# Reading 32 - CFAI EOC question #33

I have a question regarding the calculation/timing of the terminal value. I searched through old AnalystForum threads, but could not find a concise answer.

The vignette provides three years of EPS and dividends as well as beginning book value per share. Question 33 asks us to solve for intrinsic value using a multi-stage residual income model. It indicates that residual income per share will be constant from year 3 into perpetuity. Thus the cash flows used to calculate intrinsic value are RI1, RI2, and the terminal value calculated based off of RI3.

This seems a little confusing, as I attempted to use RI1, RI2, RI3, and a terminal value based off of RI4. Is the terminal value calculated based off of RI3 because the problem states that “residual income per share will be constant from year 3 into perpetuity.”

Would be greatly appreciated if someone could help (paging S2000 Magician lol), thanks!

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Hi, anyone have a good explanation for this?

I get the same answer regardless of whether I calculate terminal value at t = 2 based on RI3 or at t = 3 based on RI4 (which is the same as RI3), given we know from the passage and exhibits that cost of equity is the same at all time periods and that RI3 = RI4 = RI5 = and so on.

Can you explain how that makes sense? If you push the terminal year out a year, I don’t see how you would get the same answer because you would be including one additional year of non-terminal RI. I can see how your un-discounted terminal value does not change because its simply a perpetuity, but its discounted value definitely depends on when the terminal year occurs.

Let’s say I have a perpetuity of 10% on a notional amount of \$100 and my required rate of return is 5%.  Let’s calculate PV in two ways:

1) Directly doing PV formula: \$10 / 0.05 = \$200

2) Enumerating cash flows for year 1 and 2, and then doing PV formula:

• The PV formula applied to Year 3 cashflow gives us a value of \$200 at t = 2, to which we add the Year 2 payment of \$10 for a total value of \$210 at t = 2.
• Discounting back to t = 1 at 5% gives us a value of \$200, to which we add the Year 1 payment of \$10, which once again gives a value of \$210.
• Discounting back to t = 0 at 5% gives us \$200.

Once the residual income reaches a point that it grows at a constant rate (which could be zero, as here), you can use start at any point for the terminal value, and you’ll get the same present value.  Just remember to discount all of the other (i.e., previous) residual incomes separately and tot them all up.

Simplify the complicated side; don't complify the simplicated side.

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If this is the question I am thinking of - and I think it is - the key is that ROE remains constant as of year 3 onwards, so you use the T=3 ROE in the continuing RI model to obtain the TV and T=2. It’s a bit of a trick question, since you are given T 1-3 and assume that the “constant” begins after year 3 instead of in it…

Or maybe this is an entirely different question than the one I am thinking of…