One of the key equity valuation metrics for most industries is the Price to EPS or the PE ratio. All else held constant, the company with a lower PE ratio is considered cheaper than others.

But this ratio is not suitable for insurance companies for two reasons:

(i) A large portion of the premium incomes that a company reports are from contracts signed in prior years. So, even if a company signed zero new contracts in the current year, they may report profits. Thus, the profit reported for a year does not really reflect the complete business performance

(ii) Secondly, significant income earned by an insurance company comes from their investment income. These income may fluctuate depending external market condition. Thus a profit reported in one year may not fully reflect what is sustainable in future.

That is why we look at valuation using Price / Embedded value per share (EVPS) ratio. Before we understand the ratio or the embedded value, let us briefly understand the component of intrinsic value of an insurance company.

**Intrinsic value of an insurance company has four components**

If one were to apply the principles of DCF to an insurance company, we can break its value into four components:

**Free surplus**: Value of surplus assets that can be freely distributed to the shareholders**Required capital**: It refers to surplus assets (i.e. assets â€“ liabilities) that are held to meet solvency requirements, and thus cannot be distributed.Present value of expected profits from policies currently in force

**(value in force)**Present value of expected

**profit from new business to be underwritten in future**

These four components can be combined together as follows:

**Free surplus + Required capital = Adjusted net asset value**

**Adjusted net asset value + Value in force = Embedded value**

**Embedded value + value of new business = Appraisal value**

A simplified hypothetical illustration of calculating the embedded value is presented in the appendix. But the proper calculation of embedded value and appraisal value requires the application of actuarial techniques and hence most analysts do not derive them.

However, insurance companies do report their embedded values. Since it is not possible for equity analysts to calculate appraisal value, they simply try to value a stock by taking it as a multiple of embedded value.

**What is Embedded value?**

If you know DCF valuation, think of embedded value as the DCF value of the company assuming they don't underwrite any more policies. It has three components: (i) Free surplus (ii) Required capital and (iii) value in force.

We have already explained the meaning of free surplus and required capital, above. You can also refer to the appendix, below, to get more clarity. Value in force refers to the present value of all cash flows that would be distributed to the shareholders from the policies that are currently in force. Let us understand this part in a little bit more detailed.

Insurance companies receive premiums. These premiums are allocated to policy assets (assets held to meet policy obligations), which generate investment income. But with these amounts, the company has to pay claims and meet expenses. The company will also be declaring bonuses to policyholders. And the balance amount, net of taxes, will belong to the shareholders.

The expected premium and claim outflows can be estimated using historical mortality rate and persistency ratios. The actuary estimates these cash flows taking into consideration only the policies that are already underwritten.

The value of these cash flows is then discounted at an appropriate discount rate to arrive at the value in force (VIF). The illustration in the appendix is an oversimplistic illustration of the calculation of VIF. You may refer to it to get a broader understanding of VIF calculation. But it is not entirely accurate as several minor factors have been ignored in it.

**What does Price / EVPS mean?**

As mentioned above, the fair value of an insurance company is its appraisal value, which includes the Embedded value + value of the new business.

So, if we equate fair value to X times of embedded value, then we are assuming that the value of the new business will be (X-1) times of current embedded value.

For instance, if we say that the Price/EVPS ratio should be 3, then we are assuming that the present value of profits from future business would be twice that of the current embedded value. Here is a step-by-step derivation of it for those interested:

If â€“

Fair Price /EVPS = 3

==> Fair Price = 3 * EVPS

We know that

Fair price = EVPS + Value of new future business per share (VFBPS)

In other words,

3 * EVPS = EVPS + VFBPS

Therefore

VFBS = 2 * EVPS

**What are the limitations of Price / EVPS as a valuation metric?**

As we mentioned earlier, a higher Price / EVPS ratio indicates that we expect the insurance company to generate much more value from its future business than from the current set of policies in force.

And this is what causes the limitation.

Companies that started just a few years ago are likely to have a much smaller insurance book. And thus, it may not be inappropriate to expect the fair value of the company to be several times more than the embedded value.

On the other hand, well-established insurance companies with a very large market share are likely to have a far higher base of insurance books. It is less likely that they would be able to multiply their value as much as newer and smaller firms.

So, if in a country we have a large and very old insurance company that has been consistently losing market share, its fair Price / EVPS ratio should be lower than the industry average, as they cannot multiply their business as much as smaller firms.

**Appendix: Illustration of embedded value calculation**

You can download the __MS Excel file from this link__.

Do note that the illustration is not entirely as per the actuarial standards but it is a far simplified illustration merely to explain the core principles.

Great Lake Insurance company has a total asset of CUR 100 million, of which CUR 5 million is considered dead assets (furniture, fittings, etc., that cannot be sold for value)

The company has a liability of 40 million and the regulators expect the company to have assets of 75 million to be meet solvency requirements.

The following are the expected cash flows from the existing policy in force.

Assume no taxes. Calculate the embedded value of the company assuming the expected cost of capital to be 12%.

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