Premium over book value

[tbarb00]

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
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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.

 

[bakbakbakgone]

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

 

[adavydov7]

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.

 

[cpk123]

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

 

[rellison]

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

 

[adavydov7]

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?

 

[adavydov7]

Anyone?

 

[rellison]

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

 

[cpk123]

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.

 

[swaptiongamma]

“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?

 

[cpk123]

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

 

[rellison]

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.

 

[swaptiongamma]

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