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      In my opinion there is no reason to differentiate between the first premium or premiums and later premiums. Such a distinction is not based on any principle. Why should the policy belong to the party who paid the first premium, without which there would have been no policy, rather than to the party who paid the last premium, without which it would normally have lapsed? Moreover, any such distinction would lead to the most capricious results. If only four annual premiums are paid, why should it matter whether A paid the first two premiums and B the second two, or B paid the first two and A the second two, or they each paid half of each of the four premiums? Why should the children obtain the whole of the sum assured if Mr. Murphy used his own money before he began to use the plaintiffs' money, and only a return of the premiums if Mr. Murphy happened to use the plaintiffs' money first? Why should the proceeds of the policy be attributed to the first premium when the policy itself is expressed to be in consideration of all the premiums? There is no analogy with the case where trust money is used to maintain or improve property of a third party. The nearest analogy is with an instalment purchase.

      Hobhouse L.J. adopted a different approach. He concentrated on the detailed terms of the policy, and in particular on the fact that in the event the payment of the fourth and fifth premiums with the plaintiffs' money made no difference to the amount of the death benefit. Once the third premium had been paid, there was sufficient surrender value in the policy, built up by the use of Mr. Murphy's own money, to keep the policy on foot for the next few years, and as it happened Mr. Murphy's death occurred during those few years. But this was adventitious and unpredictable at the time the premiums were paid. The argument is based on causation and as I have explained is a category mistake derived from the law of unjust enrichment. It is an example of the same fallacy that gives rise to the idea that the proceeds of an ordinary life policy belong to the party who paid the last premium without which the policy would have lapsed. But the question is one of attribution not causation. The question is not whether the same death benefit would have been payable if the last premium or last few premiums had not been paid. It is whether the death benefit is attributable to all the premiums or only to some of them. The answer is that death benefit is attributable to all of them because it represents the proceeds of realising the policy, and the policy in turn represents the product of all the premiums.

      In any case, Hobhouse L.J.'s analysis of the terms of the policy does not go far enough. It is not correct that the last two premiums contributed nothing to the sum payable on Mr. Murphy's death but merely reduced the cost to the insurers of providing it. Life cover was provided in return for a series of internal premiums paid for by the cancellation of units previously allocated to the policy. Units were allocated to the policy in return for the annual premiums. Prior to their cancellation the cancelled units formed part of a mixed fund of units which was the product of all the premiums paid by Mr. Murphy, including those paid with the plaintiffs' money. On ordinary principles, the plaintiffs can trace the last two premiums into and out of the mixed fund and into the internal premiums used to provide the death benefit.

      It is true that the last two premiums were not needed to provide the death benefit in the sense that in the events which happened the same amount would have been payable even if those premiums had not been paid. In other words, with the benefit of hindsight it can be seen that Mr. Murphy made a bad investment when he paid the last two premiums. It is, therefore, superficially attractive to say that the plaintiffs' money contributed nothing of value. But the argument proves too much, for if the plaintiffs cannot trace their money into the proceeds of the policy, they should have no proprietary remedy at all, not even a lien for the return of their money. But the fact is that Mr. Murphy, who could not foresee the future, did choose to pay the last two premiums, and to pay them with the plaintiffs' money; and they were applied by the insurer towards the payment of the internal premiums needed to fund the death benefit. It should not avail his donees that he need not have paid the premiums, and that if he had not then (in the events which happened) the insurers would have provided the same death benefit and funded it differently.

      In the case of an ordinary life policy which lapses if the premiums are not paid, the Vice-Chancellor's approach gives the death benefit to the party whose money was used to pay the first premium, and Hobhouse L.J.'s approach gives it to the party whose money was used to pay the last premium. In the case of a policy like the present, Hobhouse L.J.'s approach also produces unacceptable and capricious results. The claimant must wait to see whether the life assured lives long enough to exhaust the amount of the policy's surrender value as at the date immediately before the claimant's money was first used. If the life assured dies the day before it would have been exhausted, the claimant is confined to his lien to recover the premiums; if he dies the day after, then the claimant's premiums were needed to maintain the life cover. In the latter case he takes at least a proportionate share of the proceeds or, if the argument is pressed to its logical conclusion, the whole of the proceeds subject to a lien in favour of the trustees of the children's settlement. This simply cannot be right.

      Hobhouse L.J.'s approach is also open to objection on purely practical grounds. It must, I think, be unworkable if there is an eccentric pattern of payment; or if there is a fall in the value of the units at a critical moment. Like the Vice-Chancellor's approach, it prompts the question: why should the order of payments matter? It is true that the premiums paid with the plaintiff's money did not in the event increase the amount payable on Mr. Murphy's death, but they increased the surrender value of the policy and postponed the date at which it would lapse if no further premiums were paid. Why should it be necessary to identify the premium the payment of which (in the events which happened) prevented the policy from lapsing? Above all, this approach makes it impossible for the ownership of the policy to be determined until the policy matures or is realised. This too cannot be right.

      The trustees argued that such considerations are beside the point. It is not necessary, they submitted, to consider what the plaintiffs' rights would have been if the policy had been surrendered, or if Mr. Murphy had lived longer. It is sufficient to take account of what actually happened. I do not agree. A principled approach must yield a coherent solution in all eventualities. The ownership of the policy must be ascertainable at every moment from inception to maturity; it cannot be made to await events. In my view the only way to achieve this is to hold firm to the principle that the manner in which an asset is converted into money does not affect its ownership. The parties' respective rights to the proceeds of the policy depend on their rights to the policy immediately before it was realised on Mr. Murphy's death, and this depends on the shares in which they contributed to the premiums and nothing else. They do not depend on the date at which or the manner in which the chose in action was realised. Of course, Mr. Murphy's early death greatly increased the value of the policy and made the bargain a good one. But the idea that the parties' entitlements to the policy and its proceeds are altered by the death of the life assured is contrary to principle and to the decision of your Lordships' House in D'Avigdor Goldsmid v. Inland Revenue Commissioners [1953] A.C. 347. That case establishes that no fresh beneficial interest in a policy of life assurance accrues or arises on the death of the life assured. The sum assured belongs to the person or persons who were beneficial owners of the policy immediately before the death.

      In the course of argument it was submitted that if the children, who were innocent of any wrongdoing themselves, had been aware that their father was using stolen funds to pay the premiums, they could have insisted that the premiums should not be paid, and in the events which happened would still have received the same death benefit. But the fact is that Mr. Murphy concealed his wrongdoing from both parties. The proper response is to treat them both alike, that is to say rateably. It is morally offensive as well as contrary to principle to subordinate the claims of the victims of a fraud to those of the objects of the fraudster's bounty on the ground that he concealed his wrongdoing from both of them.

      The submission is not (as has been suggested) supported by Professor David Hayton's article "Equity's Identification Rules" in Professor Peter Birk's Laundering and Tracing (1995) at pp. 11-12. Professor Hayton is dealing with the very different case of the party who decides to purchase an asset and has the means to pay for it, but who happens to use trust money which he has received innocently, not knowing it to belong to a third party and believing himself to be entitled to it. In such a case his decision to use the trust money rather than his own is independent of the breach of trust; it is a matter of pure chance. This is a problem about tracing, not claiming, and has nothing to do with mixtures, as Professor Hayton's article itself makes clear. It is a difficult problem on the solution to which academic writers are not agreed. But it does not arise in the present case. It was Mr. Murphy's decision to use the plaintiffs' money to pay the later premiums. The children are merely passive recipients of an asset acquired in part by the use of misappropriated trust money. They are innocent of any personal wrongdoing, but they are not contributors. They are volunteers who derive their interest from the wrongdoer otherwise than for value and are in no better position than he would have been if he had retained the policy for the benefit of his estate. It is not, with respect to those who think otherwise, a case where there are competing claimants to a fund who are both innocent victims of a fraud and where the equities are equal. But if it were such a case, the parties would share rateably, which is all that the plaintiffs claim.

      I should now deal with the finding of all the members of the Court of Appeal that the plaintiffs were entitled to enforce a lien on the proceeds of the policy to secure repayment of the premiums paid with their money. This is inconsistent with the decision of the majority that the plaintiffs were not entitled to trace the premiums into the policy. An equitable lien is a proprietary interest by way of security. It is enforceable against the trust property and its traceable proceeds. The finding of the majority that the plaintiffs had no proprietary interest in the policy or its proceeds should have been fatal to their claim to a lien.

      The Court of Appeal held that the plaintiffs were entitled by way of subrogation to Mr. Murphy's lien to be repaid the premiums. He was, they thought, entitled to the trustee's ordinary lien to indemnify him for expenditure laid out in the preservation of the trust property: see In re Leslie (1883) 23 Ch. D. 560. Had Mr. Murphy used his own money, they said, it would have been treated as a gift to his children; but the fact that he used stolen funds rebutted any presumption of advancement.

      With all due respect, I do not agree that Mr. Murphy had any lien to which the plaintiffs can be subrogated. He was one of the trustees of his children's settlement, but he did not pay any of the premiums in that capacity. He settled a life policy on his children but without the funds to enable the trustees to pay the premiums. He obviously intended to add further property to the settlement by paying the premiums. When he paid the premiums with his own money he did so as settlor, not as trustee. He must be taken to have paid the later premiums in the same capacity as he paid the earlier ones. I do not for my own part see how his intention to make further advancements into the settlement can be rebutted by showing that he was not using his own money; as between himself and his children the source of the funds is immaterial. He could not demand repayment from the trustees by saying: "I used stolen money; now that I have been found out you must pay me back so that I can repay the money". Moreover, even if the presumption of advancement were rebutted, there would be no resulting trust. Mr. Murphy was either (as I would hold) a father using stolen money to make further gifts to his children or a stranger paying a premium on another's policy without request: see Falcke v. Scottish Imperial Insurance Co. (1886) 34 Ch. D. 234.

      But perhaps the strongest ground for rejecting the argument is that it makes the plaintiffs' rights depend on the circumstance that Mr. Murphy happened to be one of the trustees of his children's settlement. That is adventitious. If he had not been a trustee then, on the reasoning of the majority of the Court of Appeal, the plaintiffs would have had no proprietary remedy at all, and would be left with a worthless personal claim against Mr. Murphy's estate. The plaintiffs' rights cannot turn on such chances as this.

The relevant proportions

      Accordingly, I agree with Morritt L.J. in the Court of Appeal that, on well established principles, the parties are entitled to the proceeds of the policy in the proportions in which those proceeds represent their respective contributions. It should not, however, be too readily assumed that this means in the proportions in which the insurance premiums were paid with their money. These represent the cost of the contributions, not necessarily their value.

      A mixed fund, like a physical mixture, is divisible between the parties who contributed to it rateably in proportion to the value of their respective contributions, and this must be ascertained at the time they are added to the mixture. Where the mixed fund consists of sterling or a sterling account or where both parties make their contributions to the mixture at the same time, there is no difference between the cost of the contributions and their sterling value. But where there is a physical mixture or the mixture consists of an account maintained in other units of account and the parties make their contributions at different times, it is essential to value the contributions of both parties at the same time. If this is not done, the resulting proportions will not reflect a comparison of like with like. The appropriate time for valuing the parties' respective contributions is when successive contributions are added to the mixture.

      This is certainly what happens with physical mixtures. If 20 gallons of A's oil are mixed with 40 gallons of B's oil to produce a uniform mixture of 60 gallons, A and B are entitled to share in the mixture in the proportions of 1 to 2. It makes no difference if A's oil, being purchased later, cost £2 a gallon and B's oil cost only £1 a gallon, so that they each paid out £40. This is because the mixture is divisible between the parties rateably in proportion to the value of their respective contributions and not in proportion to their respective cost. B's contribution to the mixture was made when A's oil was added to his, and both parties' contributions should be valued at that date. Should a further 20 gallons of A's oil be added to the mixture to produce a uniform mixture of 80 gallons at a time when the oil was worth £3 a gallon, the oil would be divisible equally between them. (A's further 20 gallons are worth £3 a gallon--but so are the 60 gallons belonging to both of them to which they have been added). It is not of course necessary to go through the laborious task of valuing every successive contribution separately in sterling. It is simpler to take the account by measuring the contributions in gallons rather than sterling. This is merely a short cut which produces the same result.

      In my opinion the same principle operates whenever the mixture consists of fungibles, whether these be physical assets like oil, grain or wine or intangibles like money in an account. Take the case where a trustee misappropriates trust money in a sterling bank account and pays it into his personal dollar account which also contains funds of his own. The dollars are, of course, merely units of account; the account holder has no proprietary interest in them. But no one, I think, would doubt that the beneficiary could claim the dollar value of the contributions made with trust money. Most people would explain this by saying that it is because the account is kept in dollars. But the correct explanation is that it is because the contributions are made in dollars. In order to allocate the fund between the parties rateably in proportion to the value of their respective contributions, it is necessary to identify the point at which the trust money becomes mixed with the trustee's own money. This does not occur when the trustee pays in a sterling cheque drawn on the trust account. At that stage the trust money is still identifiable. It occurs when the bank credits the dollar equivalent of the sterling cheque to the trustee's personal account. Those dollars represent the contribution made by the trust. The sterling value of the trust's contribution must be valued at that time; and it follows that the trustee's contributions, which were also made in dollars, must be valued at the same time. Otherwise one or other party will suffer the injustice of having his contributions undervalued.

Calculating the plaintiffs' share

      I finally come to the difficult question: how should the parties' contributions, and therefore their respective shares in the proceeds, be calculated in the case of a unit-linked policy of the present kind? This makes it necessary to examine the terms of the policy in some detail.

      All the reported cases have been concerned with ordinary policies of life assurance. In all the cases the insurance moneys have been shared between the parties in the proportions in which their money has been used to pay the premiums irrespective of the dates on which the premiums were paid. This favours the party who paid the later premiums at the expense of the party who paid the earlier ones. There is therefore a case for adding interest to the premiums in order to produce a fair result. This cannot be justified by the need to compensate the parties for the loss of the use of their money over different periods. It is not merely that this branch of the law is concerned with vindicating property rights and not with compensation for wrongdoing. It is that ex hypothesi the money has not been lost but used to produce the insurance money. But I think that taking account of interest can be justified nonetheless. The policy and its proceeds are not the product of the uninvested premiums alone. If they were, the sum assured would be very much smaller than it is. They are the product of the premiums invested at compound interest. It does not matter, of course, what the insurance company actually does with the money. What matters is how the sum assured is calculated, because this shows what it represents. In practice it represents the sum which would be produced by the premiums over the term of the expected life of the assured together with compound interest at the rate available at the inception of the policy on long term government securities. But the question has not been the subject of argument before us, and having regard to the mechanics of the present policy the calculations may not be worth doing. I agree therefore with my noble and learned friend Lord Hoffmann that there is no need to explore this aspect further.

      Unit-linked policies, however, are very different. These policies have become popular in recent years, and are commonly employed for personal pension plans taken out by the self-employed. Under such a policy the premiums are applied by the insurance company in the acquisition of accumulation units in a designated fund usually managed by the insurance company. The bid and offer prices of the units are published daily in the financial press. The value of the units can go down as well as up, but since they carry the reinvested income their value can be expected to increase substantially over the medium and long term. The policy is essentially a savings medium, and (subject to tax legislation) can be surrendered at any time. On surrender the policyholder is entitled to the value of the units allocated to the policy. Early policies provided that on death the policyholder was entitled merely to the return of his premiums with interest, but more modern policies provide for payment of the value of the units in this event also.

      Where money belonging to different parties is used to pay the premiums under a policy of this kind, it cannot be right to divide the proceeds of the policy crudely according to the number of premiums paid by each of them. The only sensible way of apportioning the proceeds of such a policy is by reference to the number of units allocated to the policy in return for each premium. This is readily ascertainable, since policyholders are normally issued with an annual statement showing the number of units held before receipt of the latest premium, the number allocated in respect of the premium, and the total number currently held. But in any case these numbers can easily be calculated from published material.

      This would obviously be the right method to adopt if the policyholder acquired a proprietary interest in the units. These would fall to be dealt with in the same way as grain, oil or wine. There would of course still be a mixed substitution, since after the mixture neither party's contributions can be identified. Neither can recover his own property, but only a proportion of the whole. Unlike Roman law, the common law applied the same principles whenever there is no means of identifying the specific assets owned by either party. In the United States they have been applied to logs, pork, turkeys, sheep and straw hats: see Dr. Lionel Smith, The Law of Tracing, at p. 70. In fact unit-linked policies normally provide that the policyholder has no proprietary interest in the units allocated to the policy. They are merely units of account. The absence of a proprietary interest in the units would be highly material in the event of the insolvency of the insurance company. But it should have no effect on the method of calculating the shares in which competing claimants are entitled to the proceeds of the policy. This depends upon the proportions in which they contributed to the acquisition of the policy, and the question is: in what units of account should the parties' respective contributions be measured? Should they be measured in sterling, this being the currency in which the premiums were paid? Or should they be measured by accumulation units, if this was the unit of account into which the premiums were converted before the admixture took place? Principle, and the cases on physical mixtures, indicate that the second is the correct approach. A unit linked policy of the kind I have described is simply a savings account. The account is kept in units. The mixing occurs when the insurance company, having received a premium in sterling, allocates units to the account of the insured where they are at once indistinguishably mixed with the units previously allocated. The contribution made by each of the parties consists of the units, not merely of their sterling equivalent. The proceeds of a unit-linked policy should in my opinion be apportioned rateably between the parties in proportion to the value of their respective contributions measured in units, not in sterling.

      The policy in the present case is only a variant of the unit-linked policy of the kind I have described. It is also primarily a savings medium but it offers an additional element of life assurance. This protects the assured against the risk of death before the value of the units allocated to the policy reaches a predetermined amount. On receipt of each premium, the insurance company allocates accumulation units in the designated fund to the policy ("the investment element"), and immediately thereafter cancels sufficient of the units to provide "the insurance element." This is in effect an internal premium retained by the insurance company to provide the life cover. The amount of the internal premium is calculated each year by a complicated formula. The important feature of the formula for present purposes is that the internal premium is not calculated by reference to the sum assured of £1m. but by reference to the difference between the current value of the units allocated to the policy and the sum assured. As the value of the units increases, therefore, the amount of the internal premium should reduce. When their value is equal to or greater than the sum assured, no further internal premiums are payable. Thenceforth the policy is exactly like the kind of unit-linked policy described above. The policyholder is entitled to the investment element, ie. the value of the accumulated units, on death as well as on surrender.

      If the policyholder dies at a time when the investment element is less than the sum assured, then he receives the sum assured. This is paid as a single sum, but it has two components with different sources. One is the investment element, which represents the value of the accumulated units at the date of death. The other is the insurance element, which is merely a balancing sum. It will be very large in the early years of the policy and will eventually reduce to nothing. It is the product of the internal premiums and is derived from the cancelled units. The internal premiums, however, though derived from the cancelled units, were credited to the account in sterling. The proceeds of the internal premiums, therefore, should be apportioned between the parties pro rata in the proportions in which those premiums were provided in sterling.

      In my opinion the correct method of apportioning the sum assured between the parties is to deal separately with its two components. The investment element (which amounted to £39,347 at the date of death in the present case) should be divided between the parties by reference to the value at maturity of the units allocated in respect of each premium and not cancelled. The balance of the sum assured should be divided between the parties rateably in the proportions in which they contributed to the internal premiums. This is not to treat the allocated units as a real investment separate from the life cover when it was not. Nor is it to treat the method by which the benefits payable under the policy is calculated as determinative or even relevant. It is to recognise the true nature of the policy, and to give effect to the fact that the sum assured had two components, to one of which the parties made their contributions in units and to the other of which they made their contributions in the sterling proceeds of realised units.

      These calculations require the policyholder's account to be redrawn as two accounts, one for each party. The number of units allocated to the policy on the receipt of each premium should be credited to the account of the party whose money was used to pay the premium. The number of units so allocated should be readily ascertainable from the records of the insurance company, but if not it can easily be worked out. The number of units which were cancelled to provide the internal premium should then be ascertained in similar fashion and debited to the appropriate account. In the case of the earlier premiums paid with Mr. Murphy's own money this will be the trustees' account. In the case of the later premiums paid with the plaintiffs' money, the cancelled units should not be debited wholly to the plaintiffs' account, but rateably to the two accounts. The amount of the internal premiums should then be credited to the two accounts in the same proportions as those in which the cancelled units were debited to provide them.

      This approach is substantially more favourable to the children than a crude allocation by reference to the premiums. By taking account of the value of the units, it automatically weights the earlier premiums which should have bought more units than the later ones. And it gives effect to the fact that, under the terms of the policy, both parties contributed to the later internal premiums which produced the greater part of the death benefit.

      It is, of course, always open to the parties in any case to dispense with complex calculations and agree upon a simpler method of apportionment. But in my opinion the court ought not to do so without the parties' consent. If it does, anomalies and inconsistencies will inevitably follow. Take the present case. The method of apportionment, with greatly differing results, ought not to depend upon whether the value of the units at the date of death is slightly more or slightly less than the sum assured. Yet once their value exceeds the amount of the sum assured, the policy becomes an ordinary unit-linked pension policy without an insurance element. If the sum assured is divided crudely in proportion requires that the same method be adopted for pension policies, which is surely wrong. If it is adopted for pension policies, then it is difficult to see how foreign currency assets can be treated differently, which is certainly wrong. There is an enormous variety of financial instruments. For present purposes they form a seamless web. Cutting corners in the interest of simplicity is tempting, but in my opinion the temptation ought to be resisted.

Conclusion

    Accordingly I would allow the appeal. In my opinion the insurance money ought to be divided between the parties in the proportions I have indicated. But I am alone in adopting this approach, and as the question was not argued before us I am content that your Lordships should declare that the money should be divided between the parties in proportions in which they contributed to the premiums. For the reasons given by my noble and learned friend Lord Hope of Craighead, with which I agree, I would dismiss the children's cross-appeal.