Question #15
Reading: Reading 23 Residual Income Valuation
PDF File: Reading 23 Residual Income Valuation.pdf
Page: 8
Status: Incorrect
Correct Answer: A
Your Answer: B
Question
Krieger String & Twine expects to generate a return on equity (ROE) of 13.6% in each of the next five years. The required ROE is 8.7%. Current book value is $12.40 per share and the firm pays no dividends. Krieger previously assumed residual income falls to zero immediately after five years, but has now decided to recalculate its estimated value using a persistence factor of 35%. The difference between the new valuation and the old one is closest to:
Answer Choices:
A. $0.64 per share
B. $0.16 per share
C. $0.32 per share
Explanation
To answer this question, we need to establish the residual values using the following
equations:
Earnings = prior year book value × ROE
Equity charge = prior year book value × required ROE
Residual income = earnings − equity charge
Here is a table containing the relevant values.
Year
Earnings
(ROE =
13.60%)
Book
Value
Equity Charge
(Required ROE =
8.70%)
Residual
Income
PV of
Residual
Income
0
$12.40
1
$1.69
$14.09
$1.08
$0.61
$0.56
2
$1.92
$16.00
$1.23
$0.69
$0.58
3
$2.18
$18.18
$1.39
$0.78
$0.61
4
$2.47
$20.65
$1.58
$0.89
$0.64
5
$2.81
$23.46
$1.80
$1.01
$0.67
Company value = $12.40 + the sum of the residual incomes
Assuming residual value drops to zero after year five, the company is valued at $15.46 per
share.
Now, we modify the model to reflect the persistence factor of 35%. The only value that
persistence factor effects is the terminal value. Instead of discounting the Year 5 residual
income by 1 + required ROE, we discount it by 1 + required ROE − persistence factor. The
new values are as follows:
Book Value
Year 1
Year 2
Year 3
Year 4
Value
$12.40
$0.56
$0.58
$0.61
$1.62
Year 4 CF = Residual income in year 4 + PV Continuing residual income = 0.89 +
1.37 = 2.26
PV of continuing residual income (T=4) = RI(year 5)/1+r-w = 1.01/(1+0.087-0.35) =
1.37
PV(T=0) of 2.26(T=4)=1.62
For a total value of $15.78 per share, or $0.32 higher than the original value.