Question

Before negotiating a long-term construction contract, build- ing contractors must carefully estimate the total cost of completing the project. Benzion Barlev of New York University proposed a model for total cost of a long-term contract based on the normal distribution(Journal of Business Finance and Accounting, July 1995). For one particular construction contract, Barlev assumed total cost, x, to be normally distributed with mean $850,000 and standard deviation $170,000. The revenue, R, promised to the contractor is $1,00,000.

Required:
a. The contract will be profitable if revenue exceeds total cost. What is the probability that the co ntract will be profitable for the contractor?
b. What is the probability that the project will result in a loss for the contractor?
c. Suppose the contractor has the opportunity to renegotiate the contract. What value of R should the contractor strive for in order to have a .99 probability of making a profit?

Answer 1

Benzion Barlev of New York University

NEGOTIATION OF A LONG-TERM CONSTRUCTION CONTRACT

a. The probability that the contract will be profitable for the contractor is:

= 81%

b. The probability that the project will result in a loss for the contractor is:

= 19%

c. The value of R that the contractor should strive for in order to have a .99 probability of making a profit is:

= $1,246,100.

Step-by-step explanation:

a) Data and Calculations:

Mean total cost (x) = $850,000

Standard deviation = $170,000

Revenue = $1,000,000

Probability of being profitable = (R - x)/std deviation

= ($1,000,000 - $850,000)/$170,000

= $150,000/$170,000

= 0.882

From Z table, 0.882 = 0.81057 = 81%

Probability of loss = 19% (100 - 81%)

To have a 99% (0.99) probability of making a profit, Z value = 2.33 from the Z table:

(R - x)/std deviation = 2.33

(R - x) = 2.33 * $170,000

= $396,100

(R - $850,000) = $396,100

R = $396,100 + $850,000

R = $1,246,100