VBM – Solution sketch SS 2012: Note: This is a solution sketch , not a complete solution. Distr ibution of points is not binding for the corrector. 1 EVA, free cash f low, and f inancial rat ios (45)

1.1 EVA without adjustments (14)

NOPAT 2010 2011

Operating income 760.00 630.00

- Provision for income taxes 262.85 215.95 [1 P] each

- Tax shield 3.15 4.55 [1 P] each

( = Tax rate * Interest expenses)

= NOPAT 494.00 409.50

Invested Capital 2009 2010 2011

Total assets 4,750 5,010 5,830 [1 P] each

- Non-interest bearing liabilities 410 390 440 [1 P] each

( = Current liab. - s.-t. debt)

= Invested Capital 4,340 4,620 5,390

Average 2009/2010 4,480 [1 P]

Average 2010/2011

5,005 [1 P]

EVA 2010 2011

NOPAT 494.00 409.50

- Capital charges 425.60 475.48

( = WACC * Invested Capital)

= EVA 68.40 -65.98 [1 P] each

1.2 Free cash f low (9)

2009 2010 2011

Current assets 1,500 1,670 2,000

- (Current liabilities - s.t. debt) - 410 - 390 - 440

Working Capital Requirement 1,090 1,280 1,560 [1 P] each

Change in WCR 190 280

Free cash f low 2010 2011

Operating income 760.00 630.00

Taxes (= Tax rate * operating income) 266.00 220.50

NOPAT 494.00 409.50

+ Depreciation and amortization 1200 1400 [1 P] each

- Capital expenditures - 610 - 780 [1 P] each

- Changes in WCR - 190 - 280 [1 P] each

= Free cash f low 894.00 749.50

1.3 Link between EVA and free cash f low (8) See lecture 3, slide 15:

¨ A project creates value if NPV > 0. [3 P] ¨ The present value of future EVAs plus the value of the invested capital is equal to the

present value of future free cash flows (Preinreich-Lücke): [3 P]

¨ Consequently, using EVA for investment decisions arrives at the same investment decision as using free cash flows. [2 P]

1.4 Working Capital (8)

Working capital = current assets – current liabilities. [1 P] Good working capital management reduces the working capital and therefore the invested capital. This results in a higher EVA. [3 P]

WC is not equally important in all industries:

- If the company is working on a cash basis (e.g. department or grocery stores, fast food chains), it does not need a lot of WC. [2 P]

- If the company sells large, expensive items on a long-term basis (e.g. airplanes), it needs relatively high WC. [2 P]

1.5 Liquidity rat ios (6) Cash ratio = (Cash + marketable securities) / current liabilities = 700 / 550 = 1.27 [1 P] Current ratio = current assets / current liabilities = 2,000 / 550 = 3.64 [1 P] These ratios measure the relation between (parts of) current assets to current liabilities. They are liquidity ratios / working capital ratios. [2 P] With a high cash position, value-creating investments are possible using the company’s own ressources. [2 P] Alternative: Debt/ investors can be paid back.

( ) ( )∑∑==

=+

=++

T

1tt

tT

1t0tt

t

WACC1FCFCapital Invested

WACC1EVA

2 Financial and non-financial value drivers (15) 2.1 (7)

[1 P] for each definition. Alternative definition for capital turnover: Relation to EVA:

- Revenue Growth: It affects operating profitability and consequently the NOPAT. In contrast to profitability, there is no real limit for growth. [2.5 P]

- Capital Turnover: It is a measure for long-term investment efficiency and therefore effects invested capital. [2.5 P]

2.2 See lecture 9, slide 12: [2 P] each ¨ Some shortcomings of f inancial drivers:

– Short-term performance might be achieved at the cost of the long run (maximizing the present value of future EVAs must be the objective)

– “milking assets”, reduced production quality at the cost of customer satisfaction and future revenues etc.

– Financial ratios are of historical nature ( lagged indicators) ¨ Non-financial drivers might help to cope with these problems:

– Leading indicators of future EVA like market share, customer satisfaction, product innovation, the number of new customers or employee skills and employee satisfaction…

– …might be more under control of operating managers and – …capture problems quicker (customer complaints as signal of problems of

product quality or distributional problems).

Assets Total AverageSales Turnover Asset Total =

3 Cost of Capital (14) 3.1 Cost of Equity (4) Cost of equity reflects an investor’s expectations on the return for investing in a risky asset/ in a company. [2 P] The calculation of EVA incorporates the WACC, and cost of equity is part of the WACC:

[2 P]

S = market value of equity (stock) B = market value of debt (bonds) rS = cost of equity rB = cost of debt TC = corporate tax rate 3.2 CAPM (10)

CAPM-formula

𝐸 𝑅! = 𝑅! + 𝛽! ∙ (𝐸 𝑅! − 𝑅!) with

𝐸 𝑅! = expected return on the risky asset 𝑖 𝑅! = return of a risk-free asset

𝛽! = measure of risk of asset i (company risk factor) 𝐸 𝑅! = expected return of the stock market. [3 P]

Basic idea: A risk premium needs to be paid on the return of a risk-free asset. [1 P] This premium is dependent

– on the volatility of the firm compared to the market (reflected in 𝛽!) [1 P]

– on the returns of the market compared to the risk-free interest rate (market risk premium) [1 P]

In the CAPM, only the market risk is incorporated (systematic risk), [2 P] and not the company risk (unsystematic risk), because the company risk is diversifiable. [2 P]

( )CBS TrBSBr

BSSWACC −⋅⋅

++⋅

+= 1

3.3 Calculation of 𝜷𝑨 (14)

Year Market returns

Stock price f irm

(EUR)

Returns on f irm

([0.5 P]

each, max [2.5 P])

(𝑹𝑴 − 𝑹𝑴)𝟐

([0.5 P] each, max [2.5 P])

𝑹𝑴 − 𝑹𝑴 ∗ (𝑹𝑨 − 𝑹𝑨)

([0.5 P] each, max [2.5 P])

2005 100

2006 0.18 120 0.20 0.00 0.00

2007 -0.10 110 -0.08 0.05 0.05

2008 0.24 140 0.27 0.02 0.02

2009 0.12 155 0.11 0.00 0.00

2010 0.14 180 0.16 0.00 0.00

Σ 0.58 0.66 0.07 0.07

Mean market return:

Mean return f i rm A:

Variance (RM):

Covariance (RA,RM):

Beta f irm A:

0.116 [1 P]

0.1319 [1 P]

0.0167 [1.5 P]

0.0172 [1.5 P]

1.0335 [1.5 P]

3.4 Calculation of cost of equity (2)

𝑟! = 0.02 + 1.0335 ∙ 0.116 − 0.02 = 0.119 [2 P]

With 𝛽! = 1.1: 𝑟! = 0.02 + 1.1 ∙ 0.116 − 0.02 = 0.126

4 Goal congruent performance measures (30) 4.1 Definit ion of goal congruence (4) Managers should have incentives for value increasing decisions [1 P] independently of manager’s planning horizon [1 P], discount rate [1 P] or the particular compensation rules [1 P]. 4.2 Profitabi l i ty of the project: net present value (6)

𝑁𝑃𝑉 𝜃 = −1.400 + 𝛾 ∙ 500 ∙ 𝜃 + 𝛾! ∙ 600 ∙ 𝜃 + 𝛾! ∙ 800 ∙ 𝜃

𝑁𝑃𝑉 𝜃 = −1.400 + 𝜃 ∙ 𝛾 ∙ 500 + 𝛾! ∙ 600 + 𝛾! ∙ 800 = −1.400 + 1566.35 ∙ 𝜃 [3 P]

Accept the project if 𝜃 ≥ 0.89,

Consequently: Accept project if realized cash flows are equal to 𝑋, don’t accept project if cash flows are only 80% of it. [3 P]

4.3 Calculation of residual income using the RBCA rule (9)

The part of the total cost of investment (depreciation and interest) allocated to period t:

𝑧! = 𝑧! 𝑥 =𝑥!𝛾! ∙ 𝑥!!

!!!

𝑡 1 2 3

𝒛𝒕

0.32

0.38

0.51

[1 P] each

𝒛𝒕 ∙ 𝒃 446.90 536.28 715.04

𝑹𝑰𝒕 = 𝜽 ∙ 𝒙𝒕 − 𝒛𝒕 ∙ 𝒃 𝜽 = 0.8 -46.90 -56.28 -75.04

[1 P] each

𝜽 = 1 53.10 63.72 84.96 [1 P] each

4.4 Goal congruence achieved? (6)

                 𝑅𝐼! = 𝑧! 𝑥 ∙ 𝑁𝑃𝑉 𝜃              ∀  𝑡

Each period’s residual income is proportional to the project’s NPV (and thus has the same

sign). In the case of θ = 0.8 (negative NPV of the project) the residual income is also

negative in each period. In the case of θ = 1 (positive NPV of the project) the residual

income is also positive in each period. If paid on the basis of such a residual income

measure, the manager will thus act in the interest of the shareholders regardless of his own

time preferences (because the time preference doesn’t matter for the decision about the

acceptance of the project if the performance measure has the same sign as the NPV of the

project in each period possibly taken into account by the manager).

Discount rate of the manager differs from those of the shareholders due to a shorter time horizon, risk averseness and not the same access to capital markets. 4.5 Straight-l ine depreciation (5) With straight-line depreciation, depreciation charge = 1,400 / 3 = 466.67 each year.

Consider the case of 𝜽 = 1 (project is beneficial for the company). Residual income in first period:

𝑅𝐼! = 500 − 466.67 − 0.095 ∗ 1,400 =  −99.67   So if the manager is paid based on residual income, and if he intends to leave the company after the first period, he will not invest into the project.