Cost comparison calculation

The cost comparison calculation is a method of investment calculation and is used to compare several investment alternatives. The total costs of the alternatives are determined and the most cost-effective one is selected.

invoice

The total costs result from the fixed and the variable costs . Since the cost comparison calculation considers the average costs of a period, the purchase payment must be taken into account accordingly within the fixed costs. These capital costs result from the imputed depreciation and the imputed interest . The total costs are made up as follows:

{\ displaystyle K _ {\ mathrm {total}} = K _ {\ mathrm {f}} + k _ {\ mathrm {v}} \ cdot x + {\ begin {matrix} \ underbrace {\ frac {I_ {0} -L_ {T}} {n}} \\ {} ^ {\ rm {calc. Depreciation}} \\ [- 4.0ex] \ end {matrix}} + {\ begin {matrix} \ underbrace {{\ frac {I_ {0} + L_ {T}} {2}} \ cdot i} \\ {} ^ {\ rm {kalk.Zins}} \\ [- 4.0ex] \ end {matrix}}}

There are:

${\ displaystyle K _ {\ mathrm {f}}}$ : The total fixed costs
${\ displaystyle k _ {\ mathrm {v}}}$ : The average variable unit cost
${\ displaystyle x}$ : The average amount sold / produced
${\ displaystyle I_ {0}}$ : Purchase payment d. Investment / investment amount at time 0
${\ displaystyle L_ {T}}$ : The liquidation proceeds / residual value at the end of the useful life
${\ displaystyle n}$ : Expected useful life; this can be found in the corresponding depreciation tables
${\ displaystyle i}$ : The discount rate

The imputed interest results from the average capital tied up , multiplied by the imputed interest rate . ${\ displaystyle {\ frac {I_ {0} + L_ {T}} {2}}}$ ${\ displaystyle i}$

example

Within a company the following data is given for two mutually exclusive investment alternatives. With the help of the cost comparison calculation, the most cost-effective alternative should be selected (sales are secured for the next 8 years).

	Appendix I.	Appendix II
Plant data
Cost (€)	80,000.00	120,000.00
Useful life	8 years	8 years
Capacity (year)	15,000 LE	15,000 LE
Occupancy (year)	10,000 LE	10,000 LE
Discount rate (year)	10%	10%
Fixed costs (€ / year)	1,000.00	1,700.00
Variable costs (€ / year), with the above capacity
Wages and ancillary wage costs	16,000.00	8,000.00
Tools, supplies, etc. a.	3,800	4,000.00
Energy and other variable costs	1,900.00	2,700.00

(LE = power unit)

Invoice for Annex I.

With a residual value of 0 EUR of the asset after the depreciation period, the following calculation results:

{\ displaystyle {\ begin {matrix} {\ mbox {Depreciation}} & = & {\ frac {80,000.00EUR-0.00EUR} {8years}} = 10,000.00 {\ frac {EUR} {year}} \ \ && \\ {\ mbox {Imputed interest}} & = & {\ frac {80,000.00EUR + 0.00EUR} {2}} \ cdot 10 {\ frac {\%} {year}} = 4,000.00 { \ frac {EUR} {year}} \\ && \\ k_ {v} & = & {\ frac {16,000.00 {\ frac {EUR} {year}} + 3,800.00 {\ frac {EUR} {year }} + 1,900.00 {\ frac {EUR} {year}}} {10,000.00 {\ frac {LE} {year}}}} = 2.17 {\ frac {EUR} {LE}} \ end { matrix}}}

{\ displaystyle {\ begin {matrix} K_ {total} & = & 1,000.00 {\ frac {EUR} {year}} + 2.17 {\ frac {EUR} {LE}} \ cdot 10,000.00 { \ frac {LE} {year}} + 10,000.00 {\ frac {EUR} {year}} + 4,000.00 {\ frac {EUR} {year}} \\ && \\ & = & 36,700.00 { \ frac {EUR} {year}} \ end {matrix}}}

.

Note: The calculation of the average variable costs ( ) can also be skipped in this case, since the variable costs in the table above are already available as total variable costs per period ( ). ${\ displaystyle k_ {v}}$ ${\ displaystyle k_ {v} \ cdot x}$

Invoice for Annex II

{\ displaystyle {\ begin {matrix} {\ mbox {Depreciation}} & = & {\ frac {120,000.00EUR-0.00EUR} {8years}} = 15,000.00 {\ frac {EUR} {year}} \ \ && \\ {\ mbox {Imputed interest}} & = & {\ frac {120,000.00EUR + 0.00EUR} {2}} \ cdot 10 {\ frac {\%} {year}} = 6,000.00 { \ frac {EUR} {year}} \\ && \\ k_ {v} & = & {\ frac {8,000.00 {\ frac {EUR} {year}} + 4,000.00 {\ frac {EUR} {year }} + 2,700.00 {\ frac {EUR} {year}}} {10,000.00 {\ frac {LE} {year}}}} = 1.47 {\ frac {EUR} {LE}} \\\ end {matrix}}}

{\ displaystyle {\ begin {matrix} K_ {total} & = & 1,700.00 {\ frac {EUR} {year}} + 1.47 {\ frac {EUR} {LE}} \ cdot 10,000.00 { \ frac {LE} {year}} + 15,000.00 {\ frac {EUR} {year}} + 6,000.00 {\ frac {EUR} {year}} \\ && \\ & = & 37,400.00 { \ frac {EUR} {year}} \ end {matrix}}}

Appendix I is preferable for the given input data. However, it can be seen that Annex II has significantly lower variable unit costs . At this point it is interesting to know from what number of units Annex II is preferable. This critical number of pieces can be determined by simply equating the functions .

{\ displaystyle K_ {f1} + k_ {v1} \ cdot x = K_ {f2} + k_ {v2} \ cdot x}

{\ displaystyle x = {\ frac {K_ {f2} -K_ {f1}} {k_ {v1} -k_ {v2}}}}

{\ displaystyle x = {\ frac {22,700.00 {\ frac {EUR} {year}} - 15,000.00 {\ frac {EUR} {year}}} {2.17 {\ frac {EUR} {LE} } -1.47 {\ frac {EUR} {LE}}}}}

{\ displaystyle x = 11000 {\ frac {LE} {year}}}

From a quantity of 11,001 service units per year, Appendix II is preferable to Appendix I in terms of costs. The cost comparison calculation cannot answer whether the higher production can be sold on the market and also bring a higher profit. At this point, however, the profit comparison calculation helps .

criticism

So that the alternatives can be compared in an economically meaningful way, they must meet the following assumptions:

Since only the costs are compared here, the yields must be the same for all alternatives. d. H.:

the returns per period must be the same.
the useful life of the various alternatives must be the same.

For the same reason, no general statement of advantageousness is possible.

By considering only one period, the statement is generally to be viewed critically.

This investment calculation method requires certain expectations .

In the case of economic investments , the use of the cost comparison calculation for alternative decisions and rationalization decisions is useful.

As a static method of investment calculation, the cost comparison calculation is one of the so-called "auxiliary methods of practice" or "practitioner method ", their application

only in a few cases really useful and
unsuitable for complex decisions with varying excess payments

is because, in contrast to dynamic methods , they do not take the course of time into account.

Individual evidence

^ ^A ^b ^c Ostendorf / Mays: Investment calculation method: a time series analysis . LIT, Munster et al. 2018, ISBN 978-3-643-13944-3 , pp. 6th ff .
↑ ^a ^b Becker: Investment and Financing Fundamentals of Business Finance . 7th, updated Edition 2016. Gabler, Wiesbaden 2016, ISBN 978-3-658-11070-3 , pp. 41 ff .

[:0-1] A ^b ^c Ostendorf / Mays: Investment calculation method: a time series analysis . LIT, Munster et al. 2018, ISBN 978-3-643-13944-3 , pp. 6th ff .

[:1-2] Becker: Investment and Financing Fundamentals of Business Finance . 7th, updated Edition 2016. Gabler, Wiesbaden 2016, ISBN 978-3-658-11070-3 , pp. 41 ff .