2. (10 pts) Topgun Records and several movie studios have decided to sign a reve

Question

2. (10 pts) 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 $1.5. Topgun in turn prices a CD at S12 and forecasts demand to be normally distributed, with a mean of 5,000 and a standard deviation of 2,000. Any unsold CDs are discounted to S0.50, and all sell at this price. Topgun will share 45 percent of the revenue with the studio, keeping 55 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

Production cost = v = $1 per CD

Wholesale price = c = $1.5 per CD

Retail price = p = $12 per CD

Discount price = s = $0.5 per CD

Demand distribution: (µ, ?) (5000, 2000)

Profit sharing:

Top Gun share = 55%

Studio share = f = 45%

Cu = under-stocking cost = Sales price/unit – Cost/unit = (1 – f)(p) – c = (1 – 0.45)(12) – 1.5 = $5.1

Co = Over-stocking cost = Cost/unit – Salvage value/unit = c – s = 1.5 – 0.5 = $1

The service level or probability of not stocking out, is set at,

Service Level = critical ratio = Cu/( Cu + Co) = 5.1/(5.1 + 1)

Service Level = critical ratio = 0.836

a)

Optimal Order Quantity = [=Norminv(service level,µ, ?)] = [=Norminv(0.836,5000, 2000)]

Optimal Order Quantity = O = 6857 CDs

b)

Expected Overstock = (O - µ)NORMDIST((O - µ)/?,0,1,1) + ?NORMDIST((O - µ)/?,0,1,0)

Expected Overstock = (6857 - 5000)NORMDIST((6857 - 5000)/2000,0,1,1) + (2000)NORMDIST((6857 - 5000)/2000,0,1,0)

From excel: Expected Overstock = 2130 CDs

2130 CDs are expected to be sold at discount rate.

c)

Expected sales at Topgun = Optimal Order quantity – Expected Overstock = 6857 – 2130 = 4826 Cds

Expected Profit at Topgun = (1 – f)(p)(expected sales) + (s)(overstock) – (c)(O) = (1-0.45)(12)(4826) + (0.5)(2130) – (1.5)(6857)

Expected Profit at Topgun = $22,484

d)

Expected profit at Studio = (c – v)O + (f)(p)(expected sales) =

= (1.50 – 1)(6857) + (0.45)(12)(4826) = $29,541

Expected profit at Studio = $29,541

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