Eppen Handgun Manufacturing, Inc. is considering building a plant in New Haven, Connecticut. If built, the plant will be worth $190 million. Eppen does not know the cost of the plant; it is between $150 million and $200 million, with equal probability for all costs within that interval; this implies that the expected cost is $175 million. The manager of Eppen’s Northeast Division, Rick Antle, knows the cost. Eppen delegates decision rights to its divisional managers by setting capital budgets. Antle will build the plant if the capital budget chosen by Eppen, B, exceeds the cost of the plant, C, and not otherwise. For example, if Eppen chooses B = $180 million, the plant will be build when Antle sees that the cost is between $150 million and $180 million (a 60% chance), and not when the cost is between $180 million and $200 million (a 40% chance.) What happens to the excess of the budgeted amount over the cost (B – C) depends on the quality of Eppen’s internal control system.

a. Suppose Eppen’s internal control system prevents Antle from spending any slack in the budget, B – C, so any funds budgeted in excess of the cost of the plant go back to Eppen. What budget B should Eppen set? What is the expected payoff to Eppen? (Note that Antle’s payoff is zero in this case.)

b. Suppose Eppen has no internal control system, so Antle spends any slack in the budget on perquisites that benefit Antle but not Eppen. This implies that Eppen will spend B whenever the plant is built; C for the plant (as in part a), and B – C to Antle. What budget B should Eppen set? What is the expected payoff to Eppen? What is the expected payoff to Antle?

c. You should find that Eppen’s expected payoff in in part a is greater than the sum of the expected payoffs to Eppen and Antle in part b. Explain the difference intuitively.

[This problem is based on Rick Antle’s and Gary Eppen’s “Capital Rationing and

Organizational Slack in Capital Budgeting,” Management Science (Spring 1983).]