Another course 2 question

[bg23516]

Company A invests $10,000 in machinery that is expected to yield net cash flows of $7000 in each of the next 2 years. Company A intends to record depreciation costs of $5000 in each of the next 2 years.

Find the Economic Rate of Return and Book Rate of Return on Investment if cost of capital is 10%.

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I understand how to find the the economic rate of return....
Economic Income = CF1 + PV1 - PV0 = 1215
EROR = EI/PV0 = 10%

My problem is with finding book ROI...
BROI = Book Income / BV0 where:
Book Income = CF1 + BV1 - BV0

According to the solutions, BV0 = 10,000 (2*5000) and BV1 = 5000. Why is book value equal to the depreciation, and why is it just added, despite the different years?

[Gandalf]

Why am I trying to discuss course 2 having none of the study material?

That said, I suspect BV0 = 10,000 because that's what you paid for it. It's somewhat of a coincidence that it equals 2 * 5,000, but not completely coincidence. It is true that BV0 = sum of depreciation in all future periods + any residual value after the depreciation, and that in many situations such as this one residual value (at least residual book value) is 0.

Normally BV1 does not equal depreciation. BV1 = BV0 - depreciation during 1. Here, BV1 = 10,000 - depreciation just happens to equal depreciation.

Those are my guesses, anyway.

[ASA_Woman]

Gandalf is correct. BV0 is the initial value of the machinery, ie 10,000. BV1 is the value at the end of 1 year, ie after one year's worth of depreciation. So BV1 = BV0 - 5,000 = 10,000 - 5,000 = 5,000.

The question states that the depreciation is 5,000 each year. It just works out this time that BV0 is 2 times the depreciation. That will not always be the case.

[GuyInWestGrove]

Sorry to resurrect this thread two years later, but ..

This appears to be problem 47 from the sample exam (Adobe PDF at http://casact.org/admissions/studytools/exam2/sampleExam2.pdf

The original post seems to indicate that the economic income calculation in the solution was in error. The solution shows CF = 7, PV at beginning of year = 10, PV at EOF = 7/1.1 = 6.36. Economic income = 7 - (10-6.36) = 3.36. Return = 3.36 / 10.

Calculating the PV's from the discounted future cash flows as bg23516 has jives with what Braeley and Meyers seem to do.

A couple of questions --

1. Is the solution in the PDF correct?

2. How would you know to look at the return in only the first year, and not over say both years, or even just the second year?

3. What is the origin of the sample exam? (i.e. Did these questions appear on real exams in the past? They seem harder than the other published exams.)

[Svak]

B&M are referring to year when calculating Rate of Return either Economic Rate of Return or Book Rate of Return.

If we assume question is on return during the "first year", then,

Economic Rate of Return

Change in PV (from year 0 to year 1) /PV at year 0

[CF₁+ PV₁- PV₀]÷PV₀
[7000+6363.63-12147.70]÷12147.70
=10%

Solution is different from this that it is using 10000 as PV₀
It makes sense to take 10000 in the denominator, since this is what we are investing. But is it the Present Value at time zero?

Book Rate of Return

Book Rate Return, I think is straight forward. There is no confusion.
[CF₁+BV₁-BV₀]÷BV₀

[7000+5000-10000]÷10000

Investing 10000 and receiving 2000 net income (7000 cash flow and losing 5000 as depreciation).

[Gandalf]

B&M is referring to year when calculating Rate of Return either Economic Rate of Return or Book Rate of Return.

If we assume question is on return during the "first year", then,

Economic Rate of Return
Change in PV (from year 0 to year 1) /PV at year 0

[CF<sub>1</sub>+ PV<sub>1</sub>- PV<sub>0</sub>]÷PV<sub>0</sub>
[7000+6363.63-12147.70]÷12147.70
=10%

Solution is different from this that it is using 10000 as PV<sub>0</sub>
It makes sense to take 10000 in the denominator, since this is what we are investing. But is it the Present Value at time zero?
You really need to see if the text specifies what to do. One thing that seems clear to me is that you must use the same value for PV0 in both numerator and denominator.

Which to use depends on what is meant by "first year" (and the problem itself didn't even specify "first year" :swear: )

If the first year is from the time you had 10,000 and ends 1 year later, then PV0 should be 10,000. You started with 10,000, and added economic value during the period by making the investment.

If the first year is one year starting immediately after the moment the investment was made, then the economic gain at the moment of investment is before the first year, and PV0 should be 12,148.

[Becoming Actuary]

In book rate of return -

The initial value BV0 is always equal to initial investment (10,000). and book value at time 1, BV1 is BV0-depr (which in this case is 5000. sometimes they say its a st. line depr. for lets just say 5 years then you calculate the depr = initial invest./#of yrs.=10,000/5 = 2000).

san