Selected Further Applications of Investment Appraisal Methods

Abstract

This chapter examines some further applications of the investment appraisal methods already discussed: the inclusion of taxes in investment appraisals; the assessment of foreign investments; and the use of selected investment appraisal methods for determining optimum economic lives, replacement times and investment timing (under the assumption of certainty). All these applications require specialised procedures described in the chapter. Optimum economic life decisions are important and different target measures, points in time and the number and type of subsequent projects have to be considered. The use of different investment appraisal methods for this decision problem is shown in this chapter illustrated by a number of examples

Appendices

Assessment Material

1.1 Exercise 5.1 (Taxes in the Investment Appraisal)

The following investment decision problem should be solved considering tax issues.

• (a) Calculate the net present values of investment projects I and II, the data relating to Exercise 4.2 and a tax rate of 40 %. Assume that depreciation is linear.

• (b) Assess the absolute profitability of project II using the visualisation of financial implications (VoFI) method and assuming a tax rate of 40 %.

1.2 Exercise 5.2 (Economic Life)

A company in the metal processing industry is planning to acquire a new machine to produce special parts. Calculate its optimum economic life using the net present value method.

The following data have been forecasted for the machine:

• Initial investment outlay: €500,000

• Technical economic life: 8 years

Table 5.11 Cash flows and liquidation values for the new machine

The uniform discount rate is 10 %.

• (a) Calculate the machine’s net present value assuming that the machine will be in operation until the end of its technically useful life.

• (b) Calculate the machine’s optimum economic life and the related net present value assuming that the machine:

  • (b1) Will not be replaced.

  • (b2) Will be replaced with an identical project at the end of its economic life.

  • (b3) Will be replaced twice with an identical project at the end of the economic life (i.e. an investment chain consisting of three machines in total).

  • (b4) Will be replaced by an infinite number of times with identical projects.

• (c) What is the reason for—possibly—differing terms of optimum economic life?

1.3 Exercise 5.3 (Economic Life)

The initial investment outlay for a machine is €54,000. In addition, the following data is available:

The sales price of products manufactured with this machine is €9 per unit. The cash outflows for each unit depend on the accumulated production volume, as follows:

Table 5.12 Cash outflows per unit according to the accumulated production volume

The maximum volume that can be produced is 27,000 units; there should be no further cash outflows.

The unit’s liquidation value at the end of each year depends on its age as well as on the production volume. It falls by €1 per unit produced plus another €7,000 in the first year, €5,000 in the second, €3,000 in the third and €2,000 in each year thereafter.

The annual production volume amounts to 3,000 units; the uniform discount rate is 10 %.

• (a) Calculate the machine’s net present value assuming it will be used until the end of its economic life.

• (b) Calculate the machine’s optimum economic life and related net present value if:

  • (b1) The machine will not be replaced.

  • (b2) The machine will be replaced once with an identical project.

  • (b3) The machine will be replaced an infinite number of times with identical projects.

1.4 Exercise 5.4 (Economic Life and Replacement Time)

A company wants to determine the optimum economic life and replacement policy for its machines.

• (a) Machine A has the following cash flows and liquidation values in dependence on its economic life t_A (in €’000):

Table 5.13 Cash flows and liquidation values of machine A for different economic lives

The uniform discount rate is 10 %.

• (a) Determine the machines’ optimum economic life and the related net present value when:

  • (a1) There is no replacement.

  • (a2) There is one identical replacement.

  • (a3) The machines are replaced twice by identical machines.

  • (a4) The machines are replaced an infinite number of times by identical machines.

• (b) Now assume there is a machine of type A in operation that is (as at 1 January 2007) 2 years old. Assume further that there will be an unlimited stream of identical replacements, as in a4) above.

  In addition to replacements with identical machines of type A, it is now possible to replace the machines with others of type B. It is expected that there will be an infinite stream of identical replacements for these machines. The net present values of machines of type B (t_B) as a function of economic life, have already been calculated as follows (in €’000):

  Table 5.14 Net present values of machines of type B for different economic lives

  Should a machine of type A be replaced with an identical one or with a machine of type B?

  If there is to be a replacement with a machine of type B, when should this occur?

• (c) Now assume, again, the situation described in a4) (unlimited stream of identical replacements) and that a 2-year old used machine as in b) is available. Machines of type B are not available.

  Investigate whether it would be advantageous to buy used machines of type A. This is possible for machines of type A of any age, at the liquidation value given in a) plus €10,000. Assume that in the following years the economic life, differential cash inflows and liquidation values are as given in a). A further assumption is that equivalent machines are also available in the future (infinite stream).

  Only 1- and 2-year old machines are being considered for purchase. Using appropriate calculations, judge whether new, 1-year-old or 2-year-old machines should be put into operation in the future. In case that there is a change in the optimum economic life calculated compared with that found in a4), how high is the net present value now, and what is the optimum time to replace this machine?

1.5 Exercise 5.5 (Determining Economic Life)

A mining operation is investing, sequentially, in two investment projects: A (for the removal and recycling of waste) and B (for the extraction of hard coal). The cash flows contained in the following tables may be allocated to these investment projects. The uniform discount rate is 10 %.

Table 5.15 Cash flows and liquidation values of the investment projects A and B

Investment project B
t	0	1	2	3
Cash outflows (€’000)	4,500
Cash inflows (€’000)		3,500	1,800	1,300
Liquidation value in t (€’000)		3,500	2,500	1,400

• (a) Determine the optimum economic lives and the total net present value of the investment projects A and B if the investment is made firstly on a type A investment project and then on a type B.

• (b) Determine the optimum economic lives of the investment projects if, starting with investment project A and alternating between A and B, repeated investments are made over an infinite period.

1.6 Exercise 5.6 (Determining Economic Life with the Net Present Value, Internal Rate of Return and Compound Value Method)

A company wants to determine the optimum economic life for a machine.

The machine A being reviewed has the following net cash flows and liquidation values as a function of economic life t_A (in €’000):

Table 5.16 Cash flows and liquidation values of the machine for different economic lives

• (a) To determine economic life using the net present value method:

  • (a1) Assume the investment project under review will not be replaced. What is the optimum economic life that maximises the net present value (uniform discount rate is 10 %)? What is the maximum net present value?

  • (a2) Imagine that the investment project under review will be replaced by an identical one. What are the economic lives for the initial and subsequent investments that maximise the net present value (the rate of interest again is 10 %)? What is the maximum net present value?

  • (a3) Using the sample data, explain the so-called ‘chain effect’.

• (b) To determine economic life using the internal rate of return method:

  • (b1) Assume the investment project under review will not be replaced. What is the optimum economic life that maximises the internal rate of return?

  • (b2) Imagine that the investment project under review will be replaced with an identical one. What are the optimum economic lives for the initial and subsequent investment projects?

• (c) To determine economic life using the compound value method:

  Assume that the investment project under review will not be replaced. What is the optimum economic life that maximises the compound value (mandatory accounts balancing; debt rate of interest 12 %; credit rate of interest 8 %)? What is the maximum compound value?

1.7 Exercise 5.7 (Profitability Assessment and Investment Timing Decisions)

• (a) There is a choice between two investment projects, A and B, having the following data at time t = 0:

  Table 5.17 Data for the two investment projects A and B

  Assume a uniform discount rate of 10 %. Assess the absolute and relative profitability of the projects using the net present value method.

• (b) There is now an opportunity to invest in project B at time t = 1. A €15,000 reduction of the initial outlay compared to the realisation at t = 0 is expected. All other data given in part a) of this exercise remain unchanged.

  • (b1) What is the optimum investment policy now? (Support the finding with appropriate calculations.)

  • (b2) Which assumption in the basic net present value method is no longer valid?

  • (b3) How can this expanded decision problem b) be solved using the VoFI method (brief description)?

Further Reading – Part III

• Baldwin, C. Y. (1982). Optimal sequential investment when capital is not readily reversible. Journal of Finance, 37(3), 763–782.

• Blohm, H., Lüder, K., & Schaefer, C. (2012). Investition: Schwachstellenanalyse des Investitionsbereichs und Investitionsrechnung (10 ed.). München: Vahlen.

• Derbes, M. J., Jr. (1987). Economic life concepts. Appraisal Journal, 55(2), 216–224.

• Fisher, I. (1930). Theory of interest. New York: Macmillan.

• Gaddis, P. O. (1966). Analyzing overseas investment. Harvard Business Review, 44(3), 115–122.

• Götze, U. (2014). Investitionsrechnung (7th ed.). Berlin, Heidelberg: Springer.

• Grob, H. L. (1993). Capital budgeting with financial plans: An introduction. Wiesbaden: Gabler.

• Heister, M. (1962). Rentabilitätsanalyse von Investitionen. Köln: Westdeutscher Verlag.

• Jääskeläinen, V. (1966). Optimal financing and tax policy of the corporation. Helsinki: Helsinki Research Institute for Business Economics.

• Kruschwitz, L. (2011). Investitionsrechnung (13 ed.). München: Oldenbourg.

• Lessard, D. R. (1985). Evaluating international projects: An adjusted value approach. In D. R. Lessard (Ed.), International financial management. Theory and application (pp. 570–584). New York: Wiley.

• Maloney, K. J., & Selling, T. I. (1985). Simplifying tax simplification: An analysis of its impact on the profitability of capital investment. Financial Management, 14(2), 33–42.

• Miller, M. H. (1977). Debt and taxes. Journal of Finance, 32(2), 261–275.

• Modigliani, F. (1982). Debt, dividend policy, taxes, inflation and market valuation. Journal of Finance, 37(2), 255–274.

• Modigliani, F. (1983). Debt, dividend policy, taxes, inflation, and market valuation: Erratum. Journal of Finance, 38(3), 1041–1042.

• Modigliani, F., & Miller, M. H. (1963). Corporate income taxes and the cost of capital: A correction. American Economic Review: American Economic Association, 433–443.

• Preinreich, G. A. D. (1940). The economic life of industrial equipment. Econometrica, 8(1), 12–44.

• Scarf, P. A., & Hashem, M. H. (1997). On the application of an economic life model with a fixed planning horizon. International Transactions in Operational Research, 4(2), 139–150.

• Teichroew, D., Robichek, A. A., & Montalbano, M. (1965). An analysis of criteria for investment and financing decisions under certainty. Management Science, 12(3), 151–179.

• Terborgh, G. (1949). Dynamic equipment policy. New York: McGraw-Hill.

• Yu, Z., & Friend, I. (1986). The effects of different taxes on risky and risk-free investment and on the cost of capital. Journal of Finance, 41(1), 53–66.

• See also: Further Reading in Part II.