Hohenheim Management Master (HMM)
Theory of the firm – winter semester 09/10 Mini Case Study 1
Accounting vs. economic profits (here concept of residual income)
West House Inc. faces the decision of replacing is existing production technology with a new
plant. Expected useful life for the new plant is estimated at T = 5. Since West House retained
substantial (cash) profits in the firm in recent years, it will pay cash for the new technology
and investment expenditure is I = $ 250.000. West House uses straight line depreciation on its
assets. All inventories are valued at variable cost. Replacement of inventory occurs under the
LOFO-assumption. Assume for your computations that demand is first met from current
production and then depletion of inventory.
The new technology allows for the production 5.000 units of a product x in each period whose
sales price is remains constant for periods 1-5 at p = $ 60. (Cash); variable cost for the
product is $ 40 per unit in period 1-2 and will increase to $ 50 per unit in period 3-5 (higher
direct labor costs). West House’s terms of credit state for future deliveries that the firm
expects a 50% down payment receivable at the end of the order period. Orders for x are
considered certain and occur as follows:
Period 0: Payment for new plant
Period 1: Demand x: 5000 units for XY Inc., immediate cash settlement
Period 2: Demand x: 1.000 units for XY Inc., immediate cash settlement, AB Inc. orders 4.000
units, scheduled delivery date end of period 4.
Period 3: Demand x: 1.000 units for XY Inc, immediate cash settlement, AB Inc. orders 4.000
units, scheduled delivery date end of period 5.
Period 4: Demand x: 5.000 units for XY Inc., immediate cash settlement.
Period 5: Demand x: 5.000 units for XY Inc., immediate cash settlement.
The certain interest rate is 10% (0.1) for all periods.
To do:
a) Find the relevant (net) cash flow for periods 0-5. Should West House Inc undertake the
investment?
b) Find the relevant accounting profits for periods 1-5? Use the present value of accounting
profits to decide, whether West House should invest in the new plant. Explain the resulting
decision!
c) Compute the investment’s economic profit (here residual income) and find its present
value. What are the implications of this result?
d) Now assume that the relevant interest rate drops to 9% (0.09). West House’s production
manager finds that there exists an alternative plant design. Investment expenditure is I2 =
$ 250.000 and useful life is also T = 5 (plant is worthless at the end of T = 5). Straight-line
depreciation is used for this plant as well. This plant design allows for the production of a
slightly modified product x2 = 5.000 units each period and it is assumed that this output is
sold for an immediate cash settlement at the end of each period (no inventory). The price
for x2 is p2 = $ 55 per unit for periods 1-5. (Cash-) variable costs per unit are $ 40 for
periods 1-2 and $ 45 for periods 3-5. What plant design should West House choose (if
any)?
e) Delegation of investment authority: West House’s CEO is Jack Soon_to_retire, MBA.
West House’s incentive and reward scheme states that Jack receives (has to pay) 1%
(0.01) of the firms’s economic profit (here residual income) each period. Jack expects to
retire at the end of period 2 and his fixed salary is assumed sufficiently high for him to be
able to meet any payment obligations of a negative residual income. Will Jack take a
decision that maximizes shareholder wealth? Comment!
Hints:
a) Cash flow: (in thousand $) [-250, 100, -20, -70, 170, 170], NPV < 0 (Do not invest)
b) Accounting profits (in thousand $) [50, -30, -40, 80, 40], PV(AP) > 0 (investment occurs)
c) Economic profit (residual income in thousand $) [25, -50, -59, -58, 27], (Do not invest)
d) Cash flow, new plant design [-250, 75, 75, 50, 50, 50], NPV2 < 0  do not invest. Old
plant design NPV1(i = 0.09) > 0  Do invest.
e) Jack will choose the “bad” plant design with NPV2 < 0!