As indicated in the chapter, there are goal-congruency problems associated with the use of ROI as an indicator of investment-center financial performance. One such problem relates to the bias against accepting new investments because of the adverse effect on a center’s ROI metric. Assume, for example, that a manager of an investment center can invest in a new, depreciable asset costing $30,000, and that this asset has a three-year life with no salvage value. Cash inflows associated with this investment are projected to be as follows: $12,000, $14,400, and $17,280. (Ignore taxes.) This scenario leads to an estimated internal rate of return (IRR) of 20 percent. Assume that the minimum required rate of return is 15 percent.

Required

1. Demonstrate, using the IRR function in Excel, that the IRR on this proposed investment is indeed 20 percent.

2. Calculate the year-by-year ROI (accounting rate of return) on this proposed investment, using each year as the denominator of your calculation the beginning-of-year book value of the asset. Assume the asset will be depreciated using the straight-line method. What incentive effects can you anticipate based on the data you generated?

3. Recalculate the year-by-year ROI (accounting rate of return) on this proposed investment, this time using “present value” depreciation (defined as the change in the present value of the asset during the period). Use the project’s anticipated IRR (20 percent) as the discount factor in your calculations. As in (2) above, define the denominator of your calculation as the beginning-of-year book value of the investment.

(Your depreciation figures should be $6,000, $9,600, and $14,400, respectively, for years 1, 2, and 3.) What incentive effects do you anticipate based on your calculations?

4. Calculate for each of three years the residual income (RI) for this proposed investment. RI is defined as income after (present-value) depreciation and after a capital charge assessed on beginning-of-year book value of the asset. For purposes of these calculations assume a 10 percent cost of capital (discount rate).

Use the built-in function in Excel to estimate the NPV of the proposed investment. (Your answer should be approximately $5,800.) At a discount rate of 10 percent, determine the net present value (NPV) of the residual income (RI) figures you estimated. What is the potential value of using multiyear RI figures determined with present-value depreciation?