Exercises: Financial risk management and insurance

Explain with a simple example how insurance works: many people pay a small amount (premium) so that if something major happens to one person (a claim), the insurer covers it. Why is this profitable for the insurer? What does the policyholder gain even if nothing ever happens to them?

Define premium, policy, claim, and coverage in your own words, and apply them to this case: Bea pays $\$30$ per year to insure her bike against theft; it gets stolen and the insurer pays her $\$250$ because the policy covered theft away from home.

The figure shows a risk matrix for the school flea market: each risk is positioned according to its likelihood of occurring and the damage it would cause. Three risks are already placed, and you must locate a fourth one, marked with a question mark.

1. a) Explain why "fire in the venue" is in the upper left and "staining a poster" is in the lower left.
2. b) Place the question mark: "losing the cash box with the day's proceeds" is unlikely but would ruin the project. Which two risks deserve a protection plan before the others? Justify your answer.

Explain the difference between an unforeseen event (you didn't know it could happen) and a risk (you knew it could happen, but not when). Classify: it raining on the day of the April fair, a member falling ill, smoke coming out of the school's electrical panel. Which one could be best prepared for?

Define the likelihood and the harm (impact) of a risk with two examples from the end-of-year class trip: one with high likelihood and little harm, and one with low likelihood and great harm. Explain why the second deserves more attention even though it is rare.

Match each insurance concept with its definition: premium, policy, claim, deductible. Definitions: (1) the contract signed with the insurer; (2) what you pay regularly to be covered; (3) the part of the damage you pay yourself before the insurer pays; (4) the covered accident or damage that occurs. Give an example with the insurance for a bike.

Name the four strategies when facing a risk (avoid, reduce, transfer, accept) and give an example of each applied to setting up a food stand at the fair (not using a deep fryer, food safety training, event insurance, a $\$20$ cushion for unexpected expenses).

Explain what a plan B is and how it differs from insurance. Take the example of the school's outdoor concert: describe a reasonable plan B for rain and explain why having it written down before the event avoids making wild decisions on the day itself.

List four risks for a crepe stand at the fair (for example: rain, running out of an ingredient, nobody coming, someone burning themselves on the griddle). Order them by mentally multiplying likelihood by impact (high/medium/low for both), and explain which one you would address first and how.

Insuring your cell phone worth $\$240$ costs $\$24$ per year. According to your track record, the likelihood of breaking it in a year is once every $5$ years.

1. a) Calculate how much you pay in premiums over $5$ years and compare it with the cost of replacing the phone once.
2. b) Based on those figures, is insurance worth it in your case? What else should you consider besides the calculation (deductible, what is covered, whether you could pay for a new phone out of pocket)?

There are four strategies when dealing with a risk: avoid it (do not carry out the activity), reduce it (make it safer), transfer it (pay for insurance), or accept it (keep a financial buffer just in case). Classify these decisions for a summer camp and justify your choices: (a) cancelling a canyoning trip due to a storm warning; (b) taking out accident insurance for the camp; (c) providing helmets and instructors for the zip line; (d) setting aside $\$200$ in case equipment gets broken.

The school's sports tournament involves these risks: injuries (medium likelihood, high harm), teams dropping out (medium, medium), losing balls (high, low) and vandalism in the bleachers (low, high).

1. a) Draw in words the likelihood × harm matrix and order the four risks by priority of attention.
2. b) Assign each one a concrete strategy (avoid, reduce, transfer or accept) and justify the one for the highest-priority risk.

You can do it on paper and send a photo with your answer.

Insuring the concert's sound equipment ($\$800$) costs $\$45$ for the day of the event. The likelihood of something breaking, according to previous years, is $1$ in every $10$ events, with an average damage of $\$300$.

1. a) Calculate the expected loss per event (likelihood times damage) and compare it with the price of the insurance.
2. b) With that calculation in front of you, decide whether you would buy the insurance and explain which non-numerical argument could tip your decision (peace of mind, who is responsible if something happens).

Your cooperative keeps $\$350$ in cash in a classroom drawer. Identify three risks of that practice (theft, loss, the temptation to "borrow" from it) and design one risk-reduction measure for each (a small safe, a log signed by two people, a weekly deposit at the bank). Explain why these measures also protect the treasurer.

The field trip costs $\$150$ per person and the organization offers a cancellation insurance of $\$12$ that refunds the money if you fall ill before the trip. In your class of $35$, statistically one or two fall ill each year.

1. a) Calculate how much the whole class would pay for the insurance and how much the class 'loses' if nobody falls ill.
2. b) Analyze who should take it out anyway (everyone, or only those who can't afford to lose $\$150$?) and what this teaches us about what insurance is for.

Read the fine print of this fictional school policy: it covers damage to sports equipment up to $\$500$ a year, a deductible of $\$40$ per claim, a maximum of $2$ claims a year, and it does not cover losses or thefts without violence. The basketball club loses $\$60$ worth of balls a year and once had the first-aid kit ($\$70$) stolen.

1. a) Explain what the policy would and would not have covered last year and calculate how much the insurer would have paid for the first-aid kit.
2. b) Write three questions you must ask before signing a policy like this and explain what trap there is in looking only at the premium.

The school market is held outdoors. A Plan B with a covered tent costs $\$30$ out of the total budget of $\$200$. If it rains without a tent, lost sales are estimated at $\$150$; the likelihood of rain that month is $1$ in $4$.

1. a) Calculate the expected loss due to rain (likelihood multiplied by impact) and compare it with the cost of the tent.
2. b) Decide whether you would go ahead with Plan B and justify your decision using the numbers and at least one non-numerical argument.

Insurance for a cell phone worth $\$350$ costs $\$2.50$ per month and has a deductible of $\$45$ per claim. Its policy only covers one repair per year and expressly excludes theft (theft without violence or force). The usual repair for a broken screen costs $\$75$.

1. a) An advertisement states: "For only $\$2.50$ a month, stop worrying and save $\$75$ if your screen breaks." Prove mathematically why this claim is false, calculating the actual total outlay for the first year with insurance versus paying for the repair directly yourself.
2. b) Propose an alternative: if that monthly money is put into an emergency savings fund (self-insurance), determine in how many months the full cost of the repair is covered and justify economically whether it is worth taking out the policy.

Design a risk management plan for the end-of-year school trip ($\$150$ per person, $40$ students): identify the four main risks (illness, missing the bus, damage to the hostel, students running out of money), assign likelihood and impact to each, choose a strategy (avoid, reduce, transfer, accept), and calculate how much of a buffer per person you would propose and how it would be refunded if unused.

The town festival hires an inflatable bounce house for children every year. This year the liability insurance goes up from $\$60$ to $\$140$ after an accident in another town. The festival's total budget is $\$3,000$.

1. a) Set out the city council's options (paying the insurance, finding another activity, installing it without insurance) and analyze what risk it takes on with each one and who pays if something happens.
2. b) Decide and defend your decision by explaining why liability insurance protects something more than money, and calculate what percentage of the budget taking it out represents.

Your school cooperative is going to make and sell jars of artisanal jam at the local fair, with a budget of $\$120$. A classmate proposes: "To save money, let's not buy sterilization thermometers or spend on printing ingredients and allergens on labels; if someone feels sick or has an allergy, we give them back the $\$3$ for the jar and problem solved."

1. a) Rebut your classmate's proposal using a risk management matrix (likelihood vs. impact): justify why a risk with low likelihood but extreme consequences cannot be managed simply by assuming it as just another financial cost.
2. b) Design the management plan for the project's three key risks: health (food poisoning or allergy), operational (team members getting burns while cooking), and commercial (being left with unsold stock). Assign a specific technical measure to each one and classify it into one of these strategies: avoid, reduce, or transfer.

Two members of a youth cooperative are debating insurance. One states: "Insuring everything is a waste of money; it is cheaper to handle unforeseen events when they happen." The other argues: "Going without insurance in any activity is irresponsible; you have to cover everything."

1. a) Refute both extremes by applying the economic principle of risk management based on financial capacity: describe a situation where taking out insurance is a financial inefficiency and another where not taking it out would mean personal or project bankruptcy.
2. b) The cooperative has a reserve fund of $\$400$ and must manage three risks: 1) Breakage of a $\$15$ calculator; 2) Liability compensation of up to $\$60,000$ for third-party damages in a workshop (insurance for $\$45$); 3) Loss of $\$250$ in sales due to rain at a street market (weather insurance for $\$80$). Determine and justify which strategy should be applied to each risk (assume, transfer, or mitigate).

The neighborhood market is held outdoors in December. Data: if it rains, sales are estimated to fall from $\$900$ to $\$300$; the likelihood of rain that day is $30\ \%$; renting a tent costs $\$120$ and would save half of the fall.

1. a) Calculate the expected loss without the tent and the expected loss with it, and decide with the numbers whether renting it is worth it.
2. b) Add two non-numerical arguments for or against the tent (the market's image, people staying if it is covered) and reaffirm or correct your decision.

Design the complete risk management plan for the school's charity concert: a table with five risks (likelihood, harm, strategy, concrete measure, owner), the calculation of the money cushion you would propose (how much and where it comes from) and the decision rule for the big day: which conditions would cancel the event and who has the final say. Defend why writing it before the event is half the work.