Decision Analysis A small business owner is considering whether to open a new st

Question

Decision Analysis

A small business owner is considering whether to open a new store on the other side of town or wait one year and then open the store. In the meantime, she paid $10,000 for a one year option on a building. If she opens the store now it will cost $140,000 to refurbish it, but it will cost $160,000 if she waits one year.

She expects sales to depend on the economy in the area at the time she opens the store. If she goes ahead now, there is a 50% chance the economy will go up, 30% it will stay the same, and 20% it will go down. She then expects the following returns: if the economy goes up $200,000; stays the same $160,000; and goes down $20,000.               

If she waits one year, she can either open the store then or not open the store and let the option expire. If the option expires, she will lose the $10,000. One year from now she expects there is a 40% chance the economy will go up, 30% stay the same, and 30% go down. The returns she expects to get would then be: if the economy goes up $180,000; stays the same $160,000; and goes down $30,000.

a.   What is the expected value of opening the store now?

b.   What is the expected value of waiting one year to open the store?

c.   What should the small business owner do and what is the expected value of that decision?

Explanation / Answer

a)Expected value now = 0.5*200000+ 0.3*160000+0.2*-20000 -140000 = 4000

b) Expected value = 0.4*180000+0.3*160000+0.3*-30000 - 160000 = -49000

She should open the store now. Expected value = 4000 - 10000 paid=-6000

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