Question

Assume that a risk manager would like to purchase property insurance on a building. She is analyzing two insurance coverage bids. The bids are from comparable insurance companies, and the coverage amounts are the same. The premiums and deductibles, however, differ. Insurer A’s coverage requires an annual premium of $70,000 with a $3000 per-claim deductible.

Insurer B’s coverage requires an annual premium of $25,000 with a $9,000 per-claim deductible. The risk manager wonders whether the additional $55,000 in premiums is warranted to obtain the lower deductible. Using some of the loss forecasting methods just described, the risk manager predicts the following losses will occur:

Expected Number of Losses                                         Expected Size   of Losses

9                                                                                  $35000

5                                                                                  $7,000

3                                                                                  over $9,000

Answer 1

a) Expected number of losses = 9 and size $35,000

Total loss = 9 * 35,000 = $315,000

With insurer A total deductible would be 9 * 3,000 = 27,000

Total benefit received = 315,000 - 27,000 = $288,000

Risk reward ratio = 288,000/70,000 = 4.11

With insurer B total deductible would be 9 * 9,000 = $81,000

Total benefit received = 315,000 - 81,000 = $234,000

Risk reward ratio = 234000/25000 = 9.36

In this case Policy B gives better return on the premium. Hence insurer B is recommended.

b) Total loss = 5*7,000= $35,000

with insurer A total deductible would be 5 * 3,000 = $15,000

Total benefit received = 35,000 - 15,000 = $20,000

Risk reward ratio = 20000/70000 = .29

with insurer B total deductible would be 5 * 9,000 = $35,000

In this case nothing will be received as a claim from insurer B.

Hence in this scenario insurer A is recommended

c) Total loss 3*9,500(assumed over $9,000) = $28,500

with insurer A total deductible would be = 3 * 3000 =9,000

Total benefit received would be 28,500 - 9,000 = 19,500

Risk reward ratio = 19,500/70,000 = .28

with insurer B total deductible would be = 3 * 9,000 =27,000

Total benefit received would be 28,500 - 27,000 = 500

Risk reward ratio = 500/25000 =

.02

In this case also benefit derived from insurer A is more, hence it is recommended.