Question

A mid-sized chain restaurant is considering growing their business and opening additional restaurants in new markets. One of the key factors in making this decision will be the level of interest rates over the next few years. It is estimated that there is a 30% chance that interest rates will go down by 2 percentage points, a 60% chance that they will stay the same, and a 10% chance that they will go up by 2 percentage points. The expansion options that they are considering and possible payoffs are shown in the table below.

Which alternative is best, based on expected value?

	Rates down	Rates	Rates up
	2 percent	unchanged	2 percent
Open 20 restaurants	‑$200,000	$90,000.00	$150,000
Open 10 restaurants	‑$115,000	$40,000.00	$80,000.00
Do nothing	-$70,000.00	$0.00	$5,000.00

Answer 1

As given in the question the restaurant is considering growing of their business and oe of the key factor to take this decision about expansion is level of interest over next few years so the possible payoffs for posible interest rates changes needs to be considered for deciding which alternative is best from given alternatives.

The alternatives given n the questions are-1)Opening of 20 restaurants 2)Opening of 10 restaurants 3)Do nothing.

Probability of interest rates going down by 2% in next few years is 30% i.e 30/100=0.30(diveded by 100 because total of probability percent is 100%)

Probability of interest rates will remai unchanged is 60% i.e 60/100=0.60

Probability of interest rates will go up by 2% points is 10% i.e 10/100=0.10

so total payoff in each of the alternatives needs to be calculated and the alternative having highest payoff should be considered to be best alternative the total expected payoff can be obtained by multiplying the payoffs in each interst scenario into its probability:-

Payoff in case of alternative

1)Opening of 20 restaurants= -200000$*0.30+90000$*0.60+150000$*0.10= -60000$+54000$+15000$=9000$

2)Opening of 10 restaurants= -115000$*0.30+40000$*0.60+80000$*0.10= -34500$+24000$+8000$= -2500$.

3)Do Nothing = -70000$*0.30+0$*0.60+5000$*0.10= -21000$+0$+500$= -20500$

Alternative 1)Opening of 20 restaurants has the highest payoff compare to other alternatives so it is the best alternative.

so the mid-sized chain restaurant should go ahead with opening 20 restaurants.

Note-It is assumed that the payoff indicated in - is negative payoff or expenses and + is positive payoff or income.