Estimating Human Capital

CFA Level III Portfolio Management
#1

On page 141 of Schweser Book 2, there was a problem estimating Human Capital. Why is discount rate 13%?

Projected Wage is calculated as nominal (includes inflation), so shouldn’t discount rate = 3% + 10% + 4% = 17%?

#2

Question info:

Alex Hamilton is 62 and expected to retire in 3 years. His current annual wage is 100,000 and expected to increase 4% per year. The risk-free discount rate is 3%, and his continued employment is considered very risky. A 10% risk premium is assumed. Using this information and the survival probabilities in the table, calculate his HC.

Answer: Increase earnings by 4% per year for the 3 years of employment, probability weight the earnings, and discount to the present value (PV) at 13% per year. 13% is the risk-free rate plus the risk premium.

HC = 248,825

My Comments:

  • 13% is the rf rate + the risk premium
  • For year 1:
    • His wage is (100 * 1.04) = 104k
    • ​​​​​​From the mortality table, he has a 98% chance of surviving the cold winter
    • 104k(0.98) = 101.92k
    • To get the PV, bring it back 1 year using the discount rate (13%): 101.92/1.13 = 90.195k
  • Do the same for years 2 and 3, sum up the PVs and you have your Human Capital!

So the 4% is not part of the discount rate used to reflect the riskiness of his earnings. It’s used to calculate his earnings for the 3 years.

#3

I felt like the 4% is inflation for the wage. Aren’t we supposed to discount using nominal discount rate when we have nominal wage in the numerator? I still don’t understand why discount rate is not 3% + 10% + 4% = 17%

#4

Another method is to adjust the discount rate by the growth rate of wage. The adjusted discount rate will be 1.13/1.04 - 1 = 8.65% or 3%+10%-4% = 9%. Using this adjusted discount rate, you can obtain the same result.

#5

On pg. 384 of Volume 2 of the CFA text it states that you are supposed to discount by the nominal rfr plus the occupational income volatility (and the discount rate can be different then the wage growth rate). Although not listed above, it is likely rfr quoted is nominal. I remember at some point seeing commentary on why you use the rfr vs. the wage growth rate, but I cannot seem to track it down. Maybe another forum member has the answer.

#6

Thanks. Yes, I found the definition risk premium includes inflation.