Solving problems of choosing the best option for the technological process. Solving typical tasks It is necessary to determine the most profitable option
Task 7.1. There are investments in the amount of 5 million rubles. Banks offer to place capital for two years, but one proposes to invest money at 20% per annum, taking into account the accrual of simple interest at the end of each year, the second - at 20% per annum, but with quarterly accrual of compound interest. Determine the future cost of capital and choose the best option.
1. Determine the future value when calculating simple interest:
TO t \u003d K (1 + E t) \u003d 5 (1 + 0.2 ∙ 2) \u003d 7.0 million rubles.
2. Determine the rate of increase (capitalization):
3. Determine the future value when calculating compound interest:
Conclusion: the second option is more profitable.
Task 7.2. The depositor has 100 thousand rubles, free throughout the year. The bank offers three options for investing money for a period of two years at 24% per annum: with interest capitalization at the end of the next month, the next quarter, the next six months. Determine the best investment option.
1. Let's determine the future value of money with a monthly capitalization:
2. Determine the future value of money with quarterly capitalization:
3. Let's determine the future value of money with a half-year capitalization:
Conclusion: the first option is the best.
Task 7.3. The initial amount is 100 thousand rubles, the final amount is 121 thousand rubles. Determine at what percentage you need to put money in the bank for 2 years.
Let's determine the percentage that will make it possible to receive 121 thousand rubles:
Task 7.4. Determine how much you should put in the bank today at 10% per annum, so that in 2 years you will have 121 thousand rubles.
Let's determine the current amount of money:
Task 7.5. The depositor has a free amount of 100 thousand rubles. He wants to receive 121 thousand rubles. The bank offers to invest money at 10% per annum with interest capitalization after the next year. Determine how many years later the depositor will be able to receive the desired amount?
Let's determine the number of years to get the desired amount.
From the formula we derive:
Task 7.6. The bank offers 25% per annum. Determine the discount factor and the initial deposit in order to have 100 thousand rubles on the account in 3 years.
1. Let's determine the discount factor:
2. Let's define the initial contribution:
Task 7.7. There are two options for making capital investments for the construction of a new workshop, corresponding to different technologies. The construction period is 3 years. The amount of costs for the options is the same - 450 million rubles. The attachment money produced at the beginning of each year. According to the first option, the sequence of depositing funds is 150 million rubles. annually. According to the second option, the order of investment by years is 200, 150, 100 million rubles. The profitability is 10% per year. Determine the current cost by options and choose the most preferable one.
1.Let's determine the current value of funds for the first option:
2. Determine the current value of monetary investments in the second option:
Conclusion: Option I is the best, it requires a smaller initial amount.
Task 7.8. The amount of invested capital is 900 thousand rubles, the duration of the investment is 4 years, the annual cash flow is 300 thousand rubles, the interest rate is 10%. Determine the net present value.
Task 7.9. The amount of invested capital is 900 thousand rubles, the duration of the investment is 4 years. Cash inflow by years: 100, 200, 300, 400 thousand rubles. The interest rate is 10%. Determine the net present value and make a conclusion about whether it is worth investing in this project.
Let's define the net present value of the invested capital:
Conclusion: an investor should not invest money, because the project is ineffective.
Task 7.10. The organization is installing new equipment. The discount rate is 10%. Determine the net discounted income from its use according to the table. 7.1.
Table 7.1
Let's determine the NPV from the use of equipment:
NPV \u003d (14260 - 996) 0.909+ (15812 - 4233) 0.826+ (16662 - 10213) 0.751+ (18750 -
–11650) 0.683+ (26250 - 18400) 0.621+ (28750 - 20150) 0.564 \u003d 41,050.30 thousand rubles.
Task 7.11. The amount of capital investment is 900 thousand rubles, the duration of the investment is 4 years, the annual inflow of funds is 300 thousand rubles, the interest rate is 10%. Determine the internal rate of return on capital and conclude whether the investment is efficient.
1. Determine the estimated value of the discounted multiplier:
2. Determine the value of the discounted multiplier at E INR \u003d 12%:
3. Determine the value of the discounted multiplier at E BHP \u003d 13%:
4. Let's define the internal rate of return:
The investment is effective because their internal rate of return (12.6%) is higher than the interest rate (10%).
Task 7.12. The reduced integral effect is 3,792 thousand rubles, and the reduced capital investment - 2212 thousand rubles. Determine net present value and profitability index.
1. Let's define the net present value:
NPV \u003d IE given. - To lead. \u003d 3792 - 2212 \u003d 1580 thousand rubles.
2. Let's define the index of profitability:
Task 7.13. The discount rate (interest rate) at which the bank issues loans is 25%. Net present value and profitability index.
Table 7.2
1. Let's define the reduced effect:
2. Let's define the given investments taking into account their depreciation:
3. Let's define the net present value:
NPV \u003d 884.81 - 328.73 \u003d 556.08 thousand rubles.
4. Let's define the index of profitability:
Conclusion: NPV is positive, ID\u003e 1; the project is effective.
Task 7.14. According to the first option, the total construction period is 4 years, the estimated cost is 40 million rubles; investment sequence - 10 million rubles. annually. According to the second option, construction begins one year later and is carried out for three years. The estimated cost is 42 million rubles, the procedure for investing funds by year is 6, 10, 26 million rubles. Funds are invested at the end of each year. The standard for bringing costs at different times is set at 10%. Determine the most effective option.
1. Let's define the amount of capital investments according to the first option, reduced to the fourth year, i.e. by the year of completion of construction:
K 4 \u003d 10 (1 + 0.1) 3 + 10 (1 + 0.1) 2 + 10 (1 + 0.1) 1 + 10 \u003d 46.41 million rubles.
2. Determine the amount of capital investments according to the second option, reduced to the third year, i.e. by the year of completion of construction:
K 3 \u003d 6 (1 + 0.1) 2 + 10 (1 + 0.1) 1 + 26 \u003d 44.26 million rubles.
Despite the higher cost, option II is the best.
Task 7.15. The loan amount is 200 million rubles, the duration of the loan is 4 years, the annual interest rate is 20%, the share of capital investments by years is 0.25. There are two options for repayment of a long-term loan: upon completion of the term of its advance; annually taking into account the interest rate. Determine the amount of the loan to be repaid and choose the best refund option.
1. Determine the amount of loan repayment for the option providing for its payment at the end of the advanced period:
2. Let's determine the amount of the loan repayment for the option providing for the annual payment of a part of the loan:
Conclusion: the second option is the best, as it gives a smaller return.
Task 7.16. The contractor commissioned the facility under construction on 1 September with the contractual deadline of 1 December and the contractual price of 1,000 million rubles. The expected efficiency of the facility is 0.12 rubles / rub. in year. In accordance with the contracting agreement, the contractor must receive an additional payment of 0.5% of the disbursed investment for each month of accelerated commissioning. Define economic effect from early commissioning of an object for an investor and a contractor.
1. Let's define the additional profit that the investor should receive for the additional time of the capital investments functioning:
2. Determine the amount additional payment, which the investor is obliged to transfer to the contractor in connection with the early commissioning of the facility:
In order to create economic interest, the investor transfers to the contractor half of the profits received in connection with the early commissioning of the facility.
Task 7.17. Overhead costs according to the estimate - 60 million rubles. The share of conditionally fixed costs is 0.5. The firm can shorten the construction period from 12 to 10 months. Determine the savings from reducing the construction time.
Let's determine the savings from reducing the construction period:
Task 7.18. Three variants of capital investments in the construction of a plant are compared with different investments by years (Table 7.3). Choose the most effective option for investing funds if the rate of return on invested capital is 20%.
Table 7.3
Let's determine the amount of discounted capital investments by options:
The best option is III, it requires less initial.
EXERCISE 1
Four options developed technological process manufacture of slate, ensuring the quality of products in accordance with applicable standards and technical conditions... The main indicators of the use of various variants of the technological process are given in table 2.1.
Table 2.1
Initial data on the technological process of manufacturing slate
Note:
The specified indicators have the following dimensions:
q - annual production volume, mln.m²;
s - unit cost, thousand rubles / m2;
K - capital investments by option, mln. Rubles.
The choice of the best variant of the technological process should be carried out by calculating the coefficients of the comparative efficiency of additional capital investments and confirm the solution obtained by calculating the reduced costs.
The choice of the best option is carried out by one of the methods:
1) by the coefficient of efficiency add. capital investments,
The efficiency factor is determined by the formula:
where: S1 and S2 - the cost of the annual production volume for two comparative options;
K1 and K2 - investments in two comparative options.
For E\u003e En, a more capital-intensive option is introduced, for E< Ен - менее капиталоемкий.
2) by calculating the reduced costs.
The given costs are determined by the formula:
P \u003d S + En * K min, (2.2)
where: S - the cost of the annual volume of products produced by the option;
Yong - standard coefficient the effectiveness of additional investments;
K - capital investment for the option.
The option is being introduced, for which the reduced costs will be the least.
Let's present the initial information in the form of table 2.2.
Table 2.2
Standard coefficient of efficiency of additional investments
Since E\u003e
Since E\u003e
Since E\u003e
P1 \u003d S1 + En * K1 \u003d 3000 * 76.5 + 0.200 * 115000 \u003d 252500 rubles.
P2 \u003d S2 + En * K2 \u003d 3000 * 78 + 0.200 * 110000 \u003d 256000 rubles.
P3 \u003d S3 + En * K3 \u003d 3000 * 71 + 0.200 * 116000 \u003d 236200 rubles.
P4 \u003d S4 + En * K4 \u003d 3000 * 85 + 0.200 * 86000 \u003d 272200 rubles.
Thus, the calculation of the reduced costs for the options confirmed that option 3 is the best, since its costs turned out to be the lowest.
ASSIGNMENT 2
For the conditions that are presented in the previous assignment, it is necessary to determine the best option for the technological process, if investments are made within four years in shares of the total amount of investments (Table 2.3).
Table 2.3
Share of investments by years
Before starting the search for the best option for the technological process, it is necessary to prepare information on capital costs by years of investment (Table 2.4). Their structure (in percentage) is given in the assignment.
Table 2.4
Investments by years and variants (thousand rubles)
|
Ordinal year |
Option 1 |
Option 2 |
Option 3 |
Option 4 |
|
Third year |
||||
|
Second year |
||||
|
First year |
||||
The numbers in the above table were determined as follows:
Option 1:
Year 0: K10 \u003d 40% * 115 \u003d 46 thousand rubles.
1st year: K11 \u003d 30% * 115 \u003d 34.5 thousand rubles.
2nd year: K12 \u003d 20% * 115 \u003d 23 thousand rubles.
3rd year: K13 \u003d 10% * 115 \u003d 11.5 thousand rubles.
Investments for options 2, 3, 4 are calculated in a similar way.
Let's recalculate investments taking into account the time factor.
Option 1:
Thus, taking into account the time factor, capital investments in option 1 will not amount to 115 thousand rubles, but 117.32 thousand rubles.
Attachments for other options are calculated in a similar way:
In the future, calculations are made of the coefficients of additional capital investments and reduced costs according to options by analogy with the first task, but using the newly obtained values \u200b\u200bof capital investments:
Since the manufacturing cost indicator is set in rubles / thousand. mІ, then capital investments should be converted into rubles, multiplying them by 1000.
Let's compare options 1 and 2:
Since E\u003e En, a more capital-intensive option is accepted for implementation, i.e. Option 1. Option 2 is excluded from further analysis as ineffective.
Let's compare options 1 and 3:
Since E\u003e En, a more capital-intensive option is accepted for implementation, i.e. Option 3. Option 1 is excluded from further analysis as ineffective.
Let's compare options 3 and 4:
Since E\u003e En, a more capital-intensive option is accepted for implementation, i.e. Option 3. It is effective of all the alternatives.
Let's check the received conclusion by calculating the reduced costs.
P1 \u003d S1 + En * K1 \u003d 3000 * 76.5 + 0.200 * 117320 \u003d 252965 rubles.
P2 \u003d S2 + En * K2 \u003d 3000 * 78 + 0.200 * 112220 \u003d 256444 rubles.
P3 \u003d S3 + En * K3 \u003d 3000 * 71 + 0.200 * 118340 \u003d 236687 rubles.
P4 \u003d S4 + En * K4 \u003d 3000 * 85 + 0.200 * 87740 \u003d 272548 rubles.
Thus, the calculation of the reduced costs for the options confirmed that the most economical option is option 3.
ASSIGNMENT 3
Five options for the technological process of making bricks have been developed, which are characterized by different productivity, but ensure the release of products in accordance with the current standards and technical conditions. The selling price of one brick is 0.285 rubles. Determine which of the technological process options is more economically profitable if the efficiency standard adopted by the company is En. The rest of the initial data are given in tables 2.5 and 2.6.
Table 2.5
Initial data
Table 2.6
Information on the volume of brick production and the standard of efficiency of capital investments
The choice of the best option is carried out according to the given effect. The reduced effect is determined by the formula
E \u003d q * Z - (s + En * Ku) max, (2.3)
where: E is the annual reduced economic effect for the option;
q is the annual production volume in physical terms;
Z is the selling price of the product;
S is the cost of production of a unit of production for a variant;
En - the standard of efficiency of capital investments;
Ku - specific capital investments for the option.
Specific capital investments are determined by the formula:
where: K - capital investment for the option.
Option 1:
Option 2:
Option 3:
Option 4:
Option 5:
Thus, option 5 is the most beneficial of all, since the effect is the most significant.
ASSIGNMENT 4
Five variants of the technological process for the manufacture of tiles have been developed, each of which differs from the others in quality finished products and the performance of the equipment used. Determine which of the options is more economically profitable with the following initial data (tables 2.7, 2.8).
Table 2.7
Variants of the technological process for the manufacture of tiles
Table 2.8
Information about the price of tiles and the standard of efficiency of capital investments
According to the given initial data, the alternatives differ in the volume of brick production. Therefore, to select the best variant of the technological process, the formulas of the reduced costs should not be applied. The solution to this problem is possible only by applying the formula for the reduced effect.
In the process of calculations, it is necessary to ensure that the dimension of the indicators is strictly observed. Taking this requirement into account, let us define the reduced effect.
Option 1:
Option 2:
Option 3:
Option 4:
Option 5:
Thus, option 4 is the most beneficial of all, since the effect is the most significant.
ASSIGNMENT 5
A technical design for construction and operation has been developed brick factory production capacity M (thousand pieces / year). The period of construction and development of the production capacity of the new enterprise (? T) is 0.8 years.
It was found expedient to use 10% of the plant's production capacity as a reserve.
In accordance with the project, annual fixed costs plant are C (thousand rubles / year), and the variables - Y (rubles / piece). The market price of bricks at the time of plant design is determined as Zr (rubles / piece). Predicted studies show that by the beginning of the plant's operation the price of bricks will change: from min \u003d 1.14 to max \u003d 1.2. Investment in the creation of the plant is defined as K (thousand rubles). The rate of efficiency of capital investments (En), established by the firm, is 0.20. The expected demand for brick is 1.25 M. The magnitude of inflation expectations can be neglected. All data are presented in table 2.9.
Table 2.9
Initial data on the production program
Note:
a - change in the commodity mass supplied by competitors to the market, share of units;
af - market share of the new firm in relation to the volume of commodity mass of the base period, share of units;
Katz - coeff. price elasticity of demand for goods, share of units;
D - coeff. changes in the income of consumers of goods, share of units;
Cad - coeff. elasticity of goods by consumer income, share of units.
Everything necessary calculations carry out in two ways:
a) with costly pricing;
b) with market pricing.
In the calculations, we assume that the planned brick production is 85% of the production capacity of the enterprise, and taxes are determined as \u003d 0.215 of the value of fixed costs (conditionally constant annual taxes) and \u003d 0.28 of the company's balance sheet profit (variable taxes, depending on the production activity of the enterprise).
It is necessary to determine the value following indicatorscharacterizing the effectiveness of the future business:
Annual production program;
The expected selling price of bricks per unit of production;
Annual proceeds from the sale of bricks;
Annual variable operating costs;
Conditionally fixed current costs per unit of production;
Unit cost of production;
Annual production cost commercial products;
The value of the annual balance sheet profit of the enterprise
The profitability of brick production;
Annual production program of self-sufficiency of the enterprise;
Characteristics and degree of reliability of the future business;
The amount of the annual aggregate tax (in the absence of tax benefits);
Annual production program of the enterprise's self-sufficiency, taking into account its taxation;
The share of the proceeds remaining at the disposal of the enterprise after taxes have been paid;
The share of the balance sheet profit withdrawn to the budget as taxes (aggregate tax as a percentage of the balance sheet profit);
The efficiency ratio and the payback period of capital investments (taking into account the risk of entrepreneurship).
After all the calculations, it is necessary to draw a conclusion about the feasibility of the business (the main production indicators are given in the table).
The results of the performed calculations should be entered into a summary table. Build a schedule of costs and results of production, depending on the production program of the enterprise. Compare the calculated results for different types pricing and draw conclusions to explain the discrepancy between these results.
AND) Based on costly pricing.
Let's define the annual production program of the plant according to the formula:
q \u003d Km * M \u003d 0.85 * 10,000 \u003d 8500 thousand pieces, (2.6)
where: M is the annual production capacity of the enterprise;
Km is the utilization factor of production capacity.
Let's determine the expected price of one brick by the formula:
Z \u003d 0.5 * (1.14 + 1.20) * 0.823 \u003d 0.9629 rubles / piece.
Let's determine the annual proceeds from the sale of bricks by the formula:
B \u003d q * Z (2.8)
B \u003d 8,500,000 * 0.9629 \u003d 8,184,735 rubles / year.
Let's define the annual variable costs of the enterprise using the formula:
Uper \u003d Y * q (2.9)
Uper \u003d 0.220 * 8,500,000 \u003d 1,870,000 rubles / year.
Let us determine the conditionally fixed costs per unit of production using the formula:
c \u003d C: q (2.10)
c \u003d 2,500,000: 8,500,000 \u003d 0.294118 rubles / piece.
Let's determine the cost of production of a unit of production by the formula:
s \u003d Y + c (2.11)
s \u003d 0.220 + 0.294118 \u003d 0.514118 rubles / piece.
Let's determine the cost of the annual marketable products by the formula:
S \u003d s * q (2.12)
S \u003d 0.514118 * 8,500,000 \u003d 4,370,000 rubles / year
Let's determine the value of the annual balance sheet profit of the enterprise according to the formula:
Пб \u003d q * (Z - s) (2.13)
PB \u003d 8,500,000 * (0.9629 - 0.514118) \u003d 3,814,735 rubles / year.
Let's define the profitability of brick making by the formula:
Pi \u003d (Z - s): s (2.14)
Pi \u003d (0.9629 - 0.514118): 0.514118 \u003d 0.8729, or 87.29%
Let's define the annual production program of self-sufficiency of the enterprise according to the formula:
Qc \u003d C: (Z - Y) (2.15)
Qc \u003d 2,500,000: (0.9629 - 0.220) \u003d 3,365,145 pieces / year.
Let's define the characteristics and degree of reliability of the future business. The ratio of production capacity to a self-sustaining production program is:
M / Qc \u003d 10,000,000 / 3,365,145 \u003d 2.97
The resulting figure indicates that the business takes into account the uncertainty of the future market situation and will be quite reliable, since its level of risk is below average, and the correction rate for the efficiency of capital expenditures Ер, which takes into account the investment risk, is:
Ep \u003d Km * En \u003d 0.85 * 0.20 \u003d 0.17.
Let us determine the amount of the annual aggregate tax of the enterprise (in the absence of tax benefits) according to the formula:
H \u003d Hpos + Hper \u003d * C + * Pb (2.16)
H \u003d 0.215 * 2 500 000 + 0.28 * 3 814 735 \u003d 1 605 626 rubles / year.
Let's define the annual production program of self-sufficiency, taking into account taxation, according to the formula:
Qc \u003d \u003d 4 370 015 pcs / year.
The result obtained indicates that, taking into account taxation, the production program of self-sufficiency has grown significantly (from 3 365 145 to 4 370 015 units / year), i.e. increased by 1.3 times. This significantly reduces the amount of net profit, increases the risk of investments in this business.
Let us determine the share of the proceeds remaining at the disposal of the enterprise after taxes, according to the formula:
Let us substitute the initial and calculated data into this formula (18) and get:
This means that almost 27% of all revenue remains at the disposal of the enterprise after taxes are paid, or:
Оn * B \u003d 0.27 * 8 184 735 \u003d 2 209 109 rubles / year.
Let's define the total tax as a percentage of the balance sheet profit using the formula:
n \u003d N / Pb (2.19)
n \u003d 1 605 626/3 814 735 \u003d 0.4209, or 42%
This is a fairly high result, which allows us to conclude that almost 42% of the balance sheet profit remains for the enterprise for social and industrial development.
Let us determine the efficiency ratio and the payback period of capital investments, taking into account the risk of entrepreneurship, using the following formulas:
Substitute the available data into the formula (2.20) and get:
Consequently, taking into account the risk, the efficiency of capital investments fully meets the requirements of the theory and the limitation of the efficiency rate established by the entrepreneur. Now you can determine the payback period of capital investments using the formula (2.21):
The project of the future business provides the entrepreneur with a sufficiently high income and can be recommended for implementation, taking into account the uncertainty of the future market situation and the investment risk. Based on the calculated data, we will construct a graph of the dependence of the costs and results of production on the volume of output (Figure 2.1).
Figure 2.1.
B) Based on market pricing.
1) First of all, it is necessary, according to the initial data and taking into account the adopted production program, to determine the price of one brick according to the following formula:
2) Since the obtained value does not represent the price of a brick itself, but its index, then to finally determine the desired price value, it is necessary to carry out the following calculation operation:
Z \u003d Z * d \u003d 0.9629 * 0.8194 \u003d 0.789 rubles / piece.
3) Let's determine the company's revenue by the formula:
В \u003d q * Z \u003d 8,500,000 * 0.789 \u003d 6,706,572 rubles / year.
4) The cost price of one brick remains unchanged, i.e. the same as with costly pricing, and amounts to:
s \u003d 0.514118 rubles / piece.
5) The cost of the annual product release also remains unchanged:
S \u003d 4 370 000 rubles / year.
6) Determine the annual balance sheet profit by the formula:
PB \u003d q * (Z - s) \u003d 8,500,000 * (0.789 - 0.514118) \u003d 2,336,572 rubles / year.
7) Determine the profitability of brick making by the formula:
Pu \u003d (Z - s): s \u003d (0.789 - 0.514118): 0.514118 \u003d 0.5346.
8) Determine the amount of the annual total tax by the formula:
Н \u003d * С + * PB \u003d 0.215 * 2,500,000 + 0.28 * 2,336,572 \u003d 1,191,740 rubles / year.
9) Let us determine the share of the proceeds remaining at the disposal of the enterprise according to the formula (2.18):
0.1251 or 13%
Thus, after settling with the budget, the company will have at its disposal approximately 13% of the proceeds, or:
В * Оn \u003d 6 706 572 * 0.1251 \u003d 838 832 rubles / year.
10) Determine the total tax as a percentage of the balance sheet profit using the formula:
N \u003d N / Pb \u003d 1 191 740/2 336 572 \u003d 0.5100, or 51%.
11) Determine the efficiency ratio and the payback period of capital investments using formulas (2.20) and (2.21):
In the context of market pricing, the business is not profitable and reliable enough.
Let's compare the calculated results on cost and market pricing with each other and present all the information in Table 2.10.
Table 2.10
Calculation results for cost and market pricing
|
Indicator name |
Indicator value |
|
|
with costly pricing |
at market pricing |
|
|
1) Annual production program, thousand pcs. |
||
|
2) Price per unit of production, rubles / piece. |
||
|
3) Annual revenue of the enterprise, rubles / year |
||
|
4) Annual variable costs, rubles / year |
||
|
5) Conditionally fixed costs, rubles / piece. |
||
|
6) Unit cost, rubles / piece. |
||
|
7) Cost of marketable products, rubles / year |
||
|
8) Annual balance sheet profit, RUB / year |
||
|
9) Profitability of brick production,% |
||
|
10) Manufacturing program self-sufficiency, pcs / year |
||
|
11) Correction rate of efficiency for investment risk |
||
|
12) Annual gross tax, rubles / year |
||
|
13) Production program of self-sufficiency, taking into account taxation, units / year |
||
|
14) The share of proceeds remaining at the disposal of the enterprise,% |
||
|
15) Total tax in relation to balance sheet profit,% |
||
|
16) The coefficient of efficiency of capital expenditures taking into account risk (with En + Ep \u003d 0.37) |
||
|
17) Payback period of capital investments, years |
Conclusion
The obtained result indicates that under conditions of market pricing, production efficiency indicators with fixed initial data are worse than under conditions of costly pricing. This is due to the fact that the price of a product decreases with an increase in the total mass in the market, therefore, all indicators formed on the basis of the price of a product deteriorate (revenue, balance sheet profit, production profitability, etc.).
At the same time, it can be stated that with market pricing after taxes, the enterprise has less money at its disposal for further development... It should be emphasized that in this case, in the conditions of market pricing, an entrepreneurial project cannot be recognized as expedient, future business - insufficiently effective and reliable.
There are three options for capital investment. In the first option out of 120 cases, the profit is UAH 800. was received in 40 cases, the profit is UAH 200. - in 80 cases. In the second option, out of 180 cases, the profit is UAH 600. was received in 100 cases, the profit is 450 UAH. - in 60 cases, the profit is UAH 300. - in 20 cases. In the third option out of 100 cases, the profit is UAH 300. was received in 50 cases, the profit is UAH 260. - in 30 cases, the profit is 220 UAH. - in 20 cases.
Choose the most profitable investment option.
Decision.
To find the most profitable investment option, you need to find the expected profit using the formula for calculating the mathematical expectation:
For the first option, the probability of making a profit is 800 UAH. will be:
The probability of making a profit is 200 UAH. will be:
The sum of all probabilities for the first option is equal to one.
As a result, the expected profit for the first option will be equal to:
The expected profit for the second option will be:
The expected profit for the third option will be:
Conclusion: The most profitable investment option is the second option.
Problem 2
The board of the car manufacturing firm must adopt strategic decision about a promising production profile. In this case, there are four preference options: cars, trucks, minibuses, sports cars. Depending on the situation on the market, the experts determined the following profit indicators (table);
Based on the risk minimization rules - the pessimism-optimism criterion, the minimax risk rule and the Laplace rule, choose the most profitable strategy.
Decision.
Laplace criterion .
This criterion is based on calculating the mathematical expectation in the absence of the likelihood of the onset of options - the arithmetic mean value is determined by the formula 
:
Strategy 1. 
cu
Strategy 2. 
cu
Strategy 3. 
cu
Strategy 4. 
cu
Since the criterion of optimality is the maximum value of the average expected value, the best strategy for the production of trucks.
The criterion of pessimism - optimism .
We assume that the probability of an event occurring with the minimum profit is 0.70, then the probability of an event occurring with the maximum profit is 0.30.
The expected profit value is determined by the formula 
:
for the car manufacturing strategy:
for a truck manufacturing strategy:
for the minibus production strategy:
for the sports car strategy:
Since the greatest value of the expected profit corresponds to the strategy for the production of trucks, then based on this criterion, this strategy is optimal.
Minimax risk criterion .
To solve the problem according to the criterion of minimax risk, it is necessary for each option to determine the maximum value of the profit indicator and subtract from it the corresponding values \u200b\u200bfor other options. The second step is to determine the maximum value of the difference for each strategy, i.e. lost profits. The minimum value of the maximum values \u200b\u200bof the lost benefits will correspond to the optimal strategy.
Calculation of indicators of lost profit (c.u.)
Based on this criterion, the optimal strategy for the production of passenger cars.
Problem 3
The entrepreneur is faced with a choice as to how much to buy 400 or 500 units. When purchasing 400 units, the purchase price is 90 UAH, and when purchasing 500 units. - 70 UAH. The entrepreneur will sell this product for 110 UAH. for a unit. The demand for the goods is not known for sure: the probability of selling 400 and 500 units is initially estimated at 60: 40. All goods not sold on time can be returned for 30 UAH.
How many items should you buy? What is the price for additional sales information?
Decision.
The profit from the purchase of 400 units of the product and the demand for the product in the amount of 400 units will be
The profit from the purchase of 400 units of goods and the demand for goods in the amount of 500 units will also amount to 8000 UAH.
The average expected profit from the purchase of 400 units of goods is determined by the formula for calculating the mathematical expectation: 
The profit from the purchase of 500 units of the product and the demand for the product in the amount of 400 units will be:
The profit on the purchase of 500 units of the product and the demand for the product in the amount of 500 units will be
The average expected profit for the purchase of 500 units of goods is determined by the formula: 
Data calculation
The risk-averse person will choose a purchase volume of 500 units. A risk-neutral person will choose a purchase volume of 500 units of goods, since for a given purchase volume, the average expected profit is higher. A risk-averse person will also choose a purchase volume of 500 units of goods, since for any demand, the profit will be greater (12,000 or 20,000 UAH) than 8,000 UAH. when purchasing 400 units of goods. Wherein additional Information future demand is unnecessary. Let us confirm this by calculations.
The cost of additional information is defined as the difference between the expected profit under conditions of certainty and the expected profit under conditions of uncertainty.
The expected profit in conditions of certainty (i.e. when the exact volume of demand is known - 400 or 500 units) will be.
The expected profit under conditions of uncertainty will be UAH 15200.
Cost of additional information: i.e. information should not be bought.
Problem 4
When providing a loan to a firm, a forecast of possible losses and corresponding values \u200b\u200bof probabilities is carried out. Numerical data are presented in the table.
Initial data
Determine the expected amount of risk, that is, losses.
Decision.
The amount of risk (expected damage) is determined by the formula 
:
those. the firm should not provide a loan, since the amount of the expected loss is UAH 16 thousand.
Investments, million rubles 20 10
Net profit, million rubles / year 9 5
The annual rate of amortization of investments is 15%.
5 + 1.5 \u003d 6.5 \u003d\u003e the first option is more efficient
Determine the current cost of 23 billion rubles, which should be spent in 3 years. During this period, interest was charged at a rate of 7% per annum.
23 * (1 + 0.07) 3 \u003d 23 * 1.225 \u003d 28.175 billion rubles. - the current cost is 23 billion rubles.
Three variants of the invention for the production technology of the product have been developed. Calculate the best option according to the table. Calculations should be made using the method of reduced costs.
Decision. Using the method of reduced costs, we will determine the most
an effective version of the invention according to the following formula:
С - annual production costs of the product;
K - investments;
En - coefficient of economic efficiency \u003d 0.2
Option 1 - (13600 * 750) + 0.2 * 22500 \u003d 14,700 million rubles.
Option 2 - (14700 * 1150) + 0.2 * 27900 \u003d 22485 million rubles.
Option 3 - (13700 * 2500) + 0.2 * 19700 \u003d 38190 million rubles.
Conclusion: the most effective option proposed for use
inventions - this is 1 option, that is, the lowest reduced costs.
Define: change total costs for creating samples, changing the total costs by changing the costs of creating one sample, changing the total costs by changing the number of samples created, in absolute and relative terms.
The average cost of developing one sample was 2,200 thousand rubles in the base year, and 2,260 thousand rubles in the current year. The number of created images is 210 and 220, respectively.
З 0 \u003d 2200 * 210 \u003d 462000 thousand rubles.
З 1 \u003d 2260 * 220 \u003d 497200 thousand rubles.
497200 / 462000 = 1,08 (108%)
The total cost of creating samples increased (497,200 - 462,000) by 35,200 thousand rubles. by 8%.
Cost index for one sample: (2260 - 2200) * 220 \u003d 13200 thousand rubles.
The number of created samples increased (220 - 210) by 10 units (220/210 \u003d 1.05 (105%)) by 5%.
The cost of manufacturing 1 sample increased (2260 - 2200) by 60 thousand rubles.
(2260/2200 \u003d 1.03 (103%)) by 3%.
The total cost of creating samples has changed as follows:
2200 * (220 - 210) \u003d 22000 thousand rubles.
The total cost of creating samples increased by 35,200 thousand rubles compared to the base year. However, an increase in the cost of creating one sample by 60 thousand rubles. led to an increase in total costs by 13,200 thousand rubles. At the same time, an increase in the number of created samples by 10 units contributed to an increase in total costs by 22,000 thousand rubles.
Hence, general changes:
DЗ \u003d 13,200 + 22,000 \u003d 35,200 thousand rubles.
Topic 6. Personnel management of an innovative enterprise
By choosing one of the list of organizations:
educational institution;
a company providing services for the design and renovation of premises;
veterinary clinic;
legal consultation;
fitness center,
medical clinic;
beauty saloon;
home of life;
or suggesting any other, at your discretion, develop the plot of an innovative game by performing, for this, the sequence of actions:
define and articulate possible problemtaking place in the selected organization within the following thematic fields:
"Improving the management system in the organization"
Human Resource Development Management;
"Management of the introduction of new technologies";
"Development of new markets";
"Attracting new sources of raw materials and resources";
formulate the goal of an innovative game, adequate to the problem;
select unambiguous criteria for assessing the effectiveness of an innovative game (criteria for achieving the goal of the game) that do not require additional costs and time;
identify the main roles of the participants in the innovative game (describe who and what will do during the game);
list the main organizational forms assumed in the innovation game;
describe the course of the game (stages, steps in the game should be logically justified, they should be enough for the game);
guess what additional effects the organization might get after the game ends.
Omsk Machine-Building Plant.
"Development and implementation of a system for training and promotion of managers."
The plot of an innovative game:
The objectives of the game are as follows:
outline the main directions for improving the system of training managerial personnel of the plant, a project for such a system and a program for its further development and implementation;
use the work of leaders to solve this problem to teach them how to collectively making decisions, increasing the level of their managerial training;
determine the composition of the initiative group, which will continue to work on the system project after the end of the game.
To achieve all these goals, an innovative game is built as a special type of social technology, including programs for problem solving, research and development of participants and the entire organization. The program of the innovative game includes eight subprograms: development of innovative solutions, design of innovations, programming of their implementation, education and training of participants, recreation of participants and organizers, research and organization of the game process. Each organizer implemented in the business game his own, drawn up at the preparatory stage, work program, where, in a time sequence, all types of work were identified and docked to achieve meaningful goals. Each such work program (and there were four main and two auxiliary) contained specific stages in the movement of participants to solve the problem posed and the tasks of the organizer, a description of the tools and organizational forms of work.
Game participants:
customers;
organizers;
researchers;
participants.
Customers are engaged in developing solutions, designing and programming their implementation.
Participants pursue educational goals - to master some new means of work, the development of new means of work, self-development, development of the organization. The researchers involved in the game do research on the organization.
The organizers of the game - along with all of the above, sets specific goals for organizing constructive relationships with all (and between all) groups for further joint activities, and also focuses on the constant enrichment and development of the entire system of goals in the game.
Organizational form: planning, design, research, training, implementation.
Development of solutions. Development of an innovative solution for the organization of this problem.
Design. The solution obtained at the previous stage is deeply worked out and justified. This work is carried out in the form of design.
Programming. At this stage, the development of organizational measures for the introduction of innovations is carried out, it is determined what the results and consequences of the implementation of the project may be, the factors that promote and hinder the implementation of the project are identified.
Training. In the course of work, the organizer suggests ways that the participants have not yet used - they learn to solve problems more effectively in the process of practical mastering and application of these methods. The next stage of training is the creation of a situation of the need for independent development of new means and new points of view, positions.
Study. A complete study of the problem posed.
The main characteristic of such a complex system should be the level of its self-organization and self-development. The basis for assessing the preparedness of leaders should be the results of his participation in group decision-making work. The management system should be based on the principles of command management, including both teams of permanent managers and specialized target (problem) groups. The system of training managers should operate at all levels of enterprise management. One of the basic principles of training should be the principle of ensemble learning (joint training of leaders and their subordinates).
Participants receive the following advantages for use in further work: the opportunity to look at their work more broadly, not from a technocratic standpoint, a means of deep analysis of the situation before making a decision, a means of assessing the consequences of their decisions, confidence in their abilities, that a lot depends on them. , understanding that organizational issues are the most important thing in the work of a leader, the conviction of the need to abandon the psychological impact of routine, increased responsibility for decisions, a better understanding of others, oneself, the situation, mastering the technology of group work, and much more.
Issues for discussion
- What is the relationship between innovation and investment?
- What is the role of innovation in enterprise development?
- What does the full innovation cycle include?
- What forms and stages of technical preparation of production are known to you?
- What are the criteria for evaluating investment projects?
Topics for reports and abstracts
- The main components and directions of innovation.
- Standards governing the process of technical preparation of production.
- Economic efficiency of improving the quality of industrial products.
- The effectiveness of investment projects in the banking sector.
- Uncertainty and risk factors in assessing the effectiveness of the project.
Tasks for mastering the calculation of economic efficiency by different methods
The economic efficiency of capital investments is the result of the implementation of an appropriate measure, which can be expressed in savings from a decrease in production costs, an increase or increase in profits, an increase in national income.
Distinguish between absolute and comparative economic efficiency capital investments, which are calculated in different ways.
Problem 1
Formulation of the problem:
Capital investments per unit of production are 80 rubles, and the unit cost is 160 rubles. The enterprise has established a wholesale price of 200 rubles. The annual volume of production is 100,000 units. The level of profitability of the enterprise is 0.2. Determine the overall economic efficiency of capital investments for the construction of a new workshop.
Problem solving technology:
This problem can be solved by two methods.
The first method is based on the calculation of the profitability ratio as the ratio of profit from sales to capital investments:
| (1) |
where R R – profitability ratio;
K -capital investments for construction;
Etc -profit from sales.
Taking into account the fact that the annual production volume is 100,000 units, capital investments in this problem will be equal to:
K \u003d 80 * 100,000 \u003d 8,000 thousand rubles.
To determine the profit from sales, you need to subtract the cost of the annual volume of products from the sales proceeds. The proceeds from sales will be calculated as the product of this volume by the wholesale price of the enterprise: Vyr p \u003d 200 * 100,000 \u003d 20,000 thousand rubles.
The cost price of the annual production volume in this task will be: s \u003d 160 * 100,000 \u003d 16,000 thousand rubles.
Thus, the profit from sales will be equal to
P p \u003d 20,000 - 160 * 100 \u003d 4,000 thousand rubles.
Let's use formula (1) to calculate the profitability ratio 
Since the resulting value ( R p \u003d 0.5) more than the normative (R n \u003d 0.2), - we recognize the project as effective.
The second method is based on assessing the ratio of profit from the sale of a unit of production and the volume of capital investments per unit of production: 
The calculated efficiency ratio also turned out to be higher than the normative one, therefore, the project is efficient.
Answer : the efficiency of capital investments for the construction of a new workshop can be achieved with design factorequal to 0.5.
Problem 2
Formulation of the problem:
The estimated cost of building a new industrial enterprise is 45 million rubles. Capital investment for creation working capital equal to 15 million rubles. The profit from the sale of finished products is 120 million rubles. It is known that the estimated profitability is not less than 0.25. Determine the economic efficiency of capital investments for the construction of a new industrial enterprise.
Problem solving technology:
Efficiency this project it is advisable to evaluate on the basis of comparing the estimated payback period with the standard. If the estimated payback period does not exceed the standard, then the project is recognized as effective.
The estimated payback period is defined as the ratio of the need for capital investments to the profit from the sale of finished products:
The calculated value ( R p\u003d 2) more than standard ( R n\u003d 0.25), therefore, the project is recognized as effective.
Answer : the estimated payback period does not exceed the standard, therefore the project is effective.
Tasks to determine the most effective option for making capital investments
The most efficient option for the implementation of capital investments is established on the basis of comparative efficiency, and in the presence of a large number of options - at the minimum of the reduced costs.
Problem 1
Formulation of the problem:
There are three possible investment options. Standard profitability 0.3. The initial data for these options are given in table. 1. Determine the most effective option.
Problem solving technology:
To determine the most effective option, we will use the following formula for calculating the reduced costs:
The third option provides the minimum of the given costs, therefore it is the most effective.
Answer: as calculations have shown, the third option is the most effective with reduced costs equal to 16.7 million rubles.
Problem 2
Formulation of the problem:
There are two possible investment options. Standard profitability 0.2. The initial data for these options are given in table. 1. Determine the most effective option.
Problem solving technology:
First, we calculate the specific capital investment and unit cost. To do this, we refer the aggregate values \u200b\u200bknown to us to the volume of production. The calculation results are summarized in a table.
By comparing the specific values \u200b\u200bof capital investments and costs, we will determine additional capital investments and savings per unit of production.
Additional investment per unit of production:
K beats \u003d 4 - 3 \u003d 1 rub.
Saving: E unit \u003d 2.5 - 2 \u003d 0.5 rubles.
Thus, the return on investment will be T p = 1/0,5 = 2.
Calculated efficiency factor R R \u003d ½ \u003d 0.5. This value is greater than the normative one, so we come to the conclusion that the second option is the most economical.
Answer: the most economical is the second option.
Problem 3
Formulation of the problem:
There are two possible investment options. The given costs for these options are, respectively, 138 rubles / piece and 147 rubles / piece, and the annual production volume is 20 thousand pieces. The given costs of the basic variant are equal to 150 rubles / piece. Calculate the conditional annual economic effect when implementing the best option.
Problem solving technology:
Before proceeding with the calculation of the conditional annual economic effect, we will select the option that is optimal. If we proceed from the criterion of minimizing the reduced costs, then in this problem the first is optimal. Now let's calculate the conditional annual economic effect E according to the formula:
|
(5) |
where Z pr bases - reduced costs of the base case, rubles;
Z pr 1 - reduced costs of the optimal variant, rubles;
Q 1
Using this formula, we find that the conditional annual economic effect is equal to E \u003d (150 - 138) 20,000 \u003d 240 thousand rubles.
Answer: the annual economic effect from the implementation of the optimal option will be 240 thousand rubles.
Problem 4
Formulation of the problem:
There are two possible options for implementing the investment, the first of which is optimal. The cost of production for the first option is 105 rubles / piece, and for the second - 118 rubles / piece. The annual production volume is 20 thousand pieces. The price of the product is 250 rubles / piece. Calculate the annual profit when implementing the best option.
Problem solving technology:
Annual profit by the best option define by the formula:
|
(6) |
where N g - annual profit according to the optimal variant, rubles;
C - product price, rubles / piece;
s wholesale - cost of production according to the best option, rubles / piece;
Q 1 - volume of production according to the optimal variant, pcs.
So, the annual profit for the best option
Answer: annualoptimal profit volume will amount to 1,900 thousand rubles.
Tasks for mastering methods for assessing the effectiveness of an investment project
When assessing the effectiveness of an investment project, indicators such as gross and net profit, economic effect by years, discounted income, integral effect (NPV), profitability index and investment payback period are used as criteria.
Problem 1
Formulation of the problem:
Considered investment project, the volume of capital investments for which in the first year will amount to 5 million rubles, in the second - 1.5 million rubles. Determine the total amount of capital investments without discounting and taking into account discounting at a discount rate of 0.3.
Problem solving technology:
The total amount of capital investments without discounting is calculated by simply summing the investment funds:
K \u003d 5 + 1.5 \u003d 6.5 million rubles.
Total capital investment, discounted:
|
(7) |
where TO t - capital investments in year t, rubles.
E - discount rate.
Substituting the data known from the condition into the formula, we get:
Answer: the total amount of capital investments without discounting will amount to 6.5 million rubles, and taking into account discounting - 4.7 million rubles.
Problem 2
Formulation of the problem:
The net profit of the enterprise, according to calculations, will be: in the first year 800 thousand rubles, in the second - 2,100 thousand rubles, in the third and fourth - 3,500 thousand rubles each. Determine the effect by years of calculation if depreciation in the first year is 300, and in all subsequent years - 400.
Problem solving technology:
The effect by year of calculation can be determined by summing net profit and depreciation. For convenience, we will summarize the calculation results in a table.
Year |
Effect, thousand rubles |
800 + 300 = 1100 |
|
2100 + 400 = 2500 |
|
3500 + 400 = 3900 |
|
3500 + 400 = 3900 |
Answer: the effect over the years of calculation is 1100 thousand rubles. in the first year, 2500 thousand rubles. - in the second and 3900 thousand rubles each. - in the third and fourth.
Problem 3
Formulation of the problem:
Problem solving technology:
Discounted income is the sum of the effects shown. Let us calculate the reduced effects by formula (8):
Year |
E t, thousand rubles |
E n, thousand rubles |
|
||
|
||
|
||
|
||
Answer: the discounted income as a whole will amount to 5466 thousand rubles.
Problem 4
Formulation of the problem:
According to the results of calculations, the reduced income will amount to 5466 thousand rubles. Calculate the cumulative effect (NPV), if the total volume of investments, taking into account discounting, is 4.7 million rubles.
Problem solving technology:
The integral effect, or net discount income (NPV), is calculated as the difference between the present (discounted) income and the total volume of capital investments, calculated taking into account discounting: NPV \u003d 5466 - 4700 \u003d 766 thousand rubles.
The result is positive, which means that the project under consideration is effective, and you can consider the issue of its adoption.
Answer: the integral effect will amount to 766 thousand rubles.
Problem 5
Formulation of the problem:
According to the results of calculations, the reduced income will amount to 5466 thousand rubles. Calculate the profitability index if the total capital investment, taking into account discounting, is 4.7 million rubles.
Problem solving technology:
The profitability index is calculated as the ratio of the reduced (discounted) income to the total volume of capital investments, calculated taking into account discounting: 
Profitability index value 1,16 indicates that the project is cost-effective, since the main criterion looks like ID\u003e 1.
Answer: the calculation of the profitability index showed that the project is economically efficient.