SOA Exam ALTAM Sample Question 34

Study guide: Exam ALTAM

XYZ Insurance Company sells two year term policies to lives age $x$ . The death benefit of 1,000,000 is payable at the end of the year of death. Premiums are payable annually.

The insurer holds reserves of 0 for this policy at time $t = 0$ and at time $t = 1$ .

The assumptions used for profit testing this policy are:

(i) Precontract underwriting expenses are 3,000 per policy.

(ii) Commissions are 20% of premium in year 1 and 5% of premiums each year thereafter. The extra 15% of premium commissions in the first year is treated as a pre-contract cash flow for profit testing purposes.

(iii) Maintenance expense is 100 per policy at the beginning of every year including the first year.

(iv) The earned interest rate is 7%.

(v) Mortality is $q_{x+t} = 0.05 + 0.05t$ for $t = 0, 1, 2$

(vi) At the end of the first year 10% of the surviving policyholders withdraw.

(vii) There are no cash values.

(viii) $\Pr_1 = 31{,}213$ .

XYZ uses a gross premium of 80,000 in its first profit test for this two year term policy.

Part a (1 point)

Determine $\Pr_0$ .

Part b (2 points)

Determine $\Pr_2$ .

Part c (1 point)

Determine the profit signature for this policy.

Part d (1 point)

The NPV for this policy using a risk discount rate of 20% is negative. Calculate the NPV to the nearest 1.

Part e (1 point)

Calculate the internal rate of return for this policy.

Part f (1 point)

Your boss questions how you can have a positive IRR but a negative NPV. Explain how this is possible.

Part g (2 points)

Calculate the NPV if the lapse rate increases to 15%.

Part h (1 point)

Policies where profits increase as the lapse rate increases are called lapse supported policies. Explain why such policies are risky to the insurance company.

(This is Question 2 from the Fall 2021 Form A Written Answer exam.)

Answer this question and see the worked solution