# Equity QBank Question

Expert Systems (ES) has a beginning book value per share of \$6.00, an expected growth rate of 15 percent, forecasted earnings per share of \$1.50, and a required rate of return of 17 percent. Assuming that the dividend remains constant at \$0.75 per share, what is next year’s expected residual income per share? A) \$1.73. B) \$0.50. C) \$0.58. D) \$7.73.

I’d go with C) \$0.58

Residual income = Net income - Cost of Equity = \$1.5-6\*17% = 0.48 -> B

EPS(t+1) = 1.725 BVPS(t+1) = 6 + 1.5 - 0.75 = 6.75 RIPS (t+1) = 1.725 - 6.75*0.17 = 1.725 - 1.1475 = 0.5775 = C?

B Bt-1 = \$6.00 r = 17% Equity Charge = Bt-1 * r = 6.00 * .17 = \$1.02 Residual Income = EPS - Equity Charge = 1.50 - 1.02 = \$0.48 so B is the closest answer

B.

what maratikus and budfox said… definitely B.

Actually: i got (ROE-r) x B which is (1.50/6 - .17) * 6 = .48 but both methods should lead to the same answer, no? why does the first method get you to .50? i only tried it this way after i couldn’t get the answer the other way.

Doesn’t the Q ask for next year’s Res Income? So wouldn’t we need to increase BV by EPS - Divs, grow earnings, and then calculate NI - Ke*BV?

They were asking about “next year’s expected residual income per share” So we need to calculate RIPS (t+1), no??? Has the caffine not yet flown into my veins yet? EDIT: Bingo ilvino!! I thought the same thing at the same time… lol

the book value to use is the previous year’s though. i don’t have my books. i’m at work… can someone confirm please?

dinesh I think we’re on the same wavelength here.

ilvino, if you’re estimating RI in year t, you’ll need to use t-1 metrics, I think. So in this case you ARE estimating next year’s RI using this year’s BV, ROE, etc cfasf1, they both do. The first one gets you 0.48 as well.

but it asks for next year’s expected RI, so we would need to use the bV as of the end of the current year, which would be the first available BV + this year’s EPS - this year’s divs paid. This will give us the ending BV for this year, which is the beginning BV for next year’s estimated RI… i think.

ilvino Wrote: ------------------------------------------------------- > Doesn’t the Q ask for next year’s Res Income? So > wouldn’t we need to increase BV by EPS - Divs, > grow earnings, and then calculate NI - Ke*BV? I can see how that if BV = 6 + 1.5-.75 = 6.75 and RI = 1.5*(1+15%) - 6.75*17% = .58 but decided that all the numbers given are for the beginning of next year. Wording is not very clear …

but I think we’re estimating for year T+1 - or at least that’s how I understood the question. If it had asked for THIS year’s RI, I would use a book value of t-1. But since it asked for NEXT year’s RI (or T+1), I would use the book value from t.

Correct, hence I used… RIPS (t+1) = EPS(t+1) - BVPS(t+1)*RRR Let’s wait for maaagian to post the official answer. I don’t have the books with me to confirm it.

Why has the RRR been given? First off, we need the rate of return for Equity to determine the equity charge. Second, the growth rate has been given. Then how can the dividend payout remain the same? Very weird question.

Your answer: C was correct! EPS next year = 1.50 × 1.15 = \$1.73. Forecast book value per share = BV0 + EPS – D = 6.00 + 1.50 – 0.75 = \$6.75. The per share equity charge is 6.75 × 0.17 = \$1.15. Thus, residual income is expected to be 1.73 – 1.15 = \$0.58. But I agree. The only reason I recalculated was beacuse 0.48 wasnt among the alternatives. According to the book and the formulas: Bt-i (or beginning book value) = 6.00 r: 17% Et (or forecasted EPS): 1.50 So using the formula: RIt: Et - (r*Bt-1) and accordingly 1.5 - (0.17*6) = 0.48 Therefore, wouldnt the 0.58 answer only be correct if they asked us to calculate RI in 2 years? When I did the equity section I noticed a couple of these questions so just wanted to make sure

I think you need to draw a timeline, like we used to for TVM questions on Lvl 1