Either I’m too tired and am making a dumb error, but I just do not understand nominal vs real cash and the discount rates used to discount things.
I thought you discount nominal stuff by the nominal rate and you discount real stuff by the real rate… Right?
So in Reading 10: Estate Planning in a Global Context on page 281, there’s a chart of annual spending and discounted value for Ernest and Beatrice.
Those two individuals need $500,000 a year inflation adjusted in retirement. In the chart, $500,000 is multiplied each year by the inflation rate of 3% to get the nominal spending amount each year, and then discounted by the real risk free rate of 2%…
Then on page 284, Kenroy and Alicia need $1,000,000 a year inflation adjusted in retirement. In the chart, $1,000,000 IS NOT mutliplied by the inflation rate of 3%, so we are left with the real spending amount each year. That real spending amount is then discounted also by the real risk free rate of 2% as the nominal risk free rate is 5%.
You simply need to READ better. Please note that the CFAI puts a LOT of matter right around tables, right around their examples - and in the white text matter.
The Websters’ inflation-adjusted annual spending needs are calculated based on their current spending of €500,000 per year and are increased annually using a 3 percent real growth rate (that is, 3 percent annual spending growth after inflation). The Websters’ expected spending need each year is presented in the column labeled Expected Spending (Column 8). It is calculated as the product of their joint survival probability and their required spending for that year (Annual Spending, Column 7). Each year’s expected spending is discounted back to the present, using in this case a real risk-free discount rate of 2.0 percent.
So the 3% is a REAL GROWTH RATE (It is AFTER inflation). Hence the REAL need is divided by the real rate to arrive at the core capital needs for Ernest and Bernice.
=====
For Kenroy and Alicia
They would like to maintain annual spending of ZAR 1,000,000 on an inflation-adjusted basis. Inflation is expected to be 3 percent, and the nominal risk-free rate is 5 percent.
They need 1000000 ZAR on an INFLATION ADJUSTED basis - so it is a REAL need. They say that just before they calculate the core capital as well.
The capitalized value of their core capital spending needs equals the product of the joint probability of survival and the real spending need for each year dis- counted using the real risk-free rate. Alternatively, one may discount the nominal expected cash flow at the nominal risk-free rate. Using the first approach, the real cash flows will remain constant and be discounted at 2 percent (or 5 percent less 3 percent).- (with footnote 16 providing some extra clarity Two percent is an approximation. A more precise calculation is: (1.05/1.03) − 1 = 1.94%.)