Seminar finances
Break even point, investment evaluation


Task 10.4 A and B Evaluation of investment options - calculation comparing costs
•The static cost method is based on a comparison of operating and one-time costs. It is based on
the fact that one variant has higher operating costs, the other higher one-off costs, but they do
not differ in their revenues.
•Example: We have to decide between two investment variants of the same capacity. Variant A has
one-time costs of CZK 250,000 and annual operating costs of CZK 160,000, variant B CZK 300,000 and
CZK 140,000. The estimated lifetime of both variants is 4 years.
•10.4 A: Compare the benefits of each alternative using absolute lifetime cost values.
•10.4 B: assess the profitability of both investment variants by calculating the payback period of
additional investment costs d n .
•

Task 10.4 A Solution
•Compare the benefits of individual alternatives using absolute lifetime cost values.
•
•Option A will incur lifetime costs:
•250,000 + 4 * 160,000 = 890,000 CZK
•
•Option B:
•300,000 + 4 * 140,000 = 860,000 CZK
•

Task 10.4 B Solution
•payback period d n =
•
•where: NP is operating costs (think of their difference as "profit" - the difference between
costs)
•NJ is a one-time cost (think of it as an investment)
•A, B - investment options
•Calculation:
•
(50 thousand (300-250) will be paid in 2.5 years, while the investment will be in operation for
another 1.5 years)
Again, option B is more advantageous, as the increased fixed costs of option B will pay off in just
2.5 years with the costs variants A thanks lower operational moods . So after 2.5 years they will
start the total costs of variant A exceed the total costs of variant B

Task 10.5
•Example: We have to decide between two investment variants of the same capacity. Variant A has
one-time costs of CZK 250,000 and annual operating costs of CZK 160,000, variant B CZK 300,000 and
CZK 140,000. The estimated lifetime of both variants is 4 years.
•Compare the profitability of individual investment alternatives by discounting future costs. Based
on the above example, the one-time cost was incurred in year 0 and the cost of capital is 14%.
•For the calculation, use the breakdown of the individual variants of the calculation tables:
•
Year
Costs
Disinheritor
(14%)
Discounted costs
0
1.0000
1
0.8772
2
0.7695
…
…
…
…

Task 10.5 Solution
Year
Costs
Disinheritor
Discounted costs
0
250,000
1
250,000
1
160,000
0.8772
140,352
2
160,000
0.7695
123 120
3
160,000
0.675
108,000
4
160,000
0.5921
94,736
890,000
716 208
Year
Costs
Disinheritor
Discounted costs
0
300,000
1
300,000
1
140,000
0.8772
122,808
2
140,000
0.7695
107,730
3
140,000
0.675
94,500
4
140000
0.5921
82,894
860,000
707,932
Option B is again more advantageous (716208 for A versus 707932 for B). This procedure is
especially advantageous if operating costs are different in individual years.
Variant A
Option B

Task 10.6 Evaluation of investment options - financial and mathematical procedures
•Flows of cash expenses and cash income are assessed until the end of the economic life or a
certain planning horizon.
•Example: There are two investment options (A and B) for which the same capital expenditure of CZK
1,000,000 is assumed, but a different distribution of annual net cash flows (see table). The cost
of capital is 10%, the lifetime for both variants is the same (6 years). Compare the listed
variants.

Task 10.6 A and B
Year
Cash flow A
Monetary flow B
Executor (10%)
0
-1000
-1000
1,000
1
300
100
0.909
2
600
200
0.826
3
400
300
0.751
4
300
400
0.683
5
200
500
0.620
6
100
600
0.564
Distribution of net income of investment options A and B

Task 10.6 A Evaluation of investment options – simple cash flow
Year
Cash flow A
Cash flow B
0
-1000
-1000
1
300
100
2
600
200
3
400
300
4
300
400
5
200
500
6
100
600
Distribution of net income of investment options A and B
900
1,100

Task 10.6 B Evaluation of investment options – discounted cash flow
Year
Cash flow A
Cash flow B
0
-1000
-1000
1
300
100
2
600
200
3
400
300
4
300
400
5
200
500
6
100
600
Distribution of net income of investment options A and B
454
403
 K A = -1000 + 300 * 0.909 + 600 * 0.826 + 400 * 0.751 + 300 * 0.683 + 200 * 0.620 + 100 * 0.564 =
454
 K B = -1000 + 100 * 0.909 + 200 * 0.826 + 300 * 0.751 + 400 * 0.683 + 500 * 0.620 + 600 * 0.564 =
403

Task 10.7
•The cost function TC = 18,000 + 1.4 Q is given
•Determine the break-even point in pieces if the price of 1 piece is 5 CZK
•

Task 10.7 Solution
•Q BEP = FC/(P-AVC)
•
•Q BEP = 18000/(5-1.4)
•
•Q BEP = 5000
•

Task 10.8
•The cost function TC = 18,000 + 1.4 Q is given. Sell price is 5 CZK.
•What quantity of products must the company produce in order to make a profit of CZK 43,200
•

Task 10.8 Solution
•Q BEP = ( FC+Profit )/(P-AVC)
•
•Q BEP = (18000+43200)/(5-1.4)
•
•Q BEP = 17000
•

Task 10.9
•The price of the product is CZK 5/pc. The required profit for the period is CZK 36,000. The
company is able to produce 15,000 pieces of products during this period.
•What is the limit of fixed costs, if the variable costs per 1 piece are CZK 1.40?
•
•
•
•

Task 10.9 Solution
•Q BEP = ( FC+gain )/(P-AVC) --- FC = Q * (P-AVC) - gain
•
•FC = 15000 * (5-1.4) – 36000
•
•FC = 18000
•

Task 10.10
•The company produces 2 types of products at the same time. More detailed information is given in
the following table:
•
•
•
•
•Determine the break-even point of products A and B when producing both of them simultaneously.
•
Product
Production volume in tons
Var. cost per 1 ton
Fixed. costs
Price for 1 ton
AND
600
20
50
B
200
40
60
in total
800
11,000

Task 10.10 solution - equation



Task 10.10 solution - logic
Product
Production volume in tons
Var. cost per 1 ton
Fixed. costs
Price for 1 ton
A
600
20
50
B
200
40
60
in total
800
11,000
pú A = 50 – 20 = 30
pú B = 60 – 40 = 20
110 = 3 * 30 + 1 * 20
Q A = 100 * 3 = 300
Q B = 100 * 1 = 100
Šipky ve tvaru V se souvislou výplní

Task 10.11
•Find out for which production volumes the individual technological procedures listed in the
following overview will be suitable. The variants are technologically equivalent, they differ in
their cost function.
•
Technological variant
Fixed costs
Variable cost per 1 piece
1
2000
300
2
10,000
200
3
50,000
100

Task 10.11 Solution
•TC 1 = 2000 + 300Q
•TC 2 = 10,000 + 200Q
•2000 + 300Q = 10000 + 200Q
• Q = 80 pcs
•TC 2 = 10,000 + 200Q
•TC 3 = 50,000 + 100Q
•10,000 + 200Q = 50,000 + 10Q
• Q = 400 pcs
•With a production volume of up to 80 pieces, variant 1 is the most suitable, between 80 and 400
pieces, variant 2, and over 400 pieces, variant 3
•

Task 10.12
•The company BOTAS, as is considering the production and sale of a new type of sports shoes. The
estimated annual production volume is 60,000 units at a unit price of CZK 650. Annual fixed costs
are budgeted at CZK 18,000,000.
•
a)Find out the maximum variable costs for 1 product.
b)By how many CZK would the unit variable costs have to be reduced if the company requires a
pre-tax profit of CZK 1,500,000, taking into account the need to replenish the reserve fund, pay
the required dividends for shareholders and resources for investments?
•

Task 10.12 Solution of a and b



•Thank you for your attention