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