Visualisation of Financial Implications VoFI Method

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Description of the method

The visualisation of financial implications (VoFI) method is based on the ideas of Heister (1962) that were later developed by Grob (1993). Its defining feature is a comprehensive financial plan that considers all cash flows connected with an investment project.

Key Concept:

The VoFI comprehensive financial plan considers the economic consequences of an investment project, specifically in regard to:

• The amounts and proportions of internal funds and debt capital used.

• The amounts and timing of debt redemption from cash inflows.

• The alternate yield on the long-term financial investment of the initial internal funds (the opportunity interest rate that generates the so-called opportunity income value) - not necessarily identical to the yield on short-term financial investments during the project's economic life.

• The existence of different forms of loans, with differing payback and interest conditions.

The VoFI method explicitly analyses both the cash flow profile of an investment project itself (the so-called original cash flows) and the cash flows from the project's financing and financial investments (the derivative cash flows). Assumptions (e.g. about payback structures, financial investment opportunities and balancing differences in capital tie-ups and economic lives) that are only implicit in other models (such as NPV and IRR) are made explicit in the VoFI method. Moreover, different assumptions can be applied to different financial arrangements when there are different forms of loan or financial investment.

Target measures for the VoFI method can be compound values, initial values, intermediate values, withdrawals, or specific rates of return. Compound values are considered here, primarily because of their clarity. They represent the value of the accounts (including the loans) at the end of the economic life of an investment project, and are discernable directly from comprehensive financial plans.

Key Concept:

An investment project is absolutely profitable if its compound value exceeds the opportunity income value at the end of its economic life.

An investment project is relatively profitable if its compound value exceeds the compound values of alternative projects.

Standardised tables can be used to work out comprehensive financial plans. Figure 4-2 shows the structure of such a table.

t=0 t=1 t=2 t=3 t=4 ...

Series of net cash flows Internal funds

- Withdrawal of capital + Contribution of capital

Instalment loan

+ Borrowing

- Redemption

- Debt interest

Loan with final redemption

+ Borrowing

- Redemption

- Debt interest

Annuity loan

+ Borrowing

- Redemption

- Debt interest

Current account loan

+ Borrowing

- Redemption

- Debt interest

Financial investment

- Reinvestment + Disinvestment + Credit interest

Financial balance

Loans:

Instalment loan Loan with final redemption Annuity loan Current account loan Financial investment

Net balance

Fig. 4-2: The VoFI table

The first part of this table contains the cash flows, consisting of: the cash flow profile of the investment project; the project-assigned internal funds and their changes; the borrowing, repayments and interest payments for four typical forms of loans; and the payments resulting from the execution, release and interest transactions of financial investments taken. The comprehensive financial plan always has to be balanced, i.e. the balance of all cash flows is zero in every point in time. In the second part of the table relevant loans and financial investments, together with their resulting net balances, are recorded. At the end of the economic life, the net balance obtained corresponds to the compound value of the investment project.

The comprehensive financial plan and compound value calculation for an investment project require the following steps:

Step 1: at t = 0 the initial outlay of the investment project and allocated internal funds are recorded. In addition, the loan amount to be raised is calculated and the status of loans and financial investments is recorded.

Step 2: for t = 1 and every subsequent period the net cash flows of the investment project are recorded. Interest payments, any borrowing or redemption of loans, and any making or discontinuation of financial investments is calculated in order to update the status of loans and financial investments.

To assess absolute profitability, a compound value is calculated using a comprehensive financial plan. Then, the project-assigned internal funds are compounded with an opportunity interest rate into an opportunity income value, which is compared to the expected compound value of the project. To assess relative profitability, the inclusion of supplementary investments may be required under specific circumstances. This issue will be addressed in the example below.

Before that, the use of alternative target measures should be explained. For example, a rate of return for the internal funds invested (rIF) can be derived from the expected compound value (CVT) at the end of the economic life (T) (assumed to be non-negative) using formula 3.6 below. This formula assumes that internal funds (IF) at the beginning of the planning period yields at a constant annual (interest) rate:

An investment project is considered absolutely profitable if its rate of return exceeds the opportunity interest rate. The project with the highest rate of return is relatively profitable. Assuming identical allocated internal funds and economic lives, results for both absolute and relative profitabilities are identical to those achieved by using the compound value as the target measure.

Another possible target measure is the periodic withdrawal which can be realised assuming a given compound value. The withdrawal amounts need not be constant throughout the different years, as it is also possible to consider a series of timed withdrawals as a target measure. The maximum withdrawal, or series of withdrawals, that a project can sustain can be determined iteratively (as in the IRR interpolation procedure) or with the help of spreadsheet software such as Lotus 1-2-3 or Microsoft Excel. In an imperfect capital market - as it is often assumed in VoFI models - differing assessments of profitability can arise from analyses of withdrawal maximisation and compound value maximisation.

Example 4-3

Example 4-2 can be usefully extended by assuming that €20,000 is available in cash (representing the allocated internal funds) at the beginning of the planning period. Its alternate use is a financial investment opportunity yielding 7% interest. The interest

rate available for the short-term investment of surpluses is 6%. To finance the investment project - A or B - a loan with final redemption and an instalment loan, each about 25% of the initial investment outlay are available at 9% interest for a term of four years. Any remaining financing can be raised as a current account loan (at 11% interest). All payments are made at the period end, and the interest charges are based on the capital employed at the beginning of each period.

Using this data, and assuming that surpluses are used for the immediate redemption of the current account loan, the comprehensive financial plan for investment project A is as follows:

t=0

t=1

t=2

t=3

t=4

t=5

Series of net cash flows

-100,000

28,000

30,000

35,000

32,000

- Withdrawal of capital + Contribution of capital

20,000

+ Borrowing

- Redemption

- Debt interest

25,000

-6,250 -2,250

-6,250 -1,687.50

-6,250 -1,125

-6,250 -562.50

0 0 0

Loan with final redemption

+ Borrowing

- Redemption

- Debt interest

25,000

-2,250

-2,250

-2,250

-25,000 -2,250

+ Borrowing

- Redemption

- Debt interest

+ Borrowing

- Redemption

- Debt interest

30,000

-13,950 -3,300

-16,050 -1,765.50

0 0

0 0

0 0

Financial investment

- Reinvestment + Disinvestment + Credit interest

-1,997

-25,494.82 119.82

1,624.73

Financial balance

0

0

0

0

0

0

Balances

Instalment loan Loan with final redemption

Annuity loan Current account loan

25,000 25,000

0

0

0

Financial investment

1,997

27,491.82

27,078.83

63,703.56

Net balance

-80,000

-59,800

-35,503

-3,758.18

27,078.83

63,703.56

Fig. 4-3: VoFI plan for investment project A

The compound value of project A amounts to €63,703.56. Because this exceeds the opportunity income value (by €20,000 ■ 1.075 = €28,051.03), the project is absolutely profitable.

The VoFI financial plan for investment project B is shown in Figure 4-4:

t=0

t=1

t=2

t=3

t=4

Series of net cash flows

-60,000

22,000

26,000

28,000

- Withdrawal of capital + Contribution of capital

20,000

+ Borrowing

- Redemption

- Debt interest

15,000

-3,750 -1,350

-3,750 -1,012.50

-3,750 -675

-3,750 -337.50

Loan with final redemption

+ Borrowing

- Redemption

- Debt interest

15,000

-1,350

-1,350

-1,350

-15,000 -1,350

Annuity loan

+ Borrowing

- Redemption

- Debt interest

+ Borrowing

- Redemption

- Debt interest

10,000

-10,000 -1,100

0 0

0 0

Financial investment

- Reinvestment + Disinvestment + Credit interest

-4,450

-20,154.50 267

-23,701.27 1,476.27

-10,460.85 2,898.35

Financial balance

0

0

0

0

0

Balances

Instalment loan Loan with final redemption Annuity loan Current account loan

15,000 15,000

0

0

Financial investment

4,450

24,604.50

48,305.77

58,766.62

Net balance

-40,000

-21,800

2,104.50

29,555.77

58,766.62

Fig. 4-4: VoFI plan for investment project B

Fig. 4-4: VoFI plan for investment project B

Investment project B is also absolutely profitable, because its compound value (€58,766.62) exceeds the opportunity income value (which is €20,000 ■ 1.074 = €26,215.92).

Assessing relative profitability requires determining the extent to which the projects are comparable, given their differences in investment outlay and economic life, and, if necessary, working out how comparability can be achieved. The VoFI method explicitly considers the manner in which the initial investment outlay is financed. Therefore, different initial investment outlays impair project comparability only if one (or more) of the mutually exclusive projects has an initial outlay less than the allocated internal funds. In that case (not shown in the example), an assumption about a supplementary investment is needed to balance the difference in the allocated equity. For example, it can be assumed that the excess amount is invested to yield the opportunity interest rate.

Economic life differences must be balanced in every case; otherwise compound values referring to different points in time will not be comparable. The capital available at the end of the shorter investment project has to be compounded by an appropriate interest rate to balance the life differences. In the example given, the compound value of project B has to be compounded by a further year before it can be compared with the compound value of project A. Assuming an interest rate of 7%, the compound value of B is €62,880.28 at t = 5 (€58,766.62 ■ 1.07). Because the compound value of the project A (€63,703.56) is higher, A is relatively profitable.

The rates of return derived from the VoFI are:

Both projects are absolutely profitable, because their rates of return exceed the opportunity interest rates. Project A emerges as relatively profitable due to its higher VoFI capital profitability.

Assessment of the method

The VoFI method is a relatively simple method for assessing alternative investment projects. Data required are: the cash flow profiles of the investment projects; the amounts of available internal (financial) funds; debt capital components and their relevant financial conditions (redemption types, interest rates etc.); the opportunity income interest rate; and the credit interest rate for short-term investments. Some of this data are determined independently of which investment appraisal method is chosen and, therefore, have to be available in each case. other data would have to be obtained especially for the VoFI method, in which case it should be asked whether the additional effort is justifiable. Since financing and investment policies are usually tailored to the whole company rather than to individual projects, the allocation of internal funds and specific loans to individual projects can be difficult. However, this problem does not occur with, for example, strategically important investments (e.g. foundational investments for new plant or business locations, and foreign investments) or with certain projects such as real-estate purchases, which require their own financial plans.

The assumptions of the VoFI method are largely the same as those of the NPV method: only one target measure is pursued (although various target measures may be employed); a given economic life is assumed; other decisions concerning production, sales etc. are assumed to be already made and therefore cash flows are attributable to specific projects and points in time; and the data is assumed to be certain. It should additionally be pointed out that the VoFI method can also be used to determine the optimum economic lives and the replacement times and that uncertainty can be included in VoFI models as well. For instance, a payback period can be determined (it ends when the existing net balance equals the compounded opportunity income value). In the examples given, it was assumed that all payments take place at the end of a period (year). This assumption can be changed by adjusting the VoFI analysis to a monthly (or other) timeframe (although this might be problematic when calculating the tables manually without spreadsheet software).

Decisions in other company areas are considered solely in relation to financial decisions, because at the beginning of the second and following periods decisions may be needed about the extent of debt use (or repayment) that results from net cash outflows (or inflows). Moreover, in an extension to the examples presented here, the optimum financing of individual investment projects can be determined. This may be useful because in an imperfect capital market the optimum investment and financing decisions are not independent (i.e. the Fisher separation theorem does not apply). The way in which investment projects are financed is, therefore, relevant to the assessment of those projects. In the case of decisions about a single investment project, the aim is to identify the optimum set of financing alternatives and use this as a basis for the project appraisal. Therefore, a compound value can be calculated for every combination of investment and financing using the comprehensive financial plan. The combination with the maximum compound value represents the optimum. Alternatively, optimisation models, which include financing possibilities as variables, can be used to determine the optimum financing for each project. In the same way, it can be determined whether any financial surpluses should be used to pay back loans. However, the VoFI method cannot assist with optimising the allocation of funds between different investment projects. The VoFI approach does not consider all interdependencies between different investment projects and financial investments, so optimum investment and financing programmes cannot be determined (for models allowing this see Chapter 7).

In contrast with the NPV method, the VoFI method does not assume that cash flows are reinvested and differences in capital tie-up and/or economic life are balanced at a uniform discount rate - assumption (f) of the NPV method. The short-term investment of cash flow surpluses is assumed to earn an adequate credit interest rate, at least for the standard case (which can be modified). Capital tie-up differences are limited to the internal funds available at the beginning of the planning period, and can be balanced individually. The same applies to economic life differences although it can be difficult to determine the relevant interest rate. In summary, the VoFI method also requires simplifying assumptions about financing and investment opportunities in order to avoid the planning scenario becoming too complicated.

An advantage of the VoFI method over other investment appraisal methods is that assumptions about the reinvestment of surpluses and the balancing of differences in capital tie-up are transparent within the standardised tables. Also, the comprehensive financial plans can be modified in regard to assumptions (f) and (g) (see Section 3.2) in order to illustrate the premises of the other dynamic investment appraisal methods such as NPV. Overall, VoFI analysis results are well suited to presentation and control, so they are likely to be highly acceptable to decision-makers.

A major difference between the VoFI and NPV methods concerns assumptions about the capital market. While the NPV method assumes a perfect capital market (assumption g), the VoFI method can include not only differences between credit and debt interest rates (like the compound value method), but also the capacity for self-financing and a huge variety of loan and financial investment conditions (especially different interest rates for short and long term investment opportunities). This is a second reason for preferring the VoFI method.

In an imperfect capital market, investment and consumption decisions are not separable, but under the VoFI method consumption can be considered in a simplified form by maximisation of the withdrawals attainable. Moreover, where capital markets are imperfect, certainty - assumed throughout Chapters 2 to 4 - cannot exist. In reality, investing companies do face an imperfect capital market and uncertainty, so to assume otherwise is a simplification. However, the arguments presented here reflect the view of the authors that these simplifying assumptions can be appropriate in some situations. In other cases, the models presented here are a first step towards dealing with uncertainty and imperfect capital markets within the investment appraisal process.

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  • Lillie
    What are the financial implications of investing in project?
    3 years ago

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