Can you please explain in detail the calculation done in Page 9 of Chapter 3 at a step level? Why are we dividing by 11.39? from where is 12.2% calculation coming in? Please explain!
Hi Muskan The reserve is the amount of the annuity (A) multiplied by the annuity factor using the valuation assumptions (12.85), ie A x 12.85. However the question doesn't tell us the amount of the annuity. Ignoring initial expenses and commission, the price is the amount of the annuity multiplied by the annuity factor using the pricing assumptions (11.39). We want to work in percentages, so it is easiest to assume a premium of 100. Ignoring the initial expenses and commission gives us a premium of 95. So 95 = A x 11.39. Hence A = 95 / 11.39. Substituting this back into the equation for the reserve gives us A x 12.85 = 95 x 12.85 / 11.39 = 107.2. The solution says that 12.2 = 107.2 - 95. This is the cost of capital per 100 of premium, ie 12.2%, where the cost is the difference between the net income at the start (95) and the cost of the reserves (107.2). Best wishes Mark
