reading 38: Risk management/Private Wealth: the Schmitt family (

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


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)?

Use 53,650 instead of 80,000.

thanks, I get a result of HC 1083755 for Jessica, close enough :slight_smile:


In the same example, page 344,“need analysis method”, I am not able to recompute the PV of survivor’s income:

For Jessica: CFAI shows 777,000 for PV of survivor income

periods=20 (currently age 45, until retirement at 65)

adjusted rate=(1+discount 3%)/(1+nominal increase 1%)-1= 1.98%

after-tax salary: assume 53,650

PV(1.98%,20,53650,1) = 896,337

Could you review my numbers?


That’s off from my number. Try this.

END Mode

PMT = 53650

FV = 0

N = 20

I/Y = -0.95238095 (It works with -0.95)

[CPT] [PV] -1,187,914.944

Then 92% × 1,187,914.944 = -1,092,881.748

I think you misunderstood the context of “survivor” in this case.

For the column on Jessica, if she dies today, the survivor is Paul , hence the PV of survivor income is computed as:

BGN mode (Annuity due)

PV = 46,510 (Paul’s after-tax income)

I/Y = 1.9802

N = 20

FV = 0

[CPT] [PV] -$777,049

Thank you for your help!

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!

I got the same number as you. Can anyone explain this ?



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

Am I missing anything?

Mode: BGN

PMT = 53,650

N = 20

Adjusted rate [I/Y]
= (1 + 3% discount rate + 1% risk adjustment)/(1 + 1% growth) - 1
= 2.9703%

FV = 0

[CPT] [PV]

Thanks a lot fino_abama!

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You’re welcome :ok_hand:

Have you been able to recompute Paul’s HC (798k)?

Nah, still the same number I got before. Any idea how I might get this wrong? Or it’s just some “Significant” rounding for the computed value

To everyone, including EugeneNYC, make sure your number of periods (P/Y) = 1. I was getting funky numbers because my periods were not 1.

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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.