^{Thurber Company made an investment that resulted in an $80 cash outflow at the beginning of year 1 (shown as time 0 below) and will return $55 cash inflow at the end of year 1 and $60.5 cash inflow at the end of year 2. This $80 investment was financed by a combination of debt and equity with a WACC (weighted average cost of capital) of 10%. Thurber does not pay any income tax. The cash flows associated with this investment over time can be depicted as:}

^{Time 0 Time 1 Time 2}

^{80 55 60.5}

^{The present value of a dollar amount n periods in the future discounted at an interest rate i per period is the amount multiplied by a factor equal to (1+i)-n (see Datar and Rajan pp. 447-448 for an example). Thus, based on the facts and formula above, the net present value (NPV) of the cash outflow and inflows, discounted back to time 0 at the 10% WACC, is}

^{NPV = 80 + (55 / 1.10) + (60.5 / (1.10)2) = 80 + 50 + 50 = 20}

^{Parts 1, 2, and 3 below ask you to consider how this investment is accounted for in financial statements prepared under generally accepted accounting principles (GAAP). In all three parts, assume the revenue is recognized at the time of the cash inflows, i.e., $55 of revenue at time 1 and $60.5 at time 2. In contrast, the timing of the recognition of expense is different across the three parts and specifically depends on whether the $80 cash outflow represents an investment in}

^{1) research and development (where GAAP requires the entire expenditure to be recognized as an expense when incurred),}

^{2) Land (where GAAP generally recognizes no expense until disposal of the Land), or}

^{3) Plant and Equipment (where GAAP generally recognizes expense by allocating the cost across the periods benefited).}

^{EVA is conceptually equivalent to NPV. While the present value of the entire stream of EVA is independent of the accounting method used, EVA in individual years depends strongly on the accounting method used, which demonstrates that EVA is not operationally equivalent to NPV.}

^{1. Suppose this is an $80 investment in R&D. Assume R&D expenditures are accounted for as expense when incurred (as required under GAAP). The effect of this accounting on the income measure, net operating profit after tax (NOPAT), is straightforward, but the effect on the cost of capital invested requires more explanation.}

^{Because the $80 is expensed immediately, it is immediately deducted from equity (so Debt+Equity is immediately reduced by the full $80) and immediately deducted from Net Assets (the reduction in Cash reduces Net Assets by the full $80). Therefore, for this first example the cost of capital invested in every period is always zero capital invested multiplied by the WACC for the period, and this product is of course always zero.}

^{One additional consideration in calculating the cost of invested capital applies to all three examples. The cost of capital is the amount invested multiplied by the WACC for the period invested, so the WACC depends on the length of the period. The WACC for 1 year (10% throughout this example) is about twice as large as the WACC for 1/2 year (or about 5% in this example) and about four times as large as the WACC for 1/4 year. In the extreme, as the length of the period goes to zero, the WACC for the extremely short period also goes to zero. Therefore, in all three parts of the example, the WACC for time 0 is always zero, so the cost of invested capital deducted from NOPAT for time 0 is always zero. To remind you that the cost of invested capital in time 0 is always zero because the WACC is always zero, the investment throughout the preceding year is missing in the tables below for all three parts of the exercise. In contrast, there is a non-zero amount shown as the investment in the year preceding time 1 and the year preceding time 2 in parts 2 and 3 (though not here in part 1), so the tables always show the amount invested during the preceding year for time 1 and 2.}

^{Under this assumption, the effects of this investment on GAAP measures of NOPAT and invested capital at times 0, 1, and 2 are:}

Year 0 1 2

^{Revenue 0 55 60.5}

^{Less: Expense 80 0 0}

^{NOPAT 80 55 60.5}

^{Investment during preceding year}

^{Net Assets = Debt + Equity 0 0}

^{a. Calculate the incremental effect of this investment on EVA for each of the years 0, 1, and 2, where the incremental effect on EVA for the year is the NOPAT less the cost of the capital invested during the preceding year multiplied by the 10% WACC.}

^{b. Calculate the present value of the incremental effects on EVA for years 0, 1, and 2. (Note that for part 1, the stream of EVA across years 0, 1, and 2 is exactly the same as the stream of cash flows so your calculation of the present value of the stream of EVA will be the same as your calculation of the present value of the stream of cash flows.)}

^{2. Suppose this is an investment in Land where the land is rented out for $55 in year 1, for $60.5 in year 2 and then sold at the end of year 2 for its residual value, which is assumed to be $0. (A zero residual value at disposal is unusual for land, but we want to hold the facts about total cash flows consistent across all three parts of this example.)}

^{Under this assumption, land is an asset at the time it is purchased and the cost of the land ($80) is expensed at the time of sale. Therefore, the effects of this investment on NOPAT and invested capital for years 0, 1, and 2 are:}

^{Year 0 1 2}

^{Revenue 0 55 60.5}

^{Less: Expense 0 0 80}

^{NOPAT 0 55 19.5}

^{Investment during preceding year}

^{Net Assets = Debt + Equity 80 80}

^{a. Calculate the incremental effect of this investment on EVA for each of the years 0, 1, and 2.}

^{b. Calculate the present value of the incremental effects on EVA for years 0, 1, and 2.}

^{3. Suppose this is an investment in Plant and Equipment where the cost of this P&E is accounted for as an asset and then depreciated on a straight line basis at times 1 and 2. The effects of this investment on NOPAT and invested capital at times 0, 1, and 2 are:}

^{Year 0 1 2}

^{Revenue 0 55 60.5}

^{Less: Expense 0 40 40}

^{NOPAT 0 15 20.5}

^{Investment during preceding year}

^{Net Assets = Debt + Equity 80 40}

^{a. Calculate the incremental effect of this investment on EVA for each of the years 0, 1, and 2.}

^{b. Calculate the present value of the incremental effects on EVA for years 0, 1, and 2.}