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 |