# Core Capital Estimation with Mortality Tables

## Introduction

Core capital is defined as ” the amount of capital required to fund spending to maintain a given lifestyle, fund goals, and provide adequate reserves for unexpected commitments”. In another way, it is the money “needed” for the rest of the one’s life.

The concept of core capital is pretty important. In estate planning, one will need to clearly understand how much capital you have to pass on to others (family, charity, etc). Just like financial reporting for a company, it is not too difficult to come up with something similar for a family, list the total asset and liabilities. If we factor in the total liability including the future spending (core capital) and also the human capital of all future projected employment income. We will be able to find the “excess capital”. In that case, to accurately quantify the core capital is an important element in estate planning.

In order to calculate that, we will need know people’s life expectancy, spending for each year and take the time value into account to calculate the total present value.

## Mortality Table

It is surprisingly predictable at an aggregated level regarding people’s lifetime expectancy. Just like for a group of kids, it is very likely all of them will survive for another 10 years and as certain as almost none will survive another 50 years post 65.

There is a table that listed many of the statistics related to survival of different age called mortality table. By a quick Google search, one can easily find several published mortality table listed by US CDC (United State Center for Disease Control).

The document that I found was categorized into different tables based on demographics, Hispanic, White and Black and the corresponding male and female.

Most of the statistics are fairly easy to understand and you can refer to this report – National Vital Statistics Report for the detailed definition and explanation of each field. (quite a fun read!)

Of course, if we need to calculate the core capital required for a family, then one will need to use the joint probability calculated as subtracting one by the probability that both couple will die.

## Discount

Given the probability of surviving each year, we will need to estimate the spending needs for each year and adjust it accordingly. For example, there is the risk free rate which we can use, however, we also want to take inflation into consideration so our discount rate is likely going to be the nominal risk free rate minus the inflation rate.