Spolier - CFAI Sample Exam 1 #13

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outq13

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Had a quick question. On the sample (Question 13), I had calculated the return by taking the total invested amount $100 * 7.4% and subtracted out the cost of borrowed funds ($40 * 4.25%) and divided the sum by the total equity of $60 ( I used 100 as the total portfolio).
(7.40 - 1.70) / (60) = 9.5%
Can someone explain why this is wrong.
The answer key stated it was 8.66%
Portfolio return 7.40%
40% of the portfolio is financed
Borrowing rate 4.25%
 
your formula is incorrect. you need to use Rp = Ri + [(B/E) * (Ri - c)] = 7.4% + [40% * (7.4% - 4.25%)] = 8.66%
there’s been a discussion about the 40% that you can do a search for…
 
lolly, I believe you can calculate using the formula or by calculating the return and subtracting out the cost of borrowing. In other problems I have used the methodology and it has worked fine (CFA and Schweser problems).
I will look for the thread. Thanks
 
Lolly, if you could point me to the thread I would appreciate it. I went through 12 pages searching 40% and was unable to find it.
Thanks
 
outq13,
you’re right, that is another way you should be able to solve it. there must be something fishy with that leverage ratio. we have (1) gross profit, (2) cost of borrowed funds, (3) net profit, and (4) equity amount. are you sure all the terms were defined as you have it?
the thread was titled: Error(s) in Sample #1 ?! Q on leveraged portfolio return
anyone with insight?
 
lolly,
I took a look at the other thread and there seems to be a lot of confusion. I am 99% sure on the facts of the problem as stated above. It is fustrating b/c it is straightforward and this is not the type of problem you want mess up.
 
Looking at the previous thread, the only way you get back to the answer is if you assume a portfolio size of $140 and $40 of margin and a total equity amount of $100.
Based on the facts that were given (40% leverage) The leverage is only then 28.57%.
Is this a mistake?
 
btt - This question is really bothering me. Anyone else have problems with this one on the sample test?
 
Did anyone ever come to a conclusion on this one? I solved it exactly as outq13 did and I can’t seem to figure out how that is wrong given the facts in the question.
 
I faced the same problem and was depressed when I got this wrong. However, following is my understanding about the solution.
Generally, in most of the we are given the total assets value ($A), % of equity ($E), % of debt ($D), return on assets (RA) and cost of debt (CD) and we do the calculation as follows.
Return on portfolio = (A*RA - D*CD)/(E)
Now, A = D + E
So, return on portfolio = ((D+E)*RA - D*CD)/E = RA + (D/E)*(RA - CD)
and D/E is the leverage ratio. In the sample test problem, they have provided this ratio and since we had been used to using the first formula, we are mistakenly taking the leverage ratio as D/A, by multiplying 40% and 4.25.
So if at all we multiply 4.25% by 40%, we should multiply the overall return by 140%, since its the total asset value (100% equity + 40% debt (as a % of equity)). Hope this clears the confusion.
 
(100+40)*7.4%-40*4.25%=8.66
8.66/100=8.66%
“our mandate allows us to borrow between 0 and 75% of the EQUITY of the portfolio”
 
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