.tfp aočc% i % 3C ^mswp*^ ^ FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES Dirk Kaiser Treasury Management Lessons in Finance and Investment at Masarykova univerzita Ekonomicko-správní fakulta Fall Term 2007/2008 MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management Page one ^yOĚSa ■r % \ \ j- ^»JíSÍAf*^ *-- ř Trilingual index 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES English-German-Czech index of key terms in investment English German Czech annual equivalent Äquivalente Annuität ekvivalentní anuita Any volunteers? MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management Trilingual index ^yOĚSa ■r % \ \ j- ^»JíSÍAf*^ *-- / Treasury Management Survey 1 Basics (units 1-5,10) a 2 Cash flow from flnancial activities (units 6-8) 3 Cash flow from operations (unit 9) 4 Cash flow from investment activities (units 11-16) • Complete account of an investment • Dominance • Net present value • Annual equivalent • Internal rate of return • Payback period 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES > J MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management Survey iMOff ^uŕ*^ Exercise 7-2 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES Make up a source income statement for the Brnenské Marcipánové a Nugátové Kontor by restructuring the 2025 income statement according to the following form! Source income statement (form) 2025 2024 Revenues Changes in inventories of finished goods and work in progress Production for own fixed assets capitalized Cost of purchased materials and services Personnel expenses Depreciation and amortization on tangible and intangible assets Core operating profit Other operating income Other operating expenses Other operating profit Operating profit ("EBIT") Income from participations Income from other financial assets Other interest income Depreciation and amortization on financial assets and financial current assets Interest expenses Financial profit ("1") Extraordinary income Extraordinary expenses Extraordinary items Earnings before tax ("EBT") Income tax }("T") Other taxes J Earnings after tax ("EAT") MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from operating activities iMOff ^uŕ*^ IV. Schmalenbach' s Bar Graph revisited (Incoming - outgoing payments =) CF from operating activities (Income - expenses =) EBIT minus T > 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES (Fig. 7-1) within operations !!! EBIT minus T + expenses that do not affect cash & cash equivalents (correction type I) within - income that does not affect cash & cash equivalents (correction type II) operations!!! - non-expense applications of cash & cash equivalents (correction type III) + non-expense originations of cash & cash equivalents (correction type IV) = Cash flow from operating activities MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from operating activities iMOff ^iJísuŕ*^ Exercise 7-3 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES Starting point is exercise 4-4. As you can easily check, this is CFP's source income statement for the fiscal year 2025. Bridge the gap between EBIT minus T and cash flow from operating activities by making up a calculation considering for the four different types of corrections! Source income statement for CFP v.o.s., Brno, for the time period from January 01, 2025, to December 31, 2025 (TCZK) 2025 Revenues Changes in inventories of finished goods and work in progress Production for own fixed assets capitalized Cost of purchased materials and services Personnel expenses Depreciation and amortization on tangible and intangible assets Core operating profit Other operating income Other operating expenses Other operating profit Operating profit ("EBIT") 700 0 0 400 180 5 115 20 0 20 135 Income from participations Income from other financial assets Other interest income Depreciation and amortization on financial assets and financial current assets Interest expenses Financial profit ("I") 0 0 0 0 35 -35 Earnings before tax ("EBT") Income tax L("T") Other taxes J 100 0 0 Earnings after tax ("EAT") 100 MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from operating activities ^iJísuŕ*^ -h 3C B/1 WT- ^-v m« ^k-S ä^I *"X ^T 1 FACHHOCHSCHULE BOCHUM ■"^ ^kŕ C-l W^š 1 ^k«-^ / M UNIVERSITYOF APPLIED SCIENCES After receipt of a corresponding purchase order by fax as of September 01, 2026, the Brnenské Marcipánové a Nugátové Kontor still on the same day delivers 3 kg of crude marzipan amounting to CZK 450 to Jemná Čokoláda. As the Kontor grants September 30, 2026, as time of payment, Jemná Čokoláda pays the amount due only at the end of the month of September. Assume Jemná Čokoláda's perspective and translate the transactions between buyer and supplier into the symbolism known to you from exercise 2-2! To this end, first register the transactions on a "gross"-level by means of two exchange contracts and then on a "net"-level by only one contract! MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from operating activities \ V«(*^ Management Cybernetics System-Theoretic Approach (Hans Ulrich) I (1) Steering of economic SVSteiTlS (2) ... by means of a close-meshed network... of directives or... (3) ... by granting extensive freedom of decision to lower hierarchy levels. (4) possible instruments: internal accounting prices, profit centers, intrapreneurship (5) dynamic version: feedback control system i PO(C)-Concept Erich Gutenberg Management is ... planning, organisation and control, 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management Treasury Management ^yOĚSa ■r % \ \ ^»JíSÍAf*^ >* Feedback Control Systems: An Example -h 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management Treasury Management iMOff ^ur*^ Treasury Management (Financial Management) 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES S Steering of the money cycle S Management of the cash flow statement Incoming & outgoing payments ĽL — a\ ~~ \v* \ \ /._ ,_. ^ >' nancial accounting M Receipts & expenditures lil____________ÍSL m ĽL Income & expenses ___________(8)___________ J9) Revenue & cost ŕ- Management accounting Consolidated cash flow statement (€ million) 2006 2005 EBIT Depreciation and amortization of tangible and intangible assets Change in provisions for pensions and other provisions Change in net working capital Income taxes paid Elimination of negative difference first-time consolidation Other 1.983 1.250 273 1.137 -543 -410 -427 1.738 1.200 -19 66 -499 0 -452 Cash flow from operating activities of continuing operations Cash flow from operatinq activities of discontinued operations 3.263 0 2.034 150 Total cash flow from operating activities (+ls+l0-OM-OL-O0-OT) 3.263 2.184 First-time consolidation Company acquisitions Investments in tangible assets (excl. Finance leases) Other investments Company divestments Divestment of stores Disposals of fixed assets 108 -205 -1.824 -268 0 484 403 19 0 -1.922 -253 48 670 313 Cash flow from investing activities of continuing operations Cash flow from investinq activities of discontinued operations -1.302 0 -1.125 -43 Total cash flow from investing activities -0F+lF-0E+lP+lw-0D+lF+lR -1.302 -1.168 Profit distribution - to parent company stockholders - to other stockholders Raising of financial liabilities Redemption/repayment of financial liabilities Interest paid Interest received Profit and loss transfers and other financinq activities -334 -122 1.423 -1.571 -610 169 50 -334 -72 935 -1.415 -637 137 -6 Cash flow from financing activities of continuing operations Cash flow from financinq activities of discontinued operations -995 -1.392 23 Total cash flow from financing activities +lE-0P-Ow+lD-0|-0R -995 -1.369 Total cash flows Exchanqe rate effects on cash and cash equivalents 966 -1 -353 13 Overal change in cash and cash equivalents Cash and cash equivalents on January 1 M0 Cash and cash equivalets on December 31 M1 965 1.767 2.732 -340 2.107 1.767 MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management Treasury Management iMOff ^uŕ*^ 3C Objectives of Treasury Management FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES V S S V S Assuring the company's ability to pay (^> sufficient liquidity) Little annoyance or (even better) strong support of operations (=> no affluent liquidity) Great contribution to the company's rentability (=> efficient use of liquidity reserves) Efficient risk management (=> implementation of hedging, insurance contracts, derivatives etc.) Little restriction of entrepreneurial freedom (^> avoidance of too many covenants) MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management Treasury Management ^yOĚSa ■r \ X ^iJísuŕ*^ >* The POC-Structure of Treasury Management -Y 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES Treasury Management (Financial Management) I I I r "Financial Controlling" A Financial organisation Financial planning Financial control Strategic financial planning Operative financial planning Financial organisational structure Financial process organisation Targets of Treasury Management (Financial Targets) MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management Treasury Management í Smí \ X.^Financial Organisational Structure: The US Model »^ i„c • 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES 1st level monistic corporate governance (where appropriate) 3rd level Financial Accounting Cash Management (AR, Credit Collection, AP) Management Accounting Forex Management Tax Banking Relationships Legal Financial Risk Management Internal Audit Financial Controlling etc. etc. MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management Treasury Management í Smí \ X^/Tinancial Organisational Structure: The European Model 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES (here: AG) 1st level (where appropriate) 3rd level Dualistic corporate governance J I I MB member for operations MB member for commercial affairs etc. Legal Department (Head of LD) Finance and Accounting (Head of F&A) Controlling (Head of C) etc. Accounting Tax Finance Risk management etc. MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management Treasury Management ^yOĚSa ■r \ X.^/Questions of Strategie Financial Planning s How many main banking relationships? y y y y y Which banks? Securitization and going public (Debt:) Fix-floating mix Target rating Three years budget Etc. 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management Treasury Management ^iJísuŕ*^ -h 3C B j1 w-r ^y -a^ ^^ * ^ ^y 'í /^ 'í FACHHOCHSCHULE BOCHUM ■"^ ^kŕ C-l l^M 1 ^^B-* I "^ M I UNIVERSITYOF APPLIED SCIENCES The Inovativny obchod a.s. from Brno is listed on the stock exchange and with 21,000 employees and 150 locations one of the leading department store companies in Europe. Within the management board, Mrs. Alice Babičková is in charge of the entire commercial affairs of the company. Among other organisational units, the treasury department directed by Mr. František Kohut belongs to her area of responsibility. /) Is the corporate governance of the company monistic or dualistic? Does the organisation of the financial sphere of Inovativny obchod follow the European or the US-Model? The accumulated lines of credit of the company amount to CZK 7,000,000. As of December 31, 2025, the company reports the subsequent data (consolidated balance sheet, consolidated income statement, consolidated cash flow statement). MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management Treasury Management iMOff = h 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES ^iJísuŕ*^ Consolidated balance sheet, Inovativny obchod a.s., Brno, as of December 31, 2025 Assets 25, CZK mio. % 24, CZK mio. % Liabilities 25. CZK mio. % 24, CZK mio. % Fixed assets Equity Intangible assets 20,0 1,4% 18,0 1,3% Capital stock 240,0 16,9% 240,0 17,2% Tangible assets 315,0 22,2% 300,0 21,5% Additional paid-in capital 20,3 1,4% 20,3 1,5% Financial assets 125,0 8,8% 115,0 8,2% Reserves from retained earnings 103,3 7,3% 97,3 7,0% 460,0 32,4% 433,0 31,0% Net profit 59,1 422,7 4,2% 29,8% 86,0 443,6 6,2% 31,8% Current assets Inventories 810,3 57,1% 805,2 57,7% Provisions Accounts receivable 10,9 0,8% 12,3 0,9% Provisions for pensions & similar commitments 198,5 14,0% 154,2 11,1% Other receivables 62,4 4,4% 69,5 5,0% Other provisions 125,9 8,9% 55,2 4,0% Cash, cash equivalents etc. 70,8 5,0% 70,8 5,1% 324,4 22,8% 209,4 15,0% LCash, cheques 4,1 0,3% 6,2 0,4% Liabilities 2. Bank deposits 61,4 4,3% 59,8 4,3% Financial liabilities 257,0 18,1% 261,2 18,7% 3. Securities 5,3 0,4% 4,8 0,3% Accounts payable 256,3 18,0% 310,1 22,2% 954,4 67,2% 957,8 68,7% Other liabilities 155,6 668,9 11,0% 47,1% 165,8 737,1 11,9% 52,8% Deferred tax assets 2,2 0,2% 1,8 0,1% Deferred tax liabilities 1,3 0,1% 1,9 0,1% Prepaid expenses & deferred charges 3,4 0,2% 2,6 0,2% Prepayments & deferred income 2,7 0,2% 3,2 0,2% 1420,0 100,0% 1395,2 100,0% 1420,0 100,0% 1395,2 100,0% MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management Treasury Management iMOff ^uŕ*^ Consolidated cash flow statement, Inovativny obchod a.s., Brno, 2025, CZK mio. 2025 2024 EBIT Depreciation and amortization of tangible and intangible assets Change in provisions for pensions and other provisions Chenge in net working capital Income taxes paid Other Cash flow from operating activities 153,4 89,6 50,0 -52,4 10,3 -20,3 230,6 221,7 84,3 45,0 -60,3 40,4 -60,3 270,8 Investments in tangible assets (excl. Finance leases) Other investments Company acquisitions & divestments Cash flow from investing activities -100,0 -16,2 -10,2 -126,4 -105,9 -15,8 -30,8 -152,5 Profit distributions - to parent company stockholders - to other stockholders Raising of financial liabilities Redemption/repayment of financial liabilities Interest paid Interest received Profit & loss transfers and other financing activities Cash flow from financing activities -80,0 -1,0 301,2 -281,6 -70,5 25,1 2,1 -104,7 -80,0 -1,0 350,4 -299,1 -87,4 24,3 -10,5 -103,3 Total cash flows Cash and cash equivalents as of January 1 Cash and cash equivalents as of December 31 -0,5 66,0 65,5 15,0 51,0 66,0 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management Treasury Management iMOff = h 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES Consolidated income statement, Inovativny obchod a.s , Brno, CZK mio. 2028B % % change 2027B % % change 2026B % % change 2025A Gross sales 4813,0 115,1% 2,2% 4710,0 115,1% 2,4% 4600,0 115,1% 2,7% 4477,4 Sales tax 633,0 15,1% 2,2% 619,5 15,1% 2,4% 605,0 15,1% 3,0% 587,4 Net sales 4180,0 100,0% 2,2% 4090,5 100,0% 2,4% 3995,0 100,0% 2,7% 3890,0 Cost of sales 2435,0 58,3% 2,3% 2380,0 58,2% 2,1% 2330,0 58,3% 2,2% 2279,5 Gross profit on sales 1745,0 41,7% 2,0% 1710,5 41,8% 2,7% 1665,0 41,7% 3,4% 1610,5 Selling expenses 1705,0 40,8% 2,1% 1670,0 40,8% 1,8% 1640,0 41,1% 2,6% 1598,8 General administrative expenses 114,0 2,7% 3,6% 110,0 2,7% 2,8% 107,0 2,7% 5,8% 101,1 Other operating income 298,0 7,1% 1,0% 295,0 7,2% 0,7% 293,0 7,3% 0,4% 291,8 Other operating expenses 35,0 0,8% -22,2% 45,0 1,1% 12,5% 40,0 1,0% 2,8% 38,9 EBITA 189,0 4,5% 4,7% 180,5 4,4% 5,6% 171,0 4,3% 4,7% 163,4 Amortization good will 10,0 0,2% 0,0% 10,0 0,2% 0,0% 10,0 0,3% 0,0% 10,0 EBIT 179,0 4,3% 5,0% 170,5 4,2% 5,9% 161,0 4,0% 5,0% 153,4 Result from associated companies -1,0 0,0% 50,0% -1,5 0,0% 40,0% -2,1 -0,1% -5,0% -2,0 Interest result -49,0 -1,2% -4,1% -47,0 -1,1% -4,3% -45,0 -1,1% 0,0% -45,0 Other financial result 1,3 0,0% 0,0% 1,3 0,0% -7,1% 1,4 0,0% 0,0% 1,4 Financial profit -48,7 -1,2% -3,1% -47,2 -1,2% -3,2% -45,7 -1,1% -0,2% -45,6 EBT 130,3 3,1% 5,7% 123,3 3,0% 6,9% 115,3 2,9% 7,1% 107,7 Income taxes 51,5 1,2% 5,7% 48,7 1,2% 6,9% 45,5 1,1% 6,9% 42,6 Net profit for the period 78,8 1,9% 5,7% 74,6 1,8% 6,9% 69,8 1,7% 7,0% 65,2 Allocable to minorities 9,1 0,2% 3,4% 8,8 0,2% 25,7% 7,0 0,2% 14,8% 6,1 Net profit 69,7 1,7% 6,0% 65,8 1,6% 4,8% 62,8 1,6% 6,2% 59,1 ii) Make yourself familiar with the data by elaborating the three immediately recognisable links between the three calculations! MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management Treasury Management iMOff -h 3C Aj ljÍii be scrutinized here, Mr. Kohuťs treasury department has mackkup "^ŕ .+■' *> ». UNIVERSITY OF APTOEI thŽMiíťernal budgeting and reporting form similar to the cash flow statement according to IAS/IFRS: BOCHUM ED SCIENCES Consolidated Cash Flow Statement (Budget), Inovativny obchod a.s., Brno, CZK mio. 2028 2027 2026 Net sales Costs of goods sold Wages Overheads Other incoming payments from operations Other outgoing payments from operations Income taxes Cash flow operations Cash flow investment Profit distribution Increase in capital Debt finance Redemption Interest result Other Cash flow finance Total cash flows Cash & cash equivalents as of January 1 Cash & cash equivalents as of December 31 Hi) Does the treasury department for internal purposes calculate the cash flow from operating activities in a direct or in an indirect manner? MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management Treasury Management iMOff =5 3C VuTTjuil^eting purposes 2026-2028, the treasury department deems tneľstrtí^equent projections to be valid: => incoming payments from net sales will be like in the consolidated budget income statement => outgoing payments for cogs will be like in the consolidated budget income statement => outgoing payments for wages per capita will equal CZK 30,000 in 2026; from then onwards yearly increase of 2.3% => outgoing payments for overheads will amount to 49% of consoli- dated total assets in 2026; from then onwards yearly increase of 2.0% => other incoming payments from operations amount to 10% of other operating income in the consolidated budget income statement => other outgoing payments from operations amount to 60% of other operating expenses in the consolidated budget income statement => income taxes paid will equal the expenses for income taxes in the consolidated budget income statement => profit distribution remains on the 2025 level visible in the consoli- dated cash flow statement FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management Treasury Management ÜSHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES Icžřsh flow investment: CZK 230 mio. in 2026, CZK 240 mi Wm*í*CZK 250 mio. in 2028 => debt finance and redemption, respectively, will in 2026, 2027 and 2028 equal the amounts of the year 2025 visible in the consolidated cash flow statement rounded to CZK 10 mio. => interest results on the payment level will equal the interest results in the consolidated budget income statement => other financial items will equal the total of result from associated companies and other financial result in the consolidated budget income statement iv) Make up a first draft of the strategic treasury budget of Inovativny obchod by using the internal form and taking into consideration the aforementioned projections! Then comment on your result! MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management Treasury Management ■- X ^/ Series of Cash effectiveness e + Timely difference ŕ = 0,1,...,í MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES Series of payment Treasury Management CF from investing activities 1 ■- 3C %,_*/ Investment Projects An investment project (sometimes called "investment" in short) is a series of payment > that begins with an outgoing payment, > that features at least one change in sign > and whose realisation still has to be decided on. Types: ■ Real investments ■ Financial investments FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 1 ^uŕ*^ -h 3C B/1 WT- ^-v m« ^k-S ä^I *"X ^T 1 FACHHOCHSCHULE BOCHUM ■"^ ^kŕ C-l W^š 1 ^k«-^ ^^ M I UNIVERSITYOF APPLIED SCIENCES The Jemná Čokoláda a.s. wants to acquire a machine for the production of chocolate bars. The price of the machine due for immediate payment in t=0 amounts to CZK 100,000. The machine would for three years allow the production of 5,000 chocolate bars per year. Each bar could be sold for instant incoming payment of CZK 20. On the other hand, ingredients (secret recipe!) and other production factors would require outgoing payments of CZK 10 per bar. At the end of the physical life of the machine, disassembly cost would induce outgoing payments of CZK 40,000. Assume Jemná Čokoláda's point of view and determine the series of payment of the project uchocolate bar machine"! MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 1 ■- -v 3C v,..»/ Financing projects FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES A financing project is a series of payment > that begins with an incoming payment, > that features at least one change in sign > and whose realisation still has to be decided on. Many of the concepts developed subsequently for investment projects can be transferred mutatis mutandis to financing projects. MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 1 ^yOĚSa ■r % \ \ j- ^»JíSÍAf*^ *-- ř Exercise 6-1 -h 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES The financial contract known from exercise 4-1 is again taken into consideration. From whose perspective is the signing of this contract a financing project, from Candice's or Quentin's? MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 1 3C ? "^^^^^"~ ^ B j* -W-7- ^-v m« ^k-B *"1 ^-V ^T ^^ FACHHOCHSCHULE BOCHUM %ň H V 1-iPf 'IWI-I ^^ — X UNIVERSITY OF APPLIED SCIENCES The Jemná Čokoláda a.s. has entered the stage of a more intense scrutiny of the chocolate bar machine known from exercise 5-1. To this end, it is to be compared with the status quo. Determine the series of payment of the status quo for this scenario ! MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 1 ^yOĚSa ■r % \ \ j- ^»JíSÍAf*^ *-- ř Investment Decisions -h 3C (Fig. 5-1) FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES An investment decision is a selection from a catalogue of investment projects and the status quo. Investment decisions Single investment decisions One project single investment decisions Multi project single investment decisions Typical of TREASURY management: Selection from a catalogue of investment projects or from a catalogue of financing projects, but not from a catalogue of investment and financing projects. Investment program decisions MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 1 9 ^yOĚSa ■r % \ \ j- ^»JíSÍAf*^ *-- ř Investment calculus -h 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES Investment calculus offers procedures for investment decisions (i. e.: for the comparison of certain series of payment). 6D's (Economic calculus is the more general concept and offers procedures for investment desisions and financing decisions.) • Complete account • Dominance • Net present value • Annual equivalent • Internal rate of return • Payback period MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 1 ■- *v._y "w&ki... 3C %^ ' "# # 1 I * 1^ S» FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES ...Dynamic Investment Calculus... Dynamic investment calculus (1) starts off from incoming and outgoing payments (upmost level of Schmalenbach's bar graph)and (2) takes the timely differences between different payments explicitly into consideration. (In other words: Dynamic investment calculus is based on series of payment.) If one of the two aforementioned criteria is not fulfilled, it is STATIC INVESTMENT CALCULUS. MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 1 ^yOĚSa ■r % \ \ j- ^»JíSÍAf*^ *-- ř Scalars and Vectors, -h 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES Norm of a Vector payment in t=1 payment int=2 Mathematically speaking, investment calculus requires the comparison of vectors, i. e. of multidemsionsal figures in the vector space. Scalar: onedimensional figure in vector space Vector: multidemsional figure in vector soace MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 1 ^yOĚSa ■r % \ \ j- ^»JíSÍAf*^ *-- ř Exercise 8-1 -h 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES The chocolate bar machine known from exercises 5-1 and 5-2 is again taken into consideration. Determine the norm of the series of payment of this investment project and interpret on your result from an economic point of view! MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 1 -h w^ Our Catalogue of Assumptions for Investment Calculus . Payments do only occur at points in time like t=0 and t=l and not inbetween (discrete time) . Payments relating to a period of time (like interest) are realised at the end of the relevant period and not at its beginning (payments in arrear, no payments in advance) . Deterministic payments and interest rates (no stochastic) . Timely invariant interest rates (homogenous term structure of interest rates) . No taxes FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 1 iMOff ^uŕ*^ The Relevance of the 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES Interest Rate t=o t=i —h- \CZK\\ ----1— \CZK\\ time r>0 Usual scenario: rB > rL; borrowing rate exceeds lending rate (a market imperfection) It is better to receive CZK 1 today than tomorrow. It is worse to be obliged to pay CZK 1 today than tomorrow. edl > After transformation to a fixed point in time by means of the interest rate, the absolute value of CZK 1 paid in the present is greater than the absolute value of CZK 1 oaid in the future. MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 2 ■- -v 3C V,.,x# Complete Account of an Investment Project (preliminary definition) FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES Explicit clearing of a series of payment by means of a simple account complying with the following conventions: i. Except for the final point in time, the account may never be overdrafted. To this end, possible deficits have to covered by a separate credit at borrowing rate r. (Please turn over.) MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 2 iMOff III IV. 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES Except for the final point in time, the account may never display a positive balance. To this end, possible surpluses have to be invested in a term money at lending rate rL. Credits and term moneys each have a duration of one period. At the final point in time, no credits may be raised and no term money investments are possible anymore. The final balance of the account is represented by the symbol FWP, i. e. the final wealth generated by the project in consideration For the time being, the initial wealth of the holder of the account (or the decision taking entity, respectively) equals zero: IWS = 0 MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 2 3C ? "^^^^^"~ ^ B j* -W-7- ^-v m« ^k-B *"1 ^-V ^? ^^ FACHHOCHSCHULE BOCHUM %ň Wl V 1-iPf 'IWI-I ^^H / UNIVERSITY OF APPLIED SCIENCES The chocolate bar machine known from exercises 5-1, 5-2 and 8-1 is again taken into consideration. The borrowing rate is r =0.05 per period, the lending rate r =0.01. Determine by means of a complete account complying with the aforementioned conventions i. to v. the final wealth FWP of the project (and thus the increase in final wealth compared to the status quo!) MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 2 ^yOĚSa ■r % \ \ j- ^»JíSÍAf*^ *-- / The Objective of Investment Calculus (Or more general: The Objective of Economic Action in a Dynamic Context) 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES r=0 t=\ t = t i time Final Wealth Maximization MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 2 ■- 3C \,s^y Complete Account: Decision Rule a) For ONE PROJECT SINGLE INVESTMENT DECISIONS, the proj'ect taken into consideration is favourable if it generates an increase in final wealth compared to the status quo. b)For MULTI PROJECT SINGLE INVESTMENT DECISIONS, the proj'ect that maximizes the increase in final wealth compared to the status quo is favourable. (If none of the projects taken into consideration generates an increase, at all, the status quo is favourable.) FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 2 ■- -v 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES \^y Equivalent Initial Wealth of a Project Fictitious back-calculation of the final wealth caused by a project that complies with the following two conventions: L After the point in time of decision (t = 0), for t > 1 no further payments occur in t = l,...J. This means that in t = 0 there is one single investment of a term money or one single raising of credit, respectively. ii. If FWP >0, the equivalent initial wealth iwp can only be generated by means of an investment in a term money in r = 0; rL is the relevant interest rate then. For FWP <0, the equivalent initial wealth IWP can only go back to an initial credit raising; in this case, rB is the relevant interest rate. MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 2 3C ? "^^^^^"~ ^ B j* w-y. ^y -a^ ^^ * ^ ^y ^) /l ^^ FACHHOCHSCHULE BOCHUM The chocolate bar machine known from exercises 5-1, 5-2, 8-1 and 8-2 is again taken into consideration. Like before, the borrowing rate is r =0.05 per period, the lending rate r =0.01. Determine by means of a complete account following the aforementioned conditions i. and ii. the initial wealth IW that is equivalent with the final wealth FWP calculated in exercise 8-21 MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 2 iMOff ^uŕ*^ Non-Zero Initial Wealth (Fig. 8-3) 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES money' 120,000~ 100,000 80,000 60,000 40,000 20,000 -20,000 -40,000 -60,000 -80,000 -100,000 -120,000 -140,000 -160,000 -180,000 -200,000 FW = IW =-] In genera^ the increase 3 time in final wealth generated by an investment project is not independent from the level of the initial wealth of the decision taking entity. MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 2 ■- -v 3C V,.,x# Complete Account of an Investment Project (final definition) Explicit clearing of a series of payment by means of a simple account complying with the following conventions: i. Except for the final point in time, the account may never be overdrafted. To this end, possible deficits have to covered by a separate credit at borrowing rate r. ii. Except for the final point in time, the account may never display a positive balance either. To this end, FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 2 possible surpluses have to be invested in a term chschulebochum ■ ■ "Y OF APPI IFn SniFNCFS money at lending rate rL. iii. Credits and term moneys each have a duration of one period. iv. At the final point in time, no credits may be raised and no term money investments are possible anymore. The final balance of the account is represented by the symbol FWP, i. e. the final wealth generated by the project in consideration Compared to the preliminary definition of the complete account, the decision rule remains unchanged. (See separate slide.) MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 2 3C ? "^^^^^"~ ^ B j* -W-7- ^-v m« ^k-B *"1 ^-V ^? ^T FACHHOCHSCHULE BOCHUM %ň Wl V 1-iPf 'IWI-I ^^«^^ UNIVERSITY OF APPLIED SCIENCES The chocolate bar machine known from exercises 5-1, 5-2, 8-1, 8-2 and 8-4a is again taken in consideration. In contrast to exercise 8-2, the initial wealth of the decision-taking entity IWS is different from zero and amounts to i) CZK 100,000 and ii) CZK -100,000. Determine the increase in final wealth caused by the machine in case i) and in case ii), respectively, transfer your results to figure 8-3 and comment on them! MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 2 ^yOĚSa ■r \ \ Jakob Bernoulli, 1655-1705 (with a view to stochastics) X * ^»JíSÍAf*^ *-- / Dominance: Defínition and Decision Rule 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES Let £ and £ be non-identical series of payments (or, speaking differently, vectors of dimension i +1). £ DOMINATES £ if and only if in pairwise comparison every element et of £ is greater or equal the corresponding element et of £ . Formally: (D) e > e V f = 0,l,...,ř If a series of payments DOMINATES another one, it is also PREFERABLE to the other one in the sense of final value maximization. MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 2 3C ? "^^^^^"~ ^ B j* -W-7- ^-v m« ^k-B *"1 ^-V ^? jC FACHHOCHSCHULE BOCHUM %ň Wl V 1-iPf 'IWI-I ^^H I ■ UNIVERSITY OF APPLIED SCIENCES In addition to the well established brands hazelnut and brittle, the Jemná Čokoláda a.s. is currently having marzipan chocolate in contemplation. An investment in the marzipan project would have the following consequences (all data in CZK and as change compared to the status quo): t=0 (1) Acquisitions amounting to 10,000,000 (immediately payment effective) (2) Employee Lissi, who has always dreamt of marzipan chocolate when she was working at the conveyor belt and proposed the idea MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 2 \ > lu JĚhe staff suggestion scheme, is to receive an immediately patrne» ^ .4-^ °° y «/A •'UNIVERSITY OF ŕ ^ ^effective premium amounting to 10,000. t=l, 2,..., 10 (figures per year) (3) Incoming payments caused by increased sale of chocolate amounting to 3,000,000 (4) Additional outgoing payments for (a) crude chocolate amounting to 1,000,000, (b) marzipan amounting to 300,000, (c) wages amounting to 200,000 (5) Lissi would be much more content with her work. (6) Writeoffs of the new machinery in the financial accounting amounting to 600,000 (7) Writeoffs of the new machinery and the good will in the management accounting amounting to 400,000 (8) The supplier Brněnské Marcipánové a Nugátové Kontor would encounter a payment effective surplus amounting to 260,000. HULE BOCHUM APPLIED SCIENCES MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 2 iMOff "Wuŕ*^ ^termine the series of payment of project marzipam 3C ClflHOCHSCHULE BOCHUM ľ^RSITY OF APPLIED SCIENCES Being deeply impressed by Lissi's idea, the marketing department of the Jemná Čokoláda a.s. has instantaneously calculated the projects nougat, walnut, strawberry yoghurt, raisin nut and peanut. The following series' of payment are presented to the board of directors: brand t=0 t=l, 2,..., 10 (per year) Nougat -10,010,000 1,400,000 Walnut -10,010,000 1,300,000 Strawberry yoghurt -10,300,000 1,500,000 Raisin nut -5,000,000 600,000 Peanut -2,000,000 300,000 ii) Preselect efficiently those chocolate brands that are under no circumstances consistent with the objective of final wealth maximization ! MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 2 ^yOĚSa ■r \ -v 3C x ^»JíSÍAf*^ >* Implicit Consideration of Accompanying Financial Activities FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES Discounting 80 = 8r(1 + rLT 80 = 8r(l + rS if 8i>0 if 8,<0 Compounding 8, = 8o-(1 + rJ' gf = 8o-(1 + rJ if 8t>0 if 8,«* MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 3 3C ? "^^^^^"~ ^ B j* -W-7- ^-v m« ^k-B *"1 ^-V ^? ^T FACHHOCHSCHULE BOCHUM %ň Wl V 1-iPf 'IWI-I ^^H / UNIVERSITY OF APPLIED SCIENCES The initial wealth of the decision taking entity be zero, i. e.: IVS = 0. Consider an investment project with the following series of payment: (-980.00, 1,100.00, -10.00) As it is shown in the draft (margin number 161, table 8-5), the final wealth of the project for rL = 0.01 and rB = 0.05 per period is 71.81, i. e. FVP =71.81. Check whether it is possible to calculate the final wealth of the project by means of compounding! To this end, apply (a) the lending rate, (b) the borrowing rate and (c) a more subtle strategy! MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 3 ^yOĚSa ■r \ X ^iJísuŕ*^ >* Deviation Analysis for Exercise 8-7 (and thus for More Complex Series of Payment) 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES What interest rate is relevant? The answer to this question in general requires a complete account!!! Final wealth of the project FVP = Ml + rfl) + e1]-(l + Ü + c2 = e0'(l + rB)'(l + rL) + er(l + rL) + e: Equivalent initial wealth of the project FW e-(l + r) e. e„ IW„ = P ___ (1 + 0 + l+rL \ + rL (1 + rJ MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 3 3C ? '^^^^^^ ..'■' B j* -W-7- ^-v m« ^k-B *"1 ^-V ^? ^? FACHHOCHSCHULE BOCHUM %ň Wl V 1-iPf 'IWI-I ^^H^^ UNIVERSITY OF APPLIED SCIENCES The investment project known from exercise 8-7 is again taken into consideration. The initial wealth of the decision taking entity remains at zero (i. e.: IWS = 0), lending rate and borrowing rate remain at rL = 0.01 and rB = 0.05 per period, respectively. Check whether it is basically possible to calculate the final wealth and the equivalent initial wealth of the project implicitly on the basis of the preceeding deviation analysis! MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 3 3C ^Uf*^ Perfect Financial Markets hhssbshh (PERFIMA) Perfect financial markets comply in particular with the following three criteria: L There are no quantitative restrictions on accompanying financial activities (absence of rationing). ii. The same interest rates are relevant for the raising of credit and the investment in term money (borrowing rate equals lending rate). iii. The one-period investment in term money as well as the one-period raising of credit are possible. (finest timely scaling of financial contracts). MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 3 ^yOĚSa ■r \ X ^iJísuŕ*^ >* PERFIMA Fisher-Separation 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES (Fig 8-4) r c¥ rT Q C^^-a + r)-^ high time preference c1T = /(;)=/(c0-c0T) Q c„ better direction low time preference -0'*-0 '*-0 Ow perfect financial markets, the real investment decision ("firms") is independent of the time preference and the intertemporal consumption decision ("households"). The opposite does not hold true. MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 3 ^yOĚSa ■r % \ -v 3C v. ^»JíSíAf*^ >* PERFIMA => Implicit Calculus Evo« of More Complex Series of Payment FACHHOCHSCHULE BOCHUM ITY OF APPLIED SCIENCES Final wealth FVP = e0-{l+rB)-{l+rL)+el-{l + rL)+e2 -rl =r = e0-(l+rY+ei-(l + r)+e2 = £é?ř-(l+r)'~ř = FW rB =r, =r t=\ Net present value iwP = <^±lA + + r =r =r \ + rL l + r, (l + rj e0 + e, • (1 + r)"1 + e2 ■ (l + r)"2 = Ze-(l + r)" s JVPV r=0 MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 3 iMOff ^uŕ*^ Net Present Value and Final Wealth Maximization 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES Final wealth maximization: The difference between the final wealth of the project and the final wealth in the status quo case has to be maximized. For arbitrary initial wealth of the decision taking unit IWS, the final wealth of the project FWP may inspite of the aforementioned problems be formulated in the following manner: FWP = Ééf-n(l+rs,L(r)) t=0 T=0 where e0 + IWS for t = 0 for t = 1,2,...,t Continuing on this approach, the final wealth in the status quo case is given by: FWS = IWs-t\{l + rBJt)) t = 0 MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 4 iMOff = h 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES As we have reduced the timely accrual of the initial wealth in the status quo case on t=0, this more subtle terminology is apparently redundant in the last equation. (In this case, the borrowing rate or the lending rate has to be applied, but not a combination of them. On the other hand, the terminology allows to prove the result even for whole timely sequences of initial wealth.) Now: PERFIMA t-t fwp = z v n (!+>-,») ŕ=0 r=0 rfí =rT =r Zv(l + rf r=0 As this expression is more simple now, a back-transformation from et to et is possible for the final wealth of the project: FW, = /Ws.(l + r/ + 5>ř-(l + rr ř=0 MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 4 C- |Ĺ*tX | Ur Accordingly, the final wealth in the case of the status quo may for PERFIMA be = h 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES formulated like follows: FWS = IWs-f\{l + rBJt)) rB=rL=r r=0 Now let us take the difference of both expressions: FW p - FWS = IWS ■ (l + rj + X et ■ (l + r)~l -IWS ■ (l + rj t=0 = Zvíl + rľ' = FV t=0 The resulting expression was already defined as the final value FV of a project. If we now multiply by (l + r)~f, we obtain the following expression which is exactly the net present value of a project: MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 4 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES t £é?ř-(l + r)~ř = FV-(l + r)"ř= (FWp-FW^il + rY* ř=0 In other words: (i) The PERFIMA-assumption is crucial for the NPV-concept. (ii) The NPV-concept is in full accordance with the objective of final wealth maximization. (iii) The NPV is completely independent of the initial wealth of the decision-taking entity in the status quo case. [UO& ^iJísuŕ*^ NPV MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 4 3C ? "^^^^^"~ ^ B j* -W-7- ^-v m« ^k-B *"1 ^-V f\ ~\ FACHHOCHSCHULE BOCHUM %ň Wy V l-iPf 'IWI-I ^W ^ I UNIVERSITY OF APPLIED SCIENCES The initial wealth in the case of the status quo be zero, i. e.: IWs=0. The chocolate bar machine known from exercises 5-1, 8-1 and 8-2 is again taken into consideration. The financial market has become perfect now and the interest rates for borrowing and lending both equal 4% now, i. e.: r = 0.04. /) Calculate the final value as well as the net present value of the project! ii) Now check the preceeding statement as to which the net present value equals the increase in final wealth discounted to the present! MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 4 iMOff ^uŕ*^ Explicit Definition of the Net Present Value and Corresponding Decision Rule The net present value of a series of payment e0,el,...,el equals the sum of all its discounted future payments and the initial payment, i. e.: (NPVl) K= Íe,-(l+ry = í>,-<7~' ř=0 ř=0 IL 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES Simon Stevin, 1548/49-1620 (the concept of discounting) Gottfried Wilhelm Leibniz, 1646-1716 (dto.) a) For one project single investment decisions, the project considered is PREFERABLE if and only if it has a POSITIVE NET PRESENT VALUE. b) For multi project single investment decisions, the project featuring the MAXIMUM NET PRESENT VALUE is PREFERABLE if the latter one is POSITIVE. (If no project features a positive net present value, at all, the status quo is preferable.) MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 4 ■- 3C \»~y Special Computational Methods for the Net Present Value Annuity (NPV2) KAmui,y = e^+e-1—^ = e0+e-Q(f,r) q-\ (Q: annuity factor) Perpetuity {NPV3) KPemtlúty = e0+- r (1/r: multiplier) FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 4 iMOff ^uŕ*^ Exercise 9-2 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES Determine efficiently the net present values of those new chocolate brands kown from exercise 8-6 that cannot be eliminated by means of the dominance criterion! To this end, start off from an interest rate amounting to 5% per period, i. e.: r - 0.05/ MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 4 ■- -v 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES V^/ Annual Equivalent: Definition and Decision Rule The ANNUAL EQUIVALENT ě of a project featuring the series of payment eQ9el9...9ei is a constant payment occurring in t = 1,2,...,f the net present value of which equals the net present value of the project: (AE\) e = -}—;-K(r) a) For one project single investment decisions, the project considered is PREFERABLE if it has a POSITIVE ANNUAL EQUIVALENT. b) For multi project single investment decisions, the annual equivalent criterion is ON PRINCIPLE NOT APPLICABLE (inconsistent with the objective of final wealth maximization) MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 5 ^yOĚSa ■r % \ \ j- ^»JíSÍAf*^ *-- ř Exercise 9-4 -h 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES Determine the annual equivalent of the chocolate bar machine by going back to the results of exercises 5-/ and 9-1 and starting off from an unchanged interest rate amounting to 4%perperod, i. e.: r - 0.04/ MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 5 ■- -v 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES Vsu./ Special Computational Methods for the Annual Equivalent Annuity (AE2) eAm"">' = e+ 6° Q(r,f) (l/Q: reciprocal of the annuity factor) Perpetuity (AE3) ěp"pMUy = e + r-e0 MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 5 3C ? "^^^^^"~ ^ B j* -W-7- ^-v m« ^k-B *"1 ^-V f\ ^T FACHHOCHSCHULE BOCHUM %ň H V 1-iPf 'IWI-I ^#™^^ UNIVERSITY OF APPLIED SCIENCES Interest rate per period: 5%, i. e.: r = 0.05 /) Determine efficiently the annual equivalent of project marzipan (which is known from exercises 8-6 and 9-2)1 ii) Would the annual equivalent criterion in the context of exercise 8-6 be apt to select the optimal chocolate brand? Hi) Now assume project marzipan had an infinite duration and determine once more its annual equivalent! MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 5 m ■- -h 3C _______ -v ------Í? FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES X_.^ ^iJísuŕ*^ Exercise 9-6 Starting point is the chocolate bar machine known from exercise 5-1. /) Make up a table of values for the project by calculating the net present values for the following interest rates: a) 0%; b) 2%; c) 4%; d) 6%; e) 8%;f) 10%; g) 12%; h) 15%; i) 20%! Round up or down to even CZK amounts! ii) Draw the net present value function of the project for positive interest rates! MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 5 ■r /Z^S \ X M. 3C ^»JíSÍAf*^ >* The Net Present Value Function FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES Face value ř=0 ř=0 (the sum of all the elements of the series of payment) Asymptotic behavior lim^(r) = lim^č (l + r) =lim (converges asymptotically against the initial payment) t=\ = eo Slope and curvature SK . S2K . <0 ; — >0 č 2 (strictly monotonously decreasing and strictly convex for standard investment projects) MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 5 i fin x ^..„„»/Standard Investment Projects =r 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES Standard projects are projects the series of payments of which features exactly one change of sign (be they standard financing projects or standard investment projects). The series of payment of a STANDARD INVESTMENT PROJECT begins with an outgoing payment e0 > 0 which is then followed by incoming payments only, i. e.: et > 0 V t = l,2,...,ř, where at least one of these payments is strictly positive, i. e.: 3 t: e > 0. MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 5 3C ? '^^^^^^ ..'■' B j* -W-7- ^-v m« ^k-B *"1 ^-V f\ ^? FACHHOCHSCHULE BOCHUM %ň Wl V 1-iPf 'IWI-I ^W ^ ^^ UNIVERSITY OF APPLIED SCIENCES Start off from the following series of payment (all elements in CZK): (-100,000, 158,900, 20,000, -80,010) Make up a table of values for the project by calculating the net present values for the following interest rates: a) 0%; b) 2%; c) 4%; d) 6%; e) 8%; f) 10%; g) 12%; h) 15%; i) 20% and rounding to even CZK amounts and then draw the net present value function of the project for positive interest rates! MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 5 iMOff Eugen von Böhm-Bawerk, 1851 (Brno) - 1914 (Vienna) 3C x.rf/The Internal Rate of Return: Definition and Decision Rule FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES The INTERNAL RATE OF RETURN r * of a project featuring the series of payment eQ9el9...9ei is given by the interest rate that makes the net present value equal to 0, i. e.: (IRR1) K(r*) = 5>-(l + r*)"ř = ° r=0 a) For one project single investment decisions, a standard investment project is PREFERABLE if ITS INTERNAL RATE OF RETURN EXCEEDS THE MARKET RATE (r* > r). If the internal rate of return is lower than the market rate (r* < r), it is disadvantageous compared to the status quo. For non-standard investment projects, the IRR-criterion is on principle NOT APPLICABLE. b) For multi project single investment decisions, the IRR-criterion is on principle not applicable. MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 5 ßcl FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES ^irsttr*^ ^The Internal Rate of Return for Standard Investment Projects (SIP's) Descartes9 Rule of Signs (applied to investment calculus): The NUMBER OF INTERNAL RATES OF RETURN of a project is either equal to the number of sign changes of its series of payment or less than it by a multiple of 2, René Descartes, 1596-1650 Conclusion: A standard investment project with a strictly positive face value has exactly one internal rate of return. MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 5 g yaxEÜ % V^Special Computational Methods for the Internal Rate of Return 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES SIP, finite annuity part immediately after initial outgoing payment (IRR3) Q(r*,t) = -^ => Table III SIP, perpetuity immediately after initial outgoing payment {IRR4) r * e eo MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 6 if hot SIP, outgoing payment, then fixed interest, then redemption in grand total 3C ACHHOCHSCHULE BOCHUM INIVERSITY OF APPLIED SCIENCES {lRR5a) i + z-a * a i: interest rate; z: payback rate; a: payout rate SIP, outgoing payment, then fixed interest and instalment redemption (lRR5b) i + z-a * T T = f + r+1 t =t-f a 2 f : years free of redemption; t: years with redemption; T: "medium" term Base formula for regula falsi rL-K{rR)-rR-K{rL) (IRKS) r(1) L: left of the zero: _ 'L ^VRS 'R JM'L K(rR)-K(rL) R: right of the zero MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 6 ■- 3C V...y Regula Falsi-Algorithm i. Find interest rates rL and rR that comply with the conditions (a) rL< rR (as close as possible) and (b)K(rL)-K(rR)<0. ii. Determine r{l) by means of formula (IRR&). iii. If K(r(l)) = 0, the procedure ends. Otherwise substitute rL or rR, respectively, by f(1) so that again (b) K{rL)-K{rR)<0 is valid. iv. Go back to steps ii. and iii. and apply the rules mutatis mutandis to determine f(2) (ř(3),ř(4) and so on). FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 6 m ■- -h 3C _______ -v ------Í? FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES X_.^ ^iJísuŕ*^ Exercise 9-9 (All payments in CZK.) Consider an investment project whose series of payment consists of an outgoing payment in t=0 amounting to -10,000.00 and an incoming payment in the amount of 11,576.25 in t=3. /) Determine the internal rate of return of the project! ii) Which payment in t=3 would instead result in an internal rate of return of 6%? MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 6 ^yOĚSa ■r % \ \ j- ^»JíSÍAf*^ *-- ř Exercise 9-10 -h 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES Determine efficiently the internal rates of the return of the different chocolate brands known from exercise 8-6! MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 6 ^yOĚSa ■r % \ \ j- ^»JíSÍAf*^ *-- ř Exercise 9-11 -h 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES Approximate the internal rate of return of project marzipan known from exercise 8-6 by assuming its annuity payment would cover an infinite time horizon and compare your result with the one from exercise 9-101 MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 6 3C ? "^^^^^"~ ^ B j* w-y. ^y -a^ ^^ * ^ ^y í~\ 'Í ^% FACHHOCHSCHULE BOCHUM ■■í,. .+-^ ■*! yŕ •-■ l^B 1 ^kÉ-* ^W M I /, UNIVERSITY OF APPLIED SCIENCES A fixed income credit contract that is redeemed in grand total after a maturity of t = 2 years is considered. The interest rate is / = 0.05 per period, the payout rate a = 0.95 and the payback rate z = 1.05. Approximate the internal rate of return of this finan cial contract! MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 6 3C ? "^^^^^"~ ^ B j* w-y. ^y -a^ ^^ * ^ ^y í~\ 'Í /^ FACHHOCHSCHULE BOCHUM %ň H V l-iPI'IWl-l ^W ^ M "^ UNIVERSITY OF APPLIED SCIENCES A fixed income credit contract with a face value amounting to CZK 100,000 that is paid out in the amount of CZK 94,714.62 is taken into consideration. The interest per year amounts to CZK 5,000. Repayment will be at face value. Determine the internal rate of return of this financial contract for the following repayment patterns: (a) redemption in grand total, (b) instalment redemption (no free years), (c) annuity redemption and (d) zerobond! Then comment on your result! MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 6 m ■- -h 3C _______ -v ------Í? m 1 • ^"V -^ M FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES V..*/ Exercise 9-14 The chocolate bar machine known from exercises 9-6 and 5-1 is again taken into consideration. /) Make a first linear estimate r{l)for its internal rate of return by implementing the regula falsi-algorithm and choosing (intentionally in a suboptimal manner) rL = 0.04 and rR = 0.08/ ii) Now round r{1) from part i) to entire percent and make a second linear estimate r{2)! MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 6 ■- -v 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES \y Payback period: Definition and Decision Rule The payback period [0,t *] of a project featuring the series of payment e0,el,...,ei is given by the point in time ŕ* < f at which its net present value becomes positive for the first time, i. e.: (PBP1) I>( • (1 + r)' <0* A Special Computational Method for the Payback Period 3C FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES Annuity {PBP2) Q(t*-l,r) < -Sl < Q(t*,r) table III MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 6 m ■- -h 3C _______ -v ------Í? m 1 • ^"V -^ ^ FACHHOCHSCHULE BOCHUM UNIVERSITY OF APPLIED SCIENCES V..*/ Exercise 9-15 Consider an investment project that is characterized by the subsequent series of payment (all figures in CZK): eo = -500, ex = 200, e2 = 100, e3 = 60 /) Start off from a market rate amounting to r = 0.05 and determine the payback period of the project! ii) Determine efficiently the payback period of project marzipan known from exercises 8-6, 9-2 and 9-5 for r = 0.05/ MU ESF Brno / FH Bochum Prof. Dr. Dirk Kaiser Treasury Management CF from investing activities 6