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Lecture 4

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Mathematics Electives
David Kohler

MTHEL131 week 4 Oct. 2, 2013 For life insurance there is always two questions: 1. How much coverage is necessary? • Funeral costs (ex: $1500) • Debt (ex: $80, 000) • Mortgage (ex: $200, 000) • Emergency fund  3 months of the new target income (ex: $15, 000) • Education fund (ex: $80, 000) o Total Immediate coverage needed (ex: $390, 000) • Shortage per month for 15 years x factor o The factor produces the amount of total money needed for 15 years (including inflation) that would be provided at death o This is the ongoing income (ex: $360, 000) and will normally be invested o Risk is that the investment could do very well (money left over after 15 years) or poorly (money runs out before 15 years) • Total for 15 years is $750, 000 If the customer is not comfortable with this risk, they may choose to purchase an annuity contract instead. This contract would give them a guarantee from the insurance company to pay the shortage every month (ex: 2500). Now the insurance company is taking on the risk of the investment instead of the policy owner. If the customer has external sources of insurance (ex: group insurance from en employer), the amount is deducted off of the total required coverage. The entire amount will be provided to the beneficiary and it is up to them to spread it out responsibly according to the plan. 2. What type of coverage is necessary? • Term or permanent Old Equitable What are the three variables considered in the pricing of policies? (Establishing the premium) 1. Mortality (age, life expectancy) 2. Investment returns (on the premiums) 3. Expenses of the company (cost of business) *Buffer (in case they don’t have enough money) Insurance companies take the premiums, and put the money into a reserve. The required amount of money put into the reserve to ensure the payment of claims is calculated given the ages of the policy owners and when they’re estimated to die (usually the amount is overestimated to be safe). When the calculation was done 40 years after the opening of the company, the Old Equitable’s reserve had an excess of $1M. How did this excess occur? Possibilities: MTHEL131 week 4 Oct. 2, 2013 • The old equitable had over charged for the premiums to keep themselves safe. • Investments were more successful than predicted • Not as many people died as predicted • The expenses were lower than predicted • Because of the experience the company had with mortality, investment returns and expenses • Today the surplus check for EXPERIENCE DIVIDENDS is done annually Experience Dividends: How to give this back to the policy owners: 1. Lower the premiums for an extended amount of time. PRO (Premium Reduction Option) 2. Cash option 3. Accumulation option (on deposit) a little bit would be deposited to a person every year ? 4. PUA (Paid Up Additions) additional insurance with no premium payment to guarantee coverage (most common) Why is it that the Experience Dividends of the company are paid back to the policy holders? • Owners of a mutual company are the policy holders • Participating (PAR) policy- PAR policy holders participate in any experience dividend distributed • Non-par policies: policy holders do not participate in the distribution of any surplus Experience dividend is never guaranteed. Ex: Accumulated option takes in portion of surplus every year. Policy owners can withdraw from that account at any time. If untouched, this extra coverage will grow with interest. Types of Companies: • Mutual company (non-stock company) o The owners are the participating policy holders. o No take-over possible - advantage o Can’t sell stocks to raise funds - disadvantage • Stock company o Another company could come and take-over with a bidding war (own 51% of the shares) – disadvantage o Can raise funds (for expansion) by issuing more shares (people will buy because they expect a high investment return) – advantage Raise capital ? Demutualization MTHEL131 week 4 Oct. 2, 2013 Four major insurance companies: (all mutual) 1. Mutual (first mutual company in Canada) 2. Canada 3. Sun 4. Manulife Were able to compete with banks, envisioned expansion. All mutual companies owned by the policy owners. Want to become stock companies. T demutualize, they first, valued the company (ie. Assets) Mutual life was worth $2B, with 1M par policy owners When the mutual company becomes a stock company, the par policy owners will become sharehold
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