Chapter 5 – Residual Income Valuation
Solutions
1.
Yes, VIM earned a positive residual income:
EBIT
300,000
Interest
120,000
(2,000,000
×
6%)
Pretax income
180,000
Tax expense
72,000
Net income
108,000
Equity charge
= Equity capital × Required return on equity
= (1/3)(3,000,000) × 0.10
= 1,000,000 × 0.10 = 100,000
Residual income
= Net income – Equity charge
= 108,000 – 100,000 = 8,000
2.
According to the residual income model, intrinsic value for a share of common
stock equals book value per share plus the present value of expected future per
share residual income. Book value per share was given as $20. Noting that debt is
(2/3)($3,000,000) = $2,000,000 so that interest is $2,000,000 × 6% = $120,000,
we find that VIM has residual income of $8,000 calculated (as in Problem 1) as
follows:
Residual income = Net income – Equity charge
= [(EBIT – Interest)(1 – Tax rate)]
– [(Equity capital)(Required return on equity)]
= [($300,000 – $120,000)(1 – 0.40)] – [($1,000,000)(0.10)]
= $108,000 – $100,000
= $8,000
Therefore, residual income per share is $8,000/50,000 shares = $0.16 per share.
Because EBIT is expected to continue at the current level indefinitely, we treat the
expected pershare residual income of $0.16 as a perpetuity. With a required
return on equity of 10 percent, we have
Intrinsic value = $20 + $0.16/0.10 = $20 + $1.60 = $21.60
3.
With
g
=
b
× ROE = (1 – 0.80)(0.15) = (0.20)(0.15) = 0.03,
P/B
= (ROE –
g
)/(
r
–
g
)
= (0.15 – 0.03)/(0.12 – 0.03)
= 0.12/0.09 = 1.33
or
P/B
= 1 + (ROE –
r
)/(
r
–
g
)
1
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= 1 + (0.15 – 0.12)/(0.12 – 0.03)
= 1.33
4.
In this problem, interest expense has already been deducted in arriving at NMP’s
pretax income of $5.1 million. Therefore,
Net income = Pretax income × (1 – Tax rate)
= $5.1 million × (1 – 0.4)
= $5.1 × 0.6 = $3.06 million
Equity charge: Total equity × Cost of equity capital
= (0.1 × $450 million) × 12%
= $45 million × 0.12 = $5,400,000
Residual income = Net income – Equity charge
= $3,060,000 – $5,400,000 = –$2,340,000
NMP had negative residual income of –$2,340,000 in 2001.
5.
To achieve a positive residual income, a company’s net operating profit after
taxes as a percentage of its total assets can be compared with the weighted
average cost of its capital. For SWI:
NOPAT/Assets = 10 million/100 million = 10 percent
WACC
= (0.5)(Aftertax cost of debt) + (0.5)(Cost of equity)
= (0.5)(0.09) (0.6) + (0.5)(0.12)
= (0.5)(0.054) + (0.5)(0.12) = 0.027 + 0.06 = 0.087 = 8.7%
Therefore, SWI’s residual income was positive. Specifically, residual income
equals (0.10 – 0.087) × €100 million = €1.3 million.
6.
A.
EVA
= NOPAT
– WACC × (Beginning book value of assets)
= 100 – (11%) × (200 + 300) = 100 – (11%)(500) = $45
B.
RI
t
=
E
t
–
rB
t
–1
= 5.00 – (11%)(30.00) = 5.00 – 3.30 = €1.70
C.
RI
t
= (ROE
t
–
r
) ×
B
t
–1
= (18% – 12%) × (30) = €1.80
7.
A.
Economic value added = Net operating profit after taxes – (Cost of capital
×
Total capital) = $100 million – (14%
×
$700 million) = $2 million. In
the absence of information that would be required to calculate the
weighted average cost of debt and equity, and given that Sundanci has no
longterm debt, the only capital cost used is the required rate of return on
equity of 14 percent.
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 Winter '07
 YAXUAN
 Interest, Valuation, Generally Accepted Accounting Principles, residual income

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