Modelling rare events - house sales

[jqewr]

I would like to model sales for construction project (building 10 cottages near the sea and sale them). The problem is that i need to take into account the uncertainty related to when cottages will be sold (term) and price. For example, I do not know when all 10 cottages will be sold - 1 can be sold in 2 month after construction, 3 cottages can be sold in 5 month etc. I was advised to use Poisson distribution to model sell term for every cottage, but for this reason I need to access parameter (lambda). 1) Can you advise please any means how I can access this parameter? 2) Can you help please with calculation - after I get the value of this parameter, i get the probability, but I need to get term (1 month/3 month etc). How can I calculate it? Maybe my approach for this reserach is not correct? My plan is to further prepare different scenarios (perhaps using Monte Carlo modelling) and based on it calculate NPV of the project

 

[BigBeachBanana]

I would like to model sales for construction project (building 10 cottages near the sea and sale them). The problem is that i need to take into account the uncertainty related to when cottages will be sold (term) and price. For example, I do not know when all 10 cottages will be sold - 1 can be sold in 2 month after construction, 3 cottages can be sold in 5 month etc. I was advised to use Poisson distribution to model sell term for every cottage, but for this reason I need to access parameter (lambda). 1) Can you advise please any means how I can access this parameter? 2) Can you help please with calculation - after I get the value of this parameter, i get the probability, but I need to get term (1 month/3 month etc). How can I calculate it? Maybe my approach for this reserach is not correct? My plan is to further prepare different scenarios (perhaps using Monte Carlo modelling) and based on it calculate NPV of the project

Lambda is the rate at which the event occurs within an interval of time. For example, if you sold, on average, 1.5 houses per year, then lambda = 1.5. The parameter of distributions is estimated based on historical data.

 

[jqewr]

Lambda is the rate at which the event occurs within an interval of time. For example, if you sold, on average, 1.5 houses per year, then lambda = 1.5. The parameter of distributions is estimated based on historical data.

Thanks. What about 2nd question?

 

[BigBeachBanana]

Thanks. What about 2nd question?

You can convert lambda into a different time interval and recalculate the probability. For example, if lambda = 1.5/year then the adjusted monthly lambda is 1.5/12.

 

[jqewr]

You can convert lambda into a different time interval and recalculate the probability. For example, if lambda = 1.5/year then the adjusted monthly lambda is 1.5/12.

I see, but the question is that How can I convert probability to term (month)? because I need term, not the probability

 

[BigBeachBanana]

I see, but the question is that How can I convert probability to term (month)? because I need term, not the probability

I don't understand what "term" means.
Assuming you want to calculate the NPV incorporating interest rate and probability of selling. A simple example
The house is 100,000, the interest rate is 5%, probability of selling the house in 1 year is 10%

[math]NPV = 100,000(1.05)^{-1}(0.1)[/math]
Extend this to multiple houses and timing.

 

[jqewr]

I don't understand what "term" means.
Assuming you want to calculate the NPV incorporating interest rate and probability of selling. A simple example
The house is 100,000, the interest rate is 5%, probability of selling the house in 1 year is 10%

[math]NPV = 100,000(1.05)^{-1}(0.1)[/math]
Extend this to multiple houses and timing.

Term means period when house will be sold (for example 1st house will be sold in 1 month, 2nd in 5 month etc). I need this figures. Then I would like to calculate npv as :
[imath]NPV = - Initial_Investment + Price_1/(1+i)^term1 +Price_2/(1+i)^term2...[/imath]
Where price_1 is price for 1st house, term_1 - period when 1st house will be sold

 

[BigBeachBanana]

Term means period when house will be sold (for example 1st house will be sold in 1 month, 2nd in 5 month etc). I need this figures. Then I would like to calculate npv as :
[imath]NPV = - Initial_Investment + Price_1/(1+i)^term1 +Price_2/(1+i)^term2...[/imath]
Where price_1 is price for 1st house, term_1 - period when 1st house will be sold

Then you're not looking for the probability a house is sold within a period of time. You're looking for the waiting time until the next house is sold which is the inverse of the Poisson. The exponential distribution is what you're looking for with the parameter [imath]\theta = \dfrac{1}{\lambda}[/imath], where [imath]\lambda[/imath] is the parameter of the Poisson.

 

[jqewr]

Then you're not looking for the probability a house is sold within a period of time. You're looking for the waiting time until the next house is sold which is the inverse of the Poisson. The exponential distribution is what you're looking for with the parameter [imath]\theta = \dfrac{1}{\lambda}[/imath], where [imath]\lambda[/imath] is the parameter of the Poisson.

Thanks