APE, VNB margin and mix

A life insurer writes, in a quarter, regular first-year premiums of ₹1,500 cr in unit-linked (ULIP), ₹900 cr in non-participating savings, ₹300 cr in protection and ₹600 cr in participating products, plus ₹2,000 cr of single premiums (annuities). Illustrative VNB margins on APE: ULIP 10%, non-par 35%, protection 60%, par 15%, single-premium business 20%. (a) Compute APE, VNB and the VNB margin. (b) Next year ULIP premiums rise 40% and everything else is unchanged. Compute APE growth, VNB growth and the new margin. Split the VNB change into a volume effect (the APE change at the old margin) and a mix effect. (c) By analogy with (6A.17), a steady-state insurer is worth $\text{P/EV} = (\text{RoEV} - g)/(k - g)$. Compute it for RoEV 16%, $g$ = 12%, $k$ = 13%; then with $g$ = 11%; then with $k$ = 13.5%. What does the sensitivity say about headline P/EV comparisons between insurers?