LONG, J.

Introduction

This is a partition action between three sisters plaintiff Donna Brennan and defendants Diane Burke and Sandra McIntosh who are the children of the late Joseph and Lena Rigoli. The property at issue (registered land) is the single family house at 37 Lawrence Street in Falmouth, built by the Rigolis and left to the sisters in accordance with various trusts and other instruments. These instruments were the subject of prior proceedings in this court, which determined that they divided the property as follows. [Note 1]

* The underlying fee in the property, currently titled in the name of the Rigoli Realty Trust, is beneficially owned by the sisters in the following percentages: Ms. Brennan (16 2/3%), Ms. Burke (41 2/3%), and Ms. McIntosh (41 2/3%).

* That fee is subject to the following life estates: Ms. Brennan and Ms. Burke, each with a present 50% undivided life estate in the property, and then Ms. McIntosh with a subsequent life estate, i.e. one that vests after Ms. Brennan and Ms. Burke have died, assuming she outlives them.

Ms. Burke and Ms. McIntosh currently live in the house. Ms. Brennan does not, and has not for many years.

By agreement of the parties, partition will be through Ms. Burke's and Ms. McIntosh's buyout of Ms. Brennan at the price set by this court after due proceedings. As discussed more fully below, determining this price the present value of Ms. Brennan's life estate plus the present value of her remainder interest, and then adjusting that figure to account for appropriate set-offs, if any has the following five steps: (1) determining the present market value of the property, (2) determining the present value of each of the respective life estates in that property, (3) determining the present value of each of the remainder interests in the property (i.e., the present value of the sisters' respective fee interests once all of the life estates have expired), (4) adding the present value of Ms. Brennan's life estate and the present value of her remainder interest together to get the total value of her interests, and then (5) if appropriate, adjusting that figure to reflect disproportionate contributions to the property's improvement or maintenance (if any) and, if Ms. Brennan was "ousted" from her right of occupation, to compensate her for that ouster. See G.L. c. 241, §§23; Stylianopoulos v. Stylianopoulos, 17 Mass. App. Ct. 64 , 66-70 (1983).

The parties agreed to be bound by the findings of a mutually chosen real estate appraiser, Steven Backus, regarding the present market value and gross rental value of the property. [Note 2] Mr. Backus found those to be $700,000 and $2,375 per month, respectively, as of May 11, 2015. The remaining issues were then tried before me, jury-waived.

Based on Mr. Backus' findings, the testimony and documents admitted at trial, my assessment of the credibility, weight, and appropriate inferences to be drawn from that evidence, and as explained more fully below, I find and rule that the present value of Ms. Brennan's life estate is $101,610.70 and her remainder interest has a present value of $81,097.34, for a total of $182,708.04. Ms. Burke's corresponding figures are $89,754.11 (the present value of her life estate) and $202,743.33 (the present value of her remainder interest) for a total of $292,497.44, and Ms. McIntosh's corresponding figures are $22,051.19 (the present value of her life estate) and $202,743.33 (the present value of her remainder interest) for a total of $224,794.52. These three sets of interests total up to $700,000, the present market value of the property. I further find and rule that (1) Ms. Brennan was not ousted from the property and is thus not owed any rent for that reason, and (2) for equitable and other reasons, no one is owed any contribution towards any "disproportionate" amount of maintenance, renovation, or improvement to the property they may have paid or caused. There are thus no adjusting set-offs. Accordingly, Ms. Burke and Ms. McIntosh may buy out Ms. Brennan's interest, in its entirety, for $182,708.04. If buyout does not occur within 90 days of the Judgment, which I find to be a reasonable time for Ms. Burke and Ms. McIntosh to obtain any necessary financing, [Note 3] interest on the buyout amount shall begin accruing from and after that date at the statutory rate (12% per annum) see G.L. c. 231, §6C, thus increasing the buyout price by that amount. If buyout does not occur within six months of the date of Judgment, Ms. Brennan may purchase Ms. Burke's and Ms. McIntosh's interests at the values set forth above.

Facts

These are the facts as I find them after trial.

The property at issue, 37 Lawrence Street in Falmouth, is a single family home, registered land, and was previously owned by the late Joseph and Lena Rigoli who conveyed its title to the Rigoli Realty Trust, the owner currently reflected on the Certificate of Title. [Note 4] The beneficiaries of that trust were two other trusts (one Joseph's, and one Lena's), and there were also subsequent additional instruments that addressed the property's ownership after their deaths. That ownership was adjudicated in a prior proceeding in this court, Brennan v. Burke and McIntosh, 11 SBQ 04286, Mass. Land Ct., Order on Respondents' Motion for Summary Judgment, (Foster, J., Oct. 6, 2014) in which, as noted above, it was determined to be as follows:

(1) Ms. Brennan and Ms. Burke each have a present 50% undivided life estate in the property; (2) Ms. McIntosh has a subsequent life estate, i.e. one that vests after Ms. Brennan and Ms. Burke have died, assuming she outlives them; and (3) the underlying remainder interest (the fee) is owned 16 2/3 % by Ms. Brennan, 41 2/3 % by Ms. Burke, and 41 2/3 % by Ms. McIntosh.

Ms. Burke and Ms. McIntosh currently live in the house. Ms. Brennan does not, and brought this action to partition her interest. The parties agree that partition shall be through buy-out of Ms. Brennan by Ms. Burke and Ms. McIntosh, with the buy-out price as determined by this court.

As previously noted, that determination has five steps. The first is finding the present market value of the house. [Note 5] The second is finding its net fair rental value, which is relevant for two purposes (1) calculating the income stream the house would generate (used in the valuation of the life estates), and (2) if "ouster" has occurred and compensation to the ousted tenant is appropriate, calculating the amount to be paid as compensation for the ouster. [Note 6] The third is finding the present value of the respective life estates. The fourth is finding the present value of the respective remainder interests (the present market value of the house, minus the present value of the life estates, and then divided in accordance with the parties' respective percentage interests). And the fifth is the calculation of appropriate "set-offs", if any.

By agreement of the parties, the fair market value and gross fair rental value were determined by Steven Backus, their mutually-chosen real estate appraiser. [Note 7] Based on his analysis of comparable properties, appropriately adjusted for the differences between them, Mr. Backus found that, as of May 11, 2015, the fair market value of the property was $700,000, and its gross fair rental value was $2,375 per month. Ms. Brennan's subsequent motion to strike those findings was denied by the court, as the parties had previously agreed to abide by them. [Note 8]

As noted above, once the value of the respective life estates has been determined, the calculation of the respective remainder interests is a simple mathematical calculation: it is the total property value ($700,000) minus the total value of the life estates, with what remains (the "remainder interest") then allocated to the parties according to their percentage shares. The challenge, of course, is calculating the value of the three life estates. On that the parties differed.

Ms. Brennan's expert, Edward Berger (not an actuary), [Note 9] was not persuasive and did not adequately explain or support his methodology. I thus do not accept his calculations. Among other things, he based them on an incorrect gross monthly rental figure of $2500 (not $2375), he did not adjust that figure for expenses to arrive at a net (I explain below why rental income is crucial to the analysis, and why net is the appropriate measure), he assumed a 2% per year rise in rental income, year after year, despite the aging of the property (an assumption I find unrealistic and not supported by the evidence), and he calculated the parties' life expectancies based on outdated and inadequately identified mortality tables, which he then adjusted in ways not persuasively explained.

In contrast, the defendants' expert, Steven Ricci, who is an actuary, [Note 10] took a different and far more persuasive approach, fully supported by the source documents he relied upon and in accordance with standard actuarial analysis, which I fully credit and adopt. [Note 11] Importantly, he used the correct $2375 per month ($28,500 per year) gross rental value figure, and then (again correctly) subtracted the property's operating expenses to arrive at the net. These expenses (what is actually being paid now) are (1) normal maintenance ($8510/ year; $709.17/month), (2) insurance ($1,642/year; $136.83/month, (3) property taxes ($4,536/year; $378/month), and (4) water ($956/year; $79.67/month), for a total of $15,644/year ($1303.67/month). I find that these are appropriate expense figures to use, and that the net rental figure the monetary value of the life estate for a particular period of time and thus the proper figure to use in the life estate calculations is $1071.33/month ($12,856/year). Based on a generally-accepted IRS table, [Note 12] he used a 2.2% interest rate to calculate the present value of the future income stream. [Note 13] I concur.

Just as importantly, because people die at all ages and not just at the end of their so-called life expectancy, and because the three life estates at issue in this case depend upon the others, [Note 14] Mr. Ricci calculated the probability of each individual party being alive at any particular time (his "custom mortality tables"), which enabled him to calculate the value of each life estate in light of the probability that its particular constituent events would occur for example, the probability, year by year, that Ms. Brennan would be alive after Ms. Burke's death, and for how long she would still be alive, year by year, after that. Given the vagaries of the rental market and the aging of the house over the course of the life estates, Mr. Ricci also assumed that rental income would be constant. I agree with this assumption for purposes of these valuations, particularly because expenses are also assumed to be constant, [Note 15] and so find.

Further facts, including the results of Mr. Ricci's calculations, are set forth below.

Analysis

"Faced with a battle of experts, the fact finder may accept one reasonable opinion and reject the other." Fechtor v. Fechtor, 26 Mass. App. Ct. 859 , 863 (1989) (internal citations omitted) (judge free to reject opinion of [one party's] expert and the valuation methods on which it was based). [Note 16] As noted above, I do not credit the testimony and methodology of the plaintiff's expert Edward Berger, but instead credit the testimony and methodology of the defendants' expert Steven Ricci. His analysis, which I accept as the correct one, was as follows.

Valuation of the Three Life Estates

Mr. Ricci used the net rental income figures ($1071.33/month; $12,856/year) as the value of occupancy, and thus the value of the life estate entitled to that occupancy. I agree that this is the correct approach to use in valuing the life estates, and that the net rather than gross rental income figure is the proper number to use because it accounts for necessary maintenance costs. The tables he used are from the IRS, which I accept as a standard, authoritative and reliable source. The IRS § 7520 Interest Rates table was used to determine the appropriate interest rate for calculating the present value of the rental income stream during each of the life estates. [Note 17] IRS Table 2000CM, a table of life expectancies showing the number of survivors at each age out of a population of 100,000 starting at age 0 and going up through age 110, was used to determine the parties' respective probabilities of life versus death at the various ages. And, from these respective probabilities, Mr. Ricci created custom tables to aid in the calculation of the present value of income streams for the different possible scenarios, depending upon which of the sisters outlived the others. This is exactly the methodology he uses in his actuarial work, in particular for calculating the present value of retirement plans, and I find it was appropriately used here.

As noted above, in making his calculations, Mr. Ricci assumed that the fair market rental value of the property and the associated property-related expenses would remain constant. I concur that this was a reasonable assumption to use in making these calculations. There may be minor fluctuations from time to time, but for this type of property and its location (Cape Cod), these fluctuations will likely even out over time, and it is doubtful, as the property ages, that steadily increasing rents can realistically be expected. And, if rents are assumed to be constant, expenses are appropriately assumed to be constant as well to enable an "apples to apples" analysis.

Because there were three life estates at issue, [Note 18] each with the potential for varying lengths, Mr. Ricci calculated the probabilities of each possible scenario and based his valuation calculations on those probabilities in accordance with standard actuarial practice. I concur that this was the proper method of analysis to use in this case.

First, he calculated the present value of the income stream during the period, year by year, in which it was probable that both Ms. Brennan and Ms. Burke would be alive and, in accordance with their 50% shares during that time period, divided it 50-50. [Note 19] In his opinion, the present value of this period of their life estates (their "shared" period) is $54,783.23 apiece. I agree and so find.

Second, he addressed the situation where, upon the death of Ms. Burke or Ms. Brennan, 100% of the net income would go to the survivor for as long as the survivor was alive. This had two alternatives Ms. Burke outliving Ms. Brennan, and Ms. Brennan outliving Ms. Burke each of which had a probability of occurring and, in each, a length of time during which the survivor (whichever it was) would continue to live, the probabilities of which he also calculated, year by year. Based on these probabilities (for Ms. Burke, the probability of her outliving Ms. Brennan, the probability of how long a period that would be, and the 100% of the net income she would receive during this period calculated in accordance with these probabilities; and for Ms. Brennan the probability of her outliving Ms. Burke, the probability of how long a period that would be, and the 100% of the net income she would receive during this period calculated in accordance with these probabilities), he calculated the present value of this portion of Ms.Burke's life estate (her "survivor" period) as $34,970.88 and the present value of this portion of Ms. Brennan's life estate (her "survivor" period) as $46,827.47. [Note 20]

The total present value of Ms. Burke's life estate is thus the addition of her "shared" period ($54,783.23) and her "survivor" period ($34,970.88) for a total of $89,754.11, and for Ms. Brennan $101,610.70 ($54,783.23 + $46,827.47). I agree and so find.

The present value of Ms. McIntosh's life estate must also be calculated so that the "remainder" will be known [Note 21] and can then be divided according to the parties' respective percentage interests in the fee. This is the instance in which 100% of the net income would be payable to Ms. McIntosh after the death of both Ms. Brennan and Ms. Burke, i.e. where she outlives them both. Once again, Mr. Ricci made this calculation based on the possible scenarios under which this could occur (here, there were three), and the respective probabilities of their occurrence.

The first scenario is if Ms. Burke and Ms. Brennan both die in the same year and Ms. McIntosh is still alive. This involves calculating the probability of that occurring (and when), the probable length of Ms. McIntosh's life after that, and then the present value of the income stream during that period of time. Mr. Ricci calculated this present value as $1,607.45.

The second scenario is if Ms. Burke dies before Ms. Brennan. This involves calculating the probability of that occurring and the probable length of Ms. Brennan's life thereafter, the probable length of Ms. McIntosh's life after that, and then the present value of the income stream during that period of time. Mr. Ricci calculated this present value as $10,619.94.

The third scenario is if Ms. Brennan predeceases Ms. Burke. This involves calculating the probability of that occurring and the probable length of Ms. Burke's life thereafter, the probable length of Ms. McIntosh's life after that, and then the present value of the income stream during that period of time. Mr. Ricci calculated this present value as $9,823.80.

The three figures are then added together (there is no double-counting because each has already been discounted by the probability of it occurring), giving a total present value of Ms. McIntosh's contingent life estate of $22,051.19. I agree and so find.

The Parties' Remainder Interests

As noted above (see n.21), once the present value of the three life estates is known, the present value of the remainder interest is simple math: it is the property's current fair market value ($700,000) less the total of the life estates ($213,416), i.e. $486,584. This is then divided according to the parties' respective percentage interests in the fee: Ms. Brennan 16 2/3% ($81,097.34), Ms. Burke 41 2/3% ($202,743.33), and Ms. McIntosh 41 2/3% ($202,743.33). I agree and so find.

Offsets

Ms. Burke and Ms. McIntosh contend that, because Ms. Brennan has a current 50% life tenancy in the property, she should be responsible for 50% of the property's expenses from and after 2010. [Note 22] I disagree. [Note 23] Any such assessment would be inequitable. It is a single family house, fully occupied by the defendants, and Ms. Brennan last lived there in 2009. She has also not received any income from it. If such an expense contribution is in order, it should come from Ms. McIntosh to avoid her unjust enrichment (unlike Ms. Brennan, Ms. McIntosh has no present right to occupancy). To her credit, Ms. McIntosh has been doing so, paying half these expenses.

On the flip side, because I find she was not ousted and could have continued to reside in the property even if uncomfortable, Ms. Brennan is not entitled to any past rents or profits. See generally Chandler v. Simmons, 105 Mass. 412 (1870) (petitioner only entitled to "rents, profits and other damages" when respondent denied petitioner's right and title to the premises). Had it been necessary, Ms. Brennan could have brought eviction proceedings against Ms. McIntosh and, aside from Ms. Burke, the other family members living there, but chose not to do so.

I do not award Ms. Brennan any compensation for work she performed on the property prior to leaving in 2009. Although she testified that she worked on renovations for five days a week from 7 a.m. to 3:00 p.m. or 4:00 p.m., for approximately four months, she provided no evidence of how those efforts added market value to the property or, if they did so, how much. See G.L. c. 241, §23 (to be compensable, improvements must have increased market value of common land).

I likewise do not award Ms. Burke or Ms. McIntosh any compensation for the renovations and repairs they claim, all of which they concede took place between 2002 and 2006 and were paid for by the sisters' parents (Mr. and Mrs. Rigoli), not the sisters themselves. And, again, there was no evidence (and certainly none persuasive) of how they added market value to the property or, if they did, how much.

Conclusion

For the foregoing reasons, I find and rule that the present value of Ms. Brennan's life estate is $101,610.70 and her remainder interest has a present value of $81,097.34, for a total of $182,708.04. Ms. Burke's corresponding figures are $89,754.11 (the present value of her life estate) and $202,743.33 (the present value of her remainder interest) for a total of $292,497.44, and Ms. McIntosh's $22,051.19 (present value of life estate) and $202,743.33 (present value of remainder interest) for a total of $224,794.52.

I further find and rule that (1) Ms. Brennan was not ousted from the property and is thus not owed any rent for that reason, and (2) for equitable and other reasons, no one is owed any contribution towards any "disproportionate" amount of maintenance, renovation, or improvement to the property they may have paid or caused. There are thus no adjusting set-offs. Accordingly, Ms. Burke and Ms. McIntosh may buy out Ms. Brennan's interest, in its entirety, for $182,708.04. How Ms. Brennan's interest is re-allocated between Ms. Burke and Ms. McIntosh is not adjudicated in these proceedings.

If buy-out does not occur within 90 days of the Judgment, interest on the buyout amount shall begin accruing from and after that date at the statutory rate (12% per annum) see G.L. c. 231, §6C, thus increasing the buy-out price thereafter by that amount. If buy-out does not occur within six months of the date of Judgment, Ms. Brennan may purchase Ms. Burke's and Ms. McIntosh's interests at the values set forth above.

Judgment shall enter accordingly.

SO ORDERED.

FOOTNOTES

[Note 1] See Brennan v. Burke and McIntosh, 11 SBQ 04286, Mass. Land Ct., Order on Respondents' Motion for Summary Judgment, (Foster, J., Oct. 6, 2014).

[Note 2] The relevance of the property's rental value is explained below.

[Note 3] Ms. Burke's and Ms. McIntosh's need for time to obtain such financing was implicit in the parties' agreement to partition by buyout. For this reason, interest shall not accrue until the 90 days has passed.

[Note 4] Because it is the owner of record, the Rigoli Realty Trust was thus named as a nominal defendant in the case. There are currently no trustees of the trust, and thus no trustees to be served. However, the three sisters own the entire beneficial interest in the property, so the court deemed service on them to be sufficient service on the trust for purposes of this adjudication.

[Note 5] All present values are calculated as of 2015, when the case was filed and tried. I find this to be the fairest approach, for three reasons. First, the parties prepared and tried the case in reliance on these figures. Second, as shown by Mr. Backus' previous appraisal, the values associated with this property have not materially changed for many years. And third, it is also in accordance with the general proposition that matters of title are adjudicated as of the time the case is filed since that is when title is put in issue. See, e.g., Pugatch v. Stoloff, 41 Mass. App. Ct. 536 , 542 n. 8 (1996) and cases cited therein.

[Note 6] See Stylianopoulos, 17 Mass. App. Ct. at 66-67 ("no recognition is to be given fair rental value unless the occupying tenant has agreed to pay rent or has ousted the other tenant or tenant in common from the property in question").

[Note 7] See Docket Entry (Feb. 26, 2015).

[Note 8] See Docket Entry (Feb. 26, 2015) & Docket Entry (May 28, 2015).

[Note 9] Actuaries are trained and certified professionals whose specialty is compiling and analyzing statistics in order to calculate insurance risks and premiums. See Concise Oxford Dictionary (10th Ed.) at 13 (1999).

[Note 10] Mr. Ricci, an Enrolled Actuary, has a BA in mathematics from the University of Notre Dame, an MA in mathematics from the University of Michigan, and a PhD in mathematics from the University of Michigan. He is a member of the New England Employee Benefits Council, the Society of Actuaries, the American Academy of Actuaries, the Conference of Consulting Actuaries, the American Mathematical Society, and the Mathematical Association of America.

[Note 11] See Mr. Ricci's testimony at the Evidentiary Hearing (Sept. 28, 2015) and the exhibits admitted in connection with his testimony, which further detail his methodology and assumptions.

[Note 12] IRS Section 7520 Interest Rates (Aug. 21, 2015).

[Note 13] "Present value" is the current sum of money that, with compound interest, would amount to a specified sum at a specified future date, i.e. future value discounted to its value today. See Black's Law Dictionary (7th Ed., 1999) at 1203. It is the answer to the question, "what is money received in the future worth today?, the notion being that the current sum would have earned interest at the specified rate from now until that future date(s). Here, in accordance with the IRS guidance, the interest (discount) rate used in making this calculation was 2.2%

[Note 14] See the discussion below.

[Note 15] The calculation will thus be apples to apples.

[Note 16] See also L.L. v. Com., 470 Mass. 169 , 183 (2014) (An "[e]xperts' opinions are not binding on the trier of fact, who may accept or reject them in whole or in part," citing Com. v. O'Brien, 423 Mass. 841 , 854 (1996)); Com. v. Hawkesworth, 405 Mass. 664 , 672 (989) ("[t]he judge was not bound by the views of the defendants' experts on the issue of rehabilitation"); Com. v. Watson, 388 Mass. 536 , 539 (1983) (affirming judge who found "the views of certain experts unpersuasive"); Ward v. Com., 407 Mass. 434 , 438 (1990) (judge not bound by views of experts and "was entitled to resolve the conflict between [the petitioner's three experts'] testimony and that of the court-appointed expert by crediting the opinion of the latter"); Com. v. Matthews, 406 Mass. 380 , 386 (1990) ( judge is "entitled to resolve the conflicting testimony" and determine witness' credibility as the judge saw the witnesses); Piemonte v. New Boston Garden Corp., 377 Mass. 719 , 731 (1979) ("[a]s the trier of fact, the judge was not bound to accept the valuation [or view] of either one expert or the other. He was entitled to reach his own conclusion").

[Note 17] An interest rate (more properly, the "discount" rate) is used to calculate the present value of a future income stream. Broadly speaking, it tells you what amount of money now, accruing interest at that rate, is needed to produce a certain amount of money at future dates.

[Note 18] Ms. Brennan's and Ms. Burke's joint life estate, followed by Ms. McIntosh's life estate after both Ms. Brennan and Ms. Burke had died.

[Note 19] For a fuller explanation of this and each of the following, see Mr. Ricci's custom mortality tables and probability calculations, the other exhibits admitted in connection with his testimony, and his testimony itself.

[Note 20] Ms. Brennan is the younger of the two by some years. Mr. Ricci's calculations take into account Ms. Brennan's heavy smoking which, for mortality-calculation purposes, deems her four years older than she actually is.

[Note 21] As previously noted, the "remainder" is the present value of the fee after the present value of the life estates has been deducted. The present value of the life estates plus the present value of the remainder = $700,000 (the present market value of the property).

[Note 22] Up until 2010, all of the property's expenses were paid by the parties' father, Joseph Rigoli.

[Note 23] See G.L. c. 241, §23 (recognizing the court's discretion, guided by "justice and equity," to award or deny compensation in connection with a partition proceeding). See also Sanborn v. Johns, 19 Mass. App. Ct. 721 , 724 (1985) ("The task of a court in partition proceedings is to make the portions of the parties just and equal, that is, just and equitable [T]he choice of charges to be made and their allocation varies according to the circumstances [with] the judge [ ] given considerable leeway") (internal quotations and citations omitted).