MODULE 1-3 ACTIVITIES
Expected Value
Problem 1
White Covered Store sells “balut” in the city’s central bus terminal. For this coming weekend, the
probability distribution of the demand for “balut” is as follows:
Estimated Sales in Units
750 Units
900 Units
1,300 Units
Probability
0.20
0.25
0.55
Compute for the estimated demand of “balut” for this coming weekend:
ANSWER:
Event
(𝒂)
750
900
1,300
Probability
Units
(𝒃)
(𝒂 × 𝒃)
0.20
150
0.25
225
0.55
715
1.0
1,090 Units
The expected demand for balut in the coming weekend is 1,090 units.
Payoff (Decision table)
Problem 2
Mr. B. Hon cooks and sells “Pansit in a Box”. Each box of pansit is sold for P50 during regular hours, that
is, from 10am to 8pm. If every box is sold by 8pm, Mr. B. Hon calls it a day. However, all unsold boxes by
8pm are sold at half of the regular price up to 9pm. The variable cost per box is P30. The contribution
margin per box is as follows:
From 10am to 8pm
Selling Price
Variable Cost
CM per box
P50
30
P20
After 8pm
Selling Price
Variable Cost
Loss per box
P25
30
P5
Past experiences have shown that the daily sales
demand (up to 8pm) and their probabilities are as
follows:
Sales per day
Probability
500 boxes
0.20
600 boxes
0.70
700 boxes
0.10
If the sales demand will be the same as in the past,
make a payoff table showing the contribution
margin for the possible sales quantities under
each production level strategy, as well as the
expected value of such contribution margin.
ANSWER:
CM is computed as follows: each box is multiplied by the CM per box P20 (from 10am to 8pm), and
excess unit will result a loss of P5.
State of Nature =
Actual Sales Demand
(up to 8pm)
Make 500 boxes
Make 600 boxes
Make 700 boxes
500
P10,000
10,000 – 500 (loss) =
P9,500
600
10,000
12,000
10,000 – 1,000 (loss) =
P9,000
12,000 – 500 (loss) =
11,500
14,000
700
10,000
The probabilities of the season’s demand are:
12,000
Sales per day
Probability
500 boxes
0.20
600 boxes
0.70
700 boxes
0.10
The expected value is calculated as follows:
Make 500 boxes
Make 600 boxes
Make 700 boxes
0.20 * P10,000
0.20 * P9,500
0.20 * P9,000
0.70 * 10,000
0.70 * 12,000
0.70 * 11,500
0.10 * 10,000
0.10 * 12,000
0.10 * 14,000
EV (500) = P10,000
EV (600) = P11,500
EV (700) = P11,250
The best decision is to make 600 boxes of pansit per day, with the greatest expected value of P11,500.
Problem 3
Using the data on problem 2 (Pansit in a box), assume that if Mr. B. Hon knew the daily sales demand for
pansit with certainty, he would prepare exactly the number of boxes demanded. Compute for the
expected value of perfect information (EVPI).
Probability (Pr)
State of Nature
Best Action
Best Action Payoff
0.20
0.70
0.10
Demand = 500
Demand = 600
Demand = 700
Produce 500
Produce 600
Produce 700
P 10,000
P 12,000
P 14,000
Expected Value with Perfect Information
Expected Value without Perfect Information
EVPI
P 11,800
P (11,500)
P
300
Expected Value
(𝑃𝑟 × 𝑃𝑎𝑦𝑜𝑓𝑓)
P 2,000
P 8,400
P 1,400
P 11,800
Problem 4
Nitz’ Company is planning to produce a new product, Duhat soap. A marketing consultant prepared the
following payoff probability distribution describing the relative likelihood of monthly sales volume levels
and related contribution margin for Duhat soap:
Monthly Sales Volume
15,000 units
18,000 units
27,000 units
36,000 units
45,000 units
•
Probability
40%
30%
15%
10%
5%
Contribution Margin
P 75,000
P 90,000
P 135,000
P 180,000
P 225,000
If Nitz’ Company decides to market Duhat Soap, the expected valued of the monthly sales volume is?
Answer:
Event
(𝒂)
15,000 units
18,000 units
27,000 units
36,000 units
45,000 units
Probability
(𝒃)
40%
30%
15%
10%
5%
100%
The expected value of monthly sales volume is computed as follows:
Units
(𝒂 × 𝒃)
6,000
5,400
4,050
3,600
2,250
21,300 Units
21,300 * P5 (CM per unit) = P 106,500
•
If Nitz’ Company decides to market Duhat Soap, the expected value of the monthly contribution
margin is?
Monthly Sales Volume
15,000 units
18,000 units
27,000 units
36,000 units
45,000 units
Probability
40%
30%
15%
10%
5%
100%
The expected value is P106,500.
Contribution Margin
P 75,000
P 90,000
P 135,000
P 180,000
P 225,000
Expected Value
(Pr * CM)
P30,000
27,000
20,250
18,000
11,250
P106,500
Problem 5
NGO, a charitable organization, was given a special permit by the city government to conduct games of
chance for fund-raising purposes. From this project, NGO expects to earn profit from admission fees and
sales of refreshments, and wants to merely break-even on the games of chance.
In on the games, a player draws one card from a standard deck of 52 cards. If a player draws any one of
the four “queens”, he wins P50; if he draws any one of the 13 “hearts”, he wins P20.
•
What is the probability that a “heart” would be drawn?
There is a 25% probability that a heart will be drawn from the deck. It is computed as follows:
13 ÷ 52 = 0.25 or 25%
• How much price should be charged per draw so that the total amount paid out for the winning draws
would equal to the total amount received from all draws?
Paid amount for four queens = 4 * P50 = P200
Paid amount for thirteen hearts = 13 * P20 = P460
Price to be charged = (460 + 200) ÷ 52 = P8.85
Problem 6
Leevoi Scan Company is developing its operating budget for 20xx. It has developed the following range of
sales forecast and associated probabilities for the year:
Sales Estimates
Probabilities
P48,000
10%
P68,000
50%
P80,000
40%
Leevoi Scan Company’s gross profit rate averages 20% of sales. What is the expected value of Leevoi Scan
Company’ budgeted cost of goods sold for 20xx?
Sales Estimates
Probability
P48,000
P68,000
P80,000
10%
50%
40%
100%
Expected Value
(Pr * Sale Estimates)
P4,800
34,000
32,000
P70,800
The Expected Value is P70,800.
Problem 7
Health Conscious, Inc. is planning to open a spa in the city. A market study conducted by an independent
market researcher shows the following estimates of the number of clients (and their probabilities) during
a period:
Number of Clients
Probabilities
0-40
10 %
41-80
40%
81-120
30%
121-160
20%
• What is the probability of having between 81-160 clients in the spa during the period?
30% + 20% = 50%
• What is the best estimate of the expected number of clients in the spa during the period?
Number of Clients
Probabilities
Expected Value (maximum
clients * Pr)
0-40
10 %
4
41-80
40%
32
81-120
30%
36
121-160
20%
32
100%
104
Problem 8
The local chapter of JPIA is planning to conduct a fund-raising project by selling roses on Valentine’s
Day. The roses, which can be purchased from a nearby supplier at P5 each, will be sold to the students
for P15 each. Any unsold roses at the end of the day will be discarded.
The estimated numbers of roses that can be sold on such day, as well as their probabilities, as follows:
•
Units of Roses
Probability
600
0.20
800
0.30
1,000
0.40
1,200
0.10
What is the estimated sales of roses (in units) using an expected value approach?
Event
(𝒂)
600
800
1,000
1,200
•
Probability
(𝒃)
0.20
0.30
0.40
0.10
1.0
Units
(𝒂 × 𝒃)
120
240
400
120
880 Units
The estimated sales of roses in units are 880 Units.
What is the estimated unit sales of roses on Valentine’s Day using an expected value approach?
Event
(𝒂)
600
800
1,000
1,200
Probability
(𝒃)
0.20
0.30
0.40
0.10
1.0
Units
(𝒂 × 𝒃)
120
240
400
120
880 Units
The estimated sales of roses in units are 880 Units.
•
What is the conditional profit of purchasing 1,000 units of roses but selling only 800 units?
Buy 1000 units of roses:
800 (800 * P15) – (200 * P5)
Less: Cost of Roses (5 * 800)
Conditional profit
Expected Value
P 11,000
4,000
7,000
MODULE 4-6 ACTIVITIES
Problem 1