You are considering purchasing an apartment complex. Before deciding, you would

Question

You are considering purchasing an apartment complex. Before deciding, you would like to do a risk analysis of the situation to assess whether or not the investment is a good idea for you. The complex has 40 units. Historical data indicate that the number of units rented in a given month is distributed uniformly between 30 and 40 units. The rent per unit, which you are not likely to change since demand is very price sensitive, is $600 per month. Monthly expenses for the entire complex seem to be normally distributed with mean $17,000 and standard deviation $1,500. a. Develop an @RISK simulation

b.According to your simulation results what is the expected monthly profit

c.According to the simulation results what is the probability of making a profit in any given month?

d.Suppose your debt payments on this complex will be $2,400 per month. Would you take this investment? Defend your decision using the simulation output data.

e.How many trials would you need to estimate mean profit within $50 for a 95 percent confidence level?

Explanation / Answer

solving first 4

a)

we run a simulation of 1000 points using R and the code below

units<-sample( 30:40, 10000, T)
revenue = units*600
cost = rnorm(10000, 17000, 1500)
profit = revenue-cost
mean(profit)

b)

we get expected value =4047.963

theoretical expected value = .

revenue=5(30+40)*600

cost 17000

profit= 4000

c)

from R we calulate the probability that profit is greater thaa . 0 as

> sum(profit >0)
[1] 947
> 947/1000
[1] 0.947

so probablity ~.95

d)

now profit =

profit = revenue-cost-2400

so

> sum(profit >0)
[1] 715

probabilty is ~.7

yeswecan still go for the investment

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