Case 025Long pitches and valuationHard

Ambrel General Insurance writes Rs 8,000 crore of premium at a combined ratio of 104%, holds invested assets of Rs 10,000 crore earning 7%, has Rs 4,000 crore of equity and a 25% tax rate. The stock trades at 2.5x book. What ROE does it earn, what does the price imply, and what would change your view?

The situation

Ambrel General Insurance sells motor, health and property insurance. It writes Rs 8,000 crore of premium a year. Its combined ratio, claims plus operating expenses as a share of premium, is 104%: for every Rs 100 of premium it pays out Rs 104. Because premiums arrive before claims are paid, it holds invested assets of Rs 10,000 crore, mostly this float of policyholder money, earning 7% a year.

Ambrel has Rs 4,000 crore of shareholders' equity and pays tax at 25%. The stock trades at 2.5x book value. For the exercise, take a cost of equity of 13% and long-run growth of 8% as your assumptions.

Your task

What return on equity does Ambrel earn, what does 2.5x book imply, and what would change your view?

Quick check

Roughly what return on equity does Ambrel earn today?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

Ambrel earns an ROE of about 7.1%, and 2.5x book implies an ROE near 20.5%, which needs a combined ratio of about 95% instead of 104%. Underwriting loses Rs 320 crore, investments earn Rs 700 crore, and Rs 285 crore after tax on Rs 4,000 crore of equity is 7.1%. Even at a 100% combined ratio ROE is only about 13%. The price is betting on a large underwriting turnaround.

Step 1Where does Ambrel's profit come from?

An insurer earns in two places: underwriting, premiums less claims and costs, and investing the float, the money it holds between collecting premiums and paying claims. It is like a wedding caterer who takes advances months ahead: even if the catering itself breaks even, the advances earn interest in the meantime. At a 104% combined ratio Ambrel loses Rs 320 crore on underwriting, and Rs 700 crore of investment income more than covers it, leaving Rs 380 crore before tax and Rs 285 crore after. On Rs 4,000 crore of equity that is an ROE of 7.12%.

Investment income carries an underwriting loss; what is left is a 7% ROE-320Underwriting+700Investment380Before tax-95Tax at 25%285After tax104% combined7% on 10,000ROE 7.1%Rs crore a year
Ambrel loses Rs 320 crore on underwriting at a 104% combined ratio, earns Rs 700 crore on Rs 10,000 crore of invested assets, and keeps Rs 285 crore after 25% tax, an ROE of 7.1% on Rs 4,000 crore of equity.
Step 2What does 2.5x book imply?

For a company that grows steadily and earns a stable return on its book, a common valuation link is price to book equals ROE minus growth, over cost of equity minus growth. With a 13% cost of equity and 8% growth, 2.5x book needs an ROE of 8% plus 2.5 times 5%, which is 20.5%, almost three times what Ambrel earns. At its actual 7.1% ROE, below the cost of equity, growth destroys value; even with no growth the same formula gives about 0.55x book. The gap between 0.55x and 2.5x is what the market is paying for a turnaround.

The relationship
PB=ROE−gk−g  ⇒  ROE=g+PB(k−g)=8%+2.5×5%=20.5%\frac{P}{B} = \frac{ROE - g}{k - g} \;\Rightarrow\; ROE = g + \frac{P}{B}(k - g) = 8\% + 2.5 \times 5\% = 20.5\%
P/Bprice to book value, 2.5x
ROEreturn on equity
kcost of equity, assumed 13%
glong-run growth, assumed 8%
What it says in wordsRearranging the price to book formula gives the return on equity the current price requires.
Step 3What combined ratio would the price need?

Work backwards. An ROE of 20.5% on Rs 4,000 crore is Rs 820 crore after tax, Rs 1,093 crore before. Investments supply Rs 700 crore, so underwriting must earn Rs 393 crore. That is a combined ratio of about 95.1%, nine points better than today's 104%, and even a break-even 100% would only lift ROE to about 13.1%. Each point of combined ratio is worth Rs 80 crore of pre-tax profit, about 1.5 points of ROE, which is why insurance analysis lives and dies on that one ratio.

2.5x book needs a combined ratio near 95%, not today's 104%0%10%20%108%104%100%96%92%Combined ratio (claims and expenses over premium); better to the rightReturn on equityROE the price needs: 20.5%cost of equity 13%Today: 104%, ROE 7.1%100%: 13.1%95.1%
Ambrel's ROE rises in a straight line as its combined ratio improves, from 7.1% at today's 104% to 13.1% at 100%; the 20.5% ROE that 2.5x book requires needs a combined ratio of about 95.1%.
Step 4What would change your view?

Three things. Evidence that the combined ratio is falling for durable reasons, such as repricing of a loss-making motor book or a shift to profitable health policies, rather than a quiet year for claims. Reserve quality, because a combined ratio can look better for a few years simply by setting aside too little for future claims, which is the most common way insurers flatter earnings. And the float: its cost this year is the Rs 320 crore underwriting loss over Rs 10,000 crore, 3.2%, cheap against a 7% yield, and if the float grows fast at that cost, the investment engine is worth more. Without a credible path to the mid-90s, 2.5x book prices in more than the numbers support.

Where candidates lose it

The trap is seeing the underwriting loss and calling Ambrel unprofitable. Insurers run on float, and the investment income more than covers the loss here; the question is whether the ROE covers the cost of equity, and it does not.

The second is reading 2.5x book as expensive or cheap without asking what ROE it implies. Turning the multiple into a required ROE, and the ROE into a required combined ratio, is the move the interviewer is waiting for.

What the interviewer asks next

  • Ambrel's investment yield falls from 7% to 6%. What combined ratio does 2.5x book need now?
  • How would you test whether Ambrel's claims reserves are adequate from its public disclosures?
  • Why might an insurer with a 98% combined ratio deserve a higher multiple than one at 95%?

Company names and figures are illustrative.