B8110 Solution to Practice Exercise Set 1 Solution

B8110 Solution to Practice Exercise Set 1 Solution

Exercise 1. Cash Flow Analysis for Apple Inc. a. Apple’s reported cash flows give the impression that free cash flow for 2009 is negative, as follows: Cash generated by operating activities Cash investments Free cash flow

$10,159 17,434 $(7,275)

The problem: GAAP reports the investment of excess cash (in debt securities) as part of investment in operations. The net investment in “marketable securities” in 2009 is: Purchases of marketable securities $ 46,724 Proceeds of maturities of marketable securities (19,790) Proceeds of sales of marketable securities (10,888) Net investment in marketable securities $ 16,046 Investment (in the business) is overstated by this amount.

b.

Cash from operations reported Interest receipts Tax on interest receipts @ 38% Corrected cash from operations

2010 $ 18,595 $155 (59) 96 18,499

Cash investment reported $13,854 Net investment in marketable securities (11,075) Free Cash Flow

2009 $10,159 $326 (124) 202 9,957

$17,434 2,779 (16,046) 15,720

1,388 8,569

c. As there are no cash dividends or stock repurchases, nor any debt to service, the only thing that Apple can do is buy marketable debt securities with its free cash flow. (These are the securities incorrectly reported as cash investments.)

Exercise 2. Testing the Price of Prudential Financial, Inc. a. Outstanding Shares

= Issued shares – shares in treasury = 662.1 – 174.0 = 488.1 million

Book value per share = Book value/shares outstanding = $35,043/488.1 = $71.79 P/B = 44.01/71.79 = 0.61 b. Set up the pro forma: 2010 EPS DPS BPS ROCE

71.79

2011 6.80 1.15 77.44

2012 7.75

9.47%

10.0%

The pro forma forecasts ROCE above the 8% required return. ROCE above the required return indicates that the stock is worth more than book value. Yet the stock trades at 0.61 times book value: it looks underpriced. (You could also calculate residual earnings to reach this conclusion.) c. The only information that would convince you that it is worth less than book value would be information that indicates that ROCE after 2012 will be considerably below 8%.

Exercise 3. Valuation of Microsoft Corporation. a. Book value per share = $57,083/8,376 = 6.815 P/B = 25.05/6.815 = 3.68 Forward P/E = $25.05/$2.86 = 8.76 b. The pro forma 2011 EPS DPS BPS

6.815

Residual Earnings (RE) (9% charge)

2012 2.86 0.64 9.035

2013 3.13 0.64 11.525

2.247

2.317

The no-growth valuation: V0  B0 

RE1 RE 2  1.09 1.091.09  1.0

 $6.815 

 $32.50

2.247 2.317  1.09 1.09  0.09

c. As RE2014

= Earnings2014 – (0.09 × BV2013)

then Earnings2014 = (BV2013 + 0.09) + RE2014 RE2014 = RE2013 = 2.317 Earnings2014 = (11.525 × 0.09) + 2.317 = 3.35 per share d. The 2% growth valuation: V  $6.815 

 $39.24

2.247 2.317  1.09 1.091.09  1.02

e. Reverse engineer to solve for g: Price  25.05  6.815 

2.247 2.317  1.09 1.091.09  g 

g = 0.9586, that is, a growth rate of -4.14% (The market sees residual earnings declining.)

f. RE2014 = RE2013 x g = $2.317 x 0.9586 = $2.221 EPS2014= $(11.525 × 0.09) + 2.221 = $3.26

Exercise 4. Valuation of Hewlett-Packard a. Forward P/E = $21.71/4.84 = 4.49 Trailing P/E = $(21.71 + 0.40)/3.78 = 5.85 Note: trailing P/E adds the dividend to price in the numerator

1  11 .11 0.09 1.09 Normal trailing P/E   12 .11 0.09 (The normal trailing P/E is always 1 more than the normal forward P/E.) Normal forward P/E 

b. The Pro forma:

EPS DPS Reinvested div (0.48 × 0.09) Cum-div EPS Normal EPS (4.84 ×1.09 Abnormal earnings growth (AEG)

2011 4.84 0.48

2012 4.78 0.0432 4.8232 5.2756 (0.4524)

c. With negative AEG, the P/E should be less than normal. d. If the P/E is normal, then subsequent AEG after 2012 must be zero; a normal P/E implies the earnings grow at the required rate of return (9%) and that means AEG = 0. The valuation: V

1   0.4524  4.84    0.09  1.09 

= $49.17

Exercise 5.

Burlington Northern and Buffett’s Expectations

Price  $100 P $100   $37.59 2.66 B $ Forward ROCE  5.50 $  14.63% 37.59 B  0.376 P Book value  Price/

a. Expected return from buying at the current market price

B   B     x ROCE1   1   x g  P   P    0.376  14.63%   0.624 x 4%   5.50%  2.496%  8.0% b. Reverse engineer from the residual earnings model with the required return of 10%: Price  $100  37.59 

5.50  0.10 x 37.59 1.10  g

The solution for g = 1.0721 (a 7.21% growth rate) c. Residual earnings growth is determined by ROCE and growth in the book value (i.e., growth is net assets). If ROCE is constant, BNI would have to grow net assets by 7.21% for year through investments (but still maintain an ROCE or those investments of 14.63%). Can BNI find investment opportunities to do this?

Exercise 6. a.

Challenging the S&P 500

V  B0 

RE1 1.09  g

Price 2007 = 1527 = 530 +

g = 1.0646

73  0.09  530 1.09  g

(a 6.46% growth rate)

Price 2011 = 1136 = 593 +

94  0.09  593 1.09  g

g = 1.0152 (a 1.52% growth rate) b.

B

 

B



Expected return =  P x ROCE  1  P x 4% In 2007: B

P =

ROCE1 = Expected return = = =

530  0.347 1527 73  13 .77 % 530 [0.347 x 13.77%] + [0.653 x 4%] 4.78% + 2.6% 7.39%

In 2011: B

P =

ROCE1 = Expected return = = =

593  0.522 1136 94  15.85 % 593 [0.522 x 15.85%] + [0.478 x 4%] 8.27% + 1.91% 10.18%

It looks like the S&P 500 was a better bet in 2011 than in 2007. With an implied growth rate of 6.46% (relative to a GDP growth rate of 4%), the index looked overpriced in 2007, and yielded only an expected return of 7.39% (and the -38.5% return in 2008 proved this to be so). The opposite is the case in 2011. What is ahead in 2012?