Question

Tom Riley's life is changing dramatically. He and his wife recently bought a new home and are expecting their second child in a few months. These new responsibilities have prompted Tom to think about some serious issues, including life insurance. Ten years ago, Tom purchased an insurance policy that provides a death benefit of $40,000. This policy is paid for in full and will remain in force for the rest of Tom's life. Alternatively, Tom can surrender this policy and receive an immediate payoff of approximately $6,000 from the insurance company.

Ten years ago, the $40,000 death benefit provided by the insurance policy seemed more than adequate. However, Tom now feels that he needs more coverage to care for his wife and children adequately in the event of his untimely death. Tom is investigating a different kind of insurance that would provide a death benefit of $350,000 but also would require on-going annual payments to keep the coverage in force. He received the following estimates of the annual premiums for this new policy in each of the next 10 years:

In order to pay the premiums for this new policy, one alternative Tom is considering involves surrendering his existing policy and investing the $6,000 he would receive to generate the after-tax income needed to pay the premiums on his new policy. However, to see if this is possible, he wants to determine the minimum annual rate of return (which is compounded quarterly) he would have to earn on his investment to generate after-tax investment income that would cover the premium payments for the new policy. Tom likes the idea of keeping the $6,000 in case of an emergency and does not want to use it to pay premiums. Tom's marginal tax rate is 28%.

Year 1- $423, year 2- $457, year 3- $489, year 4- $516, year 5- $530, year 6- $558, year 7- $595, year 8 - $618, year 9- $660, year 10- $716

Note: The following are some of the formulae you will use to calculate:

(i) Annual investment income (based on quarterly return)

??????×1+?????? ??????44−??????Amount×(1+(Annual return)/4)^4-Amount

(ii) Afte- tax income

1−??? ????×??????(1-Tax rate)×Income

Answer 1

Solution: Basic understanding is that After Tax Income should cover the Premium Amount it means After Tax Income had to be minimum equal to Premium Amount.

Amount invested per year is 6000 surrender value amount only.

Annual Investment Income is calculated by understanding that given the marginal Tax Rate i.e. 28% if 72% is after Tax Income i.e. 423 in Year 1 then 100% should be Annual Investment Income=587.50 in Year 1.

Annual Investment amount should be Annual Investment i.e. 6000 plus Annual Investment Income i.e. 587.50 which yields 6587.50. This amount should be treated as Future Value.

Thus to calculate rate we have worked it based on quarterly compounding formula used for Future Value determination: FV=PV(Annual Investment)* (1+R/4)^4 here we know FV for Year 1 = 6587.50 PV for Year 1 = 6000 thus to know the Rate we can look into FVIF table and use interpolation technique to find out the exact rate. WE have used Excel RATE function which also gives the desired result. The Working Table is as under:-

Year	Premium	Amount Invested	Minimum Annual Rate (Quarterly)	Annual Investment Income	After Tax Income	Quarters in an Year	Annual Investment Amount
1	423	6000	2.36%	587.50	423	4	6587.50
2	457	6000	2.55%	634.72	457	4	6634.72
3	489	6000	2.72%	679.17	489	4	6679.17
4	516	6000	2.86%	716.67	516	4	6716.67
5	530	6000	2.94%	736.11	530	4	6736.11
6	558	6000	3.08%	775.00	558	4	6775.00
7	595	6000	3.28%	826.39	595	4	6826.39
8	618	6000	3.40%	858.33	618	4	6858.33
9	660	6000	3.62%	916.67	660	4	6916.67
10	716	6000	3.91%	994.44	716	4	6994.44

Note that the above table gives Quarterly Rates if Annual Rate of Return is required the Quarterly Rates should be multiplied by 4 for e.g. for Year 1 Annual Rate of Return should be =2.36*4= 9.45%