As a cumulative valuation, MVA should represent the stock market's assessment of a company's lifetime NPV. MVA maximisation should therefore be the primary managerial objective for any firm concerned with shareholder welfare. If we also accept our earlier proposition that for capital budgeting purposes, lifetime EVA is equivalent to lifetime net cash flow, it follows that if all future EVA is discounted to a present value using a post-tax WACC, the balance must be equivalent to the NPV of all a firm's projects. Thus we can define MVA using the following serial equality.

(5) MVA = PV (SEVA) = SNPV

To understand the equation implications for management and investors, let us examine it in more detail. We already know from Equation (2) that MVA equals market value (V) minus book value (C).

(2) MVA = V - C

According to Stewart (op cit) it is also "a mathematical truism that market value is determined by discounting anticipated EVA using a WACC and adding it to the current capital balance, since an EVA summation approximates to lifetime free cash flow". So, we can define:

(6) V = C + PV (SEVA)

And taking the difference between Equations (2) and (6)

(7) MVA = PV (SEVA)

Because EVA excludes the cost of existing and new capital investments through depreciation adjustments, the balance must represent the equivalent NPV of all a firm's projects when it is discounted using a common WACC. Thus, MVA may be redefined as follows:

MVA = PV (SEVA) = SNPV

Activity 2

Using the following data and information from Activity 1, generate the appropriate equations to calculate the P V of all future EVA to derive the NPV of all capital projects.

V

NOPAT

C

K

Opening MVA

£m

£m

£m

%

£m

200

20

100

10%

90

As a reminder, first let us recalculate the EVA for Activity 1 using Equation (1).

EVA = NOPAT - (CK) = £20m - (£100m x 0.1) = £10m

Using Equation (2) you will also remember that:

MVA = V - C = £200m - £100m = £100m

Using Equation (6) we can also define market value (V) as follows:

V = C + PV (SEVA) = £100m + £10m / 0.10 = £200m

(where PV (SEVA) is the present value of a perpetual annuity, using a WACC of 10 percent). Now let us take the difference between the Equations (2) and (6) and review its implications.

MVA = PV (SEVA) = £10m / 0.10 = £100m

According to our hypothesis, the PV of all future EVA should also be equivalent to the NPV of all a company's past and future projects. So, returning to Equation (5) it follows that:

MVA = PV (SEVA) = SNPV = £100m

The importance of Equation (5) and the pivotal role of EVA as a performance measure linking external valuation to internal investment should not be underestimated. Because NOPAT can be derived from published company accounts and WACC estimates from stock market data, EVA provides investors with an element of control over dysfunctional management behaviour.

Of course, without more data we had to assume that the NPV in the previous Activity was equivalent to MVA and EVA. So finally, let us add to the data set and prove the case.

Assume the information relates to a company launched two years ago for £100m (C). Since then total market value (V) has risen to £200m without further capital issues. In the intervening period annual net cash inflow measured by NOPAT has been £20m per annum and the after tax WACC (K) a constant 10 per cent. Now threatened by takeover, let us use NPV analysis to confirm that predators should add an MVA premium of £100m to the £100m book value (C) for a "fair" value.

We know from Part Two that the cash surplus at the end of an investment's life (even a company's) is its net terminal value (NTV) or discounted equivalent (NPV). With a post-tax discount rate (K) we can therefore introduce a fourth term into Equation (5).

(8) MVA = PV (SEVA) = S NPV = S NTV / (1+K)n

The importance of this fourth term is that we are now in a position to derive S NPV and its equivalence to MVA and PV (SEVA) independently, using NTV.

From the data we can produce the following cash statement using a bank overdraft formulation (£m) to calculate the company's overall SNPV.

S NPV = S NTV / (1+K) n = 121 / (1.1) 2 = 100

Returning to Equation (8) a serial relationship that equates MVA with NPV using EVA as the linkage is now established

Review Activity

Throughout the text we have assumed that the normative objective of strategic financial management is to maximise shareholder wealth by maximising the expected NPV of all a firm's projects. Unfortunately, because there is no legal requirement for companies to publish this information, management could be pursuing an entirely different agenda based on self-interest, leading to a catastrophe like the 2008 market meltdown. Fortunately, investors may have a life-line if they care to use it.

Assuming that NPV is financially equivalent to EVA and ultimately MVA (and there is considerable evidence to support this) then the derivation of the latter by investors from publically available information should act as a control on sub-optimal managerial behaviour.

So, finally let us work through a simple numerical example (ignoring growth, issue costs, capital gearing and fiscal policy) that clarifies the inter-relationship between shareholder wealth and investment policy with reference to NPV and the value added concept.

Suppose a company is financed exclusively by ordinary share capital. This generates a net annual cash flow of £1 million in perpetuity that is always paid out as a dividend (i.e. earnings per share equals dividend per share). Also assume that the current market yield on equity used as the firm's cut-off rate for investment is 10 percent.

Using the constant dividend valuation model from Part Three, we can define market value of the company (V) as its market value of equity (VE) based on Ke the perpetual capitalisation of dividends (Dt).

V = VE = D / Ke = £1 million / 0.10 = £10m E t

Now assume the company intends to finance a new project of equivalent risk by retaining the next year's dividend to generate a net cash inflow of £2 million twelve months later, all of which will be paid out as a dividend. The questions we might ask ourselves are:

- How does this incremental investment, financed by dividend retention affect shareholder wealth?

- Can we confirm the investments impact on wealth using NPV analysis?

The managerial investment decision can be presented in terms of the shareholders' revised future dividend stream.

If we now compare market values (V) with or without the new investment using the PV of each dividend stream (VE):

V = VE (revised) = £3 million / (1.1)2 + [(£1 million / 0.10)] / (1.1)2 = £10.744m

V = VE (existing) = £1 million / 0.10 = £10m

AV = MVA = £0.774m

Thus, if the project is accepted management creates MVA because the PV of the firm's equity capital (VE) will rise and shareholders will be £744,000 better off.

Turning to NPV analysis, we can also confirm this wealth maximisation decision without even considering that the dividend pattern has changed.

You will recall that external MVA is equivalent to the creation of internal EVA, which also corresponds to the NPV of new investments. Applying the familiar DCF capital budgeting model to the project cash flows, we can prove this as follows

So, shareholders may relinquish their next dividend but gain an increase in the value of ordinary shares (from £10m to £10.744m overall). In other words, the company has created value (MVA) by accepting a project with a positive NPV of £744,000.

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