Question

o nounouvqus on 10 10 Pony w 10 P 1 uuu E5.3. A Residual Earnings Valuation (Easy) An analyst presents you with the following pro forma (in millions of dollars) that gives her forecast of earnings and dividends for 2013–2017. She asks you to value the 1,380 million shares outstanding at the end of 2012, when common shareholders' equity stood at $4,310 million. Use a required return for equity of 10 percent in your calculations. 2013E 2015E 2016E Earnings Dividends 388.0 115.0 2014E 570.0 160.0 599.0 349.0 629.0 367.0 2017E 660.4 385.4

Answer 1

a)

Particulars (in millions)	2012	2013E	2014E	2015E	2016E	2017E
Earnings (A)		388	570	599	629	660.4
Dividends (B)		115	160	349	367	385.4
Cost of equity (C)	10%	10%	10%	10%	10%	10%
Shareholders' fund (D = D0 + A - B) D0 = previous year's Shareholders fund	4,310	4,583	4,993	5,243	5,505	5,780
Equity charge (E = C * D)	431	458.3	499.3	524.3	550.5	578
No of shares (F)	1,380	1,380	1,380	1,380	1,380	1,380
Book Value (D/F)		3.32	3.62	3.80	3.99	4.19
ROCE (A/D)		8.4%	11.4%	11.42%	11.42%	11.42%
Residual Value (A - E)		(70.3)	70.7	74.7	78.5	82.4

b)

Particulars	2013E	2014E	2015E	2016E	2017E
Book Value (A)	3.32	3.62	3.80	3.99	4.19
Residual Earnings (B)	(70.3)	70.7	74.7	78.5	82.4
Book Value growth (A1-A0)*100/A0 A1 = Current year book value A0​​​​​​, = Previous year book value		9.03%	4.97%	5%	5.01%
Residual Earnings growth (B1-B0)*100/B0 B1 = Current year residual earnings B0 = Previous year residual earnings		-200.57%	5.66%	5.09%	4.97%

The residual Earnings growth rate for 2014 is (200.57%) because the base is negative in 2013.

c) Value of equity = Book Value₂₀₁₂ * $\frac{RI1}{(1 + r) ^{n}} + \frac{RI2}{(1 + r) ^{n+1}} +....$

Value of equity = 4,310 + $\frac{(70.3)}{(1.01) ^{1}} + \frac{70.7}{(1.01) ^{2}} + \frac{74.7}{(1.01)^{3}} + \frac{78.5}{(1.01)^{4}} + \frac{82. 4}{(1.01)^{5}}$

Value of equity = 4,340 + (69.60) + 69.31 + 72.50 + 75.44 + 78.4

Value of equity = 4,556.05

Thus value of equity per share = Value of equity/No of shares =4,556.05/1380 = 3.30

d) Current book value = 4,310/1,380 = 2.35

Premium over book value = 3.30 - 2.35 = 0.95/share

Price to book ratio = 3.30/2.35 = 1.40

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Answer 2

I THINK THE ANSWER ABOVE ISN'T CORRECT, BECAUSE ROCE IS SUPPOSED TO BE (EARNING(T=1)/BV(T=0)), BUT INSTEAD IN THIS ANSWER IT'S (EARNING(T=1)/BV(T=1)),SEE BOOK FOR CLARIFICATION. MY ANSWER FOR VALUE OF EQUITY/SHARE IS 4.34

Answer 3