Ch.10, Estate Planning, Ex. 4.2

Ch.10, Estate Planning, Ex. 4

  1. This seems like a simple excercise of calculating core capital. The solution is provided with real-risk free rates. However, using nominal rates should yield the same results. In my opinion, there shouldn’t be a nominal inflation growth rate applied to first year spendings (see exhibit 2 for reference). Then, the discounted value in the first year should be 1000,000 / (1.05) = 952,380 instead of the given 980,360 and the capitalized core capital over three years totals 2.802 million vs. the given 2.882 million.

Even if I apply an inflation growth rate starting with the first year, results will differ from the values in the curriculum book.

this is true only if the ‘Annual Spending’ is given in nominal terms as below:

Year 1 1,000,000 * 1.03 = 1,030,000

Year 2 1,000,000 * (1.03)^2 = 1,060,900

Year 3 1,000,000 * (1.03)^3 = 1,092,727

in which case one needs to discount each yearly spending need using the nominal risk-free rates (see also

yes, there should be as the question is asking “What is the capitalized value of their core capital spending needs over the NEXT three years” i.e. the first year under consideration is the next and spending needs are to be calculated with infl.: 1,000,000 * 1.03 = 1,030,000 and then, in the alternative approach, using risk free + infl. to discount: 1,030,000*0.99996 = 1,029,959 / (1.03*1.02) = 980,353 which yields an equivalent result as shown in the book

if you assume that the first cashflow (spending need) under consideration is 1,000,000, (i.e. no inflation is considered in the first year) then using 5% as discount rate would be wrong: if the cashflow doesn’t incorporate inflation one needs to discount it @ the risk free (i.e. 2%).

I agree with your calculatons in principle, but the treatment is inconsistent. If you were asked to name the core capital “over the next three years” in exhibit 2 (“example of core capital calculation”), the answer should be the sum of year 1 - 3, not the sum of year 2-4. And they are not applying an inflation growth rate to year 1.

It’s just a matter of interpretation, but in exam situation I may be doing it incorrect because their explanation and practice question differ.

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Funny, I actually remember this one from last year’s studying, and I see your confusion. However, there are two points of consistency throughout finance curriculum here and in university, unless stated otherwise:

  1. Starting figures are always at t=0

  2. Cash flow calculations are presumed to be ordinary annuities (end of period cash flows)

Based on this, I would respectfully disagree with your sum of years 1-3 vs years 2-4 statement, and you would grow the initial spending value by the rate of inflation under the nominal approach in the example. Test the above out throughout your preparation and I’m sure you’ll see it to be so. Zero confusion in an exam situation.

The first figure from the top in Column 7 of Exhibit 2 should be €515,000 (i.e. the whole column should be shifted one cell up).

This exhibit was adapted from

and whoever restyled it for the CFA curriculum wasn’t too alert.

If Earnest and Beatrice are “79 and 68, respectively” and their “current spending [is] €500,000” then, when they are 80 and 69, their spending has to be €515,000.

So the inconsistency you correctly identified is due to a sloppy editor.

Practice Problem 2. at the bottom of the same reading provides further confirmation as to how to treat calculations when dealing with this topic: in the alternative method, ‘year1 spending’ is = to current annual spending * 1+infl .

^Outstanding catch on the ages!