Topgun Records and several movie studios have decided to sign a revenue-sharing

Question

Topgun Records and several movie studios have decided to sign a revenue-sharing contract for CDs. Each CD costs the studio $1 to produce. The CD will be sold to Topgun for $2. Topgun in turn prices a CD at $15 and forecasts demand to be normally distributed, with a mean of 6,000 and a standard deviation of 2,000. Any unsold CDs are discounted to $0.50, and all sell at this price. Topgun will share 40 percent of the revenue with the studio, keeping 60 percent for itself.

) 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?

A publisher sells books to Barnes & Noble at $14 each. The unit production cost for the publisher is $2 per book. Barnes & Noble prices the book to its customers at $27 and expects demand over the next two months to be normally distributed, with a mean of 18,000 and a standard deviation of 5,000. Barnes & Noble places a single order with the publisher for delivery at the beginning of the two-month period. Currently, Barnes & Noble discounts any unsold books at the end of two months down to $3, and any books that did not sell at full price sell at this price. a) How many books should Barnes & Noble order? What is its expected profit? How many books does it expect to sell at a discount? b) What is the profit that the publisher makes given Barnes & Noble’s actions above? Use the following information to solve parts c) and d). A plan under discussion is for the publisher to refund Barnes & Noble $5 per book that does not sell during the two-month period. Because Barnes & Noble shares the point-of-sales data with the publisher, the publisher does not require Barnes & Noble to return all unsold books for verification purpose. As before, Barnes & Noble will discount them to $3 and sell any that remain. c) Under this plan, how many books will Barnes & Noble order? What is the expected profit for Barnes & Noble? How many books are expected to be unsold during the two-month period? [Hint: Since Barnes & Noble gets a refund of $5 from the publisher for each unsold book as well as a $3 of clearing each unsold book after the two-month period, Co = c – b - SR. Moreover, SM = 0] d) What is the expected profit for the publisher under the plan and given Barnes & Noble’s actions in part c)?

Explanation / Answer

a) How many CDs should Topgun order

Marginal profit, MP = 15*(1-0.40) - 2 = 7, where 0.40 is the revenue sharign fraction

Margin loss, ML = 2 - 0.5 = 1.5

Optimal cycle service level = MP/(MP+ML) = 7/(7+1.5) = 0.8235

z value corresponding optimal cycle service level = NORMSINV(0.8235) = 0.9289

Optimal order quantity = + z = 6000 + 0.9289*2000 = 7858

Topgun should order, Q = 7858 CDs

b) Look for I(z) for z =0.9289 in the standard normal table.

I(z) = 1.024

Expected unsold inventory, V = *I(z) = 2000*1.024 = 2048

Top expects to sell 2048 CDs at discount

c)

Expected Sales, S = Order quantity(Q) - Unsold inventory (V) = 7858 - 2048 = 5810

Expected profit = S*MP - V*ML = 5810*7 - 2048*1.5 = $ 37,595

d) Studio profit = Order quantity by Topgun * (Wholesale price - production cost) + Expected Sales by Topgun * retail price * revenue sharing fraction = 7858*(2-1) + 5810*15*0.4 = $ 42,715

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