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Chapter 6 - Investment decisions - Capital budgetingChapter objectives Capital budgeting is vital in marketing decisions. Decisions on investment, which take time to mature, have to be based on the returns which that investment will make. Unless the project is for social reasons only, if the investment is unprofitable in the long run, it is unwise to invest in it now. Often, it would be good to know what the present value of the future investment is, or how long it will take to mature (give returns). It could be much more profitable putting the planned investment money in the bank and earning interest, or investing in an alternative project. Typical investment decisions include the decision to build another grain silo, cotton gin or cold store or invest in a new distribution depot. At a lower level, marketers may wish to evaluate whether to spend more on advertising or increase the sales force, although it is difficult to measure the sales to advertising ratio. Chapter objectivesThis chapter is intended to provide: · An understanding of the importance of capital budgeting in marketing decision making Structure of the chapterCapital budgeting is very obviously a vital activity in business. Vast sums of money can be easily wasted if the investment turns out to be wrong or uneconomic. The subject matter is difficult to grasp by nature of the topic covered and also because of the mathematical content involved. However, it seeks to build on the concept of the future value of money which may be spent now. It does this by examining the techniques of net present value, internal rate of return and annuities. The timing of cash flows are important in new investment decisions and so the chapter looks at this "payback" concept. One problem which plagues developing countries is "inflation rates" which can, in some cases, exceed 100% per annum. The chapter ends by showing how marketers can take this in to account. Capital budgeting versus current expendituresA capital investment project can be distinguished from current expenditures by two features: a) such projects are relatively large As a result, most medium-sized and large organisations have developed special procedures and methods for dealing with these decisions. A systematic approach to capital budgeting implies: a) the formulation of long-term goals The last point (g) is crucial and this is the subject of later sections of the chapter. The classification of investment projectsa) By project size Small projects may be approved by departmental managers. More careful analysis and Board of Directors' approval is needed for large projects of, say, half a million dollars or more. b) By type of benefit to the firm · an increase in cash flow c) By degree of dependence · mutually exclusive projects (can execute project A or B, but not both) d) By degree of statistical dependence · Positive dependence e) By type of cash flow · Conventional cash flow: only one change in the cash flow sign The economic evaluation of investment proposalsThe analysis stipulates a decision rule for: I) accepting or The time value of money Recall that the interaction of lenders with borrowers sets an equilibrium rate of interest. Borrowing is only worthwhile if the return on the loan exceeds the cost of the borrowed funds. Lending is only worthwhile if the return is at least equal to that which can be obtained from alternative opportunities in the same risk class. The interest rate received by the lender is made up of: i) The time value of money: the receipt of money is preferred sooner rather than later. Money can be used to earn more money. The earlier the money is received, the greater the potential for increasing wealth. Thus, to forego the use of money, you must get some compensation. a) Future values/compound interest Future value (FV) is the value in dollars at some point in the future of one or more investments. FV consists of: i) the original sum of money invested, and The general formula for computing Future Value is as follows: FVn = Vo (l + r)n where Vo is the initial sum invested Thus we can compute the future value of what Vo will accumulate to in n years when it is compounded annually at the same rate of r by using the above formula. Now attempt exercise 6.1. Exercise 6.1 Future values/compound interest i) What is the future value of $10 invested at 10% at the end of 1 year? We can derive the Present Value (PV) by using the formula: FVn = Vo (I + r)n By denoting Vo by PV we obtain: FVn = PV (I + r)n by dividing both sides of the formula by (I + r)n we derive: Rationale for the formula: As you will see from the following exercise, given the alternative of earning 10% on his money, an individual (or firm) should never offer (invest) more than $10.00 to obtain $11.00 with certainty at the end of the year. Now attempt exercise 6.2 Exercise 6.2 Present value i) What is the present value of $11.00 at the end of one year? b) Net present value (NPV) The NPV method is used for evaluating the desirability of investments or projects. where: Ct = the net cash receipt at the end of year t The discount factor r can be calculated using: Examples:
Decision rule: If NPV is positive (+): accept the project Now attempt exercise 6.3. Exercise 6.3 Net present value A firm intends to invest $1,000 in a project that generated net receipts of $800, $900 and $600 in the first, second and third years respectively. Should the firm go ahead with the project? Attempt the calculation without reference to net present value tables first. c) Annuities N.B. Introduce students to annuity tables from any recognised published source. A set of cash flows that are equal in each and every period is called an annuity. Example:
PV = $400(0.9091) + $400(0.8264) + $400(0.7513) Alternatively, PV of an annuity = $400 (PVFAt.i) (3,0,10) d) Perpetuities A perpetuity is an annuity with an infinite life. It is an equal sum of money to be paid in each period forever. where: C is the sum to be received per period Example: You are promised a perpetuity of $700 per year at a rate of interest of 15% per annum. What price (PV) should you be willing to pay for this income?
A perpetuity with growth: Suppose that the $700 annual income most recently received is expected to grow by a rate G of 5% per year (compounded) forever. How much would this income be worth when discounted at 15%? Solution: Subtract the growth rate from the discount rate and treat the first period's cash flow as a perpetuity.
e) The internal rate of return (IRR) Refer students to the tables in any recognised published source. · The IRR is the discount rate at which the NPV for a project equals zero. This rate means that the present value of the cash inflows for the project would equal the present value of its outflows. IRR of an annuity: where: Q (n,r) is the discount factor Example: What is the IRR of an equal annual income of $20 per annum which accrues for 7 years and costs $120?
Economic rationale for IRR: If IRR exceeds cost of capital, project is worthwhile, i.e. it is profitable to undertake. Now attempt exercise 6.4 Exercise 6.4 Internal rate of return Find the IRR of this project for a firm with a 20% cost of capital:
a) Try 20% Net present value vs internal rate of returnIndependent vs dependent projects NPV and IRR methods are closely related because: i) both are time-adjusted measures of profitability, and So, which method leads to an optimal decision: IRR or NPV? a) NPV vs IRR: Independent projects Independent project: Selecting one project does not preclude the choosing of the other. With conventional cash flows (-|+|+) no conflict in decision arises; in this case both NPV and IRR lead to the same accept/reject decisions. Figure 6.1 NPV vs IRR Independent projects If cash flows are discounted at k1, NPV is positive and IRR > k1: accept project. If cash flows are discounted at k2, NPV is negative and IRR < k2: reject the project. Mathematical proof: for a project to be acceptable, the NPV must be positive, i.e. Similarly for the same project to be acceptable: where R is the IRR. Since the numerators Ct are identical and positive in both instances: · implicitly/intuitively R must be greater than k (R > k); b) NPV vs IRR: Dependent projects NPV clashes with IRR where mutually exclusive projects exist. Example: Agritex is considering building either a one-storey (Project A) or five-storey (Project B) block of offices on a prime site. The following information is available:
Assume k = 10%, which project should Agritex undertake?
Both projects are of one-year duration: IRRA: Decision: Assuming that k = 10%, both projects are acceptable because: NPVA and NPVB are both positive Which project is a "better option" for Agritex? If we use the NPV method: NPVB ($1,363.64) > NPVA ($954.55): Agritex should choose Project B. If we use the IRR method: IRRA (21%) > IRRB (20%): Agritex should choose Project A. See figure 6.2. Figure 6.2 NPV vs IRR: Dependent projects Up to a discount rate of ko: project B is superior to project A, therefore project B is preferred to project A. Beyond the point ko: project A is superior to project B, therefore project A is preferred to project B The two methods do not rank the projects the same. Differences in the scale of investment NPV and IRR may give conflicting decisions where projects differ in their scale of investment. Example:
Assume k= 10%. NPVA = $1,500 x PVFA at 10% for 3 years Decision: Conflicting, as: · NPV prefers B to A
See figure 6.3. Figure 6.3 Scale of investments To show why: i) the NPV prefers B, the larger project, for a discount rate below 20% ii) the NPV is superior to the IRR a) Use the incremental cash flow approach, "B minus A" approach
IRR"B Minus A" Advantage of NPV: · It ensures that the firm reaches an optimal scale of investment. Disadvantage of IRR: · It expresses the return in a percentage form rather than in terms of absolute dollar returns, e.g. the IRR will prefer 500% of $1 to 20% return on $100. However, most companies set their goals in absolute terms and not in % terms, e.g. target sales figure of $2.5 million. The timing of the cash flow The IRR may give conflicting decisions where the timing of cash flows varies between the 2 projects. Note that initial outlay Io is the same.
Assume k = 10%
IRR prefers B to A even though both projects have identical initial outlays. So, the decision is to accept A, that is B + (A - B) = A. See figure 6.4. Figure 6.4 Timing of the cash flow The horizon problem NPV and IRR rankings are contradictory. Project A earns $120 at the end of the first year while project B earns $174 at the end of the fourth year.
Assume k = 10%
Decision: NPV prefers B to A The profitability index - PI This is a variant of the NPV method. Decision rule: PI > 1; accept the project If NPV = 0, we have: NPV = PV - Io = 0 Dividing both sides by Io we get: PI of 1.2 means that the project's profitability is 20%. Example:
Decision: Choose option B because it maximises the firm's profitability by $1,500. Disadvantage of PI: Like IRR it is a percentage and therefore ignores the scale of investment. The payback period (PP) The CIMA defines payback as 'the time it takes the cash inflows from a capital investment project to equal the cash outflows, usually expressed in years'. When deciding between two or more competing projects, the usual decision is to accept the one with the shortest payback. Payback is often used as a "first screening method". By this, we mean that when a capital investment project is being considered, the first question to ask is: 'How long will it take to pay back its cost?' The company might have a target payback, and so it would reject a capital project unless its payback period were less than a certain number of years. Example 1:
For a project with equal annual receipts:
Example 2:
Payback period lies between year 2 and year 3. Sum of money recovered by the end of the second year = $7,500, i.e. ($5,000 + $2,500) Sum of money to be recovered by end of 3rd year = $10,000 - $7,500 Disadvantages of the payback method: · It ignores the timing of cash flows within the payback period, the cash flows after the end of payback period and therefore the total project return. Advantages of the payback method: · Payback can be important: long payback means capital tied up and high investment risk. The method also has the advantage that it involves a quick, simple calculation and an easily understood concept. The accounting rate of return - (ARR) The ARR method (also called the return on capital employed (ROCE) or the return on investment (ROI) method) of appraising a capital project is to estimate the accounting rate of return that the project should yield. If it exceeds a target rate of return, the project will be undertaken. Note that net annual profit excludes depreciation. Example: A project has an initial outlay of $1 million and generates net receipts of $250,000 for 10 years. Assuming straight-line depreciation of $100,000 per year:
Disadvantages: · It does not take account of the timing of the profits from an investment. The payback and ARR methods in practice Despite the limitations of the payback method, it is the method most widely used in practice. There are a number of reasons for this: · It is a particularly useful approach for ranking projects where a firm faces liquidity constraints and requires fast repayment of investments. Now attempt exercise 6.5. Exercise 6.5 Payback and ARR Delta Corporation is considering two capital expenditure proposals. Both proposals are for similar products and both are expected to operate for four years. Only one proposal can be accepted. The following information is available:
Depreciation is charged on the straight line basis. Problem: a) Calculate the following for both proposals: i) the payback period to one decimal place Allowing for inflationSo far, the effect of inflation has not been considered on the appraisal of capital investment proposals. Inflation is particularly important in developing countries as the rate of inflation tends to be rather high. As inflation rate increases, so will the minimum return required by an investor. For example, one might be happy with a return of 10% with zero inflation, but if inflation was 20%, one would expect a much greater return. Example: Keymer Farm is considering investing in a project with the following cash flows:
Keymer Farm requires a minimum return of 40% under the present conditions. Inflation is currently running at 30% a year, and this is expected to continue indefinitely. Should Keymer Farm go ahead with the project? Let us take a look at Keymer Farm's required rate of return. If it invested $10,000 for one year on 1 January, then on 31 December it would require a minimum return of $4,000. With the initial investment of $10,000, the total value of the investment by 31 December must increase to $14,000. During the year, the purchasing value of the dollar would fall due to inflation. We can restate the amount received on 31 December in terms of the purchasing power of the dollar at 1 January as follows: Amount received on 31 December in terms of the value of the dollar at 1 January:
In terms of the value of the dollar at 1 January, Keymer Farm would make a profit of $769 which represents a rate of return of 7.69% in "today's money" terms. This is known as the real rate of return. The required rate of 40% is a money rate of return (sometimes known as a nominal rate of return). The money rate measures the return in terms of the dollar, which is falling in value. The real rate measures the return in constant price level terms. The two rates of return and the inflation rate are linked by the equation: (1 + money rate) = (1 + real rate) x (1 + inflation rate) where all the rates are expressed as proportions. In the example, (1 + 0.40) = (1 + 0.0769) x (1 + 0.3) So, which rate is used in discounting? As a rule of thumb: a) If the cash flows are expressed in terms of actual dollars that will be received or paid in the future, the money rate for discounting should be used. In Keymer Farm's case, the cash flows are expressed in terms of the actual dollars that will be received or paid at the relevant dates. Therefore, we should discount them using the money rate of return.
The project has a positive net present value of $30,540, so Keymer Farm should go ahead with the project. The future cash flows can be re-expressed in terms of the value of the dollar at time 0 as follows, given inflation at 30% a year:
The cash flows expressed in terms of the value of the dollar at time 0 can now be discounted using the real value of 7.69%.
The NPV is the same as before. Expectations of inflation and the effects of inflation When a manager evaluates a project, or when a shareholder evaluates his/her investments, he/she can only guess what the rate of inflation will be. These guesses will probably be wrong, at least to some extent, as it is extremely difficult to forecast the rate of inflation accurately. The only way in which uncertainty about inflation can be allowed for in project evaluation is by risk and uncertainty analysis. Inflation may be general, that is, affecting prices of all kinds, or specific to particular prices. Generalised inflation has the following effects: a) Inflation will mean higher costs and higher selling prices. It is difficult to predict the effect of higher selling prices on demand. A company that raises its prices by 30%, because the general rate of inflation is 30%, might suffer a serious fall in demand. However, if the future rate of inflation cannot be predicted with a certain amount of accuracy, then management should estimate what it will be and make plans to obtain the extra finance accordingly. Provisions should also be made to have access to 'contingency funds' should the rate of inflation exceed expectations, e.g. a higher bank overdraft facility might be arranged should the need arise. Many different proposals have been made for accounting for inflation. Two systems known as "Current purchasing power" (CPP) and "Current cost accounting" (CCA) have been suggested. CPP is a system of accounting which makes adjustments to income and capital values to allow for the general rate of price inflation. CCA is a system which takes account of specific price inflation (i.e. changes in the prices of specific assets or groups of assets), but not of general price inflation. It involves adjusting accounts to reflect the current values of assets owned and used. At present, there is very little measure of agreement as to the best approach to the problem of 'accounting for inflation'. Both these approaches are still being debated by the accountancy bodies. Now attempt exercise 6.6. Exercise 6.6 Inflation TA Holdings is considering whether to invest in a new product with a product life of four years. The cost of the fixed asset investment would be $3,000,000 in total, with $1,500,000 payable at once and the rest after one year. A further investment of $600,000 in working capital would be required. The management of TA Holdings expect all their investments to justify themselves financially within four years, after which the fixed asset is expected to be sold for $600,000. The new venture will incur fixed costs of $1,040,000 in the first year, including depreciation of $400,000. These costs, excluding depreciation, are expected to rise by 10% each year because of inflation. The unit selling price and unit variable cost are $24 and $12 respectively in the first year and expected yearly increases because of inflation are 8% and 14% respectively. Annual sales are estimated to be 175,000 units. TA Holdings money cost of capital is 28%. Is the product worth investing in? Key termsAccounting rate of return
Which method of evaluating capital investment proposals uses the concept of present value to compute a rate of return?Answer and Explanation: The correct answer is option a. Internal rate of return. In capital budgeting, computing the internal rate of return in evaluating capital investment proposals uses the present value concept.
Which of the following methods of evaluating capital investment proposals uses the concept of present value to compute a rate of return quizlet?-The internal rate of return (IRR) method uses present value concepts to compute the rate of return from a capital investment proposal based on its expected net cash flows.
When evaluating capital investment proposals What is the time value of money?20000 after five years.
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. Which method of capital budgeting uses time value of money?The specific time value of money calculation used in Capital Budgeting is called net present value (NPV). NPV is the sum of the present value (PV) of each projected cash flow, including the investment, discounted at the weighted average cost of the capital being invested (WACC).
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