VALUE OF INSURANCE

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VALUE OF INSURANCE
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CALCULATING THE VALUE OF INSURANCE

• Houstons theory compares the financial position
  of an organisation when it buys insurance with
  the financial position of a firm when it does not
  buy insurance
• If the fiirm net worth of a firm is better
  following the purchase of insurance then the
  organisation should not self finance

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INSURANCE PURCHASING DECISION

• Buy if FPb gt FPnb
• FPb Financial position if insurance bought
• FPnb Financial position if insurance not bought
• FPb NW - P r(NW - P)
• NW Initial net worth invested in business
• P Premium paid for insurance
• r return available to the firm on funds
  invested in the business or in non-liquid
  securities

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DONT BUY INSURANCE

• FPnb NW - P/2 r(NW - P/2 - F) iF
• where
• P/2 Average insured loss per year
• F Average fund
• i Interest on reserve
• Thus if FPb gt FPnb buy insurance

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VALUE OF INSURANCE

• The value of insurance can be derived from
  previous equations
• V F(r - i) - P(0.5 0.5r)
• Difference between i and r important as the
  greater the difference the greater the value of
  insurance
• Insurance frees reserves for internal investment

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EXAMPLE

• V F(r - i) - P(0.5 0.5r)
• F 100,000
• r 0.16
• i 0.10
• P 2000
• V 100,000(.16 - .10) - 2,000(.5 (.5 .16))
• 6,000 - 1160
• 4840
• Value of insurance 4840

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RELATIONSHIP BETWEEN I AND R

• As difference between r and i narrows
  insurance becomes less valuable.
• r rate of investment earned by the business
• i interest rate earned on investment
• Example
• r 0.11 F 100,000
• i 0.10 P 2,000
  
• V F(r - i) - P(0.5 0.5r)
• V 100,000 (0.11 - 0.10) - 2,000(.5 .50.11)
• 1000 - 1110
• -110
• This means insurance should not be bought

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DEDUCTIBLE

• Houstons model determines optimum deductible
  size
• FPd NW - Pd - Kd r(NW - Pd - Kd - F2) iF2
• FPd Financial position of firm purchasing
  deductible
• Pd Premium charged
• D Deductible
• Kd Losses below deductible
• F2 Reserve fund
• Calculated financial positions of FPd and FPb

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EXAMPLE

• Assume losses below deductible are 0.05 of
  deductible deductible 15,000 Premium
  500
• The answer depends on the size of the claims
  below the deductible and the reserve.

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EXAMPLE

• FPd NW - Pd - Kd r(NW - Pd - Kd - F2) iF2
• FPd 1000000 - 500 - .05(15000) .161000000 -
  500 - .05 (15000) - 15000 .1(15000)
• 998750 1574001500
• 1,157,650.
• Using these figures full coverage value is
  1,157,680.
• Compare deductible value with full coverage value
  of 1157680.
• 1157680 gt 1157650 thus buy insurance.

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questions?