Question

I have been getting many incorrect answers recently, if you are unsure please do not attempt. All i ask is all parts answered and with shown or explained work. Thank you (:

Delaware National Golf Club went out of business during the recent downturn in the economy (a sad day in the Donnelly household). Susan is a real estate developer who would like to build houses on a portion of it. To do so Susan will need the approval of the county government to change how the land is zoned. The following decision table shows the scenario's payoffs and probabilities.

	Market
Alternative	County Approval	No County Approval
Purchase land	$1,500,000	−$1,600,000
Don't purchase land	$0	$0
Probability	0.30	0.70

Susan has the choice of purchasing an option to buy the land next year for $30,000. This will give her the opportunity to gain the support of the homeowners on the golf course, which will increase the likelihood of the county approving the zoning change. Susan estimates there is a 40% chance she will be able to obtain the support of the residents. With the support of the residents, the probability that the county will approve the zoning change is 56.6%. Without the residents' support, the probability of the county's approval is only 12.1%.

a. Construct a decision tree to recommend a course of action for Susan.

b. What is the most that Susan should pay to purchase the option to buy the land?

Answer 1

At the first level Susan has 2 choices, buy an option or don't buy an option. Isshe does not buy the option then she has 2 choices, purchase or don't purchase the land

If she buys the option then she can obtain the support of residents or fail to obtain the support.

Either case she has 2 choices, purchase or don't purchase.

a) The decision tree is given below

To calculate the expected value, we start from rigth to left

• Node 7 (chance node)  

she has to spend $30,000 on the option

payoff if she gets approval is $1500,000-30,000 = $1,470,000 with a probability of 0.566

payoff if she does not get approval is -$1,600,000-30,000= -$1,630,000 with a probability of 0.433

The expected value of node 7 is

• Node 8 (chance node)  

she has to spend $30,000 on the option

payoff if she gets approval is $1500,000-30,000 = $1,470,000 with a probability of 0.121

payoff if she does not get approval is -$1,600,000-30,000= -$1,630,000 with a probability of 0.879

The expected value of node 8 is

• Node 4 (Decision node)

Decision is between purchase land (EV=$124,600) and don't purchase land (-$30,000)

The optiomum decision is to purchase.

EV for node 4 is $124,600

• Node 5 (decision node)

Decision is between purchase land (EV= -$1,254,900) and don't purchase land (-$30,000)

The optiomum decision is don't purchase.

EV for node 5 is -$30,000

• Node 6 (chance node)

payoff if she gets approval is $1500,000 with a probability of 0.30

payoff if she does not get approval is -$1,600,000 with a probability of 0.70

The expected value of node 6 is

• node 2 (chance node)

EV if support of residents is obtained is $124,600 with a probability of 0.40

EV if the support of residents is not obtained is -$30,000 with a probability of 0.60

EV of node 2 is

• Node 3 (decision node)

Decision is between purchase land (EV= -$670,00) and don't purchase land ($0)

The optiomum decision is don't purchase.

EV for node 3 is $0

At node 1 which is the decision node, there are 2 choices for Susan

If she buys the option then the expected payoff is $31,840

if she does not buy the option then the expected payoff is $0

Hence the optimum decision for Susan is to buy the option for $30,000

b) The expected payoff at node 2 calculated above is #31,840. This payoff is after subtracting the cost of option which is $30,000. That means the expected value of purchasing the option is 31,840+30000=$61,840

This value we will call as expected value with sample information EVwSI, as purchasing the option lets Susan to try to gauge if the residents are going to vote in favor or against the Golf course.

If she does not purchase the option then she will have to take a decision, without theextra help of the residents. The expected payoff then is $0. This we will call as expected value withpout the sample information EVwoSI

The expected value of purchaing the option then is

(expected payoff when option is purchased) - (expected payoff when option is not purchased)

=61,840 - 0 -= 61,840

Susan should be ready to pay at the most $61,840 to purchase the option to buy the land