Question

A corporation is trying to decide whether to open a new factory outlet store. The store will have high, medium, or low demand. Before it decides whether to open the store, the corporation can pay $7,000 immediately for a market survey. The market survey can predict 'high,' 'medium,' or 'low' demand. If the actual demand of the store will be high, there is a 0.6 probability the survey will predict 'high' demand, a 0.06 probability the survey will predict 'medium' demand, and a 0.34 probability the survey will predict 'low' demand. If the store will actually have medium demand, there is a 0.26 probability the survey will predict 'high' demand, a 0.36 probability the survey will predict 'medium' demand, and a 0.38 probability the store will predict 'low' demand. If the store will actually have low demand, there is a 0.04 probability the survey will predict 'high' demand, a 0.14 probability the survey will predict 'medium' demand, and a 0.82 probability the survey will predict 'low' demand. If the corporation decides not to take the market survey, there is a 0.22 probability the store will have high demand, a 0.57 probability the store will have medium demand, and a 0.21 probability the store will have low demand. If the corporation decides to open a store, the immediate cost of opening the store is $382,000, and the store must remain open for exactly 4 years. If demand is high, the store will EARN $0.5 million for each year that the store is open. If demand is medium, the store will EARN $200,000 for each year that the store is open. If demand is low, the store will LOSE $113,000 for each year that the store is open. You should assume that demand remains the same for each year that the store is open. There is no salvage value, and you can ignore taxes. If the corporation decides not to open a store, the corporation has a net present worth = $0 minus the cost of the survey (if the corporation takes the survey). The corporation's MARR is 12%. The corporation will choose the alternative with the largest expected net present worth (NPW). What is the expected NPW of the best alternative?

Answer 1

As taking the survey will only predict the demand,but actual demand will be independent from the survey it is advisable not to take survey. Eventhough survey is taken, survey will fail to predict the probabilties accurately when actual probability is lower(which has the hihger probability if survey is not taken).

Alternative 1: Store is opened

1.1 If Store has the high demand (Probability 0.22):

Total Cash Inflow would be $0.5Mn * 4 Years = $2mn

1.2 If Store has the medium demand (Probability 0.57): :

Total Cash Inflow would be $0.2Mn * 4 Years = $0.8mn

1.3 If Store has the low demand (Probability 0.21): :

Total Cash Inflow would be $ -0.113Mn * 4 Years = $ -0.45mn

Expected Cash Inflow = ($ 2mn*0.22)+($ 0.8Mn*0.57)+($ -0.45mn*0.21) = 0.80 Mn over 4 years i.e. 0.20 Mn per Year.

Present Value of Cash Inflow = 0.20 Mn / (1/1.12)^4 = 0.61 Mn

NPW = Present Value of cash inflow - Present value pf cash outflow

(Cash outflow in this case is immediate cost of opening the store I.e. $ 0.38 Mn, as it is spent immediately present value of this remain 0.38 Mn only)

NPW = $ 0.61Mn - $ 0.38Mn = $ 0.23Mn

Alternative 2: Store is not opened

NPW = $0 Mn

Conclusion:

Alternative 1 has higher NPW than Alternative 2, it is advisable to open the store.