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The Economic Value Added (EVA) is a measure of surplus value created on an investment. Define the return on capital (ROC) to be the ìtrueî cash flow return on capital earned on an investment. Define the cost of capital as the weighted average of the costs of the different financing instruments used to finance the investment.

EVA = (Return on Capital - Cost of Capital) (Capital Invested in Project)

Things to Note about EVA

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EVA is a measure of dollar surplus value, not the percentage difference in returns. It is closest in both theory and construct to the net present value of a project in capital budgeting, as opposed to the IRR. The value of a firm, in DCF terms, can be written in terms of the EVA of projects in place and the present value of the EVA of future projects.

DCF Value and NPV Value of Firm = Value of Assets in Place + Value of Future Growth = ( Investment in Existing Assets + NPVAssets in Place) + NPV of all future projects

= ( I + NPVAssets in Place) + where there are expected to be N projects yielding surplus value (or excess returns) in the future and I is the capital invested in assets in place (which might or might not be equal to the book value of these assets). The Basics of NPV

NPVj = :

Life of the project is n years

Initial Investment =

: Alternative Investment

NPVj =

= NPV to EVA (Continued)

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Define ROC = EBIT (1-t) / Initial Investment: The earnings before interest and taxes are assumed to measure true earnings on the project and should not be contaminated by capital charges (such as leases) or expenditures whose benefits accrue to future projects (such as R & D). Assume that return of capital. : The present value of depreciation covers the present value of capital invested, i.e, it is a

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DCF Valuation, NPV and EVA

Value of Firm = ( I + NPVAssets in Place) +

=

=

= In other words,

Firm Value = Capital Invested in Assets in Place + PV of EVA from Assets in Place + Sum of PV of EVA from new projects

A Simple Illustration Assume that you have a firm with IA = 100 In each year 1-5, assume that ROCA = 15%

∆ I = 10 (Investments are at beginning of each year)

WACCA = 10% ROCNew Projects = 15% WACC = 10%

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Assume that all of these projects will have infinite lives.

After year 5, assume that

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Investments will grow at 5% a year forever ROC on projects will be equal to the cost of capital (10%)

Firm Value using EVA Approach Capital Invested in Assets in Place = $ 100 EVA from Assets in Place = (.15 - .10) (100)/.10 = $ 50 + PV of EVA from New Investments in Year 1 = [(.15 - .10)(10)/.10] = $ 5 + PV of EVA from New Investments in Year 2 = [(.15 - .10)(10)/.10]/1.12 = $ 4.55 + PV of EVA from New Investments in Year 3 = [(.15 - .10)(10)/.10]/1.13 = $ 4.13

+ PV of EVA from New Investments in Year 4 = [(.15 - .10)(10)/.10]/1.14 = $ 3.76 + PV of EVA from New Investments in Year 5 = [(.15 - .10)(10)/.10]/1.15 = $ 3.42 Value of Firm = $ 170.86 Firm Value using DCF Valuation Base Year EBIT(1-t) from Assets in Place EBIT(1-t): yr 1 EBIT(1-t) in yr 2 EBIT(1-t) in yr 3 EBIT(1-t) in yr 4 EBIT(1-t) in yr 5 EBIT(1-t) - Net Capital Expenditures FCFF PV of FCFF Terminal Value PV of Terminal Value Value of Firm $170.85 10.00 -10.00 -10.00 15 1 15 1.50 2 15 1.50 1.50 3 15 1.50 1.50 1.50 4 15 1.50 1.50 1.50 1.50 5 15 1.50 1.50 1.50 1.50 1.50 16.50 10.00 6.50 $ 5.91 18.00 10.00 8.00 $6.61 19.50 10.00 9.50 $7.14 21.00 10.00 11.00 $7.51 22.50 11.25 11.25 $6.99 $236.25 $146.69 23.63 11.81 11.81 Terminal Year

In Summary

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Both EVA and Discounted Cash Flow Valuation should provide us with the same estimate for the value of a firm. In their full forms, the information that is required for both approaches is exactly the same - expected cash flows over time and costs of capital over time. A policy of maximizing the present value of economic value added over time should be the equivalent of a...