From Schweser QBank (#88663) Brown Manufacturing is expected to have a return on equity (ROE) of 15% for the next five years and 10% thereafter, indefinitely. Its current book value per share as of the beginning of year 1 (i.e., the end of year 0) is \$9.50 per share and its required rate of return is 10%. The premium over book value at the end of five years is expected to be 40%. All earnings are reinvested. The sum of the present values of the residual income estimates over the next five years is \$3.10. The projected ending book value in year 5 is \$25.00. What is the value of Brown Manufacturing using these inputs? a)\$18.81 b)\$12.60 c)13.83 answer below and a q on that answer . . . . . . . . . . . . . Answer: Applying the finite horizon residual income valuation model: V0 = B0 + sum of discounted RIs + discounted premium = 9.50 + 3.10 + [(0.40)(25.00) / (1.10)5] = \$18.81 Question: Please explain the why the terminal value is just the premium, not premium plus book.

You are already including the book value at time zero, I am not sure why you would want to account for it twice to determine the value of the shares

I have a different question: why are we discounting the premium 5 periods instead of 4? The question clearly states 9.5 is BV at time 1, and the projected BV at time 5 is 25. Since the question asks to find value today (which is time 1), the time 5 projected book value is only 4 periods away and should be discounted as such and not to time zero (since we are at time 1 not time zero), otherwise the 9.5 needs to be discounted back one period also.

5 years is to end of year 0 from end of year 5.

Hmm I’m confused. Are they using BV(0)+sum of residual income, or are they using the multi-state RI model assuming it goes to long-term average industry maturity (i.e., Terminal Value at time T-1=(Premium minus Book+RI)/(1+r)? It seems they are using book value at time 0, adding the RI from time 0-5, and then using some sort of terminal value. I know I’m bein stupid and it’s obvious but tell me real quick

cpk123 Wrote: ------------------------------------------------------- > 5 years is to end of year 0 from end of year 5. Okay lets once again do a timeline, since Schweser doesn’t seem to understand the difference between a point in time and a period of time (ex. like a year): time0…time1…time2…time3…time4…time5 year1: time0 to time1 year2: time1 to time2 year3: time2 to time3 year4: time3 to time4 year5: time4 to time5 The question clearly states that 9.50 is “Its current book value per share as of the beginning of year 1 (i.e., the end of year 0).” Apparently they don’t get you can’t have a period of time (i.e. a year) be a zero value, but whatever say we reclassify as follows to accommodate their idiocy: time0…time1…time2…time3…time4…time5 year0: time0 to time1 year1: time1 to time2 year2: time2 to time3 year3: time3 to time4 year4: time4 to time5 So we know now that \$9.50 BV at the start of year1 but this would mean that if we have to discount the premium 5 periods (meaning to time0) we would still have to discount the 9.50 BV one period as well, but the question doesn’t do this. Why?

Anyone?

Why do you add the premium over book value and have that be the terminal value? What happened to (Premium-Book+RI)/(1+r)?

Premium - BookValue is given to be 40% and the RI in the terminal year has been already taken into consideration in the 3.10 \$ number. What I mean to say is: Terminal Value = 1.4 * BookValue in the final year. So Terminal Value - Final Year BookValue = 0.4 * BookValue.

“The sum of the present values of the residual income estimates over the next five years is \$3.10” How do we know that the 3.10 contains the RI_5 inclusive?

ok. how do I know your name? How I hate myself? all rhetorical questions…

cpk one last thing: I know from the formula I memorized that: premium in time t=(book value in time t)*(Forecast P/B ratio). Why does Terminal Value = 1.4 * Book value in the final year? I get the rest of what you said though.

“The premium over book value at the end of five years is expected to be 40%” Pt = (1 + 0.40)*Bt