CFAI book 6, page 339, in the “Schmitt family” case.

At age 45, I fail to recompute Paul’s and Jessica’s human capital in the economic balance sheet.

CFAI shows Paul’s human capital = 798,000 and Jessica’s human capital = 1,093,000

Inputs:

Jessica salary before taxes = 80000

nb periods = 20

Salary growth=5%

Discount rate = 3%

Risk adjustment=1%

I compute adjusted rate as (1+discount+risk adjustment)/(1+growth):

for jessica adjusted rate = (1+3%+1%)/(1+5%)= -0.95%

PV for Jessica=PV(-0.95%,20,80000,1) as annuity due in excel = 1,754,941

then multiply by 92% probability rate (given in the text)

HC for Jessica=1,614,546

Is anyone able willing to help? Is the HC based on the after-tax salary? Or does the CFAI use a different mortality table (ie a % different from 92% at each period)?

How did you get the same number for Paul’s HC ($798,000)
Here is what I did:
END Mode
PMT = 46,510
N = 20
I/Y = (1.03/1.02) - 1 = 0.98%
FV = 0
Then I got a PV = 840,991.212
92% * 840,991.212 = 773,711.91

I will be appreciative if you can show me your calculation! Thanks!

May I know for Paul(Jessica is survivor)? I can’t seem to reach 824,000
PMT=53,650
N=20
Adjusted rate used =(1+discount 3%)/(1+nominal increase (-2%))
PV=696,776

Why are we using an annuity due here? aren’t salaries supposed to be received at end of periods? In the same case, an earlier needs based PV is calculated using end of period setting (which is how it should be)

If the spouse dies today, do you think the surviving spouse would want the first income payout now (annuity due) or at the end of the year (ordinary annuity)?

But for this particular bit (the 824,000 or the 777,000), we aren’t calculating the payouts to be received by survivor but rather the expected PV of survivor’s income (his/her salary basically), which should supposedly be received at the end of a month. I totally get why living expenses PV are calculated using Annuity Dues as these are due at the beginning of periods. In contrast, when calculating PV of survivor’s income, not sure how the annuity due assumption makes sense.

How do you calculate the Net Present Vale of Peter´s Care (exhibit 20)?

Exhibit 20. Net Present Value of Peter’s Care

The required funding for the goal of providing for Peter’s care for the rest of his life can be modelled as the present value of a deferred-start annuity (even though they would not be buying one now) that begins in 20 years’ time. Its duration would equal Peter’s life expectancy then (an additional 53 years of life up to the age of 90). The following table shows the PV of such an annuity, with different assumptions, considering a yearly cost of €30,000 in real terms. Because the Schmitts emphasized the need to address inflation risks, the calculations are performed in real terms—that is, the amounts are expressed in euros based on their value at present time when the Schmitts are 55. The discount rate represents the real discount rate.

Real Discount Rate

PV

1.0%

€1,018,000

2.0%

€669,000

3.0%

€438,000

Note: The amounts are rounded to the nearest €1000 for the present value of this annuity due lasting 53 years.