# equity fun

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) \$13.83. B) \$10.00. C) \$12.60. D) \$18.81.

yikes… probably made a million mistakes, but I’ll take c) 12.60

I got the same. I think (but I doubt it) a lot of stuff in there is to throw you off. Vo = Bo + PV(RI) 9.5 + 3.1 = 12.6 Only reason I think this may be right is because when determining value from RI, the majority of the value is in B0 which is in contrast to the DDM which derives a majority of its value from the terminal value. Confidence in answer = 1%

Niblita75 Wrote: ------------------------------------------------------- > > > Only reason I think this may be right is because > when determining value from RI, the majority of > the value is in B0 which is in contrast to the DDM > which derives a majority of its value from the > terminal value. > > Nibs - great point…that would be a good shortcut to remember to phase out BS answer choices without actually doing the math. They often throw things like that in there.

my biggest concern is the terminal value term. Where the q mentions the firm is trading at a premium to book value, you have to subtract the clean surplus book value from the premium book value, and then divide by K - G. So I get a BV premium of 10, but I get a K of .1 and a G of .1, so do I divide this all by zero? I did, and then got 9.5 + 3.1 + 0 = 12.6

Vo = BVPSo + PV(Residual Incomes) = 9.5 + 3.1 = 12.6 = C?? … they why was the other gazillion’s of data give?

This question needs a multi-stage RI model - typically there is a terminal value that you need to figure, but in this case I think the terminal value is zero because k-g = 0. But if k-g was not equal to zero, the single-stage model would not give the correct answer.

San Fran would you shine some light on this one?

I come up with 12.60 using: 9.50 + 3.10 + 10/(.10-.10) I might also just be totally crazy.

I don’t feel as bad for getting it wrong. you guys read this anywhere? The correct answer was D) \$18.81. 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

Hmm - I ended up w/ “D.” B0+RI+TV 9.50+3.1+6.21. To get TV I did (BV5*1.4)-BV5. Then discount back 5 periods at 10%. TV = (35-25)/1.10^5

so, if g was not 10%, but rather 8%, we would have had to solve for the PV of continuing RI in year 5. If so, I believe they would have to give us either a persistence factor to accommodate assumption #3 (RI declines to zero over time) or explicitly tell us the LR level of growth in the mature industry to accommodate assumption #4 (RI declines to LR level in mature industry). My question: Does the PV calc of 3.10 include the continuing RI? I found the PV for the RI’s in years 1-5 to be 2.37. Also, for anyone else who did the calcs: How did they come up with 25 as the ending BV? Again, my calcs gave me an end BV = to 19.11. Answer: C

ugghh… why did I think k-g… idiot… I needed to discount the \$10 premium by just Ke. This is a Res Income Q that Stalla hammers constantly.

Crap. Makes sense. The way to treat a premium is drilled in my mind now.

i’m spacing here because i don’t remember reading about how to treat the premium… nothing more depressing than seeing something you’ve learned/read and not even getting close to recognizing it.

You have to discount the premium over the book value given, so since it says the stock will be trading at a 40% premium to book value in five years, discount the \$10 premium back five years at the cost of equity.

yup. i know now… didn’t know when i was testing myself… i don’t even remember reading it. i just had a really bad 30 question quiz. 60%. depressing.

My trouble is wasting time doing unnecessary work. All the info i needed was right there. grrr For what it’s worth, I still don’t get how they come up with 3.10 or 25. Even if we don’t need to do the calculations, I can’t help but wonder where I went wrong.

bummer, there is a lot to review …

I agree pdx. I know we don’t need to do the calculations but you’re right they don’t jive. I just cranked through the numbers: NI=BV*ROE to get the earnings, took the equity charge. Then adding NI to Beg BV to get the next period’s BV., etc. Bottom line I came up with PV of RI’s of 2.35 and BV5 of 19.1.