Question

The Branding Iron Company sells its irons for $60 apiece wholesale. Production cost is $50 per iron. There is a 25% chance that a prospective customer will go bankrupt within the next half-year. The customer orders 1,000 irons and asks for 6 months’ credit. Assume the discount rate is 8% per year, there is no chance of a repeat order, and the customer will either pay in full or not pay at all.

a. Calculate the expected profit for the order. (A negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

The Branding Iron Company sells its irons for $60 apiece wholesale

Production cost is $50 per iron

There is a 25% chance that a prospective customer will go bankrupt within the next half-year

The customer orders 1,000 irons and asks for 6 months’ credit.

discount rate is 8% per year, = so for 6 month disount rate is half of 8% = 8 / 2 = 4%

Chances are

25% of not getting payment from customer

75% of getting payment correctly

a. Calculate the expected profit for the order.

The amount owe custmer to compay = 60 ( selling price) + 1000 ( number of iron) = $ 60000

Production cost = 50 (per unit) * 1000 = 50000

Profit from the sales = 60000 - 50000 = 10000

This profit of $ 10000, the company will earn as cash after 6 months. However here we calculate the Expected profit for the orerder at the time of sales. So we should calculate the Present Value of this profit at half year rate of 4%

calculation of PV of profit = $ 10000 * (1/1 + r )n

Here,

r = discount rate = 4% ( 8 / 2 )

n = number of period = 1 (here only one time we get the payment , the chance)

PV of profit = $ 10000 * (1 / 1 + 4% )1 = 10000 * (1/1.04)1 = 10000 * 0.9615 = $ 9615

The chance of get profit of $ 9615 is 75%

There is another chance, not pay at all. IF it happened, the company has loss of $ 60000, the full amount of sale. It is profit ( $-60000)

This profit of $ 60000, the company will earn as cash after 6 months. However here we calculate the Expected profit for the orerder at the time of sales. So we should calculate the Present Value of this loss at half year rate of 4%

calculation of PV of profit = $ 60000 * (1/1 + r )n

Here,

r = discount rate = 4% ( 8 / 2 )

n = number of period = 1 (here only one time we ghave the loss)

PV of profit = $-60000 * (1 / 1 + 4% )1 =-60000 * (1/1.04)1 = -60000 * 0.9615 = $-57690

The chance of get loss of $-57690 is 25%

After we calculate the Expected profit, there is two chance 25% to not getting payment and 75% to get payment

If we does't get payment, the company loss is $ 57690

Calculation

Profit	Probability	Profit * probability
$ 9615	75%	$ 7211
$ -57690	25%	$ -14422.5

The 25% is the chance that a prospective customer will go bankrupt within the next half-year. if she / he bankrupt, the company will not get payment, and also the compay has a loss of $ 57690

Expected Profit for the order = $ 7211 + - 14422.5 = $ - 7211.5