Question

A Risk Manager gets bids from two insurers. The coverages and policy limits are the same for each one. The premiums and deductibles are different.

Company A: $40,000 Premium, $5,000 Deductible (per claim)

Company B: $55,000 Premium, $3,000 Deductible (per claims)

The Risk Manager knows the expected losses from what’s happened in the past:

Expected # of Losses                         Expected Size of Loss

8                                                         $3,000

4                                                         $5,000

3     over $5,000                                                            

Assume an interest rate of 4%.   Premiums are paid at the beginning of the year and losses at the end. Find the Present Value of each bid:

• Company A (4 points):
• Company B (4 points):
• Which bid will the Risk Manager choose?

Answer 1

Calculating the present value of each Bid

1. For Company A:

Premium= $40,000

Interest that compnay could have gained if it doesn't invest in insurance= Premium x interest%

= 40,000 x 4%

=1600

Now, in the table, to calculate number of losse

Expected Number	Size of the Loss	Total Money paid from the pocket (Deductibles)
8	$3000	$24000
4	$5000	$20000
3	Over $5000	$15000
Total		$59000

Therefore the present value of Risk insurance by Company A

= 40,000+1600+59000

=$100,600

1. For Company B:

Premium= $55,000

Interest that compnay could have gained if it doesn't invest in insurance= Premium x interest%

= 55,000 x 4%

=2200

Now, in the table, to calculate number of losse

Expected Number	Size of the Loss	Total Money paid from the pocket(Deductibles)
8	$3000	$24000
4	$5000	$12000
3	Over $5000	$9000
Total		$45000

Therefore the present value of Risk insurance by Company A

= 55,000+2200+45000

= $102,200

Since, the present value cost of proposal by Company A is less than that of Company B, the risk manager will choose Company A.