Life Insurance Products And Finance 1st Edition David B. Atkinson, James W. Dallas - Solutions

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Review how your company (or the life insurance company with which you are the most familiar) achieves its financial goals:1. What is the company’s “story” that explains to investors, rating agencies, employees, and agents how the company will succeed?2. Which financial management techniques
Repeat the previous exercise, but assume that Tier2RC = 20% of total required capital. Calculate Tier2ChargePct and explain the result, assuming the cost of debt is 5% and that debt is 20% of capital.
Repeat the previous exercise, but assume that Tier2RC = 25% of total required capital. Calculate Tier2ChargePct and explain the result.
Assume that ROE = 15%, WACC = 13%, Tier2IntRate = 5%, CorpExp = 0, and Tier2RC = 50% of total required capital. In other words, Tier1RC = Tier2RC = 50% of RC. Calculate Tier2ChargePct using Formula 16.9.2. Explain the result.
This exercise expands on Section 16.6.5.4 to develop a theoretical basis for the charge for Tier 2 required capital. Let Tier1RC = Total Tier 1 required capital Tier2RC = Total Tier 2 required capital ROE = The company’s desired return on equity WACC = The company’s weighted average cost of
Conduct a capital management review of your company (or the life insurance company with which-you are the most familiar).L According to insurance regulations, rating agencies, company management, and a comparison to similar companies, is the company over- or undercapitalized? You may get different
Conduct an earnings management review of your company or line of business (or the life insurance company or line of business with which you are the most familiar). What changes, strategies, or actions would you recommend to 1. Reduce product-related risk without reducing sales levels.2. Increase
Conduct a risk management review of your company or line of business(or the life insurance company or line of business with which you are the most familiar). Categorize each of the risks as high, moderate, low, or insufficient information. Has your company performed a review of its risks recently?
DOB, a large insurance organization, has decided to sell its individual life insurance operation, which is respected in the industry as a national leader in the brokerage term market, with the most efficient systems for underwriting and issuing new term policies. Discuss considerations for each of
Product X earns a meager 10% ROI, before reinsurance. However, you have negotiated a reinsurance agreement that will allow you to reinsure 90% of the business at an ROI of 9%. What ROI would you expect on product X after reinsurance?
Your company is growing rapidly, selling primarily one product. Sales have increased to a level that will require the company to raise additional capital before the end of the year. A reinsurer has approached you with a proposal to reinsure up to 90% of your company’s new business. Your analysis
Financial analysis shows that the company’s newest line of business seems to be off to a poor start, with the following profits (actually, losses) and new business written in its first three years of operation.Calendar Profit (Loss) Amount of Insurance Sold Year (in Millions) (in Billions)1 =.2
Using the following variables, develop quarterly formulas equivalent to Formulas 16.2.1 and 16.2.2:DistrEarn_tot(cyq) = Future distributable earnings in calendar quarter and year cyq, for the business being analyzed iQ = Quarterly hurdle rate at which future distributable earnings will be
Refer to Table 15.8.2. For each discount rate, compare the following pairs of results to the median (50th percentile): 25th and 75th, 15th and 85th, Oth and 100th. For each discount rate, would you say there is more upside potential or downside potential, compared to the median?How would this
Describe the various ways that assets can be repaid prematurely.
Of the major asset classes presented in Section 15.7.1, which generally have the following characteristics:. The highest liquidity. The lowest liquidity. The highest quality (or lowest default cost). The lowest quality (or highest default cost). The highest yield, excluding capital gains. The
If you create a lapse rate formula to reflect the differences between credited rates and market rates, what attributes should this formula have?
What problems can be caused by always setting the credited rate equal to the earned rate less the spread needed to achieve the priced-for profit margins?
Using Formulas 15.5.1 through 15.5.3, calculate the 90-day rates and the ten-year rates for the first two periods, using the random numbers below and assuming the beginning 90-day rate is 7.50% and the beginning ten-year rate is 9.25%. Also assume that VolFactor = 0.25, Correlation = 0.35, and n =
Using the slope movement probabilities in Example 15.5.3, the slope random numbers in Example 15.5.3, and the 10-year rates in Exercise 15.7, calculate the resulting 90-day rates for 1. Period 4, assuming Period 3’s slope was 0.90 2. Period 7, assuming Period 6’s slope was 1.05 3. Period 8,
Recalculate the pattern of ten-year rates from Example 15.5.3, using the same random numbers that were generated, but assuming the following distribution function:~0.50% = 0.25% 0.00% 0.25% 0.50%| fix) 0.05 0.20 0.50 0.20 0.05| Probability of Change in Level by
Using the binomial distribution, calculate a lapse distribution function and cumulative distribution function, up to and including y = 20, where y is the number of lapses. Use n = 500 less the number of deaths calculated in Exercise 15.5 and use qw = 0.01. Note: qw = 0.01 might be viewed as an
Use Table 15.4.3 to calculate the number of deaths assuming S =,0.7896/7.
Use Formula 15.4.1 to derive Formula 15.4.5 for fratio(x).
.Using the distribution function in Table 15.3.1, calculate the following:P(Z,) = —1.09545 P(Z,) = 1.46059 PC) = 2.92119.
Using Formula 15.3.1, calculate Z, for X, = 0,5, 10, 15, 20, 25, and 30.
Use the following random values and the table below to estimate how many points the St. Louis Rams will score on any given Sunday.Random values: 0.25345, 0.32895, 0.45919, and 0.87456.Points f (Points)7 0.04224 14 0.10542 21 0.12434 28 0.08453 35 0.10266 42 : 0.30894 49 O:15295 56 0.07894
Recalculate Example 14.4.1 twice, once with each of the following changes:1. Replace the first two liability cash flows with 35.00 and 30.00, rather than —35.00 and —30.00.2. Replace the last two liability cash flows with 85.00 and 100.00, rather than —85.00 and —100.00.Explain the results.
Repeat Exercise 14.10, assuming that, if Asset 3 is sold, then half of it or all of it must be sold. Assume that your company would prefer net capital gains to net capital losses.
Your company’s primary objective when selling assets to cover cash shortfalls is to minimize net capital gains and losses. The following three assets are available to cover cash outflows; assets can be partially or wholly sold:Asset 1: Book value = 1,000.00, Market value = 1,000.00 Asset 2: Book
Recalculate free cash flow in Exercise 14.8, assuming that one-half of investment income generated during the year is from coupon payments and the other half is from an increase in the book value of assets.
Repeat Exercise 14.7 using the values shown in the following table, from policy year 4 of the pricing example that runs from Chapter 4 through Chapter 11. The value shown for AssetCashFlow is equal to the investment income earned on the assets at the beginning of the year that back solvency
The values shown in the following table were extracted from policy year 1 of the pricing example that runs from Chapter 4 through Chapter 11.If you attempt to match some of the values shown below from the pricing example in Chapters 4 through 11, remember to include the reinsurance values in
In this chapter, the emphasis has been on gross yields, which ignore the cost of defaults and investment expenses. In practice, net yields, which are calculated net of the cost of defaults and investment expenses, are often used. In general, the net yield can be calculated as Net yield for the
Using the formulas developed in Exercises 14.2 through 14.4, calculate t and Q as of the following dates for business issued at the beginning of the second quarter of 1985:1. The end of the third quarter of 2001, and 2. The end of the first quarter of the year 2005.
Building on the definitions from Exercise 14.2 and the definition below, develop formulas to calculate policy year t and policy quarter Q from cyq and iyq. Express your answer in terms of duration, to the extent possible, and using INT and MOD:INT(x) = A function that rounds x down to the nearest
Building on the definitions from Exercise 14.2, develop formulas to calculate cyq from policy year t, policy quarter Q, and iyq.
Using the definitions below, we develop a method of keeping track of calendar years and quarters assuming that time is measured by the number of calendar quarters since the beginning of calendar year 0. We pretend there was a calendar year A.D. 0 immediately before the year A.D. 1. In fact, the
Fill in the missing information below, assuming annual payment of premiums, no policy fees, and DB_pu = 1,000 for all three pricing cells for Year 3.c Prem_pu(c) NumUnits(c) SurvFactor(c,2) qd(c, 3)Issue Age 25 2.00 45,000.00 0.89 0.00115 Issue Age 45 18.00 2 0.91 0.00450 Issue Age 65 55.00
The following projection of account values shown in Table 13.13.2 assumed that the underlying investments earn a rate of 10% each year and credit interest at a spread of 1.75%. They also assume an annual lapse rate of 10% for all years until the last, when the lapse rate equals 100%.The initial DAC
As mentioned in the chapter, it is often necessary to use stochastic modeling to price aGMDB feature. Assume you are pricing a variable annuity that has a GMDB feature that pays upon death the premium accumulated at 5% interest, if that amount is greater than the account value.Given the mortality
Modify Formula 13.5.5 to reflect semimonthly income benefits instead of monthly income benefits. Assume that IncomeBen_pu(t, Q) is now 13.13. Exercises defined as the semimonthly income benefit per unit in force. How would IncomeBen(t, Q) be split between middle and end of the quarter cash flows in
Calculate AnnuitizationBen(t, Q) and its ratio to earnings, given the following: AV_pu(t, Q) = 10,000, AnnuitizationCost(t) = —0.05(this means the company makes a 5% profit on annuitization), Annuitizations(t, Q) = 0.01, Assets(t, Q) = 5,000, and ROA(t, Q) = 0.20%. What portion of earnings do
Rather than ignore death benefits for certain and life annuities, you will develop a formula for income annuity death benefits that reflects the commutation of the remaining certain period payments at the date of death. Use the following notation: |CPRemaining(t, Q) = Average number of certain
An annuity with an MVA guarantees 5.25% interest for the next three years. The three-year interest rate available on new deposits is 7.10%.The company uses an additional margin in its MVA formula equal to 0.35%. Calculate the MVA using Formula 13.2.2.
An equity indexed annuity product has a participation rate of 75% of the S&P 500 index, a cap of 18%, and a guaranteed minimum interest rate, or floor, of 3%. How much does the S&P 500 index have to rise for the cap or floor to come into play?
A variable income annuity has an AIR of 3% and experiences the following net investment returns for its first five years: 10%, 15%, 5%,—5%, and 10%. If the initial monthly income is 3,000 and it is recalculated once a year, determine the monthly incomes for years 2 through 6.
A husband age 60 and a wife age 58 purchase a five-year deferred, tenyear certain and life, JLS income annuity, with 50% payable to the survivor upon the first death. The income benefit payable while both are alive is 5,000 per month.a. Explain the resulting monthly income pattern.b. Explain how
Review Formulas 6.4.5 for mean reserves and 6.4.7 for interpolated reserves to observe that the differences between these formulas amount to mean reserves using factors of “'2” and “'A” in place of the interpolation factors “(1 — Frac)” and “Frac.”Assume* 5% of your company’s
Add together the corresponding answers from Exercises 12.8 and 12.9 and compare the results to the answers from Exercise 6.9. What relationship do you observe? How do you explain this?12.15 Answers
Using the information given for Exercise 12.8, calculate the deferred premium asset as of the end of the third and ninth policy months for policy year t, assuming premiums are paid (a) semiannually and (b)quarterly.
Given the following information, calculate the nonannual interpolated reserves as of the end of the third and ninth policy months for policy year t, assuming premiums are paid (a) semiannually and (b) quarterly:Res_pu(t —1) = 10.00 NetPrem_pu(t) = 6.00 Exp_puPrem(t) = 0.60 Exp_puBeg(t) = 0.40
Develop or describe formulas for dynamic products that redistribute monthly premiums, commissions, surrender benefits, and partial withdrawals between beginning-, middle-, and end-of-the-quarter cash flows, as suggested at the end of Section 12.6.1. Use M1, M2, and M3 to represent the three months
Change the target premium per unit in Example 12.5.1 from 7.50 to 4.50 and describe the resulting values of HighCommPrem and LowCommPrem, keeping all other assumptions the same.
Example 12.4.5 illustrates the unearned premium factors as of the end of each quarter. These factors are applied to annualized premiums to determine the premium refunded on lapses. Develop unearned premium factors for lapses that occur at the middle of policy months 2 and 5, that is, ' and “%of
Example 12.4.4 illustrates modal return of premium factors assuming premiums paid beyond the month of death are refunded. These factors are applied to annualized premiums to determine the premium refunded at death. Develop or describe a similar table assuming premiums paid beyond the date of death
Modify Formula 12.4.7 to reflect monthly calculations for dynamic products.
Assume* An annual premium rate (Prem_pu(t)) equal to 10.00* An average size of 100.0* A modal distribution of 50%, 10%, 15%, and 25% for modes 1 through 4* The modal factors and modal policy fees shown in Examples 12.4.1 and 12.4.2, and* A survivorship factor of 1.00 Calculate 1. Modal premiums per
Formulas 12.3.2, 12.3.4, 12.3.6, 12.3.8, 12.3.9, and 12.3.10 can be converted from quarterly to their monthly. equivalents merely by replacing Q with M. Develop formulas that are the monthly equivalents to*Formulas 12:3:17°12.3.3,1235:5,and 12.3%
Now let us apply the formulas developed in the previous exercise.Repeat Exercises 11.4 and 11.5 to recalculate distributable earnings and ROIs, reflecting capital contributions made at the beginning of the year.What effect did this change have on the ROIs? Why?Distributable earnings can be
Capital contributions are mainly required to provide the initial required capital and cover the strain of writing new business. Capital contributions are most common in the first policy year but sometimes occur after the first policy year as well.We calculate distributable earnings as of the end of
Review the patterns for solvency earnings, distributable earnings, and stockholder earnings from Exercises 11.4 and 11.6 and compare them to the pattern for premiums. Other than the first-year strain associated with solvency and distributable earnings, we expect earnings to roughly follow the
Using Table 11.8.1 and the results of Exercise 11.6, calculate stockholder equity and year-by-year return on equity, based on average equity.
Calculate pre-tax and after-tax stockholder earnings, using Table 11.8.1 and a tax rate of 45%.
Using Table 11.8.1, calculate simple ROI and generalized ROI. For generalized ROI, negative values should be discounted at the after-tax interest rate. The pre-tax interest rate is 7.00%. Also, calculate embedded value assuming a 15% hurdle rate.
Assuming no timing or permanent differences between solvency and tax reserves, calculate Distributable Earnings (DistrEarn), using Table 11.8.1 and a tax rate of 45%.
Demonstrate that one of the possible ROIs for the following stream of profits is —200%.™ Profit(t)aewSAn|uan Total 0 |538 Use Table 11.8.1 with Exercises 11.4—11.8. It will be easiest to solve the exercises if you type the columns into an electronic spreadsheet.539 Life Insurance Products and
Given the following data, calculate investment income on assets backing required capital, the tax on it, after-tax solvency earnings, and distributable earnings.The assets backing required capital earn a pre-tax interest rate of 6%. A tax rate of 30% applies to investment income earned on required
Calculate the weighted-average cost of capital for a company that wishes to maintain a capital structure of 85% equity and 15% debt. Assume that stockholders demand a 15% after-tax ROE. The pre-tax cost of debt is 8%. The company pays a tax rate of 40%.
Referring to Table 10.8.1, assume Company 1 and Company 2 enter into two different reinsurance transactions:Company | transfers 40 million of Cl risk to Company 2.At the same time, Company 2 transfers 6 million of C2 risk to Company 1.Which company’s risk-based capital position is improved, after
If acompany has 1 billion of required capital and an asset default factor of 1%, how much of the company’s required capital is related to the asset default risk on required capital, the so-called required capital on required capital?
A company has 100 million of universal life account value on its books.This business is supported by total capital of 5,000,000, on which the company is currently earning 15%, after tax. These universal life policies currently have no surrender charges. If the company offers an exchange program to
Using the mortality risk factors in Section 10.3.1, calculate the average mortality risk factor for a company with 4 billion of net amount at risk.If the company expects to double its net amount at risk over the next ten years, how will this impact its average mortality risk factor?
Building on the previous exercise, assume the company reinsures 50%of its business, with the following results: 50% of the company’s required capital is shifted to the reinsurer, the reinsurer provides allowances that cover 60% of new business strain, and the reinsurer retains 50% of future
a. If a company earns an interest rate of 10% on all of its assets and a tax rate of 40% applies to investment income, what is the rate of return earned on assets backing required capital? (Note: Rates of return are always after tax.)b. If the rate of return on capital other than required capital
The formulas in this chapter assume taxes are payable at the end of the policy year. Develop revised formulas for InvIncome(t) (from Chapter 8) that reflect taxes payable at the middle of the policy year, in terms of the following notation:TaxRate(t) = The tax rate that applies to a small change in
As explained at the end of Section 9.6, deferred taxes are best handled by calculating the deferred tax liability directly (as in Formula 9.6.6)and then calculating the provision for deferred taxes as the change in deferred tax liability. Using this approach in combination with Examples 9.6.1 and
If a company is taxed on total investment income less total expenses, what impact will this have on how the company is run and the types of products sold?
Assuming the nondeductible percentage of each year’s expenses is NonDedExpPct(t), expand Formula 9.2.6 for permanent differences to reflect nondeductible expenses.
If your company has cumulative tax losses that are in danger of expiring in a few years, what impact should this have on the design of the products your company sells?
If a country enacted new legislation that significantly decreased the tax rate on life insurance company earnings in five years, what impact would you expect this to have on life insurance product design?
Explain what is meant by “timing differences” and “permanent differences.” Which type of difference has a greater impact on taxes over the life of a policy? Which is more important?
In Exercise 8.6, which interest rate would apply to insurance cash flows occurring during year f?
In Exercise 8.6, it is theoretically possible for InvAssets(t, t) to be negative. How could this happen? What would it mean? How could a negative result be avoided?
In any given year, the funds that are available for investment at the new money rate come from several sources:¢ Insurance cash flows¢ Investment income cash flows (such as bond coupons and mortgage payments)* Capital cash flows (that is, capital contributions or distributed earnings), and*
Suppose a reinsurance agreement reduces solvency reserves and policy loans by a percentage equal to ReinsPct. How would Formulas 8.3.2 and 8.3.3 be adjusted to reflect this reinsurance agreement?
Suppose a Universal Life policy is expected to be supported by invested assets that earn 7% interest (net of investment expenses and asset defaults), with a credited interest rate 1.5% below the earned rate.Suppose further that (1) policy loans are charged an interest rate of only 4%, (2) annual
In Table 8.1.1, what impact would a doubling of required capital have on excess capital, apparent earnings, and true earnings?
Let AssetShare(t) = Asset share per unit in force at the end of policy year t.Develop a formula for AssetShare(t) in terms of CumCashFlow(t)and SurvFactor(t).
Let CumCashFlow(t) = Cumulative cash flows as of the end of policy year t, per unit issued.Develop a formula for CumCashFlow(t) based on CumCashFlow(t — 1), CashFlowBeg(t), CashFlowMid(tf), _ CashFlowEnd(t), InvIntRate(t), and InvIntRateMid(t). Ignore taxes.
Modified coinsurance (“modco”’) treaties require the reinsurer to pay the company a modified coinsurance adjustment calculated as (a) less(b), where (a) is the increase in the modco reserve, and (b) is modco interest, equal to the interest earned by the company on the modco reserve.To keep
Some reinsurance treaties provide for an experience refund that causes the reinsurer to return a portion of its profits if experience is favorable.Typically, the reinsurer is allowed to accumulate past losses and net them against any current profits when calculating an experience refund.For a YRT
Assume that expense allowances are not a percentage of premiums but instead are equal to an amount per unit in force plus an amount per policy in force. Develop a formula for expense allowances to replace Formula 7.5.9. Use the following additional notation:ExpAllow_pu(t) = Expense allowance per
Building on Exercise 7.2, assume that the treaty states that the reinsurer must pay an amount to the company equal to the reserve credit on the portion of the reinsurance recaptured at the end of the policy year.Assume the reserve credit is equal to the gross reserves times the percentage currently
Building on Exercise 7.1, explain how to revise formulas for coinsurance premiums, policy benefits, and reserve credits using the stand-alone method (Formulas 7.5.1 through 7.5.8 and 7.5.19).
Develop revised formulas for YRT premiums and death benefits(Formulas 7.4.4, 7.4.5, and 7.4.6) to reflect the impact of recapture.Assume that, except for the impact of recapture, a constant percentage equal to ReinsPct is reinsured. Use the following additional notation:RecapPct(t) = The percentage
Given the following information and assuming annual premiums, calculate the initial reserve, mean reserve, and interpolated reserves as of the end of the third and ninth policy months for policy year t:Res_pu(t —1) = 10.00 NetPrem_pu(t) = 6.00 Exp_puPrem(t) = 0.60 Exp_puBeg(t) = 0.40 Res_pu(t) =
For a ten-year level premium policy with acquisition costs of $5 per unit issued, calculate the acquisition cost net premium and deferred acquisition cost per unit in force at the end of each policy year using the following assumptions:a. 100% survivorship and no discounting (that is, p(t) = 1 and
Given the same realistic reserve assumptions, does the realistic net premium method or the gross premium method generally produces larger reserves? Why?
How would you change the Fackler reserve accumulation formula to reflect lapse rates and surrender benefits payable at the end of the policy year?

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Life Insurance Products And Finance 1st Edition David B. Atkinson, James W. Dallas - Solutions

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