Company is expecting an ROE of 18% over each of the next five years. Current book value is $5 per share, it pays no dividends, and all earnings are reinvested. The required return on equity is 10%. Forecasted earnings in years 1 to 5 are equal to ROE times beginning book value. 1) Calculate the intrinsic value of the company using residual income model, assuming that after five years, continuing residual income falls to zero. A) $6.25 B) $6.62 C) $7.60 2) Supposed residual income after years remains constant at $0.44 forever, calculate the new intrinsic value. A) $8.20 B) $8.98 C) $8.74 3) Supposed after five years, residual income will decay over time to zero with a persistence factor of 0.4, calculate the new intrinsic value. A) $6.40 B) $6.76 C) $6.94 4) Supposed after five years, ROE falls to a long-run average level and the price-to-book ratio falls to 1.2, calculate the new intrinsic value. A) $7.50 B) $7.15 C) $7.65
- B ----> I actually calculated $7.02 after 5 years, but if I remove the 5th year RI I get $6.62 exactly. 2. After how many years? 3. Stalla didn’t cover this, maybe this is indirectly related to the H model? 4. I actually calculated $7.74, but going with C.
Answer choices do not seem to match up. Schweser has an exactly identical problem solved but with 15% ROE - which has the above answer choices listed / matching up. 1. RI for each year 5 BV0 RI1=0.40 == 0.18*5-0.1*5, BV1=5+0.9=5.9 RI2=0.47== 0.18*5.9-0.1*5.9, BV2=5.9+1.06=6.96 RI3=0.55== 0.18*6.96-0.1*6.96, BV2=6.96+1.25=8.21 RI4=0.66== 0.18*8.21-0.1*8.21, BV2=8.21+1.48=9.69 RI5=0.77== 0.18*9.69-0.1*9.69, BV2=9.69+1.74=11.43 Terminal Value = 0.77/1.1=0.70 RI Value of firm = 5+0.4/(1.1)+0.47/(1.1^2)+0.55/(1.1^3)+(0.66+0.70)/(1.1^4)=7.09 None of the above??? 2. Terminal Value = 0.44/0.1 = 4.4 RI Value of firm = 5+0.4/(1.1)+0.47/(1.1^2)+0.55/(1.1^3)+(0.66+4.40)/(1.1^4)=9.62 3. Persistence Factor = 0.4 Terminal Value =0.77/(1+0.1-0.4) = 0.7 Same as answer choice 1? 7.09?
Hey CP can you explain this persistence factor and how we’re supposed to apply it?
A persistence factor of 1 means the RI will not fade at all. It will continue at the same level indefinitely (a perpetuity). A persistence factor of 0 => RI will NOT continue after initial forecast horizon. Higher the persistence factor - higher the stream of RI in the final stage, and hence higher the value of the firm. Persistence factor considers the long run mean reverting nature of the ROE -> assuming over time that ROE fades towards r and RI fades towards 0. Formula using a persistence factor of w: Terminal Value TV=RIt / (1+r-w) PV of TV = TV / (1+r)^(T-1)