Core Capital

CFA Level III
#1

Ok, this is a simple question but I can’t wrap my head around this.

Example 4 Volume 2 Reading 10 P. 284 Solution 2

I don’t understand why we don’t increase annual spending by the real rate of 2%?? What is throwing me off is in the question it says they want to maintain spending of ZAR 1,000,000 on an INFLATION ADJUSTED BASIS. If inflation is 3% and nominal RFR is 5%. In my mind we need to increase that number by the inflation rate and discount it back using nominal rate (5%) or increase it by real rate of 2% and discount it back by the real rate of 2%.

In Exhibit 2 (page 281) they appear to increase annual spending by 3%. I’m assuming we do this because it says “increase annual spending by 3% growth rate”

I just don’t understand why it’s 1MM ZAR each year and we don’t increase that at all? Please explain in a very basic manner. I’m probably overthinking this… ugh

#2

This is wrong. They want to maintain spending of ZAR 1,000,000 on an inflation adjusted basis. On real basis you don’t need to adjust for inflation and the only adjustment needed was for inflation, hence no adjustment needed. If you increase by real rate of 2% it means that spending is increased by 2% on an inflation adjusted basis, which is wrong because they want to maintain spending. And increasing and then discounting by 2% will cancel each other out give you 1,000,000 for all years.

#3

Inflation is accounted for in the rather simplified discount rate - increase by 3% inflation and discount by 5% portfolio return - nets out to discount by 2%

say for example yr2 - 1m x surv prob / 1.02^2

1,000,000 x .9973= 999,730 / 1.02^2 = 960,910

hth