Measuring True Profits using Embedded Value
by
Peter Luk
Plan-B Consulting Ltd.
[email protected]
May 2004
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Measuring True Profits using Embedded Value
A. Introduction
The reported profit of a company seldom gives the true indication of its value. The widely
used US GAAP has been severely criticized over the decades, particularly for the artificiality
of its DAC (deferred acquisition cost). The IASB (International Accounting Standards
Board) has been trying hard to come up with a better, universally accepted (i.e., by all
countries) accounting standard. Due to all the kinds of honest difference of opinion as well as
political bickering, it appears that this is at least anywhere between three to five years away.
Meanwhile, the use of embedded value has gained increasing acceptance. Even in the US, as
recent as five years ago, not many people have heard of the term “embedded value”. Today,
almost all major companies calculate their EV, although not all of them publish such
information.
While EV (embedded value) and AV (appraisal value) have become such important a subject,
there is little actuarial literature on it. It is hoped that what is described here can fill this gap
to some extent.
B. The anatomy of the value of a company
If somebody asks the question “How to value a life insurance company”, the simple answer
given here is: It equals “three companies plus a painting”.
What is that? It means that an insurance company can be considered as a holding company
with three subsidiaries: a service company, a sales company and an investment company, plus
a painting.
The method described below is for the valuation of a life insurance company, but the
principles are actually mostly applicable to any kind of company, not just an insurance
company.
1)
Service company
This company makes money by providing services for the existing clients. The
company needs certain capital to keep it working, but it will not keep more than
enough. Any excess will be paid back to the holding company as dividends.
Obviously, the value of this company equals the present value of those dividends
minus the initial required capital.
The present value is arrived at by discounting the dividends at the rate of i,
commonly called the hurdle rate. Alternatively, i is described as shareholder’s
rate of return or cost of capital.
As mentioned before, this company needs capital. There are two kinds of capital.
Any company will need operating capital, for equipment, machinery, space,
logistic support, etc. For banks and insurance companies, due to their fiduciary
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duty to the general public, there is another kind of capital, risk capital, mandated
by regulations (often called solvency margin or risk-based capital in the case of
insurance companies). It is like a cushion there to ensure that such financial
institutions will not fail under unfavorable economic conditions. In most cases
(though not always), the risk capital exceeds the operating capital. If there is no
regulatory restriction how such risk capital can be invested, the operating capital
can make up part of the risk capital. Under such circumstances, de facto, the
company only needs to have the risk capital. If part of the operation is outsourced
to an outside company, this outside company will have to have its own operating
capital, which will not be covered by the banks’ or insurance companies’ risk
capital.
For an insurance company, particularly a life insurance company, the maintenance
of inforce policies is akin to the function of a service company and the value of
the inforce policies is akin to the value of a service company.
The value of an inforce policy is calculated as follows. Make a year-to-year
projection of the company’s accounts using realistic (best-estimate) assumptions
about the future including investment return (j), mortality and morbidity, lapse
and surrender, acquisition and maintenance expenses, both variable and fixed,
taxes, etc. Reserve for policy liabilities is calculated using statutory basis (often
more conservative ones). Solvency margin is also calculated in accordance with
regulatory requirements.
This projection will produce for each year a
“distributable earning”, the amount that is not required to be kept by the service
company for its operation. It is assumed that these distributable earnings are
transferred to the “investment company” (see (3) below) for investment.
Prudential actuarial practice requires that the “distributable earnings” be positive
for every year in the projection. A negative number for a particular year would
imply the need for capital injection for that year. If the company has no money to
inject, the policyholders will not get paid. The fiduciary nature of the business
does not allow this to happen. The only time a loss is allowed to be incurred is at
the policy inception, i.e., at the time new business is generated. Such losses are
termed “new business strain”. The new business strain, an accounting loss, may
be considered as investments of the company to acquire new business. If a
company cannot afford the new business strain, it should stop writing new
business.
It should be noted that j and i are quite different. j refers to the return of the
portfolio of assets (consisting of bonds, equities, etc.) of the company, currently at
around 5% p.a. for many companies. On the other hand, i refers to the
shareholders’ expected rate of return. Since a business operation involves
significantly higher risk than portfolio investments, i is usually much higher. A
rate of i between 10% and 15% is not uncommon.
2)
Sales company
The sales company does nothing but generating new business. As soon as the
new business is generated, it is sold to the service company for a fee, which is the
equivalent of the present value of all the future profits the service company
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expects to make on this block of business, minus the required risk and/or
operating capital. In other words, the service company makes no profit out of it.
The sales company builds a model that estimates sales volume it can make in the
coming year (the base year) by reference to the past data. This is a static
calculation. It simply extrapolates the past into the future. It does not take into
account the dynamics of the general economic and sociopolitical environment, an
area that is reserved for the visionary.
Thus, the sales company can expect certain profit for the base year. The sales
company then projects the expected profit for each year thereafter by assuming
certain growth rates (that can vary from year to year). The period of projection
typically varies from 5 years to 30 years, depending on personal preference. Such
profits are then discounted back to the present at a rate of k, which is usually
larger than i to compensate for the extra risk of uncertainty that the projected sales
growth may or may not materialize. It is quite often to see k = i + 5% though
nobody knows the rationale behind that.
There are limited attempts to incorporate increasing competitiveness of the
business into the model. Two commonly seen methods are (a) the use of a
declining scale of growth rates over a period of, say, 10 years, which then remain
flat thereafter and (b) the use of a so-called “margin squeeze” whereby profit
margin is assumed to decline by say, 0.5% p.a. over a period of time.
The value of this sales company is the present value so arrived at in the preceding
paragraph less the operating capital required. When the sales company is part of
the insurance company, the service company can lend it part of their surplus
capital (i.e., the excess of its risk capital over its operating capital) effectively
make the sales company a zero-capital company. This would not be true if the
sales function is outsourced to an outsider broker or general agency company,
both of whom will have to put up their own operating capital, which will be a
charge to the value of the company.
3)
Investment company
When one hears about Microsoft sitting on billions of dollars of cash, possibly
investing in risk-free Treasury bonds earning minimum return, one cannot help
wondering what would happen if the money is distributed to their shareholders.
Would the stock price be affected? The rational answer is a simple no, since the
pile of cash is not affecting Microsoft’s earnings.
By the same token, the excess capital (i.e., the net worth less the solvency
margin), which is sometimes referred to as free surplus, will be kept by the
investment company investing in marketable securities. The value of the
investment company is the total market value of those securities, there being no
discounting of future income cash flow.
The analogy described above does not take into account the possible impact on a
company’s rating if such surplus cash is distributed.
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4)
Painting?
Why painting? It is used here to represent the psychological part of the investing
public. Imagine a Picasso painting costing millions of dollars (his “Boy with a
Pipe” was auctioned on 5th May 2004 in New York for US$104 million). It
generates no cash flow whatsoever, but people are nevertheless willing to pay a
hefty price for it. It does not reflect its ‘economic’ value. Rather, it reflects its
‘emotional’ or ‘psychological’ value at a particular moment. Each painting is
unique and its value changes from time to time.
The stock market ebb and flow reflects the mass psychology of the investing
public. The market value of a company can easily go up or down two or three
percent in a day’s time without the company’s fundamentals changing a bit. It
defeats any attempt at rational analysis.
We call this part of the company’s value its painting-value. The interesting thing
here, though, is that a company’s painting value can be negative. For instance,
where a company is in a “forced sale” situation, either because the company needs
cash or because the management makes a strategic decision to quit a market, the
painting value can be negative.
An often confusing item is goodwill. See the section on Debate for more detail.
C. Insurance terminology
The combined value of the service company and the investment company is called
embedded value (EV) in insurance jargon. Sometimes the value of the inforce
policies refers to the value before the solvency margin and sometimes it refers to
the value after the solvency margin. This can be confusing. One must determine
its true meaning in context. In the above anatomy, the required capital is assumed
to be kept by the service company and the investment company keeps the surplus
capital. In any event, the following expression should not cause any confusion:EV
= value of inforce + net worth − solvency margin
= value of inforce + free surplus
The combined value of the embedded value and the value of the sales company is
called appraisal value (AV).
The combined value of the appraisal value and the painting-value is the
company’s market price.
D. An illustrated example of projection
It is often helpful to illustrate complex theories by a numerical example. It is hoped that the
following example helps one understand what is discussed here.
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Revenue projection and embedded value of one policy
*acquisition *maintenance
Year *premium*commision
1
2
3
4
5
6
7
8
9
10
expense
expense
Increase in
claims* surrender* interest* reserve*
operating Increase distributable *value of *net solvency free Embedded *increase growth
profit* in SM* earnings* inforce worth margin* surplus* Value*
in EV of EV*
1,000
-300
-200
-50
-20
-60
23
-475
-82
-43
-125
798
-40
-40
-17
-73
62
-613
78
-22
56
717
-36
-16
-62
92
-589
106
-22
83
679
-34
-16
-56
120
-590
104
-23
81
657
-33
-16
-79
150
-569
111
-22
88
636
-32
-16
-105
179
-548
113
-21
92
615
-31
-16
-121
206
-529
125
-21
104
595
-30
-16
-137
233
-509
136
-20
116
576
-29
-16
-152
258
-491
146
-19
127
557
-28
-16
-5,552
283
4,913
156
213
369
====== ======= ======= ======= ====== ======= ====== ======= ====== ====== =======
Note 1:
Note 2:
Note 3:
Note 4:
Note 5:
Note 6:
Note 7:
Note 8:
323
496
515
509
504
491
473
439
390
321
0
120
43
1
497
44
65
57
571
74
15%
122
87
143
651
80
14%
230
110
231
735
83
13%
341
133
331
822
87
12%
463
154
439
912
90
11%
593
174
566
1,005
93
10%
740
194
710
1,099
94
9%
904
213
872
1,193
94
9%
1,085
0
1,285
1,285
92
8%
1,285 ====== ===== ======================
In the above table, year-start cash flow is indicated by * preceding the title whereas year-end cash flow is represented by * following the title.
Investment return =
5%
and the accumulation rate =
1.0500
Hurdle rate =
15% and the discount rate =
0.8696
The increase in reserve and increase in solvency margin are both positive. Because they are outgo items, they are shown as negative in the above table.
The rollover of inforce value works as follows:
starting value of inforce × 1.15 − profits for the year + increase in solvency margin = year-end value of inforce
For example:
439 × 1.15 − 136 + 20 = 390 (ignoring some rounding error)
The same applies to the new business. One just adds an item on the left side of the equation: year-end value of the new business.
The beginning value of inforce, 323, actually represents the value of a new policy. It is the value at the inception of the policy, before any cash flow happens. At that time,
the company has a net worth of 120, which accumulates to 120 × 1.05 = 126. However, it suffers a first-year loss (new business strain) of 82 during the year leaving a net
worth of 44, barely enough to cover the required solvency margin of 43. At that time, the new policy actually generates a future value of 496 at the end of the first year
(i.e., the same as the beginning of the second year). A similar rollover equation is as follows.
323 × 1.15 − (−82) + 43 = 496
Interest = (starting reserve + starting SM + cash flow) × interest rate. Thus, for year 2: (475 + 43 + 798 − 40 − 40) × 5% = 62
Year-end net worth = year-start net worth + profit + year-start free surplus × interest rate.
Thus, for year 6: 463 + 113 + 331 × 5% = 593
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E. Rollover of the inforce value
Embedded value calculations can be used to show the realistic operating profits as shown
below.
Let
W = Net Worth (W0 and W1)
i = discount rate used to calculate F = shareholders' expected rate of return =
hurdle rate = cost of capital
F = value of Inforce (F0 and F1) (calculated using reserve = statutory; discount
rate = i; other assumptions such as mortality, interest rate, lapse, expense,
etc. are all based on the realistic ones)
SM = solvency margin or required capital (SM0 and SM1)
R
= free surplus (R0 and R1) = W − SM
EV = embedded value (EV0 and EV1) = F + W − SM = F + R
(1)
B = year-end value of new business generated during the year
j = realistic rate of investment income for the year
W0 + statutory profits = W1
elements:
where statutory profits can be decomposed into 4
Pu = unwinding profits (profits from unwinding of F, if actual experiences
equal assumed. This includes, as mentioned previously, the interest
on solvency margin.)
Pi = investment income from the free surplus = Rj
Pe = experience profits (deviation of actual from assumed)
S = new business strain (i.e., statutory loss suffered due to the generation
of new business). This can be estimated as new business premiums −
new business commissions and overriding − allocated new business
administration expenses − year-end reserve for the new business
claims, etc. (sometimes, an interest element is also built into it).
T = True profit of the operation
There is no value creation in Pu and Pi. The former represents the unwinding of the profit
embedded in the inforce policies and the latter represents simply the interest income of the net
worth. The company incurs losses S for the generation of new business. However, it also
creates value B. The value creation of the new business is represented by B – S. On the
other hand, if Pe is positive it represents value creation. If Pe is negative, it represents value
destruction. Therefore, the true profit T = Pe + B – S is the best indicator of the strength
of the company:
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T = Pe + B – S
(2)
= Pe + ( B – S )
= Experience profits from inforce business + profits from new business
In arriving at the inforce value, we go backwards by discounting the future profits at i. It is
therefore only natural that in calculating future profits we should roll forward by multiplying
the inforce value by (1 + i ). This is, in the actuarial jargon, called unwinding (or rollover) of
the inforce value. As shown in the above illustrated example, the unwinding of the profit
embedded in the inforce policies is, ignoring new business, simply,
F0 × (1 + i) − Pu + ∆ SM = F1
With the addition of new business it becomes,
F0 × (1 + i) + B − Pu + ∆ SM = F1
(3)
Further, we have
W0 + Pu + Pi + Pe − S = W1
(4)
SM0 + ∆ SM = SM1
(5)
Combining (3), (4) and (5) together and taking note that EV = F + W − SM , Pi = Rj
and T = Pe + B – S,
EV0 + F0 i + B + R0j + Pe − S = EV1
And the most important item of profit measurement, the true profit T , equals
T = ∆ EV - F0 i - R0j
(6)
(7)
To paraphrase equation (7) into simple language: the gross value creation is ∆ EV.
However, since F0i is merely the unwinding of the interest discount originally embedded
there, it should be excluded. Moreover, the interest earned on the free surplus cannot be
considered as value creation either and therefore should be excluded too. If there is any
capital injection during the period, that should be excluded too since it is obvious that capital
injection is no value creation. If we equate true profits with value creation, then it becomes
apparent that formula (7) is universally true purely based on the first principle regardless of
the type of business and the structure of the company. Thus, a company many have many
different kinds of assets (F0, R0, etc.). Some of them (like R0 here) are to earn market-based
interest rates (j), some of them (like F0 here) are to earn the company’s cost of capital (i). The
interest so earned cannot be considered as true value creation. If we deduct them from the
gross value creation (∆ EV), what is left is the true value creation, or the true profit (T), which
is the only indication of the profitability of the company’s operation.
Sometimes, the assumptions used to calculate F0 and those for F1 are not the same due to
change of environment, etc. In such cases, it would be desirable to calculate F1 first using
the same assumptions as F0 and then calculate separately the effect of assumption changes on
F1.
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To evaluate a company’s true profits, one must go to its statutory statements, not the GAAP
statements. Fortunately, in most countries, such information is publicly available.
Statutory profits and net worth are always reported. Solvency margin is often (though not
always) reported. Embedded value is sometimes reported. Value of inforce is seldom
reported.
Equation (1) is therefore helpful in helping us arrive at the value of the inforce policies:
F = EV + SM – W = EV – R
(1a)
i, the discount rate, is sometimes reported along with the embedded value. However, j is not
often reported. Even when reported, it is often different from what we want. For instance,
investment performance from unit-linked portfolio should be excluded as it does only affects
the performance of the policyholders’ value, not the performance of the company (which is
often meant to represent the shareholders’ value). Very often, there is some information in
the published statement wherefrom j can be estimated.
One would have expected that T is, at least in most cases, positive, since one would have
expected profits to be generated from new business. B and S from equation (2) are often not
available in the form of public information, but in-house actuaries should have no problem
arriving at some kind of reasonable estimates about them. If T is negative, particularly if it is
negative for several years in succession, this should give cause to concern. Either the
experience profit is negative or the new business profit is negative. And it can be both.
In the former case, it is suggestive of unrealistic assumptions being used in the calculation of
F. While it is technically easy to recalculate the numbers using more realistic (in this case
more conservative) assumptions, it is however politically quite difficult as the management
does not like to see their EV shrink simply because of the say-so of some actuaries.
Estimating profits from the new business is quite straightforward too. S is usually positive,
meaning losses being incurred in generating new business. Should S be negative in some rare
circumstances, it would be indicative of lack of competition. In a free market, this rarely
happens as competition would quickly drive the “new business profit” into the negative
region. It is not unusual to find S in the vicinity of 10% to 50% of the new business
premiums for regular premium business or zero to 2% in the case of single premium business.
On the other hand, B is almost always positive, but it is important that B – S be also positive,
meaning that it is desirable and profitable to generate new business. In a very mature market,
one could find B – S close to zero, a strong indication that the market is overdue for
consolidation.
As actuaries could always use, in theory, aggressive assumptions to make B – S positive, it is
desirable to look for assumptions used behind B, or at least to check if B and F are calculated
using consistent assumptions. Any significant departure is a sign for serious concern.
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F. A Case Example
A Company reported the following results:
Year 2002:
Statutory net worth:
Embedded value:
Solvency margin:
Discount rate:
460,000,000
2,130,000,000
226,000,000
15% p.a.
Year 2003:
Statutory net worth:
Investment yield:
Embedded value:
Solvency margin:
Discount rate:
530,000,000
8.4% p.a.
2,189,000,000
260,000,000
15% p.a.
The company made a respectable statutory profit of 70,000,000 for the year, representing an
increase of 15.2% of its net worth.
Using equation (1a):
R0 = W0 – SM0 = 460,000,000 – 226,000,000 = 234,000,000
F0 = 2,130,000,000 – 234,000,000 = 1,896,000,000
i = 15%
j = 8.4%
∆ EV = 2,189,000,000 – 2,130,000,000 = 59,000,000
Therefore, true profit T is,
T = 59,000,000 – 1,896,000,000 × 0.15 – 234,000,000 × 0.084 = (245,000,000)
This shows that the company made a staggering loss of 245 million during year.
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G. The Debate
There are quite a number of issues where there is no consensus as yet. Discussions of a few
of the most important ones are listed below for reference.
G1. Determination of the hurdle rate i
This will be a relatively easy task if one is acting for the buyer in an M & A transaction. The
buyer would specify their expected rate of return.
On the other hand, the seller could also specify their own version of the hurdle rate.
However,
such hurdle rate normally would not exceed what the prevailing market condition would
imply, unless there are special circumstances such as (a) when the sale would give the
potential buyer the critical mass in a highly competitive market, (b) when the sale would give
the potential buyer entry into a market that is not normally easy to obtain, (c) when the sale
would give the potential buyer substantial scale of economy, (d) when the sale would give the
potential buyer control of the company, etc.
The most difficult situation is where the actuary who is performing the EV calculation is
acting in an “independent” capacity such as in the case of an IPO (initial public offering).
The hurdle rate in such cases would be equivalent to what the prevailing market would imply.
A great deal of judgment could be involved. It is not unusual to see i exceeds the prevailing
“risk-free” rate by 3% to 6% to reflect the appropriate risk premium. Sometimes, the CAPM
(capital asset pricing model) would be used to determine the risk premium as:
i = risk free rate + β × (average rate of return of the market – risk free rate)
where β can be determined from market data using the regression method. In Asia, β is quite
often between 0.7 and 1.0.
What is not seen in the usual actuarial literature is that in Asia i is often higher than what one
would normally expect. This could be due to one of the following reasons: (a) Asian stock
markets are more volatile and a higher premium is expected, (b) a risk premium for currency
risk is incorporated where the potential buyer thinks in terms of US dollar, (c) the perception
that Asian markets are less mature, less transparent and therefore more risky.
By the same token, a Chinese company listed in the U.S. should command a lower valuation
(i.e., due to a higher risk premium) than a similar company listed in its domestic stock market.
G2. Determination of the rate of return j
The rate obtained from the data disclosed by the company is often not appropriate for the
purpose here. Different companies have different risk appetite that is often reflected in the
investment performance of the company for the period under review. It is much better to
estimate j from the market average and leave the variance as part of Pe. While moderate
deviation could be ascribed to the performance of the investment managers, substantial
deviation, whether positive or negative, is often indicative of high risk appetite of the
- 12 -
company. Consequently, one should be wary of “superior investment results” in a company’s
financial statement. Contrary to what one would think, it is often not a good thing.
Another plausible method is to consider j as the current risk free rate for the period and take
any excess as the return for the risk taking and therefore represents value creation, whether
positive or negative.
G3. Dividend discount model or P/E method?
The P/E ratio method is probably the most widely used method to value a listed company.
This method assumes a certain constant growth of the annual earnings and then discounts the
stream of the earnings at the rate of the cost of capital (the hurdle rate) to arrive at the
capitalization rate. The target price then simply becomes the product of the capitalization rate
and the annual earnings.
The dividend discount model (DDM) is essentially the same as the P/E ratio method if one
assumes a constant dividend payout ratio. The following illustrates the theoretical method to
arrive at the target P/E ratio.
Let
P
E
r
D
g
i
=
=
=
=
=
=
target price of the stock
annual earnings
dividend payout ratio
r x E = annual dividend
compound annual growth rate
discount rate (or cost of capital)
Then, the following detailed formula can be obtained:
P =
r E (1 + g) 3
r E (1 + g) 2
r E (1 + g)
+ ⋅⋅⋅⋅⋅⋅
+
+
(1 + i ) 3
(1 + i ) 2
(1 + i )
(8)
Further, the previous formula can be reduced to a simple one as follows:
P
E
=
r (1 + g )
i - g
(9)
For instance, if we assume a constant dividend payout ratio of 0.65, a compound earnings
growth rate of 8% p.a. and a discount rate of 12% p.a., the above formula will produce a
target P/E ratio of 17.55.
The above DDM model is well documented in the security analysts' bible Graham and Dodd's
Security Analysis. It is actually an application of the well-known discount cash-flow (DCF)
method to an assumed stream of future earnings, a method that is the basic stock-in-trade of
all actuaries and financial analysts.
It is now apparent that while the P/E ratio method is an effective and simple method it fails to
work in circumstances where the current earnings are negative. While the future earnings can
still be positive and the DCF method is still applicable, the P/E ratio method fails because it
- 13 -
uses the simplified formula (9) as shown above instead of the detailed formula (8). In so far
as this valuation method actually incorporates the values of the “service company” and the
“sales company”, it also fails to take into account the value of the “investment company”, as
illustrated above in the case of Microsoft’s huge cash surplus.
An astute observer will notice that the above method is very sensitive to the earnings growth
rate and where g is large relative to i , the P/E ratio can be so large (or even negative) that it
can become meaningless. This is what happened to internet stocks a few years ago. In
reality, the prevailing P/E ratio is often the result of a mixture of mathematics as shown above
and investors' sentiment and preference at a particular moment. In other words, the paintingvalue plays a big role here.
G4. Appraisal value or embedded value?
As mentioned above, the combined value of the “service company” and the “investment
company” is called embedded value (EV), and the combined value of the “sales company”
and the embedded value is called appraisal value (AV). In theory, the appraisal value of a
company is the best proxy of the true value of a company (barring the impossible task of
evaluating its painting value). A good example is a 3-year comparison of the share prices of
AXA China (listed in Hong Kong before it became privatized) versus its appraisal values.
AXA China - ratio of share price over appraisal value
1.6
1.4
1.2
1
0.8
0.6
6/
96
8/
96
9/
96
11
/9
6
12
/9
6
1/
97
3/
97
4/
97
5/
97
7/
97
8/
97
10
/9
7
11
/9
7
12
/9
7
2/
98
3/
98
5/
98
6/
98
7/
98
9/
98
10
/9
8
11
/9
8
1/
99
2/
99
4/
99
5/
99
6/
99
8/
99
9/
99
11
/9
9
0.4
In recent years, however, there has been a noticeable trend away from the use of appraisal
value in favor of the use of embedded value. This is because the growth rate of a company is
(a) not a constant as suggested in formulas (8) and (9) – it fluctuates from year to year – and
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(b) it is extremely difficult, practically impossible, to determine the future growth rates of a
company with any reasonable degree of confidence.
The most popular method of valuation in recent years is to first calculate the embedded value
of a company and then apply a “multiplier” reflecting its growth potential as well as its
painting value. In a matured market, such a multiplier often varies between 0.8 to 3.0 (see
chart on the next page). In a fast developing market, a much higher multiplier is not unusual.
Another popular method, widely used in Asia, is to apply the multiplier only to the value of
“one-year’s new business” as mentioned in section B above. In such cases, the multiplier can
easily be in the order of double digits. A good example is China Life’s dual listing in New
York and Hong Kong, the largest IPO in the world in 2003. The listing document gave the
embedded value at a discount rate of 12.5% as HK$2.22 per share (the listing document
actually published embedded values for three discount rates: 10%, 12.5% and 15%). It also
gave the value of one year’s new business, also at 12.5% p.a., as HK$0.158 per share. At the
IPO price of HK$3.59, it meant a multiplier of 8.7. At its peak price of HK$7 a few weeks
later, the multiplier worked out to around 30.
G5. What assumptions?
The mathematical analysis of the actuarial science is fairly straightforward. With the advent
of the modern-day computers, the “mathematical genius” of actuaries is no longer needed.
The most difficult part of an actuary’s job is probably the determination of appropriate
assumptions.
Arguably, this is one of the areas where actuaries are susceptible to criticism. But strangely,
this is also one of the areas where the profession has spent less than adequate effort in training
new actuaries.
Actuaries are supposed to think independently and professionally. Therefore, prescribed
assumptions, apart from the regulatory context, are not considered desirable or appropriate.
However, it is not infrequent to see pricing actuaries, under the pretext of independent
thinking, use aggressive assumptions in order to make their products more saleable, only to
find them unprofitable years later. This is acceptable if, and only if the management is fully
aware of the circumstance and wants to use certain products as “loss leaders” to capture
market share. This is not acceptable if the management is not aware of the implication of
such actions on its capital adequacy.
How can one then tell what the right assumptions are? In reality, there is no such thing as the
“right” assumptions, as no one has the crystal ball to see the future. There are only varying
degrees of acceptability. For instance, for a whole life insurance policy, an assumed long
term interest rate of 4% to 6% may be considered acceptable with varying degrees of
conservativeness, whereas an assumption of 2% p.a. might be considered too conservative and
an assumption of 9% p.a. would be considered overly aggressive.
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U.K. Companies Comparison Chart (Market Price / embedded value (%) )
650
600
St. Jam es Place Capital
550
500
450
400
CGU plc
350
300
Legal & General
Prudential plc
250
200
Norw ich Union plc
150
100
50
10/00'
08/00'
06/00'
04/00'
02/00'
12/99'
Prudential plc
10/99'
08/99'
06/99'
04/99'
02/99'
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12/98'
Norwich Union plc
10/98'
08/98'
06/98'
04/98'
02/98'
12/97'
10/97'
CGU plc
08/97'
06/97'
04/97'
02/97'
12/96'
Legal & General
10/96'
08/96'
06/96'
04/96'
02/96'
12/95'
0
St. Jam es Place Capital
The best way to determine the appropriateness of the assumptions in the calculation of a
company’s EV is by full disclosure. By full disclosure it is meant that such disclosure would
enable another actuary to arrive at, approximately, a new EV if this actuary wishes to change
certain assumptions. A compromise, though less satisfying, is to publish the results of certain
sensitivity tests or alternative scenarios.
The disclosure of certain key assumptions such as discount rate, investment return, mortality
tables used, unit expenses, etc. would enable the users to determine whether the assumptions
are on the whole leaning towards the conservative side or the aggressive side.
There may be outcry against this proposal on the ground of confidentiality. The fact is that
history has taught us many lessons. In the face of inadequate disclosure, there is a tendency
on the part of potential investors to assume the worst. One might recall that there was a huge
outcry several decades ago when banks were asked to disclose their hidden reserve. The end
results are such that no banks have been hurt by the fact that they were forced to disclose their
hidden reserve. In fact, that led to a more transparent banking industry and more public
confidence in it.
G6. What is goodwill?
An often confusing item is goodwill. This term is often loosely applied to anything that is
intangible. But in most cases goodwill is not painting value. This is the case where the
existence of goodwill is based on the expectation of future economic benefits. For example,
when a company acquires another company for a substantial premium resulting in a huge
amount of goodwill on its balance sheet. Such goodwill is assumed to reflect the present
value of future benefits and is required by most accounting rules to be amortized against
future earnings. In such cases, the goodwill should not be treated as painting-value. If it is
regarded as part of the inforce value, then when we try to measure the true profit or value
creation by using formula (7) of section E, F0 in that formula should include the amount of
this goodwill.
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References
GAAP – Stock Life Companies – 1974, by Ernst and Ernst
US GAAP for life insurers – 2000, by Society of Actuaries
Actuarial Appraisals – Theory and Practice – August 1995, by Henry Essert,
Canadian Institute of Actuaries
International Measure of Profit for Life Assurance Companies – 1999, by P.J.L.
O’Keeffe and A.C. Sharp, Volume 5, Part II, No. 22 of British Actuarial Journal
Developing an International Accounting Standard for Life Assurance Business – 1999,
by D.O. Forfar and N.B. Masters, Volume 5, Part IV, No. 24 of British Actuarial
Journal
Summary and Comparison of Approaches Used to Measure Life Office Values –
October 2001, by Life Assurance Value Measurement Working Party to The
Staple Inn Actuarial Society
Use of Embedded Values at United States and European Insurance Companies
October 2001, by Milliman USA
–
The Value of a Listed Life Insurance Company and How it May be Affected by
Different Accounting Rules – August 2002, by Peter Luk to Society of
Actuaries of China at Lijiang
An Overview of Embedded Value – November 2003, by Hubert Mueller, Issue No. 55
, The Financial Reporter, Society of Actuaries
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