2. Topgun Records and several movie studios have decided to sign a revenue-shari

Question

2. Topgun Records and several movie studios have decided to sign a revenue-sharing contract for CDs. Each CD costs the studio $1.5 to produce. The CD will be sold to Topgun for $2.5. Topgun in turn prices a CD at $13 and forecasts demand to be normally distributed, with a mean of 8,000 and a standard deviation of 2,500. Any unsold CDs are discounted to $1, and all sell at this price. Topgun will share 35 percent of the revenue with the studio, keeping 65 percent for itself.

a) How many CDs should Topgun order?

b) How many CDs does Topgun expect to sell at a discount?

c) What is the profit that Topgun expects to make?

d) What is the profit that the studio expects to make?

Explanation / Answer

Facts and Figures from the Question

Cost to Produce 1 CD by any studio : $ 1.5

Cost of 1 CD for Topgun : $ 2.5

Selling Price of 1 CD : $ 13

Profit per CD for Topgun : $ 13- $ 2.5 = $ 10.5

a) How many CDs should Topgun order?

Assuming that the Demand Distribution is Normal with Mean of 8000 and Standard Deviation of 2500, Topgun should try to sell maximum and hence will Order for maximum number of CDs.

In this case, if Demand deviates towards higher side then maximum Demand will be equal to Mean + Standard Deviation

Mean: 8000

Standard Deviation: 2500

Hence Topgun should Order for 8000+ 2500 = 10,500 CDs

b) How many CDs does Topgun expect to sell at a discount?

Since Mean of the Demand is 8000 so Topgun expects that there will be Demand as per mean figures and any additional stock of CD has to be sold at discount.

Total Order of CDs by Topgun : 10,500

Total Number of CDs that has to be sold at Discount : = Standard Deviation = 2500

c) What is the profit that Topgun expects to make?

In this case we are taking total Demand of CDs= 8000

A-Revenue earned by selling these CDs @ $13 = 8000 * 13 = 104,000

Balance Number of CDs left : 2500

Selling price of extra CDs = $1 /CD

B-Revenue earned by selling extra CDs = 2500 * 1 = $ 2500

C-Total Revenue earned= A+ B = 104,000 + 2500 = 106, 500

D-Revenue for Topgun @ 65% of total = 106,500* 0.65 = 69,225

E-Revenue for Studios @ 35% of total = 106,500* 0.35 = 37,275

Now lets do cost calculation for Topgun and Studios

F-Total Number of CDs produced = 10,500

G-Cost of production of each CD by studios = $ 1.5

H-Total Cost of Production of 10,500 CDs= G*F=10,500*1.5 = 15750

I-Cost of each CD incurred by Topgun = $ 2.5

J-Total Cost Incurred by Topgun = F* I = 10,500 * 2.5 = 26,250

Therefore total profit that Topgun expects to make = D-J = 69,225 – 26,250 = $ 42,975

d) What is the profit that the studio expects to make?

Therefore total profit that Studis expects to make = E-H = 37,275 – 15,750 = $ 21,525

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