Question

Could you please solve the problem below:

Lucy Company has a current book value of $100. Lucy will have an ROE of 15% (on trailing book value) and will pay out one-third of its earnings in dividends into the foreseeable future. The required return on equity is 10%. You calculate the residual income for the next two years (year 1 and year 2). What is the residual income for year 2? (Enter your answer to the nearest $0.01. Leave the $ sign off. In other words, if your answer is $55.55, enter 55.55 for your answer.)

Answer 1

Residual income is excess income generated more than the minimum rate of return. It is the measurement of internal corporate performance, whereby a company's management team evaluated the income generated relative to the company's minimum required rate.

a simple equation for the above problem can be;

Net income - equity charge = Residual income

RIt = Et - re Bt-1

RI = Residual income per share

Et = Earning per share

re = required rate of return

Bt = Beginning book value of shares.

Here we see that the book value of the share is 100 at the beginning of year one.

re = 10% required rate of return.

equity charge is ( required rate of return * book value) = .10 * 100 = 10

Et = earning per share = Return on equity viz., 100 * .15(ROE) = 15 per share

therefore here value for residual income = 15 - (.10 * 100) year 1

= 5

provided in the information that the company will pay out 1/3rd of earnings

Therefore, End of the year book value is:-

book value at beginning + earnings - dividends

i.e., 100 + 15 - 5 = 110

Charge for equity capital for year 2 =

.10 * 110 = 11  

Residual income in year 2

= Earnings which is book value * .15, here opening book value in year 2 = 110

then, 110 * .15 = 16.5

residual income ( year 2) = 16.5 - (.10 * 110) = 5.5