 # CFAI Book 2/Reading 15/Question 13

How did Schweser come up with 7.38% Return Objective? I understand the 26K a year shortfall. Please someone break down for me. thanks,

Schweser?? Where did you find the discussion of this question in Schweser?

not schweser, my apologies. i mean CFA Institue Book 2.

If you use the TI BA ii plus. Hope this is helpful, as we are expected to arrive at the solution using one of the approved calcs. I dont know how it could be laid out matematically though and never tried the calc on HP 12 c. FV= GBP 2 million PMT= GBP 26,000 PV= GBP -1.235 million N= 18 years CPT I/Y you will arrive at the number 4.427%. 4.427%/(1-tax rate 0.4) = 7.38%

i’d be curious how to lay it out mathematically, if someone cares to opine i’ll restate the problem: 2,000,000 is needed in 18 years; current portfolio is 1,235,000; 26,000/year distribution will be required to maintain living standards what is required annual return to achive this objective? using TA BA II Plus, I also get 4.427% per year

You can lay it out mathematically: 1,235,000 = (-26,000)/(1+r)^1 + … + (-26,000)/(1+r)^18 + (2,000,000)/(1+r)^18. Solve for R. Have fun.

Actually, to those who are interested, there is a way to solve this equation with a simpler formula, using YTM approximation (I had to dig out my old finance notes for it) YTM approximation = [annual payment + (FV - Po) / T] / [0.6 * Po + 0.4 * FV) In this example: YTM approximation = [26,000 + (2,000,000 - 1,235,000) / 18] / (0.6 * 1,235,000 + 0.4 * 2,000,000) = .04445 or 4.445% (pretty close to exact answer of 4.427%)

Its interesting to see it laid out mathematically, in the morning exam we have to write out the answer, so i presume we need to know the underlying mathematics.

I don’t think this is right. (I think CFAI is wrong) the 26K is a differential between income and expense that both grow at the rate of inflation. In other words, the dollar figure cannot be constant over the years. Only the ratio between income and expense will stay constant. For example, the income number of 48K becomes 81.72 in 18 years with 3% inflation and the expense number of 74 becomes 125.98. Thus, the difference in absolute dollars figure keeps changing over the years. And, paying out a flat 26K like a coupon calculation can’t be right. I did mine differently. I calculated the % of 26K from the current portfolio of 1235K and came up with 2.11% which will have to be added to the 2.71% needed to grow the portfolio to 2mm in 18 years (without coupon payments). Thus, they sum to 4.82% and diving by .6 gives me 8.04%. Am I over thinking this?

This one’s correct MellonC00 - check out the 4th post on this threat about how to input it into your calculator - easier, quicker, and makes sense.

inflation on living expenses is not an issue here because of this sentence, “After-tax salary increases will offset any future increases in their living expenses.” So whatever the inflation is on 74k it will be offset by and after-tax salary increase on 48k and 26k shortfall will be constant during 18 years

I don’t think you guys are understanding my post. The 26K which is the difference between income and expense must also grow at the rate of inflation because both income AND expense grow at inflation rate (as according to the case). Thus, the number, 26K, must also grow with inflation. Yet, CFAI wants you to stick in a flat 26K on the calculator. Which makes no sense. Am I alone in this???

yeah you are. Income is not growing with inflation, its is growing with whatever rate of increase your employeer is giving you. Living expenses are growing with rate of inflation. So, for this problem assume inflation is 3%, then first year living expenses will grow by 2,220 (74,000 * 3%). What the case is telling us is that after-tax sallary increase will be offset inflation on living expenses. That means his after-tax salary increase in the first year will also be 2,220 which translates to 4.625% (2,220/48,000) after-tax salary increase. This leaves the shortfal of salary and expenses constant at 26K. This logic repeats for all 18 years.

Yes, you are right. I re-read the case and it looks like I mis-understood the problem. I made it harder it has to be. Thanks.

no problem