Question

Strassel Investors buys real estate, develops it, and resells it for a profit. A new property is available, and Bud Strassel, the president and owner of Strassel Investors, believes if he purchases and develops this property it can then be sold for $155000. The current property owner has asked for bids and stated that the property will be sold for the highest bid in excess of $100000. Two competitors will be submitting bids for the property. Strassel does not know what the competitors will bid, but he assumes for planning purposes that the amount bid by each competitor will be uniformly distributed between $100000 and $145000.

a. Develop a worksheet that can be used to simulate the bids made by the two competitors. Strassel is considering a bid of $125000 for the property. Using a simulation of 1000 trials, what is the estimate of the probability Strassel will be able to obtain the property using a bid of $125000? Round your answer to 1 decimal place. Enter your answer as a percent.

b. Use the simulation model to compute the profit for each trial of the simulation run. With maximization of profit as Strassel’s objective, use simulation to evaluate Strassel’s bid alternatives of $125000, $135000, or $145000. What is the recommended bid, and what is the expected profit?

Answer 1

A.

The total interval is 145000-100000 = 45000

The other 2 winners bid uniformly between the start and end points, so probabilities are uniformly distributed for win/loss

If Strassel bid is 125000

therefore Strassel wins (125000-100000)/45000 = 55.6% times against 1 bidder

Against both bidders, Strassel would have to win against each of them independently, therefore win 55.6% * 55.6% = 30.9% of the times

If Strassel bid is 135000

Against both bidders, using same logic as above, Strassel would win 77.8% * 77.8% = 60.5% of the times

If Strassel bid is 145000

Since Strassel has bid the highest, against both bidders, using same logic as above, Strassel would win 100% of the times!

We assume in these cases that in case of tie, Strassel would win.

B.

Profit:

Case 1 = 0.309 * (155000-125000) = $9,259

Case 2 = 0.605 * (155000-135000) = $12,098

Case 3 = 1 * (155000-145000) = $10,000

Therefore recommended bid is $135,000 and the estimated profit is $12,098

Worksheet is given below. Simulated by random number up to 1000 rows. I have only given first few rows due to space constraint

			random1	random2	bid1	bid2	win1	win2	win	simulated wins		total wins	percent
		1	0.355602	0.288527	4	3	1	1	1	583	554	307	31%
		2	0.514042	0.547169	5	5	1	1	1
		3	0.276026	0.727693	3	7	1	0	0
		4	0.040496	0.526015	0	5	1	1	1
		5	0.540871	0.82348	5	8	1	0	0
		6	0.315083	0.081181	3	1	1	1	1					win		profit
1	100000	7	0.859022	0.277518	9	3	0	1	0		25000	20000	45000	0.555556	0.308642	9259.259
2	105000	8	0.132149	0.08512	1	1	1	1	1		35000	10000	45000	0.777778	0.604938	12098.77
3	110000	9	0.632255	0.978488	6	10	0	0	0		45000	0	45000	1	1	10000
4	115000	10	0.915841	0.724907	9	7	0	0	0
5	120000	11	0.823775	0.174383	8	2	0	1	0
6	125000	12	0.083028	0.344359	1	3	1	1	1
7	130000	13	0.712683	0.295336	7	3	0	1	0
8	135000	14	0.067634	0.295011	1	3	1	1	1
9	140000	15	0.822325	0.095052	8	1	0	1	0
10	145000	16	0.733952	0.228798	7	2	0	1	0
		17	0.117918	0.401072	1	4	1	1	1
		18	0.334256	0.797895	3	8	1	0	0
		19	0.163273	0.346425	2	3	1	1	1
		20	0.697902	0.440001	7	4	0	1	0
		21	0.462317	0.697812	5	7	1	0	0
		22	0.858809	0.439994	9	4	0	1	0
		23	0.646317	0.952174	6	10	0	0	0
		24	0.813409	0.518206	8	5	0	1	0
		25	0.219426	0.144305	2	1	1	1	1
		26	0.692166	0.965413	7	10	0	0	0
		27	0.363265	0.740157	4	7	1	0	0