Question

A firm currently makes only cash sales. It estimates that allowing trade credit on terms of net 30 would increase monthly sales from 500 to 600 units per month. The price per unit is $75 and the cost (in present value terms) is $60. The interest rate is 1 percent per month. Should the firm change its credit policy if 5 percent of all customers fail to pay their bills under the new policy?

A) Yes, profits will increase by $1,054 per month

B) Yes, profits will increase by $965 per month

C) No, profits will not change

D) No, profits will fall by $817 per month

E) No, profits will fall by $1,173 per month

Answer 1

The answer is option E, which is calculated as follows :-

details given in the problem are as follows :

Price per unit $ 75

Cost per unit $ 60           

Current profits $7,500 based on 500 units sold

Interest rate 1% per month

Current sales = 500/month

Future sales = 600/month

We can assume that, if the firm allows credit sales,

then all customers will aply for this policy.

Payment of $75 is receivable in 1 month time.

So we have to find the PV of the revenue per unit, since the price

receives for each unit is $75, we have to find the present value of $75

in 1 month. So the PV of $75 for 1-month interest rate of 1% =

$ 75/1.01 = $74.2574

PV of revenue per unit = $74.2574.

Now we can calculate present value of profit :-

PV of profits = PV of revenue - PV of costs

We know that the PV of the cost per unit = $60.

then the PV of total costs is 60*600 = $36000.

PV of revenue per unit is $74.2574,

So, PV of total revenue is 600*74.2574=$44,554.44.

Therefore:

PV of profits = =$44,554.44 – 36,000 = $ 8554.44

It is given that 5% of customers fail to pay.

If 5% of customers don't pay, then the PV of total revenues will be 95%. Therefore, if 5% of customers don't pay:

PV of profits = 0.95*=$44,554.44- 36,000 = $6,326.718

Reduction in profit if 5% fail to pay = $7,500 - $6,326.718

                                                               = 1173.28

Rounded answer is 1,173

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