How To Calculate A Person'S Income From A Life Insurance

Transcription

1 How Much Life Insurance o You Need? Chris Robinson 1 and Vicoria Zaremba 2 Augus 14, 2012 Absrac We presen formal models of he differen mehods of esimaing a person s required life insurance coverage. The models make eviden he criical issues surrounding he esimaes: he family goals, cash flow esimaion, he discoun rae, inflaion, axes and he ime horizons assumed. We invesigaed 23 life insurance companies o see wha models hey and/or heir agens use o esimae life insurance needs of poenial cliens. In general, where we could deermine a model, i was closes o he expense model. The models and he explanaions are raher vague abou he deails and applicaion of hem could lead o widely-varying resuls. We found similar vagueness in he models ha appear in life insurance exbooks. This grea lack of aenion o how life insurance needs are calculaed suggess ha personal financial planning educaion and he insurance indusry should be working o improve boh eaching and pracice on his opic. 1 Corresponding auhor Chris Robinson Ph, CA,CFP is an associae professor of finance, School of Adminisraive Sudies, York Universiy, Torono, ON M3J 1P3. crobinso@yorku.ca 2 Vicoria Zaremba BAS is a financial planner in he Office of he Aorney General of Onario. All opinions in his paper are solely he responsibiliy of he auhors and do no reflec he opinion of he Governmen of Onario.

2 2 Simple Models for Esimaing Life Insurance Needs There are wo common mehods of esimaing he amoun of life insurance a person needs, assuming ha here will be surviving family members who are parially or wholly dependen upon he earnings of he insured person. The income mehod calculaes he presen value of all he fuure labour income of he insured, someimes wih a rule of humb adjusmen o allow for iems like income ax rae differences and saved expenses. The expense mehod calculaes he presen value of all he fuure expenses of he dependens ha he labour income was inended o suppor. In beween he income and expense mehods is he human live value or wha we call he ne human capial mehod, which we will argue is likely o serve family needs beer han eiher he income or he expense mehod. A differen approach values he insurance a he amoun needed o produce a specific beques. Le us esablish some noaion so ha we can express hese conceps more formally. P NI P NX P NH P CP P E E C 1 C k k nom R W 0 W n B Addiional insurance required using he income mehod Addiional insurance required using he expense mehod Addiional insurance required using he ne human capial mehod Addiional insurance required using he capial reenion mehod Exising insurance coverage Afer-ax real dollar labour income of he insured, year Real dollar consumpion of he family wih he insured person alive, year Real dollar consumpion of he family afer he insured s deah, year afer-ax real discoun rae afer-ax nominal discoun rae dae of reiremen dae of deah las surviving dependen, or end dae of dependence on he insured Iniial wealh available o fund fuure consumpion of he dependens Fuure value of a family s financial goal Beques o he nex generaion Then, under he income mehod, P NI R E ( 1 P Under he expense mehod, E P NX 1 C ( 1 PE W0 The family s consumpion afer he deah of he insured person needs some furher descripion. We are defining family as a surviving spouse for he res of his or her life, and he children or ohers only for as long as hey would normally remain dependen on he spouse. Once he children are expeced o sar earning heir own income and paying heir own expenses, hey are

3 3 no longer par of he family, bu have sared heir life as family unis hemselves. The expenses ha need o be insured no longer include heir expenses. The acual age of a child when independence happens can vary, and i migh be for life in he case of a disabled child. The wo expressions are quie differen, bu wha does he difference mean? If you insure your afer-ax income, including pension conribuions, hen you mus have a leas covered all he expeced expenses, because oherwise you would also no have been able o cover hem if you didn die before reiremen. We expec P NI P NX. We can say more han ha. In a world of cerainy, we would be able o calculae P NX precisely, and if he insured died, he insurance money would run ou exacly on he dae of deah of he second spouse. The difference beween he income and expense mehods of insurance is he beques o he nex generaion, or more precisely, he addiional beques o be added by he new life insurance. We can express his as: P NI P NX R E 1 ( 1 C (1 W0 In his form, as he difference beween he wo mehods of calculaing life insurance needed oday, he equaion gives he presen value of he beques. A he dae of deah, he beques will be: R 1 ( 1 C (1 W0 B E (1 In a more general sense, we can express he wealh, or perhaps he goal, of a family, a any ime n, as: W n W n n n 0 ( 1 ( E C )(1 If he specific goal is he beques o he nex generaion, hen in he absence of any insurance and wih neiher paren dying prior o reiremen, we ge: B W 0 ( 1 ( E C )(1 These wo expressions for B are no in general equal, hough hey can be in specific circumsances. They appear very similar, bu we have glossed over a number of imporan issues ha affec he value ha life insurance will have for differen families in differen circumsances. We have also reaed he problem only in a cerain world, bu life insurance is all abou risk managemen, and we canno ignore he uncerainy in hese esimaes. One of he bigges effecs is income ax. A common pracice wih he income mehod is o reduce he basic calculaion o 70 or 80% of he value, as a rule of humb adjusmen for ax and risk effecs.

4 4 However, here is a significan issue wih using he income mehod as he mehod of esimaing life insurance, and i is relaed o he family goals and a more precise consideraion of wha he human capial is worh and how much he second generaion can expec as he average beques. Ne Human Capial Model Le us sep back and consider he purpose of insurance. Wha is he family objecive in buying life insurance? One objecive is ofen said o be mainaining he family in he same life syle as if he insured did no die premaurely and coninued o conribue o he family resources. Le us reason by analogy and hink of house insurance. The usual pracice is o insure he enire value of he family home and eiher add a curren value rider or revise he insurance periodically o reflec changes in he replacemen value of he home. The purpose of he insurance is o replace he enire home wih he same qualiy home. This home insurance does no have he same objecive as he one we saed for life insurance. Recall from our previous discussion ha he family consiss of he dependens only as long as hey are dependen. Laer in he life cycle, his will be only he parens mos ofen, because he children will have moved on o form heir own families. If he objecive in insuring he house is only o mainain he sandard of living required for he dependen children and surviving spouse, i could be me more cheaply by insuring for an amoun equal o he presen value of he renal cos of an equivalen house unil he deah of he surviving spouse. Bu we do no hink of house insurance in ha way, we hink of i as replacing he enire value of wha he family already owns, he house and land freehold, wih he righ o sell i for marke value upon deah of he spouse, and leave he residual o he nex generaion. Or alernaively, o sell he house when he surviving spouse is older and needs he asse value o generae income. If we apply he logic of house insurance o life insurance, we wan o insure he enire value of he asse, which is he human capial. This seems o resolve he quesion beween he income and expense mehods in favour of he income mehod, because i is a way of measuring human capial. However, we recall also one maxim favoured by a colleague, which is ha you should never insure yourself so well ha he beneficiary is beer off wih you dead han alive! There are wo reasons why he pure income mehod will also fail o capure he value o he family of he human capial of he insured. Firs, recall ha we don value a business solely based on is revenue (which equals labour income in he human capial sense), bu raher on is ne income or cash flow. Human capial has o be mainained wih food, clohes, ec., and when he insured dies, hese expenses also disappear. The ne conribuion o he family is much less han he labour income. Second, human beings are no valuable solely for heir cash income, bu also for he value hey conribue o he family. A common misake in family insurance plans is o fail o insure he spouse who says home wih he children, ye if he or she dies, he survivor will have significan addiional expenses. Spouses working ouside he home also conribue labour o he household ha would oherwise have o be purchased. In words, he ne human capial mehod of esimaing insurance needs measures he ne conribuion o he family of he person s human capial by valuing he paid labour income, he

5 5 unpaid labour income and he savings in mainenance of he human capial. Huebner (1927) seems o be he firs o discuss insurance needs in his fashion, bu he does no provide a deailed model of how o calculae wha he calls human life values. He provides an example ha calculaes he presen value of he expeced fuure earnings of a person, minus he cos needed o care for he insured person if he had lived (Huebner, 1927, pp ). He discusses some of he issues around he esimaion, bu in fairly general erms. He does no deal wih he insured person s conribuions o household work, probably because he implicily assumes a household wih a working male and homemaking female. Our definiion of ne human capial is more inclusive. We can express he ne human capial value as: P NH R E ( 1 P E ( C C 1 )(1 Noe ha he summaion for he labour income runs unil he reiremen of he insured, bu he summaion of he ne saving or ne exra expenses required runs unil he deah of he spouse. The sign of each erm in he summaion will no necessarily be he same. If he insured is a homemaker spouse, he deah could increase expenses while he children are dependen and hen decrease hem afer he deparure of he children. We expec P NH P NX also, bu he relaionship o P NI depends on he circumsances. A homemaker who earns no ouside labour income will seem o require no life insurance, bu a proper calculaion of his or her conribuion o he family will show a posiive value. A family in which boh spouses work ouside he home and share he household duies or hire ohers o do hem will be one in which P NI P NH P NX. Specific Beques Models A beques o a spouse is simply he provision for expenses, or he capialisaion of ne human capial and should no be confused wih he models in his secion. The specific beques models are providing a beques o he nex generaion. We have already seen ha he simple ne income model provides an expeced beques o he nex generaion ha is equal wha he nex generaion would expec o receive if he insured person did no die premaurely. There are wo ypes of specific beques calculaions. In boh cases, he implici family goal is dynasic. The family wans o mainain specific asses, or perhaps jus a forune, forever. One such model is he capial reenion approach. The insurance allows he dependens o live upon he income from he family capial wihou liquidaing any of i, hus passing an esae o he nex generaion wih virual cerainy. The auhors who describe his mehod do no disinguish beween mainaining he real value of he esae and he nominal value. If we ake he goal as mainaining he real value, hen, P CP = C 1 /k - P E

6 6 Comparing his o he earlier equaions, we see ha he iniial wealh is no couned a all in he deerminaion of needed insurance, because ha is precisely wha he family wans o mainain. If insead he family believed ha he insured person would be able o increase he family forune maerially if he or she lived o he end of working life, hen here would be an addiional erm ha is he capialised value of expeced fuure excess income. If he goal is o mainain he nominal value, hen we subsiue k nom for k. The oher sor of specific beques allows he family o keep a specific asse ha he heirs would oherwise have o sell in order o pay income axes or deah duies. In Canada, asses generally can pass from one spouse o he oher a deah wihou immediae ax consequences, bu he capial gains ax will be exaced when he second spouse dies. If he asse is somehing ha has special value ouside is financial worh, like a family coage or a family business in which oher family members sill work, hen he value of he insurance is he esimae of he fuure income ax ha will be payable. Issues in he Esimaion Process We idenify six issues ha may maerially affec he esimae of life insurance needed: 1. The family s goal in buying he insurance; 2. The esimaion of fuure earnings and living expenses; 3. Time horizons ha are assumed, paricularly dae of deah of he beneficiary spouse and reiremen age of he insured; 4. Riskless or risky discoun rae; 5. Inflaion; and, 6. Income ax. These issues are iner-relaed, bu we will discuss hem separaely, while showing he connecions. Family Goal I follows from he characerisics of he hree models ha he mehod used o esimae life insurance needs depends upon he family goals. oes he family wish o leave a beques o he nex generaion, assuming i even has he means o do so? If he answer is no, hen he insured parens should use he expense mehod, since his will no produce as much of a beques o he nex generaion, if a all. If he family wishes o leave a beques, i could use he ne human capial mehod. This mehod will on average reproduce he beques ha he nex generaion could expec if neiher paren died early. The income mehod will produce an excessive beques on average, alhough a rule of humb adjusmen migh correc i by acciden.

7 7 Anoher mehod is possible, hough. If he goal is o leave a beques, he insured person could se a specific beques goal, and i could be less han he amoun ha he ne human capial mehod would produce. The mechanical calculaion is o use he expense mehod o deermine he needed insurance, and hen add as much insurance as is desired for he beques. This amoun would be in nominal dollars a he dae he insurance is purchased and so he real value of he beques would be lower. If he beques is inended o be specifically dynasic, hen he insurance is esimaed as he amoun needed o mainain whaever i is ha he family wans o be able o keep in perpeuiy. The imporan poin is ha a generic insurance model augh in a exbook or used by a life insurance agen is no suiable. The model should mach he family goal. Esimaing Cash Flows We don have a lo o conribue from he finance heory perspecive, because he challenges are all relaed o personal budgeing for long horizons. The financial planner can provide check liss and model budges, bu he clien has o do he hard work of filling in he numbers. The planner needs o remind he clien of some finance issues ha do arise. In pracice, insurance companies provide he ools, and an ineresing opic o pursue is how life agens use he ools and work wih heir cliens. Esimaing key daes In he equaions, wo daes sand ou: dae of reiremen and dae of deah of he surviving spouse. The dae of reiremen is a choice of he insured, bu he planner needs o remind him ha he average dae of reiremen is in many wesern counries, including Canada and he US, and he insurance esimaed using he income mehod may be affeced subsanially by he reiremen assumpion. The dae of deah of he second spouse is a major deerminan of he esimae under he expense mehod. Since insurance is inended o reduce risk, he planner should advise he cliens o use an age like 90 or 95, raher han he median age of deah ha will underlie he insurance company s calculaions. A he same ime, here is anoher way o hink abou his issue, following from Milevsky and Macqueen (2010). If he family does no wish o leave a beques, hen annuiising he insurance payoff, or assuming i will be annuiised, will provide a much higher payou guaraneed for life han invesing he principal can do, because of he moraliy credis. This aspec of esimaing he insurance needed deserves a paper on is own. Riskless or Risky iscoun Rae? Normal insurance pracice among many differen applicaions is o use a riskless rae. On he oher hand, one of he mos basic principles of finance is o discoun cash flows wih a rae ha is suiable o he risk involved. Fuure income sreams, dae of deah, ec. inroduce significan risk ino he esimaes.

8 8 We prefer o use a riskless rae in he belief ha he purpose of insurance is o reduce risk and hence he amoun of insurance should be enough o provide a secure fuure for he dependens. The effec of he rae choice is very large because of he long ime horizons. Use a riskless rae, and he amoun of insurance required is much larger, han ha generaed from a calculaion using a higher, risky rae. If he dependens inves he insurance proceeds in a balanced porfolio of equiy and deb for a long period of ime, hey are very likely o end up beer off financially han if he insured had survived. Whichever rae an insurance company or agen is using, he clien mus know wha i is and undersand he significance of he choice. Income Taxes Income axes are a complicaed issue in all financial planning models. In principle, life insurance needs esimaes ough o be afer-ax, wih he ax effecs buil in year by year in a spreadshee. The larges effec is he lower ax average ax rae ha a beneficiary will pay when suppor comes from a large insurance payou. The principal is no axable and so only he income on he principal will be axable each year. For example, he beneficiary could choose o annuiize par or all of he selemen. In Canada, his would be a prescribed annuiy wih a special forma for he ax calculaions o arificially spread he ineres income porion of he annuiy evenly over he life of he conrac. A homemaker spouse who received such an annuiy migh well pay no income ax a all on paymens as large as $80,000 p.a. However, an income of well over $100,000 p.a. would have been required when he insured spouse was living o generae ha amoun afer-ax. The income mehod deals wih his in an inadequae fashion by a rule of humb adjusmen. The expense and ne human capial mehods require deailed ax calculaions and he quesion is wheher companies and agens do hem in pracice. Inflaion The planner can allow for inflaion in wo ways: use real cash flows and real discoun raes or assume an inflaion rae and calculae everyhing in nominal values. Ho and Robinson (2005) generally advocae using real values because i is more compac, bu wih modern sofware i is more a maer of ase. The issues arise wih an inflaion rae assumpion, forecass of fuure changes in labour income and mixing real and nominal values. Insurance planning involves very long ime horizons and hence hese issues affec he calculaions considerably. Cliens are rarely well-educaed in how o incorporae inflaion ino heir planning. Iniial Observaions of Pracice

9 9 We invesigaed 23 life insurance companies o see wha we could learn abou heir pracical applicaion of life insurance needs models. Our findings are preliminary, bu poin he way clearly o furher research. - 9 ou of he 23, or 39% of he companies had an on-line calculaor o assis consumers in esimaing insurance needs; - 13 ou of he 23, or approx. 57% of he companies did no have a calculaor o assis consumers in esimaing insurance needs and one had a calculaor we were unable o use; - All of he companies ha had an on-line calculaor used he expense approach. - No companies used he ne human capial approach, alhough one company did have a Human Life Calculaor, bu he mehod of he calculaor was no he Human Capial approach. Some calculaors do incorporae pars of he ne human capial mehod, bu no compleely or consisenly. - Rules of humb, usually as a percenage of some measure of income muliplied by an arbirary facor, are used a leas some of he ime. - There is no consisency in he approach aken by differen companies. - We saw no evidence of an indusry sandard or norm. One company referred us o he Canada Life and Healh Insurance Indusry Associaion, which we followed up. Is calculaor is reasonable, bu no consisen wih any oher calculaor, nor is i demonsrably superior. - The variaion in he facors considered, issues raised, ec., on all he websies, wheher or no hey included a calculaor, defies easy summarizaion. - We can say ha here are clear errors and/or inadequacies in he way axes and inflaion are incorporaed ino he plans. Oher sources of income a deah and he savings and addiional coss associaed wih he loss of one paren are no compleely incorporaed in anyhing we saw. Some calculaors include employee benefis, some do no. We inerviewed six agens who sell life insurance o families in conjuncion wih he invesigaion of he websie calculaors. We had much he same observaions. The agens are more horough in wha hey consider, and mos of hem use company sofware o esimae he amoun of life insurance needed. The agens were more aware of he imporan facors we have discussed, including iems ha are par of he ne human capial model. Elger (2003) finds ha he calculaors available on he web a ha ime gave enormously varying resuls when used wih a sample case. Given he lengh of ime since ha research, i would be well worh repeaing. Our iniial examinaion of web calculaors suggess ha here would sill be huge variaions, and he imporance of various esimaes is never compleely explained. Wha o he Texbooks Say? Rejda (2010) oulines he human life approach and criiques i because i does no include all he facors ha we have oulined in he ne human capial approach. He does no explicily menion an income approach, hough of course he human life value as he explains i is closes o he income mehod. He explains he expense approach fairly horoughly, and clearly he prefers i. He also explains he capial reenion approach, noing ha i produces much higher esimaes.

10 10 Clark (2010) oulines a pure income approach, hough she calls i he human life value. She provides a deailed example of he expense approach and also he capial reenion approach. Like Rejda, she favours he expense approach, and calls he capial reenion approach overkill. Black and Skipper (2000) do no seem o discuss hese models explicily, bu he exended example hey provide (pg ) uses he expense approach. Ho and Robinson (2005) provide deailed examples of he income mehod wih a rule of humb adjusmen, he expense mehod and he ne human capial mehod. Conclusions 1. The income mehod of esimaing life insurance needs will only be accurae by luck, and will ofen oversae he requiremen. 2. The choice beween ne human capial and expense mehods depends on he family s goal for a beques o he nex generaion. 3. The expense mehod will give he lowes esimae of insurance needed of he hree mehods. 4. The difference beween he expense mehod and he oher wo mehods is he expeced beques o he nex generaion. 5. The explici beques mehods will give inflaed esimaes of insurance needs unless he family goal is dynasic reenion of specific asses or a family forune. 6. There is no consisen mehod used in pracice o esimae he amoun of life insurance an individual or family requires, and all he pracices we observed have good and bad aspecs. Where do we go from here? We need o use he formal models and our discussion of hem o beer inform a more in-deph series of inerviews and invesigaions of he models ha he companies and life insurance agens are using currenly. REFERENCES Black, Kenneh Jr. and Harold Skipper Jr. (2000), Life and Healh Insurance 13e, Prenice Hall. Clark, Coleen (2010), Risk Managemen and Insurance in Canada, Capus Press. Elger, John (2003), Calculaing Life Insurance Need: on Le he Tools Fool You, Journal of Financial Service Professional, (57), pg. 40. Ho, Kwok and Chris Robinson (2005), Personal Financial Planning 5e, Capus Press. Huebner, Solomon (1927), The Economics of Life Insurance,. Appleon and Company, New York.

11 11 Milevsky, Moshe and Alexandra MacQueen, (2010), Pensionize Your Nes Egg: How o Use Produc Allocaion o Creae A Guaraneed Income for Life, Wiley Canada. Rejda, George (2011), Principles of Risk Managemen and Insurance 11e, Prenice Hall.