A regional fast-food restaurant is considering an expansion program.The major fa

ID: 463503 • Letter: A

Question

A regional fast-food restaurant is considering an expansion program.The major factor influencing the success of such a program is the future level of interest rates.It is estimated that there is a 40 percent chance that interest rates will increase by 3 percentage points, a 35 percent chance that they will remain the same, and a 25 percent chance that they will decrease by 3 percentage points.The alternatives they are considering and possible payoffs are shown in the following table:

Rates Rates Rates

Increase No Change Decrease

Build 50 new places -$100,000 +$150,000 +$250,000

Build 25 new places -$80,000 +$100,000 +$180,000

Do Nothing -$50,000 +$50,000 +$125,000

Using decision tree analysis, calculate the expected value of each alternative, and decide which would be the best to follow.

Explanation / Answer

Expected Monetary Value (EMV) for alternative I = (Payoff of first state of nature) x (probability of first state of nature) + (Payoff of second state of nature) x (probability of second state of nature) + (Payoff of third state of nature) x (probability of third state of nature)

EMV(build 50 new places) = 0.4 x (-100000)+0.35 X (150000) +0.25 X (250000) = 75,000

EMV(build 25 new places) = 0.4 x (-80000)+0.35 X (100000) +0.25 X (180000) = 48,000

EMV(do nothing) = 0.4 x (-50000)+0.35 X (50000) +0.25 X (125000) = 28,750

States of Nature

Rates Increase

Rates No change

Rates decrease

Expected Monetary Value (EMV)

Build 50 new places

-100000

150000

250000

75000

Build 25 new places

-80000

100000

180000

48000

Do Nothing

-50000

50000

125000

28750

Probability

0.4

0.35

0.25

Largest Expected Monetary Value is 75,000 and decision is to build 50 new places