Idea Transcript
The decision to buy or lease equipment from an engineering economics perspective
By
Cebsile Mkhatshwa 28319461
Submitted in partial fulfilment for the degree of BACHELORS OF INDUSTRIAL ENGINEERING In the
FACULTY OF ENGINEERING, BUILT ENVIRONMENT AND INFORMATION TECHNOLOGY UNIVERSITY OF PRETORIA
October 2011
Executive Summary Leasing and purchasing equipment forms some of the expenses on the capital budget hence, affects the net profit of a company. When deciding whether to lease or purchase equipment it is essential to understand the cash flows associated with each option and the effects of certain parameters on the cash flows in order to select the option that will give the highest return to the investment. In this study the net present value (NPV) is used to decide whether to lease or purchase equipment, with the help of spreadsheet models that represent the cash flows associated with each option. Then the effect of inflation rates, project life, interest rates, loan payback period and percentage equity used to purchase the asset on the NPVs of the spreadsheet models is determined using sensitivity analysis.
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Table of Contents Executive Summary ................................................................................................................................ 1 CHAPTER 1: Introduction and Background .......................................................................................... 4 1.1
Background and Problem Statement ....................................................................................... 4
1.2
Project Aim ............................................................................................................................. 4
1.3
Project Scope .......................................................................................................................... 5
Chapter 2: Literature Review .................................................................................................................. 6 Capital Budget ........................................................................................................................ 6
2.1
2.1.1
Importance of the capital budget ................................................................................... 6
2.1.2
Influence of the capital structure on capital budget decisions ........................................ 6
2.1.3
Influence of interest, tax and inflation rates on cost of capital ....................................... 7
Lease of Equipment ................................................................................................................ 8
2.2
2.2.1
Typical lease agreement .................................................................................................. 8
2.2.2
Different types of leases available .................................................................................. 8
2.2.3
Tax and leasing agreements ............................................................................................ 9
2.2.4
Influence of interest changes on a lease agreement ........................................................ 9
Purchasing of equipment ....................................................................................................... 10
2.3 2.3.1
Tax implications............................................................................................................ 10
2.3.2
Depreciation.................................................................................................................. 10
2.4
Existing methodologies of making the lease-buy decision ................................................... 10
Chapter 3: Solution ............................................................................................................................... 13 3.1
Engineering methods and tools ............................................................................................. 13
3.2
Method selection and development..................................................................................... 14
Chapter 4: Analysis ............................................................................................................................... 22 Chapter 5: Conclusions ......................................................................................................................... 31 APPENDIX A – Purchasing models with different equity ................................................................... 32 APPENDIX B – Purchasing models with varying project life ............................................................. 36 APPENDIX C- Purchasing models with different pay back periods .................................................... 40 APPENDIX D-Purchasing models with different inflation rates ......................................................... 43 APPENDIX E- Leasing models with different inflation rates .............................................................. 46 APPENDIX F- leasing models with varying project lives .................................................................... 49
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Appendix G – purchasing models with varying interest rates .............................................................. 52 Appendix H- leasing models with varying interest rates ....................................................................... 55 Bibliography ......................................................................................................................................... 58
List of tables TABLE 1: INPUT DATA TO THE PURCHASE SPREADSHEET MODEL ...................................................................... 16 TABLE 2: PURCHASING SPREADSHEET MODEL................................................................................................... 18 TABLE: 3 INPUT DATA FOR THE LEASING SPREADSHEET MODEL ....................................................................... 20 TABLE: 4 SPREAD SHEET THAT REPRESENTS THEN LEASING OPTION................................................................ 20 TABLE 5: NPV AND EQUITY ................................................................................................................................ 23 TABLE: 6 CHANGE IN NPV AS THE PROJECT LIFE VARIES ............................................................................... 24 TABLE 7: NPV FOR VARYING PAYBACK PERIODS ............................................................................................... 25 TABLE 8: NPV AND INFLATION RATES WHEN PURCHASING ............................................................................................... 26 TABLE 9: NPV ASSOCIATED WITH DIFFERENT INFLATION RATES WHEN LEASING ........................................... 27 TABLE 10: NPV FOR DIFFERENT PROJECT DURATIONS IN THE LEASING OPTION ............................................. 28 TABLE 11: NPV FOR DIFFERENT INTEREST RATES ............................................................................................. 29 TABLE 12: NPV AND DIFFERENT INTEREST RATES WHEN THE ASSET IS LEASED .............................................. 30
List of figures FIGURE 1: HYDRAULIC MIXER ................................................................................................................................................. 15 FIGURE 2: SENSITIVITY ANALYSIS OF NPV TO THE VARIATION IN THE % OF EQUITY USED TO PURCHASE THE ASSET .......... 22 FIGURE 3: SENSITIVITY ANALYSIS OF NPV TO THE VARIATION IN PROJECT LIFE IF ASSET IS PURCHASED ............................. 24 FIGURE 4: SENSITIVITY ANALYSIS OF NPV TO THE VARIATION IN PAYBACK PERIODS IF ASSET IS PURCHASED ...................... 25 FIGURE 5: SENSITIVITY ANALYSIS OF NPV TO THE VARIATION IN INFLATION IF THE ASSET IS PURCHASED........................... 26 FIGURE 6: SENSITIVITY ANALYSIS OF NPV TO THE VARIATION IN INFLATION RATES IF ASSET IS LEASED .............................. 27 FIGURE 7: SENSITIVITY ANALYSIS OF NPV TO THE VARIATION IN PROJECT LIFE IF THE ASSET IS LEASED............................. 28 FIGURE 8: SENSITIVITY ANALYSIS OF THE AFFECT OF INTEREST RATE ON THE NPV AN ASSET IS PURCHASED ...................... 29 FIGURE 9: SENSITIVITY ANALYSIS OF THE AFFECT OF INTEREST RATE ON THE NPV AN ASSET IS LEASED ............................. 30
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CHAPTER 1: Introduction and Background 1.1 Background and Problem Statement Prior to the 1950s only land and buildings were leased. Today, however almost any fixed asset can be leased. For example about 50% of all new commercial aircraft sold is purchase by aircraft leasing companies (Brigham et al., 1999). At times companies make the decision to buy or lease equipment while not taking into account all the factors that will have a positive or negative effect on the cash flow associated with the decision made. This could be due to the fact that the management of a trading entity may not be aware of the long term impact that acquiring an asset through leasing or buying has on the capital budget of the company. Most published literature that discusses the decision to lease or purchase equipment only addresses the matter from a certain perspective and hence leaves out other factors that are relevant to management faced with the task of deciding to lease or purchase equipment. For example some publications present mathematical models that can be used to decide whether to lease or purchase equipment but leaves out the detailed theoretical explanations of the cash flows incorporated into the formulas of the models and the effect that these cash flows will have on the capital budget of the company, which is what management is interested in. These models can prove to be of little help since they can be difficult to understand and implement and require extensive mathematical knowledge to solve them. There is a great need for a comprehensive analysis of leasing and purchasing equipment and a simplified approach of deciding whether to lease or purchase equipment that will be relevant and easy to implement for all companies.
1.2 Project Aim The aim of this study is to provide a detailed research on the following:
The cash flows associated with leasing and purchasing equipment. The factors that companies should consider when contemplating to lease or purchase equipment. The effect that leasing and purchasing equipment has on a company’s capital budget.
Then finally provide a structured approach that can be followed by any company when deciding to lease or purchase equipment.
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1.3 Project Scope To conduct the study the following problem solving approach will be used (Tarquin, 2008:8) Step 1: understand the problem. Step 2: Collect information. Step 3: Define feasible alternative solution and make realistic estimations. Step 4: Identify criteria for decision making. Step 5: Evaluate each alternative. Step 6: Select the best alternative. To accomplish the first two steps, an in depth study of the literature currently available about buying and leasing equipment and how the capital budget is affected by leasing or purchasing equipment. The effect that the size of the loan acquired to purchase the equipment, period to pay back the loan, inflation rate and project life on the decision to purchase or lease equipment. With regards to step 3; the alternative solutions will be the different techniques of evaluating capital investment decisions. Keep in mind that the solution in this case would be the best suited technique to be used when deciding to lease or purchase equipment. According to step 4, a decision making criteria must be selected for each technique mentioned in step3. In step 5 each decision making technique will be evaluated and compared against each other. Lastly a conclusion will be reached on which technique is to be used when deciding to lease or purchase equipment.
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Chapter 2: Literature Review 2.1
Capital Budget
A capital budget consists of an outline of planned long term investments on fixed assets. Capital budgeting is the process of analyzing projects and deciding which ones to include in the company’s capital budget. Assets included in the capital budget have the following characteristics (du Toit et al., 2001):
The expected life of the asset is longer than one year. They are not traded in the normal course of the firm’s business.
The equipment to be discussed in this study present the features or characteristics mentioned above therefore they are recorded in the capital budget and can be referred to as capital budget investments.
2.1.1
Importance of the capital budget
The distribution of resources in the capital budget determines whether management will be able to produce a minimum return on the investor’s money that the investor would have received on an alternative investment. This factor determines whether investors keep investing in the company or they take their investments elsewhere (Brigham et al.,2005). From the capital budget potential investors and current investors can determine the firm’s strategic direction. The acquisition of assets or projects that the company decides to finance will affect the company’ cash flow for a number of years still to come, that is why capital budgeting is preceeded by a forecast of future expences and future income. A significant amount of this forecast is done during the analysis of the cash flows associated with leasing or purchasing equipment.
2.1.2
Influence of the capital structure on capital budget decisions
To acquire an asset buy leasing or purchasing a company needs capital. Capital structure refers to the different sources of capital that a company uses, the fixed amount of capital that the company gets from each source and the cost of each capital source. These different sources of capital are referred to as capital components. According to Brigham et al., (1999) the three major capital components are: common stock, preferred stock and debt capital. Companies may choose to use only one of these sources of capital or a combination of two sources or a combination of all three sources.
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Common stock refers to the amount that shareholders have invested in the organisation plus retained earnings, which is the amount earned from income generating activities (Walter & Charles, 2008). Preferred stock is a hybrid of common stock and long-term debt. Preferred stock can be referred to as long term debt because if it is used as capital to acquire an asset then a fixed dividend must be paid to the preferred stockholders. It can also be referred to as common stock because the dividend is not paid out to the preferred stock holders unless the board of directors declare the dividend, as this is the case with common stock (Walter & Charles, 2008). Debt capital refers to raising capital by acquiring debt; it can be through a loan or issuing bonds. Each company ought to have an optimal capital structure that is aimed at providing the highest possible economic value added (EVA). According to Brigham et al., (1999) the capital structure is used to determine the cost of capital by using the weighted average cost of capital equation (WACC).
WACC
=
𝒘𝒅 𝒌𝒅 𝟏 − 𝑻 + 𝒘𝒑𝒔 𝒌𝒑𝒔 + 𝒘𝒄𝒆 𝒌𝒔
[𝟐. 𝟏]
wd, wps and wce are the weights used for debt, preferred and common equity respectively. kd is the interest rate of the debt. T is the marginal tax of the firm. Kps is the preferred dividend divided by the net issuing price, 𝑘𝑝𝑠 =
𝐷𝑝𝑠 𝑃𝑛
Ks is the rate of return required by investors. The weights for debt, preferred equity and common equity are determined by each company on the company’s capital structure policy. Capital structure enables management to determine beforehand the projects that will require a minimum cost of capital. By considering the capital structure management can determine the capital component that costs the most at that specific time, and then use less of that capital component when financing new capital investments.
2.1.3
Influence of interest, tax and inflation rates on cost of capital
When interest rates in the economy increase the cost of debt capital will also increase because bondholders and banks will require a higher interest rate. Higher interest rates will also increase the cost of preferred equity capital. Variation in the tax rate will affect the cost of capital equity. An increased tax rate will lead to a low cost of debt capital according to the WACC equation (Brigham et al., 1999). An increase in inflation tends to
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increase the required rates of return by the investors, this leads to a higher cost of capital (du Toit et al., 2001).
2.2
Lease of Equipment
2.2.1
Typical lease agreement
Leasing is characterised by the separation of ownership of the asset and right of use of the asset between the lessor and the lessee. The lessor owns the asset but the lessee has the right to use the asset (du Toit et al., 2001). According to the Internal Revenue Service an agreement is regarded as a lease agreement if the following requirements are met (Brigham 1999):
The period of leasing the asset (including renewals and extensions of the lease agreement) should not exceed 80% of the estimated useful life of the asset. The remaining useful life of the asset after the lease term must not be less than a year. The residual value of the asset at the end of the lease term must at least equal 20% of the value of the asset at the start of the lease period. The lessee or any other party is not allowed to purchase the equipment at a price determined at the start of the lease term.
A lease agreement usually contains the following information:
The duration of the lease contract. The specific lease payments and the number of payments. Conditions of renewal of the lease agreement. Individual responsible for maintenance costs. How the residual value will be incorporated in the cash flows. The description of the leased assets.
2.2.2
Different types of leases available
Leasing takes place in four different forms, being, the operating lease, financial or capital lease and a sale and sale back lease agreement (Brigham et al., 1999).
Operating lease The lessor is required to maintain and service the leased equipment, the cost of maintaining is built into the lease payment. The lease payments are not sufficient for the lessor to cover the full capital coat of the asset. Operating lease agreements contain a cancellation clause which allows the lessee to cancel the lease and return the asset before the end of the lease term.
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Financial or capital lease The lessor does not provide maintenance services. The lease payments fully amortize the capital cost of the equipment. The lease agreement is not cancellable, unless the asset is fully amortized. Sale – and - Leaseback A company that owns an asset sells the asset to another firm and simultaneously executes an agreement to lease the equipment at specific terms and period. The seller gets the purchase price immediately from the buyer. The seller still retains the use of the equipment.
2.2.3
Tax and leasing agreements
According to the Income Tax Act 1962, administered by the Commissioner of the South African Revenue Services (SARS), tax payments and other expenditures incurred in the production of income not of capital nature can be deducted from income for tax purposes. These deductions grant tax savings for the lessee and are referred to as general deductions. The tax savings are calculated in the following manner: 𝑻𝒂𝒙 𝒓𝒂𝒕𝒆 × 𝒍𝒆𝒂𝒔𝒆 𝒑𝒂𝒚𝒎𝒆𝒏𝒕 + (𝑶𝒕𝒉𝒆𝒓 𝒆𝒙𝒑𝒆𝒏𝒅𝒊𝒕𝒖𝒓𝒆𝒔 × 𝑻𝒂𝒙 𝒓𝒂𝒕𝒆)
2.2.4
[2.2]
Influence of interest changes on a lease agreement
Interest rates influence the lease payments determined by the lessor on the lease agreement. The internal rate of return (IRR) that will allow the net present value of the cash flows experienced by the lessor equal to zero is the IRR that the lessor selects to determine the lease payments. The lessor determines the internal rate of return (IRR) required by considering the net present value of the cash flows experienced while acquiring the asset and maintaining it. These cash flows from the lessor perspective include: the net purchase price, maintenance costs, tax on residual value and lease payment, depreciation and maintenance tax savings. If the cost of capital (return required by the capital components) for acquiring and maintain the asset was high, this will result in the lessor declaring a high IRR in order to pay back the cost of capital and earn interest. This will result in high lease payments. On the other hand if the return required by the capital components is relatively low, the lessor will declare a lower IRR, hence the lease payments on the lease agreement will be lower (Brigham et al., 1999).
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2.3 Purchasing of equipment 2.3.1
Tax implications
According to the Legal and Policy division, South African Revenue Service (2009) all goods purchased from a vendor value added tax (VAT) is paid as part of the purchase price. The current vat rate is 14% is South Africa. Therefore when purchasing an asset, the VAT is included in the purchase prize. Once the asset is purchased and put to use, the tax payer can declare tax savings based on the operating expenses of the asset and depreciation expenses (S.A Income tax Act section 6, 1962). If the asset is being resold at a market value that is higher than the salvage value, a capital gains tax (CGT) is paid on the difference between the two amounts (South African Income tax Act section 11, 1962).
2.3.2
Depreciation
Depreciation refers to the reduction in the value of an asset (Tarquin, 2008). Depreciation reduces the calculated net profit even though it is not a cash charge. A high depreciation leads to a low tax bill (Brigham, 1999). Depreciation can be calculated using one of the following methods
Straight line depreciation: The difference between the initial purchase price of the asset and the estimated salvage value is divided by the economic life of the project to find the annual depreciation amount (Tarquin, 2008). This method is mainly used for stockholder reporting (or book purposes) (Brigham, 1999).
Modified accelerated cost recovery system (MACRS): This method consists of two steps. In the first step the annual depreciation is determined by multiplying the initial cost of the asset. In the second step, the book value in a particular year is determined by subtracting the sum of annual depreciations (from previous years) from the initial purchase price of the asset (Tarquin, 2008). This method is favoured when calculating income tax since it yields high net profit reductions due to high depreciation (Brigham, 1999).
2.4
Existing methodologies of making the lease-buy decision
Various tools have been suggested to assist companies make the right choice to lease or purchase equipment. The Vincil model also known as the Lease-Or-Borrow model is one of these tools (Sartoris & Paul, 1973, 46:52). The Lease-Or-Borrow model compares the cost of acquiring an asset through lease financing to the cost of acquiring the asset by purchasing the asset using debt capital. The first step of the Lease-Or-Borrow model is to determine the net present value of owning an asset, using the following formula
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𝒌
𝑵𝒆𝒕 𝒑𝒓𝒆𝒔𝒆𝒏𝒕 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒑𝒖𝒓𝒄𝒉𝒂𝒔𝒆 = −𝑪 + 𝒏+𝟏
Where C
=
Purchase Price
Dnt
=
Depreciation tax savings in year n
t
=
tax rate
i
=
Cost of capital
K
=
Life of the project
𝑫𝒏 𝒕 (𝟏 + 𝒊)𝒏
[𝟐. 𝟑]
The second step is to determine the net present value of the lease payments, using the following equation: 𝑵𝒆𝒕 𝑷𝒓𝒆𝒔𝒆𝒏𝒕 𝑽𝒂𝒍𝒖𝒆 𝒐𝒇 𝒍𝒆𝒂𝒔𝒆 = Where
𝑨𝒏 𝒕 𝒌 𝒏=𝟏 (𝟏+𝒊)𝒏
−
𝑳𝒏 𝒌 𝒏=𝟏 (𝟏+𝒓)𝒏
An
= non interest portion of the lease payment in year n.
Ln
=
r
= Basic interest rate.
k
=
Life of the asset.
i
=
Cost of capital
[𝟐. 𝟒]
Lease payment in year n.
The highest positive NPV between the NPV of the lease and the NPV of purchasing indicates the best alternative of acquiring the asset. The Lease-Or-Buy model was developed by Johnson & Wilbur (1972). This model is similar to the Lease-Or-Borrow model because it also develops the NPVs associate with leasing and owning equipment. The difference between the two models is that the Lease-Or-Buy model includes costs that are common when leasing or purchasing equipment, on the other hand the Lease-Or-Borrow model omits these costs. Another significant difference between the two models is that the Lease-Or-Buy model compares the costs of acquiring an asset through leasing to the costs of acquiring through purchasing using own equity. On the other hand the Lease-Or-Borrow model compares leasing to purchasing using debt capital. The Lease-Or-Buy model consists of the following equations 𝑵𝑷𝑽 𝒑𝒖𝒓𝒄𝒉𝒂𝒔𝒆 = −𝑪 +
𝒕𝑫𝒏 𝒌 𝒏=𝟏 (𝟏+𝒊)𝒏
+
𝑹𝒏 (𝟏+𝒕) 𝒌 𝒏=𝟏 (𝟏+𝒊)𝒏
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[2.5]
𝑵𝑷𝑽 𝒍𝒆𝒂𝒔𝒆 =
𝑹𝒏 +𝑶𝒏 (𝟏−𝒕) 𝒌 𝒏=𝟏 (𝟏+𝒊)𝒏
−
𝑳𝒏 (𝟏−𝒕) 𝒌 𝒏=𝟏 (𝟏+𝒓 𝒊)𝒏 𝒕
[2.6]
Where Ri = Operating cash flow from the project in year i. Oi = Operating costs that would occur under ownership of the asset but not under the lease agreement. rt
= after tax interest rate.
Ln
=
Lease payment in year n.
Sartoris & Paul (173, 46:52) compared the two models (Lease-Or-Borrow and Lease-OrBuy) and reached a conclusion that Lease-Or-Borrow model leads to the correct decision while Lease-Or-Buy model leads to an incorrect decision.
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Chapter 3: Solution 3.1
Engineering methods and tools
Leasing and purchasing equipment are both capital budget investments. Brigham et al.,(1999) define the following capital budgeting decision rules that should be used to decide whether a capital investment should be included in the capital budget or not.
Payback period – Compares the number of years required to recover the investment in each project. The project with the lowest payback period is selected. It is applicable to mutually exclusive projects. 𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒚𝒆𝒂𝒓𝒔 =
𝑰𝒏𝒊𝒕𝒊𝒂𝒍 𝑰𝒏𝒗𝒆𝒔𝒕𝒎𝒆𝒏𝒕 𝑨𝒏𝒏𝒖𝒂𝒍 𝒏𝒆𝒕 𝒄𝒂𝒔𝒉 𝒇𝒍𝒐𝒘
[𝟑. 𝟏]
Net Present Value (NPV) – NPV refers to the sum of the discounted cash flows at the cost of capital. If NPV = 0, then the project is acceptable because the cash inflow is sufficient to repay the initial investment at required rate of return of the capital. If NPV > 0, then the project is still acceptable since the cash inflows will pay back the cost of capital at a rate higher than the required cost of capital. If NPV < 0 then the project is not acceptable since capital will be repaid at a rate that is less than the required rate of return.
IRR (internal rate of return) –IRR is the rate of return required by a company to ensures that the NPV of cash inflows is equal to zero. If the rate of return of any project is less than the IRR of the company then that project is not included in the capital budget.
MIRR (modified internal rate of return) – This decision making rule is an improvement of the IRR. When using this rule, the terminal value (TV) has to be defined. The TV is the future value of cash inflows. The MIRR is the discount rate that ensures that the present value of cash outflows (PV cost) is equal to the present value of the terminal value.
Profitability Index (Benefit cost ratio) – Shows the relative profitability of a project. A project is acceptable if the Profitability index is greater than 1.0. 𝑷𝑰 =
𝑷𝑽 𝒃𝒆𝒏𝒆𝒇𝒊𝒕𝒔 𝑷𝑽 𝑪𝒐𝒔𝒕
[𝟑. 𝟐]
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Brigham et al.,(1999) further mention that the net present value decision rule is the most reliable and accurate decision rule.
3.2
Method selection and development
To compare purchasing equipment and leasing equipment a cash flow analysis is used and the cash flows are presented on spreadsheet models. This method is selected because it is easier to prepare and understand spreadsheet models than to set up and understand mathematical models. Hence, this method can be applied by any company. The NPV rule is used to analyse the spreadsheets that represent the options of leasing and purchasing equipment in this study because according to Brigham et al., (1999) this is the rule that managers prefer to use when comparing projects. The reason for this is that the NPV value directly links to the economic value added (EVA) to the company by a certain project and this is the information that shareholders and investors are interested in. For example the NPV refers to the present value of the EVA (Brigham et al., 1999). Brigham et al., (1999) further mentioned that well managed companies cannot purchase equipment cash because cash is usually tied up in assets. To implement the method mentioned in the paragraph above, the following steps must be followed. I. II. III. IV.
V.
State assumptions. Collect the information that will be used to develop the spreadsheet models. Present the expected cash flows on spreadsheet models. Determine the net present value in each of the spreadsheet models and decide on the best alternative. The alternative with the highest positive NPV value will be accepted. If the NPV value derived from the spread sheet calculations is negative, the option represented by that spreadsheet is not accepted. Determine how some inputs of the spreadsheet models affect the NPV, by changing one input variable while keeping all other parameters and variables the same.
The final step is optional. It can be done if the company would like to know how certain parameters will affect the cash flows associated with leasing and the cash flows associated with purchasing. This step will be demonstrated in chapter 4.
To test this methodology, the steps listed above were used to decide whether to purchase or lease an asset called the hydraulic mixer with scale (see figure 1). The relevant information about the hydraulic mixer (e.g. purchase price, lease payments, operating costs) was made available by the Turner and Morris Company located in Pretoria town Skinner Street. The trade of the Turner and Morris Company is to sell and lease out fixed assets that are used in the construction industry.
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Figure 1: Hydraulic mixer
I.
State assumptions A loan is used to finance the purchase of the asset. Payback period of the loan is 4 years. The market value of the asset once it has been purchased decreases at a 10% rate. Life of the project is 15 years. The minimum allowed rate of return (MARR) of the company is 15% since it is normally stated to be higher than the rate of return charged by banks.
The lease presented on the spreadsheet model is an operating lease whereby the lessor is responsible for the overhaul maintenance cost but the lessee is responsible for the daily maintenance cost.
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II.
Collect relevant information The data that is used to prepare the spread sheet models is presented on input tables and calculations that precede each spread sheet model.
Steps III & IV are presented simultaneously on the spreadsheet models. Below is the input table which represents data used to prepare the spreadsheet model that represents the purchasing alternative. Table 1: Input data to the purchase spreadsheet model
Cash Flow Analysis for purchasing a hydraulic mixer using a loan. Scenario:
Purchase equipment using a loan.
Input table Purchase price + VAT Loan Amount Interest on loan (i) Payback period Normal tax rate Secondary tax Life of project Tax life
254 218.86 254 218.86 7.00% 4 years 28% 10% 15 years 3 years
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Calculations:
Annuity, A (n = 4)
P(A/P,7,4) R 75 053.03
Depreciation per year: (254218.86 - 40 000)/3 R 71 406.28667
Annual interest (n = 4) :
A(P/A,7,n)*7%
Interest in year 1 Interest in year 2 Interest in year 3
17795.37 13787.32 9498.71
Interest in year 4
4910.12
Annual Income : each load = 5 litres at R50 per 5 litres In one hour = 4 loads operates for 8 hours 6 days per week Assume 52 weeks per year (6*52*8)*(4*50)
Annual operating expenses diesel (R11 per hour) 2 labourers (R18 per hour) 1 Operator ( R35 per hour) Engine oil and filter service Total Assumption: work 8 hrs 6 days a week Overhaul service every 3 years
R 499200 440 89856 87360 2000 R 179656 R 50 000
MARR After tax MARR Before Tax = 15% MARR(Before tax) (1 - Tax rate) 0.108 11%
Market Value After 15 years: 254 218.86 *( 1- g)^(15-1); g = 10% 58157.12098
The purchase price of this asset was provided by the Turner and Morris Company. The loan used to purchase this equipment covers the entire purchase price. According to Brigham et al., (1999) well managed companies cannot afford to purchase such equipment cash since the company’s cash is tied up in fixed assets. The effect that the percentage of own equity used to purchase the equipment is still to be investigated further in this study. The annuities and interest rates were calculated using discount factors published by Blank Tarquin (2008). The interest rate on the loan is 7% as this is the official rate of interest published by the Legal and Policy division South African Revenue Services, March 2011.
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The MARR before tax is 15% and it is based on the interest rate charged by the banks. The MARR expected by management in companies is always higher that the interest charged by the banks in order to declare a profit. The depreciation used is straight line depreciation (Brigham et al., 1999:446) The tax life of this equipment (cement mixer) is 3 years as stated on the Binding General Ruling (Income Tax Act): NO.7 published 11 April 2011. The Normal and Secondary tax rates are as published by the South African Revenue Services. To determine the market value at the end of the life of the project, it was assumed that the market value decreases by 10% per year. The formula used is stated under calculations. The operating expenses and income are specific to the equipment being evaluated.
Below is the spreadsheet model that represents the option of purchasing the asset. Table 2: Purchasing Spreadsheet model Year
CFBT
Depreciation
Book Value
Loan Interest
Operating cost and maintenance
Taxable Income
Loan Payment
Tax payment
CFAT
0
MV
1
499200
-71072.95
183,145.91
17795.37
2
499200
-71072.95
112,072.95
13787.32
3
499200
-71072.95
41,000.00
9498.71
4
499200
4910.12
5
230675.67
75,053.03
64,589.19
179656
234683.73
75,053.03
65,711.44
178779.52
R 229,656
R 188,972.33
75,053.03
52,912.25
R 141,578.71
179656
R 314,633.88
75,053.03
88,097.49
R 156,393.48
499200
179656
319544
89,472.32
230,071.68
6
499200
R 229,656
269544
75,472.32
R 194,071.68
7
499200
179656
319544
89,472.32
R 230,071.68
8
499200
179656
319544
89,472.32
R 230,071.68
9
499200
R 229,656
269544
75,472.32
R 194,071.68
10
499200
179656
319544
89,472.32
R 230,071.68
11
499200
179656
319544
89,472.32
R 230,071.68
12
499200
R 229,656
269544
75,472.32
R 194,071.68
13
499200
179656
319544
89,472.32
R 230,071.68
14
499200
179656
319544
89,472.32
R 230,071.68
15
499200
R 229,656
269544
75,472.32
R 194,071.68
17,157.12
4,803.99
R 53,353.13
58,157
179656
41,000.00
179901.78
NPV: 179 901.78(P/F,11,1) + 178 779.52(P/F,11,2) + 141 578.71(P/F,11,3) + 156 393.48(P/F,11,4) + 230 071.68(P/F,11,5) 194 071.68(P/F,11,6) + 230 071.68(P/A,11,2)(P/F,11,6) + 194 071.68(P/F,11,9) + 230 071.68(P/A,11,2)(P/F,11,9) + 194 071.68(P/F,11,12) + 230 071.68(P/A,11,2)(P/F,11,12) + 194(P/F,11,15) + 53 353.13(P/F,11,15)
18
1414270.19 EAA (Equivalent Annual Annuity) = P(A/P,11,15) 196682.556
All cash flows are considered to be at the end of the year. CFBT refers to cash flow before tax, and CFAT refers to cash flow after tax The CFBT is the income generated by the equipment; in this case it is determined under calculations. The depreciation is calculated as stated on the calculations above. The taxable income is calculated by subtracting the tax saving from depreciation and expenditure and loses actually incurred during the year of assessment in the production of income not of a capital nature (Income Tax Act, 1962) from the gross income. In this case these expenses include the interest rate on the loan and operating expenses. 𝑫𝒆𝒑𝒓𝒆𝒄𝒊𝒂𝒕𝒊𝒐𝒏 𝑻𝒂𝒙 𝒔𝒂𝒗𝒊𝒏𝒈𝒔 𝒂𝒕 𝒕𝒉𝒆 𝒆𝒏𝒅 𝒐𝒇 𝒕𝒉𝒆 𝒚𝒆𝒂𝒓 = 𝑫𝒆𝒑𝒓𝒆𝒄𝒊𝒂𝒕𝒊𝒐𝒏 𝒑𝒆𝒓 𝒚𝒆𝒂𝒓 × 𝑻𝒂𝒙 𝒓𝒂𝒕𝒆 𝑶𝒕𝒉𝒆𝒓 𝒆𝒙𝒑𝒆𝒏𝒄𝒆𝒔 𝒕𝒂𝒙 𝒔𝒂𝒗𝒊𝒏𝒈𝒔 = 𝑬𝒙𝒑𝒆𝒏𝒄𝒆𝒔 × 𝒕𝒂𝒙 𝒓𝒂𝒕𝒆
[𝟑. 𝟑]
[𝟑. 𝟒]
The loan payment is computed as stated under calculations. This amount includes both the interest on the loan and the principle amount. 𝑻𝒂𝒙 𝒑𝒂𝒚𝒎𝒆𝒏𝒕 = 𝑻𝒂𝒙𝒂𝒃𝒍𝒆 𝒊𝒏𝒄𝒐𝒎𝒆 × 𝟎. 𝟐𝟖 [𝟑. 𝟓] 𝑪𝑭𝑨𝑻 = 𝑻𝒂𝒙𝒂𝒃𝒍𝒆 𝒊𝒏𝒄𝒐𝒎𝒆 − 𝒕𝒂𝒙 𝒑𝒂𝒚𝒎𝒆𝒏𝒕 − 𝒍𝒐𝒂𝒏 𝒑𝒂𝒚𝒎𝒆𝒏𝒕 + 𝒅𝒆𝒑𝒓𝒆𝒄𝒊𝒂𝒕𝒊𝒐𝒏 + 𝒍𝒐𝒂𝒏 𝒊𝒏𝒕𝒆𝒓𝒆𝒔𝒕. [𝟑. 𝟔]
After the life of the project (15 YEARS) the market value of the equipment is higher than the book value (40 000). Capital gains tax is paid on the difference between the market value and book value. The capital gains tax was assumed to be 28% of the difference between the book value and the market value.
The NPV for the option to purchase equipment using a loan to finance it is positive, which means that this option is acceptable.
19
Next, the option of leasing the asset is considered. Steps III & IV will be presented in the same manner as in the option of purchasing the asset. Table: 3 Input data for the leasing spreadsheet model
Scenario:
Acquiring equipment through leasing
Input table Purchase price + VAT Annual lease payment Normal tax rate Secondary tax Life of project Tax life
254 218.86 215 162.46 28% 10% 12 years 3 years
Table: 4 Spread sheet that represents then leasing option Year
CFBT
lease payment
Operating cost
Taxable
Tax
CFAT
and maintenance
Income
payment -215162.46
0 1
499200
430324.92
179656
-110780.92
2
499200
215162.46
179656
104381.54
29226.8312
75154.7088
-110780.92
3
499200
215162.46
179656
104381.54
29226.8312
75154.7088
4
499200
215162.46
179656
104381.54
29226.8312
75154.7088
5
499200
215162.46
179656
104381.54
29226.8312
75154.7088
6
499200
215162.46
179656
104381.54
29226.8312
75154.7088
7
499200
215162.46
179656
104381.54
29226.8312
75154.7088
8
499200
215162.46
179656
104381.54
29226.8312
75154.7088
9
499200
215162.46
179656
104381.54
29226.8312
75154.7088
10
499200
215162.46
179656
104381.54
29226.8312
75154.7088
11
499200
215162.46
179656
104381.54
29226.8312
75154.7088
12
499200
179656
319544
89472.32
230071.68
NPV: - 110 780 (P/F,11,1)+ 75 154.709*(P/A,11,10) (P/F,11,1)+ 230 071.68*(P/F,11,12) 364691.2973
20
EAA (Equivalent Annual annuity) = P(A/P,11,12) 56173.40053
The lease payment is always paid at the beginning of the year. However, the first lease payment can be paid along with the second payment at the beginning of the first year. Lease payments are considered to be an expense, hence, there are tax savings experienced due to lease payments. Equation [3.4] was used to determine the tax savings associated with the lease payment. The value of operating expenses represents the expenses experienced daily, not the overhaul expenses. This value was calculated in the calculations preceding the spreadsheet model that represents the purchasing option. Equation [3.4] was used to determine the tax savings associated with this expense. The NPV is positive which makes this alternative acceptable.
When considering the NPV values on the spreadsheets we notice that the NPV on the spreadsheet that represents purchasing is higher (R 1 414 270.19) than the NPV valve on the spreadsheet that represents leasing (R 364 691.2973). These values suggest that the purchasing alternative should be implemented. According to the NPV rule the alternative with the highest positive NPV should be implemented. However, there is still another factor to consider; the lives of the projects are not the same. In order to compare projects with different lives the Equivalent Annual Annuity (EAA) value should be used (Brigham et al., 1999). In each spreadsheet the EAA value is calculated right after the NPV value. The option with the highest positive EAA value should be chosen. The EAA of the purchasing calculations is R 1960682.556 and the EAA value of the leasing calculations is R 560173.40053. The purchasing option has a higher EAA value which means the asset should be purchased rather than leased.
21
Chapter 4: Analysis To accomplish step V sensitivity analysis was carried out on both spreadsheet models, to determine how certain parameters affect the cash flows associated with leasing and purchasing. To determine how the percentage of own equity used to purchase the equipment affects the NPV, different purchasing spreadsheet models were prepared where the amount of own equity used to purchase the asset varied from 0% of the purchase price to 100% of the purchase price. The spreadsheet model representing 0% own equity can be seen on table 2 and the spreadsheet models representing 25% to 100% own equity can be found in appendix A. From figure 2 it can be seen that when the percentage of own equity used to finance the purchase price increases, the NPV or profit that is expected from a project will decrease at a constant rate. This shows that it would be best to purchase the asset using a loan rather than use own equity (company’s money) to purchase the equipment. Figure 2: Sensitivity analysis of NPV to the variation in the % of equity used to purchase the asset
Change in NPV as equity changes 1420000 1410000
NPV
1400000 1390000 NPV
1380000 1370000 1360000 0%
25%
50%
75%
100%
% of own equity used to purchase equipment
22
Table 5: NPV and Equity
NPV
Equity
1414270
0%
1406336
25%
1398381
50%
1390413
75%
1382446
100%
Figure 3, below demonstrates how the NPV of a project changes if the duration of the project decreases, when the asset is purchased using a loan. When the project life is varying the market value of the asset at the end of the project life is affected, as well as the total income generated since the number of operating years is varying. A project life of 15 years is the normal scenario depicted on table 2, for further investigation the project life was reduced to 3 years (these spreadsheet models are shown in appendix B). On figure 3 it can be shown that as the project life decreases from 15 years to 3 years the NPV or the return on the project decreases. This is simply because the number of operating years has decreased hence less profit is made.
23
Figure 3: Sensitivity analysis of NPV to the variation in project life if asset is purchased
Change in NPV as project life changes 1400000.00 1200000.00
Project life
1000000.00 800000.00 600000.00
NPV
400000.00 200000.00 0.00
3
6
9
12
15
Project life
Table: 6 Change in NPV as the project life varies
Project life
NPV
3
812085.39
6
875706.2996
9
1141355.46
12
1179742.949
15
1223340.701
The graph bellow (figure 4) depicts how the payback period of a loan used to purchase an asset affects the NPV. The payback period is increased from 4 years to 8, 12 and 15 years (spreadsheet models representing these payback periods are found in appendix C). The change in the payback period affects the annual loan payment expense. When the payback period of the loan is increased to 8 years the NPV also goes up. This is because the loan is paid over a longer period and in smaller quantities which leads to high annual after tax cash
24
flows, resulting in an increased NPV. The same manner of reasoning applies if the payback period is increased to 12 years; the NPV is increased due to higher annual after tax cash flows. On the other hand if the payback period is equal to the life of the project (15 years), this means the loan payments are spread over the entire life of the project, hence each annual income is reduced by the loan payment. This has an adverse effect on the NPV, as seen on figure 4 the NPV is drastically reduced if the payback period is equal to the life of the project.
Figure 4: Sensitivity analysis of NPV to the variation in payback periods if asset is purchased
NPV associated with different payback periods 1520000 1500000 1480000
NPV
1460000
1440000 1420000
NPV
1400000 1380000 1360000
4
8
12
15
period to pay back the loan
Table 7: NPV for varying payback periods
Payback period
NPV
4
1414297.659
8
1434815.991
12
1510699.793
15
1462319.244
25
Figure 5 below illustrates how inflation affects the NPV associated with purchasing calculations. The spreadsheets that support the information presented in figure 5 are presented in appendix D. Inflation is the annual increase in the amount of money required to purchase the same amount of goods. If the inflation rate is incorporated into the spreadsheet model that represents purchasing, this results in the operating expenses increasing yearly at the rate of inflation. As the inflation rate increases from 5% to 6.6% to 9.6% the NPV value decreases since the yearly operating expenses also increases. The current inflation in South Africa at the moment is estimated to be 6.6%, this estimate was determined through a process called inflation targeting (de Jager & Kahan, 2011).
Figure 5: Sensitivity analysis of NPV to the variation in inflation if the asset is purchased
Change in NPV as inflation changes 1200000 1000000
NPV
800000 600000 400000
NPV
200000 0 5%
6.60%
9.60%
Inflation rate
Table 8: NPV and inflation rates when purchasing
NPV
inflation rate
1016691.3
5%
795365.58
6.60%
447344.19
9.60%
Further analysis was also done on the leasing spreadsheet. To investigate the effect of inflation on the NPV if an asset is leased multiple leasing spreadsheets were prepared with varying inflation rates. These spreadsheets can be seen in appendix E. Figure 6 below
26
demonstrates the results. The change in the inflation rate affects only the operating expenses if the asset was leased. The lease payment expense is not affected because these payments are determined at the beginning of the lease period and cannot be adjusted for inflation during the duration of the lease; the inflation rate is considered when the payments are first established at the beginning of the lease period. In figure 6, as the inflation rate increases from 5%, to 6.6% and to 9.6% the NPV of the leasing spread sheet is decreasing, the reason for this is that as inflation gets higher the operating expenses get even more expensive. Once the inflation hits 9.6%, the NPV will be negative, which makes the leasing option unacceptable. If the inflation rate were to actually rise to 9.6% the asset would not be leased since the NPV when the asset is leased is negative, the asset would be purchased because as seen in figure 5 the NPV is positive when the asset is purchased and the inflation rate is 9.6%. Figure 6: Sensitivity analysis of NPV to the variation in inflation rates if asset is leased
Change in NPV as inflation changes 400000 300000 200000
NPV
100000 0 -100000
5%
6.60%
NPV
9.60%
-200000 -300000 -400000
Inflation rate
Table 9: NPV associated with different inflation rates when leasing
Inflation
NPV
5%
313449.1171
6.60%
149529.2973
9.60%
-305128.07
27
Figure 8 shows how different project lives can affect the NPV if an asset is leased. The relevant spreadsheets are in Appendix F. As the life of the project is decreased from 12 to 9 years the NPV is also decreasing. The reason is that when the project life gets shorter, there are less operating years hence, less income. When the asset is leased the market value of the asset at the end of the project duration does not affect the NPV of profit from the project. Figure 7: Sensitivity analysis of NPV to the variation in project life if the asset is leased
Change in NPV as project life increases 400000 350000
Net Present Value
300000 250000 200000 Net Present Value
150000 100000 50000 0 3
6
9
12
Project Life
Table 10: NPV for different project durations in the leasing option
Project life
Net Present Value
3
129421.4442
6
233247.6083
9
359744.6624
12
364691.2973
28
To investigate how an increase in the interest rates would affect the profit expected from a project whether the asset is leased or purchased further analysis was done on the leasing and purchasing spreadsheet models and the results are show on figure 8 and figure 9. The spreadsheet models supporting these graphs are on appendix G and appendix H respectively. Figure 8: Sensitivity analysis of the affect of interest rate on the NPV an asset is purchased
Change in NPV as interest rates increase 1420000 1415000 1410000 1405000 NPV
1400000
1395000 1390000
npv
1385000 1380000 1375000 1370000
0.07
0.08
0.11
0.14
Interest rate
Table 11: NPV for different interest rates
Interest rate
NPV
0.07
1414270.194
0.08
1410565.397
0.11
1399170.018
0.14
1387507.857
29
Figure 9: Sensitivity analysis of the affect of interest rate on the NPV an asset is leased
Change in NPV as interest rate increases 400000 350000 300000 NPV
250000 200000 150000
npv
100000 50000 0 7%
8%
11%
14%
interest rates
Table 12: NPV and different interest rates when the asset is leased
INTERST RATE
NPV
7%
364691.2973
8%
267922.9641
11%
231634.5301
14%
178398.398
From figure 8 and 9 it is evident that when the interest rate increases the return that is expected on a project decreases, whether the asset was leased or purchased. However the slope of the graph on figure 8 is –R 382 466.44 and the slope of the graph in figure 9 is -R 3.7041E-07, these values show that an increase in the interest rates will have a higher effect on the profit of a project if the assets used on the project are purchased.
30
Chapter 5: Conclusions Based on the analysis in chapter 4, certain conclusions can be made regarding the effect that inflation, interest rates and project life has on the decision to lease or purchase equipment. The analysis also gave further insight on the effect of the loan payback period and the percentage of equity used to purchase the equipment on the NPV if the asset is purchased.
The sensitivity analysis in figure 5 and 6 demonstrates the effect of different inflation rates on the NPV when an asset is purchased and leased, respectively. The slope of the graph in figure 5 is –12 277 451 and the slope of the graph in figure 6 is -13 666 561, since figure 6 has a greater slope than figure 5 this implies that inflation has a greater effect on the NPV if the asset is leased than when the asset is purchased. Therefore, when an increase in inflation rate is expected it would be best to purchase than to lease the asset. The sensitivity analysis in figure 3 and in figure 7 show how the duration of the project affects the NPV if the asset is purchased and leased respectively. The graph in figure 3 has a slope of 37 551.576 and the slope of the graph in figure 7 is 27 743.55378. The slope of the sensitivity analysis graph (37 551.576) that reflects the effect of the project life on the NPV when the asset is purchased is higher than the slope of the sensitivity analysis graph (27 743.5) that shows the effect of the project life when the asset leased. Therefore it can be concluded that it is best to lease the asset than to purchase if the project life of the asset is less than 15 years. Figure 8 demonstrates that as the interest rate increases the profit expected on a project decreases at a rate of -382466 if the asset is purchased. On the other hand figure 9 shows that as the interest rate increases the profit expected if the asset is leased will decrease at a rate of -3.041E-07. From this it can be concluded that if a rise in interest rates is anticipated it is best to lease the equipment.
If the decision to purchase the asset has been made the following conclusions can be made based on figure 2 and 4.
Figure 2 shows the effect of using different values of own equity to purchase an asset on the NPV when the asset is purchased. From this graph it can be concluded that it is best to use a loan to purchase equipment since the return or profit of a project decreases if own equity if used to finance the purchase price. Figure 4 illustrates how different payback periods affect the NPV. Based on this graph it can be concluded that as the loan payback period in increased the NPV will also increase however, if the payback period is equal to the project life this leads to a decrease in the NPV.
31
APPENDIX A – Purchasing models with different equity Scenario:
Purchase equipment using 25% equity.
Input table Purchase price + VAT Own equity Loan Amount Interest on loan (i) Payback period Normal tax rate Secondary tax Life of project Tax life Year
CFBT
Depreciation
Book Value
254 218.86 63 554.72 190 664.15 7.00% 4 28% 10% 15 years 3 years Loan Interest
Operating cost and maintenance
Taxable Income
Loan Payment
Tax payment
CFAT
0
-63,554.72
1
499200
-71072.9533
183,145.91
13346.53
179656
235124.516
56289.77553
65834.86
197419.36
2
499200
-71072.9533
112,072.95
10340.49
179656
238130.559
56289.77553
66676.56
196577.668
3
499200
-71072.9533
41,000.00
7124.034
229656
191347.013
56289.77553
53577.16
159677.061
4
499200
3682.59
179656
315861.41
56289.77553
88441.19
174813.03
5
499200
179656
319544
89472.32
230071.68
6
499200
229656
269544
75472.32
194071.68
7
499200
179656
319544
89472.32
230071.68
8
499200
179656
319544
89472.32
230071.68
9
499200
229656
269544
75472.32
194071.68
10
499200
179656
319544
89472.32
230071.68
11
499200
179656
319544
89472.32
230071.68
12
499200
229656
269544
75472.32
194071.68
13
499200
179656
319544
89472.32
230071.68
14
499200
179656
319544
89472.32
230071.68
15
499200
229656
269544
75472.32
194071.68
17,157.12
4803.994
53,353.13
MV
-63,554.72
58,157.12
41,000.00
NPV: -63 554.72 + 197 419.36(P/F,11,1) + 196 577.668(P/F,11,2) + 159 677.061(P/F,11,3) + 174 813.03(P/F,11,4) 230 071.68(P/F,11,5) + 194 071.68(P/F,11,6) + 230 071.68(P/A,11,2)(P/F,11,6) + 194 071.68(P/F,11,9) 230 071.68(P/,11,2)(F/P,11,9)+ 194 071.68(P/F,11,12) + 230 071.68(P/A,11,2)(P/F,11,12) + 194 071(P/F,11,15) + 53 353.13(P/F,11,15) 1406335.857
32
Scenario:
Purchase equipment using 50% equity.
Input table Purchase price + VAT Own equity Loan Amount Interest on loan (i) Payback period Normal tax rate Secondary tax Life of project Tax life Year
CFBT
7.00% 4 28% 10% 15 years 3 years
Book Value
Loan Interest
Operating cost and maintenance
Taxable Income
Loan Payment
Tax payment
CFAT
0
-127,109.43
1
499200
71072.95333
183,145.91
8923.956
179656
239547.091
37526.52
67073.19
214944.298
2
499200
71072.95333
112,072.95
6893.659
179656
241577.388
37526.52
67641.67
214375.814
3
499200
71072.95333
41,000.00
4749.356
R 229,656
193721.691
37526.52
54242.07
177775.41
4
499200
2455.06
179656
317088.94
37526.52
88784.9
193232.58
5
499200
179656
319544
89472.32
230071.68
6
499200
R 229,656
R 269,544
75472.32
194071.68
7
499200
179656
319544
89472.32
230071.68
8
499200
179656
319544
89472.32
230071.68
9
499200
R 229,656
269544
75472.32
194071.68
10
499200
179656
319544
89472.32
230071.68
11
499200
179656
319544
89472.32
230071.68
12
499200
R 229,656
269544
75472.32
194071.68
13
499200
179656
319544
89472.32
230071.68
14
499200
179656
319544
89472.32
230071.68
269544
75472.32
194071.68
17,157.12
4803.994
53,353.13
15 MV
Depreciation
254 218.86 63 554.72 190 664.15
-127,109.43
499200
R 229,656
58,157.12
41,000.00
NPV: -127 109.43 + 214 944(P/F,11,1) + 214 375.814(P/F,11,2) + 177 775.41(P/F,11,3) + 193 232.58(P/F,11,4) 230071.68(P/F,11,5) + 194 071.68(P/F,11,6) + 230 071.68(P/A,11,2)(P/F,11,6) + 194 071.68(P/F,11,9) 230 071.68(P/A,11,2)(P/F,11,9) + 194 071.68(P/F,11,12) + 194 071.68(P/F,11,12) + 230 071.68(P/A,11,2)(P/F,11,12) 194 071.68(P/F,11,15) + 53 353.13(P/F,11,15) 1398380.508
33
Scenario:
Purchase equipment using 75% equity.
Input table Purchase price + VAT Own equity Loan Amount Interest on loan (i) Payback period Normal tax rate Secondary tax Life of project Tax life Year
CFBT
Depreciation
Book Value
254 218.86 63 554.72 190 664.15 7.00% 4 28% 10% 15 years 3 years Loan Interest
Operating cost and maintenance
Taxable Income
Loan Payment
Tax payment
CFAT
0
-190,664.15
1
499200
71,072.95
183,145.91
4448.8436
179656
244,022.20
18763.25851
68326.2168
232,454.52
2
499200
71,072.95
112,072.95
3446.8294
179656
245,024.22
18763.25851
68606.7808
232,173.96
3
499200
71,072.95
41,000.00
2374.678
229656
196,096.37
18763.25851
54906.9832
195,873.76
4
499200
1227.5299
179656
318,316.47
18763.25851
89128.6116
211,652.13
5
499200
179656
319,544.00
89472.32
230,071.68
6
499200
229656
269,544.00
75472.32
194,071.68
7
499200
179656
319,544.00
89472.32
230,071.68
8
499200
179656
319,544.00
89472.32
230,071.68
9
499200
229656
269,544.00
75472.32
194,071.68
10
499200
179656
319,544.00
89472.32
230,071.68
11
499200
179656
319,544.00
89472.32
230,071.68
12
499200
229656
269,544.00
75472.32
194,071.68
13
499200
179656
319,544.00
89472.32
230,071.68
14
499200
179656
319,544.00
89472.32
230,071.68
15
499200
229656
269,544.00
75472.32
194,071.68
17,157.12
4803.9936
53,353.13
MV
-190,664.15
58157.12
41,000.00
NPV: -190 664.15 + 232 454.52(P/F,11,1) + 232 173.96(P/F,11,2) + 195 873.76(P/F,11,3) + 211 652.13(P/F,11,4) + 230 071.68(P/F,11,5) + 194 071.68(P/F,11,6) + 230 071.68(P/A,11,2)(P/F,11,6) + 194 071.68(P/A,11,9) + 230 071.68(P/A,11,2)(P/F,11,9) + 194 071.68(P/F,11,12) + 230 071.68(P/A,11,2)(P/F,11,12) + 194 071.68(P/A,11,15) + 53 3553.13(P/A,11,15) 1390412.58
34
Scenario:
Purchase equipment using 100% equity.
Input table Purchase price + VAT Own equity (100%) Loan Amount Normal tax rate Secondary tax Life of project Tax life Year
MV
CFBT
Depreciation
254 218.86 254 218.86 0.00 28% 10% 15 years 3 years Book Value
Operating cost and maintenance
Taxable Income
Tax payment
CFAT
0
-254,218.86
-254,218.86
1
499200
71072.95333
183,145.91
179656
248471.047
69571.89307
249972.107
2
499200
71072.95333
112,072.95
179656
248471.047
69571.89307
249972.107
3
499200
71072.95333
41,000.00
229656
198471.047
55571.89307
213972.107
4
499200
179656
319544
89472.32
230071.68
5
499200
179656
319544
89472.32
230071.68
6
499200
229656
269544
75472.32
194071.68
7
499200
179656
319544
89472.32
230071.68
8
499200
179656
319544
89472.32
230071.68
9
499200
229656
269544
75472.32
194071.68
10
499200
179656
319544
89472.32
230071.68
11
499200
179656
319544
89472.32
230071.68
12
499200
229656
269544
75472.32
194071.68
13
499200
179656
319544
89472.32
230071.68
14
499200
179656
319544
89472.32
230071.68
15
499200
229656
269544
75472.32
194071.68
17,157.12
4803.9936
53,353.13
58,157.12
41,000.00
NPV: -254 218.86 + 249972.107(P/A,11,2) + 213972.107(P/F,11,3) + 230071.68(P/A,11,2)(P/F,11,3) + 194071.68(P/F,11,6) + 230071.68(P/A,11,2)(P/F,11,6) + 194071.68(P/F,11,9) + 230071.68(P/A,11,2)(P/F,11,9) + 194071.61(P/F,11,12) + 230071.68(P/A,11,2)(P/F,11,12) + 194071.68(P/F,11,15) + 53353.13(P/F,11,15) 1382446.222
35
APPENDIX B – Purchasing models with varying project life Scenario:
Purchase equipment using a loan.
Input table Purchase price + VAT Loan Amount Interest on loan (i) Payback period Normal tax rate Secondary tax Life of project Tax life Year
CFBT
Depreciation
254 218.86 254 218.86 7.00% 4 28% 10% 12 years 3 years
Book Value
Loan Interest
Operating cost and maintenance
Taxable Income
Loan Payment
Tax payment
CFAT
0 1
499200
71072.95333
183,145.91
17795.37
179656
230675.67
75,053.03
64589.19
179901.78
2
499200
71072.95333
112,072.95
13787.32
179656
234683.73
75,053.03
65711.44
178779.52
3
499200
71072.95333
41,000.00
9498.71
229656
188972.33
75,053.03
52912.25
141578.71
4
499200
4910.12
179656
314633.88
75,053.03
88097.49
156393.48
5
499200
179656
319544.00
89472.32
230071.68
6
499200
229656
269544.00
75472.32
194071.68
7
499200
179656
319544.00
89472.32
230071.68
8
499200
179656
319544.00
89472.32
230071.68
9
499200
229656
269544.00
75472.32
194071.68
10
499200
179656
319544.00
89472.32
230071.68
11
499200
179656
319544.00
89472.32
230071.68
12
499200
229656
269544.00
75472.32
194071.68
38,776.57
10857.44
68,919.13
MV
79776.572
41,000.00
NPV: 179901.78(P/F,11,1) + 178 779.52(P/F,11,2) + 141 578.71(P/F,11,3) + 156 393.48(P/F,11,4) + 230 071.68(P/F,11,5) 194 071.68(P/F,11,6) + 230 0071.68(P/A,11,2)(P/F,11,6) + 194 071.68(P/F,11,9) + 230071.68(P/A,11,2)(P/F,11,9) + 194 071.68(P/F,11,12)+ 68 919.13(P/F,11,12) 1179742.95
36
Scenario:
Purchase equipment using a loan.
Input table Purchase price + VAT Loan Amount Interest on loan (i) Payback period Normal tax rate Secondary tax Life of project Tax life
Year
CFBT
Depreciation
Book Value
254 218.86 254 218.86 7.00% 4 28% 10% 9 years 10 years
Loan Interest
Operating cost and maintenance
Taxable Income
Loan Payment
Tax payment
CFAT
0 1
499200
71072.95333
183,145.91
17795.37
179656
230675.67
75,053.03
64589.19
179901.78
2
499200
71072.95333
112,072.95
13787.32
179656
234683.73
75,053.03
65711.44
178779.52
3
499200
71072.95333
41,000.00
9498.71
179656
238972.33
75,053.03
66912.25
177578.71
4
499200
4910.12
179656
314633.88
75,053.03
88097.49
156393.48
5
499200
179656
319544.00
89472.32
230071.68
6
499200
179656
319544.00
89472.32
230071.68
7
499200
179656
319544.00
89472.32
230071.68
8
499200
179656
319544.00
89472.32
230071.68
179656
319544.00
89472.32
230071.68
68,432.88
19161.21
90271.68
9 MV
499200 41,000.00
109432.9
NPV: 179 901.78(P/F,11,1) + 178 779.52(P/F,11,2) + 177 578.71(P/F,11,3) + 156 393.48(P/F,11,4) + 230071.68(P/A,11,5)(P/F,11,4) + 90 271.68(P/F,11,9) 1141355.46
37
Scenario:
Purchase equipment using a loan.
Input table Purchase price + VAT Loan Amount Interest on loan (i) Payback period Normal tax rate Secondary tax Life of project Tax life Year
CFBT
Depreciation
Book Value
254 218.86 254 218.86 7.00% 4 28% 10% 6 years 3 years Loan Interest
Operating cost and maintenance
Taxable Income
Loan Payment
Tax payment
CFAT
0 1
499200
71072.95333
183,145.91
17795.37
179656
230675.67
75,053.03
64589.19
179901.78
2
499200
71072.95333
112,072.95
13787.32
179656
234683.73
75,053.03
65711.44
178779.52
3
499200
71072.95333
41,000.00
9498.71
229656
188972.33
75,053.03
52912.25
141578.71
4
499200
4910.12
179656
314633.88
75,053.03
88097.49
156393.48
5
499200
179656
319544.00
89472.32
230071.68
6
649313.7
229656
419657.69
117504.2
302153.54
109113.69
30551.83
119561.86
MV
41,000.00
150113.7
NPV:
179901.78 (P/F,11,1) + 178779.52(P/F,11,2) + 141578.71(P/F,11,3) + 156393.48(P/F,11,4) + 230071.68(P/F,11,5) 302153.54(P/F,11,6) + 119 561.86(P/F,11,6) 875706.2996
38
Scenario:
Purchase equipment using a loan.
Input table Purchase price + VAT Loan Amount Interest on loan (i) Payback period Normal tax rate Secondary tax Life of project Tax life
Year
CFBT
Depreciation
254 218.86 254 218.86 7.00% 4 28% 10% 3 years 3 years
Book Value
Loan Interest
Operating cost and maintenance
Taxable Income
Loan Payment
Tax payment
CFAT
0 1
499200
71072.95
183,145.91
17795.37
179656
410331.67
75,053.03
114,892.87
309254.10
2
499200
71072.95
112,072.95
13787.32
179656
414339.73
75,053.03
116,015.12
308131.84
3
705117.277
71072.95
41,000.00
9498.71
R 229,656
624545.61
75,053.03
174,872.77
455191.47
4910.12
4
NPV:
75,053.03
309254.10 (P/F,11,1) + 308131.84(P/F,11,2) + 455 191.47(P/F,11,3) - 75053.03(P/F,11,4) 812085.39
39
-75053.03
APPENDIX C- Purchasing models with different pay back periods Scenario: Input table Purchase price + VAT Loan Amount Interest on loan (i) Payback period Normal tax rate Secondary tax Life of project Tax life
Year
MV
Purchase equipment using a loan.
CFBT
Depreciation
Book Value
254 218.86 254 218.86 7.00% 8 years 28% 10% 15 years 3 years
Loan Interest
Operating cost and maintenance
Taxable Income
Loan Payment
Tax payment
CFAT
0 1
499200
71072.95333
183,145.91
17795.56
179656
230675.48
42,574.03
64589.14
212380.83
2
499200
71072.95333
112,072.95
16061.10
179656
232409.95
42,574.03
65074.79
211895.18
3
499200
71072.95333
41,000.00
14205.04
229656
184266.01
42,574.03
51594.48
175375.49
4
499200
12219.34
179656
307324.66
42,574.03
86050.9
190919.06
5
499200
10094.47
179656
309449.53
42,574.03
86645.87
190324.10
6
499200
7820.89
229656
261723.11
42,574.03
73282.47
153687.50
7
499200
5388.17
179656
314155.83
42,574.03
87963.63
189006.33
8
499200
2785.28
179656
316758.72
42,574.03
88692.44
188277.53
9
499200
229656
269544.00
75472.32
194071.68
10
499200
179656
319544.00
89472.32
230071.68
11
499200
179656
319544.00
89472.32
230071.68
12
499200
229656
269544.00
75472.32
194071.68
13
499200
179656
319544.00
89472.32
230071.68
14
499200
179656
319544.00
89472.32
230071.68
15
499200
229656
269544.00
75472.32
194071.68
17,157.12
4803.994
53353.13
58157.121
41,000.00
NPV: 212 380.83(P/F,11,1) + 211 895.18(P/F,11,2) + 175 375.49(P/F,11,3) + 190 919.06(P/F,11,4) + 190 324.10*(F/P,11,5) + 153 687.50(P/F,11,6) + 189 006.33(P/F,11,7) + 188 277.53(P/F,11,8) + 194 071.68(P/F,11,9) + 230 071.68(P/A,11,2)(P/F,11,9) + 194 071.68(P/F,11,12) + 230 071.68(P/A,11,2)(P/F,11,12) + 194 071.68(P/F,11,15) + 53353.13(P/F,11,15) 1434815.991
40
Scenario:
Purchase equipment using a loan.
Input table Purchase price + VAT Loan Amount Interest on loan (i) Payback period Normal tax rate Secondary tax Life of project Tax life Year
CFBT
Depreciation
254 218.86 254 218.86 7.00% 12 years 28% 10% 15 years 3 years
Book Value
Loan Interest
Operating cost and maintenance
Taxable Income
Loan Payment
Tax payment
CFAT
0
MV
1
499200
71072.95333
183,145.91
15778.68
179656
232692.36
32,006.15
65153.86
222383.98
2
499200
71072.95333
112,072.95
16800.32
179656
231670.73
32,006.15
64867.8
222670.04
3
499200
71072.95333
41,000.00
15735.89
229656
182735.16
32,006.15
51165.84
186372.00
4
499200
14596.85
179656
304947.15
32,006.15
85385.2
202152.64
5
499200
13378.28
179656
306165.72
32,006.15
85726.4
201811.45
6
499200
12074.35
229656
257469.65
32,006.15
72091.5
165446.34
7
499200
10679.01
179656
308864.99
32,006.15
86482.2
201055.65
8
499200
9186.21
179656
310357.79
32,006.15
86900.18
200637.67
9
499200
7588.79
229656
261955.21
32,006.15
73347.46
164190.39
10
499200
5879.56
179656
313664.44
32,006.15
87826.04
199711.80
11
499200
4050.70
179656
315493.30
32,006.15
88338.12
199199.72
12
499200
2093.91
229656
267450.09
32,006.15
74886.03
162651.82
13
499200
179656
319544.00
319544.00
14
499200
179656
319544.00
319544.00
15
499200
229656
269544.00
269544.00
41,000.00
58157.12
17,157.12
4803.994
NPV: 222 238.98 (P/F,11,1)+ 222 670.04(P/F,11,2) + 186 372.00(P/F,11,3) + 202152.64(P/F,11,4) + 201 811.45(P/F,11,5)+165 446.34(P/F,11,6) + 201 055.65(P/F,11,7) + 200 637.67P/F,11,8) + 164 190.39(P/F,11,9) +199 199.80(P/F,11,10)+ 199 199.72(P/F,11,11) + 162 651.82(P/F,11,12) +319 544(P/A,11,2)(P/F,11,12) + 269 544(P/F,11,15) + 53353.13(P/F,11,15) 1510699.793
41
53353.13
Scenario:
Purchase equipment using a loan.
Input table Purchase price + VAT Loan Amount Interest on loan (i) Payback period Normal tax rate Secondary tax Life of project Tax life Year
CFBT
Depreciation
Book Value
254 218.86 254 218.86 7.00% 4 28% 10% 15 years 3 years Loan Interest
Operating cost and maintenance
Taxable Income
Loan Payment
Tax payment
CFAT
0 1
499200
71072.95333
183,145.91
17794.54
179656
230676.50
27,910.69
64589.42
227043.89
2
499200
71072.95333
112,072.95
17086.50
179656
231384.54
27,910.69
64787.67
226845.64
3
499200
71072.95333
41,000.00
16757.30
229656
181713.75
27,910.69
50879.85
190753.46
4
499200
15518.04
179656
304025.96
27,910.69
85127.27
206506.04
5
499200
14650.57
179656
304893.43
27,910.69
85370.16
206263.15
6
499200
13722.35
229656
255821.65
27,910.69
71630.06
170003.25
7
499200
12729.06
179656
306814.94
27,910.69
85908.18
205725.13
8
499200
11666.42
179656
307877.58
27,910.69
86205.72
205427.59
9
499200
10529.34
229656
259014.66
27,910.69
72524.11
169109.21
10
499200
9312.54
179656
310231.46
27,910.69
86864.81
204768.50
11
499200
8010.76
179656
311533.24
27,910.69
87229.31
204404.00
12
499200
6422.36
229656
263121.64
27,910.69
73674.06
167959.25
13
499200
5163.76
179656
314380.24
27,910.69
88026.47
203606.84
14
499200
3532.38
179656
316011.62
27,910.69
88483.25
203150.06
15
499200
1825.97
229656
267718.03
27,910.69
74961.05
166672.26
4803.994
53,353.13
MV
58157.12
41,000.00
17,157.12
NPV: 227 093.12(P/F,11,1) + 226 845.64(P/F,11,2) + 190 753.46(P/F,11,3) + 206 506.04(P/F,11,4) + 206 263.15(P/F,11,5) + 170003.25(P/F,11,6) + 205725.13(P/F,11,7) + 205 527.59(P/F,11,8)+ 169 109.21(P/F,11,9) + 204 768.50(P/F,11,10) + 204 404.00(P/F,11,11)+167 959.25(P/F,11,12) + 203 606.84(P/F,11,13) + 203 150.06(P/F,11,14) + 166 672.26(P/F,11,15) + 53 353.13(P/F,11,15) 1462319
42
APPENDIX D-Purchasing models with different inflation rates Scenario:
Purchase equipment using a loan.
Input table Purchase price + VAT Loan Amount Interest on loan (i) Payback period Normal tax rate Secondary tax Life of project Tax life Inflation rate Year
CFBT
Depreciation
254 218.86 254 218.86 7.00% 4 28% 10% 15 years 3 years 9.60%
Book Value
Loan Interest
Operating cost and maintenance
Taxable Income
Loan Payment
Tax payment
CFAT
0 1
499200
71072.95
183 145.91
17795.37
179656
230675.67
75 053.03
64 589.19
179901.78
2
499200
71072.95
112 072.95
13787.32
179656
234683.73
75 053.03
65 711.44
178779.52
3
499200
71072.95
41 000.00
9498.71
R 229 656
188972.33
75 053.03
52 912.25
141578.71
4
499200
4910.12
179656
314633.88
75 053.03
88 097.49
156393.48
5
499200
179656
319544.00
89 472.32
230 071.68
6
499200
R 229 656
269544.00
75 472.32
194 071.68
7
499200
179656
319544.00
89 472.32
230 071.68
8
499200
179656
319544.00
89 472.32
230 071.68
9
499200
R 229 656
269544.00
75 472.32
194 071.68
10
499200
179656
319544.00
89 472.32
230 071.68
11
499200
179656
319544.00
89 472.32
230 071.68
12
499200
R 229 656
269544.00
75 472.32
194 071.68
13
499200
179656
319544.00
89 472.32
230 071.68
14
499200
179656
319544.00
89 472.32
230 071.68
15
499200
R 229 656
269544.00
75 472.32
194 071.68
17 157.12
4 803.99
53 353.13
MV
58 157
41 000.00
NPV : 179 901.78(P/F,11,1) + 178 779.52(P/F,11,2) + 141 578.71(P/F,11,3) + 156 393.48(P/F,11,4) + 230 071.68(P/F,11,5) 194 071.68(P/F,11,6) + 230 071.68(P/A,11,2)(P/F,11,6) + 194 071.68(P/F,11,9) + 230 071.68(P/A,11,2)(P/F,11,9) + 194 071.68(P/F,11,12) + 230 071.68(P/A,11,2)(P/F,11,12) + 194(P/F,11,15) + 53 353.13(P/F,11,15)
1223341
43
Scenario: Input table Purchase price + VAT Loan Amount Interest on loan (i) Payback period Normal tax rate Secondary tax Life of project Tax life Inflation rate
Year
MV
CFBT
Depreciation
Book Value
Purchase equipment using a loan. 254 218.86 254 218.86 7.00% 4 28% 10% 15 years 3 years 6.60%
Loan Interest
Operating cost and maintenance
Taxable Income
Loan Payment
Tax payment
0 1
499200
-71072.95
183 145.91
17795.37
196902.976
213428.70
75 053.03
59 760.03
2
499200
-71072.95
112 072.95
13787.32
215805.6617
198534.07
75 053.03
55 589.54
3
499200
-71072.95
41 000.00
9498.71
R 302 350
116278.69
75 053.03
32 558.03
4
499200
4910.12
259229.2137
235060.67
75 053.03
65 816.99
5
499200
284115.2182
215084.78
60 223.74
6
499200
R 398 053
101146.80
28 321.10
7
499200
341283.746
157916.25
44 216.55
8
499200
374046.9856
125153.01
35 042.84
9
499200
R 524 050
-24850.07
10
499200
449311.2239
49888.78
13 968.86
11
499200
492445.1014
6754.90
1 891.37
12
499200
R 689 929
-190729.07
13
499200
591532.9349
-92332.93
14
499200
648320.0966
-149120.10
15
499200
R 908 314
-409114.21
58 157
41 000.00
17 157.12
4 803.99
NPV when taking in to account the inflation rate (6.6%): 167 483.96(P/F,11,1)+ 152 751.77(P/F,11,2)+ 89239.29(P/F,11,3) + 99 100.77(P/F,11,4) + 154 861.04(P/F,11,5) + 72 825.69(P/F,11,6)+ 113 699.70(P/F,11,7) + 90 110.17(P/F,11,8) - 24 850.07(P/F,11,9) + 35 919.92(P/F,11,10) + 4863.53(P/F,11,11) - 190 729.07(P/F,11,12)+ -92 332(P/F,11,13) - 149 120.10(P/F,11,14) - 409 114.21(P/F,11,15) + 53 353.13(P/F,11,15) 447344.19
44
CFAT
Scenario:
Purchase equipment using a loan.
Input table Purchase price + VAT Loan Amount Interest on loan (i) Payback period Normal tax rate Secondary tax Life of project Tax life Inflation rate
Year
CFBT
Depreciation
Book Value
254 218.86 254 218.86 7.00% 4 28% 10% 15 years 3 years 5.0%
Loan Interest
Operating cost and maintenance
Taxable Income
Loan Payment
Tax payment
CFAT
0 1
499200
-71072.95
183 145.91
17795.37
188638.8
221692.87
75 053.03
62 074.00
173434.16
2
499200
-71072.95
112 072.95
13787.32
198070.74
216268.99
75 053.03
60 555.32
165520.91
3
499200
-71072.95
41 000.00
9498.71
R 265 856
152772.81
75 053.03
42 776.39
115515.05
4
499200
4910.12
218372.9909
275916.89
75 053.03
77 256.73
128517.25
5
499200
229291.6404
269908.36
75 574.34
194334.02
6
499200
R 325 771
173428.57
48 560.00
124868.57
7
499200
270136.1978
229063.80
64 137.86
164925.94
8
499200
265433.7352
233766.26
65 454.55
168311.71
9
499200
R 356 272
142928.17
40 019.89
102908.28
10
499200
292640.6931
206559.31
57 836.61
148722.70
11
499200
307272.7277
191927.27
53 739.64
138187.64
12
499200
R 412 429
86770.82
24 295.83
62474.99
13
499200
338768.1823
160431.82
44 920.91
115510.91
14
499200
355706.5914
143493.41
40 178.15
103315.25
15
499200
R 477 438
21761.67
6 093.27
15668.40
17 157.12
4 803.99
R 53 353.13
MV
58 157
41 000.00
NPV when taking in to account the inflation rate (5%): 1016691
45
APPENDIX E- Leasing models with different inflation rates Scenario:
Acquiring equipment through leasing
Input table Purchase price + VAT Annual lease payment Normal tax rate Secondary tax Life of project Tax life Inflation rate
Year
CFBT
254 218.86 215 162.46 28% 10% 15 years 3 years 6.6%
lease payment
Operating cost and maintenance
Taxable Income
Tax payment
CFAT
0 1
499200
430324.92
191513.296
-122638.216
-122638.216
2
499200
215162.46
204153.1735
79884.36646
22367.62
57516.74385
3
499200
215162.46
217627.283
66410.25701
18594.87
47815.38505
4
499200
215162.46
231990.6837
52046.85633
14573.12
37473.73656
5
499200
215162.46
247302.0688
36735.47121
10285.93
26449.53927
6
499200
215162.46
263624.0053
20413.53467
5715.79
14697.74496
7
499200
215162.46
281023.1897
3014.35032
844.0181
2170.33223
8
499200
215162.46
299570.7202
-15533.1802
-15533.1802
9
499200
215162.46
319342.3877
-35304.84773
-35304.84773
10
499200
215162.46
340418.9853
-56381.44532
-56381.44532
11
499200
215162.46
362886.6384
-78849.09835
-78849.09835
12
499200
386837.1565
112362.8435
31461.6
80901.24733
NPV: - 110 780 (P/F,11,1)+ 75 154.709*(P/A,11,10) (P/F,11,1)+ 230 071.68*(P/F,11,12) 149529.2973
46
Scenario:
Acquiring equipment through leasing
Input table Purchase price + VAT Annual lease payment Normal tax rate Secondary tax Life of project Tax life Inflation rate
Year
CFBT
lease payment
254 218.86 215 162.46 28% 10% 15 years 3 years 5%
Operating cost
Taxable
Tax
and maintenance
Income
payment
CFAT
0 1
499200
430324.92
188638.8
-119763.72
-119763.72
2
499200
215162.46
198070.74
85966.8
24070.704
61896.096
3
499200
215162.46
207974.277
76063.263
21297.7136
54765.54936
4
499200
215162.46
218372.9909
65664.5492
18386.0738
47278.47539
5
499200
215162.46
229291.6404
54745.8996
15328.8519
39417.04772
6
499200
215162.46
240756.2224
43281.3176
12118.7689
31162.54866
7
499200
215162.46
252794.0335
31243.5065
8748.18181
22495.32466
8
499200
215162.46
265433.7352
18603.8048
5209.06534
13394.73945
9
499200
215162.46
278705.422
5332.11803
1492.99305
3839.124982
10
499200
215162.46
292640.6931
-8603.1531
11
499200
215162.46
307272.7277
-23235.188
12
499200
322636.3641
176563.636
-8603.153068 -23235.18772 49437.818
127125.8178
NPV: - 119763.72 (P/F,11,1)+ 61896.096*(P/F,11,2)+ 54765.54936(P/F,11,3) + 47278.47539(P/F,11,4) + 39417.04772(P/F,11,5) + 31162.54866(P/F,11,6) + 22495.32466(P/F,11,7) + 13394.73945(P/F,11,8) + 3839.124982 (P/F,11,9)- 8603.153068(P/F,11,10) + - 23235.18772(P/F,11,11) + 127125.8178(P/F,11,12) 313449.1171
47
Scenario:
Acquiring equipment through leasing
Input table Purchase price + VAT Annual lease payment Normal tax rate Secondary tax Life of project Tax life Inflation rate
Year
CFBT
lease payment
254 218.86 215 162.46 28% 10% 15 years 3 years 9.6%
Operating cost
Taxable
Tax
and maintenance
Income
payment
CFAT
0 1
499200
430324.92
196902.976
-128027.896
-128028
2
499200
215162.46
215805.6617
68231.8783
19104.92593
49126.95
3
499200
215162.46
236523.0052
47514.53478
13304.06974
34210.47
4
499200
215162.46
259229.2137
24808.32628
6946.331358
17861.99
5
499200
215162.46
284115.2182
-77.67823693
-77.6782
6
499200
215162.46
311390.2792
-27352.73919
-27352.7
7
499200
215162.46
341283.746
-57246.20599
-57246.2
8
499200
215162.46
374046.9856
-90009.4456
-90009.4
9
499200
215162.46
409955.4962
-125917.9562
-125918
10
499200
215162.46
449311.2239
-165273.6839
-165274
11
499200
215162.46
492445.1014
-208407.5614
-208408
12
499200
539719.8311
-40519.83108
-40519.8
NPV: - 128028*(P/F,11,1)+ 49126*(P/F,11,2)+ 34210.47*(P/F,11,3)+ 17861.99*(P/F,11,4) - 77.6782*(P/F,11,5) 27352.7*(P/F,11,6) - 57246.2*(P/F,11,7) - 90009.4*(P/F,11,8) - 125918(P/F,11,9) - 165274*(P/F,11,10) 208408(P/F,11,11) - 40519.8*(P/F,11,12) -305128.07
48
APPENDIX F- leasing models with varying project lives Acquiring equipment through leasing
Scenario: Input table Purchase price + VAT Annual lease payment Normal tax rate Secondary tax Life of project Tax life
Year
CFBT
254 218.86 215 162.46 28% 10% 9 years 10 years
lease payment
Operating cost
Taxable
Tax
and maintenance
Income
payment
CFAT
-215162.46
0 1
499200
430324.92
179656
-110780.92
-110780.92
2
499200
215162.46
179656
104381.54
29226.83
75154.7088
3
499200
215162.46
179656
104381.54
29226.83
75154.7088
4
499200
215162.46
179656
104381.54
29226.83
75154.7088
5
499200
215162.46
179656
104381.54
29226.83
75154.7088
6
499200
215162.46
179656
104381.54
29226.83
75154.7088
7
499200
215162.46
179656
104381.54
29226.83
75154.7088
8
499200
215162.46
179656
104381.54
29226.83
75154.7088
9
499200
499200
139776
359424
NPV -215 162 - 110 780.92(P/F,11,1) + 75 154.71*(P/A,11,7)(P/F,11,1) + 359 424*(P/F,11,9) 359744.6624
49
Acquiring equipment through leasing
Scenario: Input table Purchase price + VAT Annual lease payment Normal tax rate Secondary tax Life of project Tax life
Year
CFBT
lease payment
254 218.86 215 162.46 28% 10% 6 years 10 years
Operating cost
Taxable
Tax
CFAT
and maintenance
Income
payment -215,162.46
0 1
499200
430,324.92
179656
-110,780.92
-110,780.92
2
499200
215,162.46
179656
104,381.54
29226.8312
75,154.71
3
499200
215,162.46
179656
104,381.54
29226.8312
75,154.71
4
499200
215,162.46
179656
104,381.54
29226.8312
75,154.71
5
499200
215,162.46
179656
104,381.54
29226.8312
75,154.71
6
499200
179656
319,544.00
89472.32
230,071.68
MV: - 215 162.46 - 110780.92(P/A,11,1) + 75 154.71*(P/A,11,4)(P/F,11,1) + 230 071.68*(P/F,11,6) 233247.6083
50
Scenario:
Acquiring equipment through leasing
Input table Purchase price + VAT Annual lease payment Normal tax rate Secondary tax Life of project Tax life Life of equipment
Year
CFBT
254 218.86 215 162.46 28% 10% 3 years 10 years 15 years
lease payment
Operating cost
Taxable
Tax
and maintenance
Income
payment
CFAT
-215,162.46
0 1
499200
430,324.92
179656
-110,780.92
-110,780.92
2
499200
215,162.46
179656
104,381.54
29226.83
75,154.71
3
499200
179656
319,544.00
89472.32
230,071.68
NPV: -215 162.46 - 110780.92(P/F,11,1) + 75 154.71*(P/F,11,2) + 230 071.68*(P/F,11,3) 129421.444
51
Appendix G – purchasing models with varying interest rates Cash Flow Analysis for purchasing a hydraulic mixer using a loan. Scenario:
Purchase equipment using a loan.
Input table Purchase price + VAT Loan Amount Interest on loan (i) Payback period Normal tax rate Secondary tax Life of project Tax life
Year
CFBT
Depreciation
254,218.86 254,218.86 8.00% 4 28% 10% 15 years 3 years
Book Value
Loan Interest
Operating cost and maintenance
Taxable Income
Loan Payment
Tax payment
CFAT
0 1
499200
71072.95
183,145.91
20337.29
179656
228133.76
76,753.76
63877.45
178,912.79
2
499200
71072.95
112,072.95
15824.17
179656
232646.88
76,753.76
65141.13
177649.12
3
499200
71072.95
41,000.00
10950.00
R 229,656
187521.05
76,753.76
52505.89
140284.35
4
499200
5685.30
179656
313858.70
76,753.76
87880.43
154909.81
5
499200
179656
319544.00
89472.32
230071.68
6
499200
R 229,656
269544.00
75472.32
194071.68
7
499200
179656
319544.00
89472.32
230071.68
8
499200
179656
319544.00
89472.32
230071.68
9
499200
R 229,656
269544.00
75472.32
194071.68
10
499200
179656
319544.00
89472.32
230071.68
11
499200
179656
319544.00
89472.32
230071.68
12
499200
R 229,656
269544.00
75472.32
194071.68
13
499200
179656
319544.00
89472.32
230071.68
14
499200
179656
319544.00
89472.32
230071.68
R 229,656
269544.00
75472.32
194071.68
17,157.12
4803.994
53,353.13
15 MV
499200 58157.121
41,000.00
NPV 178912.79(P/F,11,1) + 177649.12(P/F,11,2) + 140284.35(P/F,11,3) + 154909.81(P/F,11,4) + 230071.68(P/F,11,5) + 194071.68(P/F,11,6) 230071.68(P/A,11,2)(P/F,11,6) + 194071.68(P/F,11,9) + 230071.68(P/A,11,2)(P/F,11,9) + 194071.68(P/F,11,12) 230071.68(P/A,11,2)(P/F,11,12) + 194071.68(P/F,11,15) + 53353.13(P/F,11,15) 1410565.397
52
Scenario:
Purchase equipment using a loan.
Input table Purchase price + VAT Loan Amount Interest on loan (i) Payback period Normal tax rate Secondary tax Life of project Tax life Year
CFBT
Depreciation
254,218.86 254,218.86 11.00% 4 28% 10% 15 years 3 years Book
Loan
Operating cost
Taxable
Loan
Tax
CFAT
Value
Interest
and maintenance
Income
Payment
payment
179656
220507.07
81,942.37
61741.98
175859.66
0
MV
1
499200
71072.95333
183,145.91
27963.98
2
499200
71072.95333
112,072.95
22026.68
179656
226444.37
81,942.37
63404.42
174197.21
3
499200
71072.95333
41,000.00
15435.89
R 229,656
183035.15
81,942.37
51249.84
136351.79
4
499200
8120.41
179656
311423.59
81,942.37
87198.61
150403.03
5
499200
179656
319544.00
89472.32
230071.68
6
499200
R 229,656
269544.00
75472.32
194071.68
7
499200
179656
319544.00
89472.32
230071.68
8
499200
179656
319544.00
89472.32
230071.68
9
499200
R 229,656
269544.00
75472.32
194071.68
10
499200
179656
319544.00
89472.32
230071.68
11
499200
179656
319544.00
89472.32
230071.68
12
499200
R 229,656
269544.00
75472.32
194071.68
13
499200
179656
319544.00
89472.32
230071.68
14
499200
179656
319544.00
89472.32
230071.68
15
499200
R 229,656
269544.00
75472.32
194071.68
17,157.12
4803.994
53,353.13
58157.121
41,000.00
NPV 175859.66(P/F,11,1) + 174197.21(P/F,11,2) + 136351.79(P/F,11,3) + 150403.03(P/F,11,4) + 230071.68(P/F,11,5) 194071.68(P/F,11,6) + 230071.68(P/A,11,2)(P/F,11,6) + 194071.68(P/F,11,9) + 230071(P/A,11,2)(P/F,11,9) 194071.68(P/F,11,12) + 230071.68(P/A,11,2)(P/F,11,12) + 194071.68(P/F,11,15) + 53353.13(P/F,11,15) 1399170.02
53
Scenario:
Purchase equipment using a loan.
Input table Purchase price + VAT Loan Amount Interest on loan (i) Payback period Normal tax rate Secondary tax Life of project Tax life
Year
CFBT
Depreciation
Book Value
254,218.86 254,218.86 14.00% 4 28% 10% 15 years 3 years
Loan Interest
Operating cost and maintenance
Taxable Income
Loan Payment
Tax payment
CFAT
0 1
499200
71072.95333
183,145.91
35589.99
179656
212881.05
87,247.91
59606.69473
172689.39
2
499200
71072.95333
112,072.95
28357.67
179656
220113.38
87,247.91
61631.7467
170664.34
3
499200
71072.95333
41,000.00
20113.96
R 229,656
178357.09
87,247.91
49939.98446
132356.10
4
499200
10714.74
179656
308829.26
87,247.91
86472.19233
145823.89
5
499200
179656
319544.00
89472.32
230071.68
6
499200
R 229,656
269544.00
75472.32
194071.68
7
499200
179656
319544.00
89472.32
230071.68
8
499200
179656
319544.00
89472.32
230071.68
9
499200
R 229,656
269544.00
75472.32
194071.68
10
499200
179656
319544.00
89472.32
230071.68
11
499200
179656
319544.00
89472.32
230071.68
12
499200
R 229,656
269544.00
75472.32
194071.68
13
499200
179656
319544.00
89472.32
230071.68
14
499200
179656
319544.00
89472.32
230071.68
R 229,656
269544.00
75472.32
194071.68
17,157.12
4803.993875
53353.13
15 MV
499200 58157.12
41,000.00
NPV 172689.39(P/F,11,1) + 170664.34(P/F,11,2) + 132356.10(P/F,11,3) + 145823.89(P/F,11,4) + 230071.68(P/F,11,5) 194071.68(P/F,11,6) + 230071.68(P/A,11,2)(P/F,11,6) + 194071.68(P/F,11,9) + 230071.68(P/A,11,2)(P/F,11,9) 194071.68(P/F,11,12) + 230071.68(P/A,11,2)(P/F,11,12) + 194071.68(P/F,11,15) + 53353.13(P/F,11,15) 1387507.857
54
Appendix H- leasing models with varying interest rates Cash Flow Analysis Scenario:
Acquiring equipment through leasing
Input table Purchase price + VAT interest rate Annual lease payment Normal tax rate Secondary tax Life of project Tax life
Year
CFBT
254,218.86 8%
232,375.46 28% 10% 15 years 3 years
lease payment
Operating cost and maintenance
Taxable Income
Tax payment
CFAT
0 1
499200
464750.9136
179656
-145206.9136
2
499200
232375.4568
179656
87168.5432
24407.1921
62761.3511
3
499200
232375.4568
179656
87168.5432
24407.1921
62761.3511
4
499200
232375.4568
179656
87168.5432
24407.1921
62761.3511
5
499200
232375.4568
179656
87168.5432
24407.1921
62761.3511
6
499200
232375.4568
179656
87168.5432
24407.1921
62761.3511
7
499200
232375.4568
179656
87168.5432
24407.1921
62761.3511
8
499200
232375.4568
179656
87168.5432
24407.1921
62761.3511
9
499200
232375.4568
179656
87168.5432
24407.1921
62761.3511
10
499200
232375.4568
179656
87168.5432
24407.1921
62761.3511
11
499200
232375.4568
179656
87168.5432
24407.1921
62761.3511
12
499200
179656
319544
89472.32
230071.68
NPV -145206.914(P/F,11,1)) + 62761.3511(P/A,11,10)(P/F,11,1) + 230071.68(P/F,11,12) 267923
55
-145206.914
Cash Flow Analysis Scenario:
Acquiring equipment through leasing
Input table Purchase price + VAT interest rate Annual lease payment Normal tax rate Secondary tax Life of project Tax life
Year
CFBT
254,218.86 11%
232,375.46 28% 10% 15 years 3 years
lease payment
Operating cost and maintenance
Taxable Income
Tax payment
CFAT
0 1
499200
477660.6612
179656
-158116.6612
2
499200
238830.3306
179656
80713.6694
22599.83
58113.84
3
499200
238830.3306
179656
80713.6694
22599.83
58113.84
4
499200
238830.3306
179656
80713.6694
22599.83
58113.84
5
499200
238830.3306
179656
80713.6694
22599.83
58113.84
6
499200
238830.3306
179656
80713.6694
22599.83
58113.84
7
499200
238830.3306
179656
80713.6694
22599.83
58113.84
8
499200
238830.3306
179656
80713.6694
22599.83
58113.84
9
499200
238830.3306
179656
80713.6694
22599.83
58113.84
10
499200
238830.3306
179656
80713.6694
22599.83
58113.84
11
499200
238830.3306
179656
80713.6694
22599.83
58113.84
12
499200
179656
319544
89472.32
230071.7
NPV -158117 (P/F,11,1) + 58113.84(P/A,11,10) (P/F,11,1) + 230071.7(P/F,11,12) 231634.5301
56
-158117
Cash Flow Analysis Scenario:
Acquiring equipment through leasing
Input table Purchase price + VAT interest rate Annual lease payment Normal tax rate Secondary tax Life of project Tax life
Year
CFBT
254,218.86 14%
232,375.46 28% 10% 15 years 3 years
lease payment
Operating cost and maintenance
Taxable Income
Tax payment
CFAT
0 1
499200
490570.4088
179656
-171026.4088
2
499200
245285.2044
179656
74258.7956
20792.46
53466.33
3
499200
245285.2044
179656
74258.7956
20792.46
53466.33
4
499200
245285.2044
179656
74258.7956
20792.46
53466.33
5
499200
245285.2044
179656
74258.7956
20792.46
53466.33
6
499200
245285.2044
179656
74258.7956
20792.46
53466.33
7
499200
245285.2044
179656
74258.7956
20792.46
53466.33
8
499200
245285.2044
179656
74258.7956
20792.46
53466.33
9
499200
245285.2044
179656
74258.7956
20792.46
53466.33
10
499200
245285.2044
179656
74258.7956
20792.46
53466.33
11
499200
245285.2044
179656
74258.7956
20792.46
53466.33
12
499200
179656
319544
89472.32
230071.7
NPV -171026 + 53466.33(P/A,11,10)(P/F,11,1) + 230071.7(P/F,11,12) 178398.398
57
-171026
Bibliography B, T. (2008). Engineering Economy. New York: Mc Graw.Hill. DE JAGER, S., & KAHAN, B. (2011). An assesment of inflation targetting. Economic History of Developing Regions , S73-93. EHRARDT, C., GAPENSKI, C., & BRIGHAM, E. (1999). Financial Mnagement, Theory and Practice 9th edition. New York: Goerge Proval. HARRISON, W., & HORNGREN, T. (2008). Financial Acounting 7th edition. London: PEARSON, Prentice Hall. NEWLAND, E., GEGEMANN, E., & DU TOIT, G. (2001). Capital Investment Decisions. Pretoria: Unisa Press. S.A department of revenue,(1962). Income Come tax Act. constitution . Pretoria, Gauteng SARS. (2010, Febuary 28). Retrieved August 27, 2011, from www.gov.sars.za. SARTOIS, L., & PAUL, S. (Summer 1973). Lease Evaluation: Another Capital budgetting decision. Financial Management, Vol 2, , 46-52. SouthAfrican, Department of legal and policy division . (2009, March 10). www.sars.gov.za. Retrieved September 20, 2101
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