenue is 220*100=$22,000. Therefore:

PV of profits = 22,000 - 17,600 = $4,400

Now, let's assume 5% of customers fail to pay. This will reduce the
revenues but not the costs. If 5% of customers don't pay, then the PV
of total revenues will be 95% of what it was when all customers paid.
Therefore, we find that, if 5% of customers don't pay:

PV of profits = 0.95*22,000 - 17,600 = $3,300

Notice, thus, that if all customers pay, the company will be better
off by adopting this trade credit policy (profits of $4,400 vs the
current $4,200); while, if 5% of customers fail to pay, then the
company should not adopt this policy (profits of $3,300 are smaller
than current $4,200 profits)


I hope this helps!
Best wishes,
elmarto

Thanks for all your help!  :-)

Assuming only additional 20 units sold are credit sales and not all 220 units
PV of revenue = 20 * 101 * .99 = 2000
PV of cost = 20 * 80  = 1600

PV of profit  = 400 (2000 - 1600)

5% fail to pay that means 20 units * 5% = 1 unit does  not pay

SAles value = 1 * 101 = 101
PV of this sale = 101 * .99 = $100

PV of profit given 5% fail = 400 - 100 = 300