HighKey Records and several movie studios have decided to sign a revenuesharing
ID: 388761 • Letter: H
Question
HighKey Records and several movie studios have decided to sign a revenuesharing contract for CDs. Each CD costs the studio $2 to produce. The CD will be sold to HighKey for $3. HighKey in turn prices a CD at $15 and forecasts demand to be the following:
Quantity Probability
1000 5%
2000 5%
3000 10%
4000 10%
5000 20%
6000 15%
7000 15%
8000 10%
9000 10%
Any unsold CDs are discounted to $1, and all sell at this price. HighKey will share 35% of the revenue with the studio, keeping 65% for itself.
a). How many CDs should HighKey order?
b). How many CDs does HighKey expect to sell at a discount?
c). What is the profit that HighKey expects to make? What is the profit that the studio expects to make?
Explanation / Answer
Construct cumulative probability table
a)
Wholesale price, w = 3
Production cost, c = 2
Retail price, p = 15
Discount price, s = 1
Revenue share fraction, f = 0.35
Optimal service level = ((1-f)*p - w)/((1-f)*p - s) = ((1-0.35)*15 - 3)/((1-0.35)*15 - 1) = 0.771
Look for this value in the cumulative probability table.
The corresponding quantity is 7000
Therefore, HighKey should order, Q = 7000 CDs
b) Expected overstock, V = (7000-1000)*5%+(7000-2000)*5%+(7000-3000)*10%+(7000-4000)*10%+(7000-5000)*20%+(7000-6000)*15% = 1800
c) Expected Sales, S = 7000-1800 = 5200
Expected profit of HighKey = (1-f)*p*S + s*V - w*Q
= (1-0.35)*15*5200+1*1800-3*7000
= $ 31,500
Expected profit of Studio = (w-c)*Q + f*p*S
= (3-2)*7000+0.35*15*5200
= $ 34,300
Quantity Probability Cumulative Probability 0% 1000 5% 5% 2000 5% 10% 3000 10% 20% 4000 10% 30% 5000 20% 50% 6000 15% 65% 7000 15% 80% 8000 10% 90% 9000 10% 100%