The concept of human capital can be thought of as the present value of an individual’s future earnings and wages. For most households, human capital represents the single largest asset on the economic balance sheet.
The formula used to calculate an individual’s human capital is as follows:
Where:
Depending on the profession, the wages used may be higher or lower and more or less sensitive to the business cycle. Additionally, the discount rates used in the model should be consistent with the risks of wage growth and consistency of the assumed profession.
Let’s assume an individual was 55 and planned on retiring when he or she reached the normal retirement age of 65. Further, this individual’s current salary is $100,000 and as a professor has consistently received a 3% cost-of-living adjustment (COLA) on an annual basis.
Since this individual has tenure, the discount rate assigned for occupational income volatility is 3%, and the risk free rate is currently 2%. What is the present value of human capital for this individual if he or she has an expected survival rate of 99% in the first year, declining at 1% thereafter on an annual basis?
First, let’s use Excel to model the future value of wage growth over the next ten years at a 3% annual COLA:
| Year | FV Wages @ COLA |
| 1 | $103,000.00 |
| 2 | $106,090.00 |
| 3 | $109,272.70 |
| 4 | $112,550.88 |
| 5 | $115,927.41 |
| 6 | $119,405.23 |
| 7 | $122,987.39 |
| 8 | $126,677.01 |
| 9 | $130,477.32 |
| 10 | $134,391.64 |
Next, we’ll need to discount the future value of wages in each year to the present period by the total discount rate, composed of the risk free rate and the discount rate assigned to occupational income volatility:
| Risk-Free Rate | Income Volatility | Total Discount Rate |
| 2.00% | 3.00% | 5.00% |
Using the total discount rate of 5%, we can expand the table above as follows:
| Year | FV Wages @ COLA | PV Wages |
| 1 | $103,000.00 | $ 98,095.24 |
| 2 | $106,090.00 | $ 96,226.76 |
| 3 | $109,272.70 | $ 94,393.87 |
| 4 | $112,550.88 | $ 92,595.89 |
| 5 | $115,927.41 | $ 90,832.16 |
| 6 | $119,405.23 | $ 89,102.02 |
| 7 | $122,987.39 | $ 87,404.84 |
| 8 | $126,677.01 | $ 85,739.99 |
| 9 | $130,477.32 | $ 84,106.84 |
| 10 | $134,391.64 | $ 82,504.81 |
Now, we will multiply the present value of wages in each year by the expected probability of survival in each given year:
| Year | FV Wages @ COLA | PV Wages | p-survival | P-adjusted Wages |
| 1 | $103,000.00 | $ 98,095.24 | 99% | $ 97,114.29 |
| 2 | $106,090.00 | $ 96,226.76 | 98% | $ 94,302.22 |
| 3 | $109,272.70 | $ 94,393.87 | 97% | $ 91,562.05 |
| 4 | $112,550.88 | $ 92,595.89 | 96% | $ 88,892.05 |
| 5 | $115,927.41 | $ 90,832.16 | 95% | $ 86,290.55 |
| 6 | $119,405.23 | $ 89,102.02 | 94% | $ 83,755.90 |
| 7 | $122,987.39 | $ 87,404.84 | 93% | $ 81,286.50 |
| 8 | $126,677.01 | $ 85,739.99 | 92% | $ 78,880.79 |
| 9 | $130,477.32 | $ 84,106.84 | 91% | $ 76,537.23 |
| 10 | $134,391.64 | $ 82,504.81 | 90% | $ 74,254.33 |
| HC | $852,875.90 |
Multiplying the present value of wages by the probability of survival in each year, yields the product which represents the probability weighted present value of wages. The summation of each of these values indicates this individual’s human capital is $852,875.90 under the given assumptions.
In other words, if this individual were to pass away today and had dependents who were counting on this income for survival, a total of $852,875.90 of life insurance would be required to replace his income if no life insurance policies were currently in force.
Keep this formula and model in mind the next time an insurance agent tries to randomly assign an arbitrary face amount to a policy when attempting to sell you life insurance.
A copy of the Excel model used to calculate the present value of human capital can be found here.