Solution to Exercise Set 1 - Columbia Business School



B8110, Fall 2009

Solution to Practice Exercise Set 1

Exercise 1. Cash Flow and Earnings: Kimberly-Clark Corporation

Part a.

Adjust cash flow from operations for after-tax net interest payments and cash investment for net investments in interest-bearing assets:

Cash flow from operations reported $2,969.6

Interest paid $175.3

Interest income (17.9)

Net interest 157.4

Tax on net interest (at 35.6%) 56.0 101.4

Cash flow from operations $3,071.0

Cash flow from investing reported $(495.4)

Net investment in debt securities (38) + 11.5 ( 26.5)

Net investment in time deposits 22.9 (499.0)

Free cash flow $2,572.0

Note: As cash interest receipts are not reported (as is usual), use interest income from the income statement.

Part b.

Accruals = Net income – Cash flow from operations

= $1,800.2 – 2,969.6

= $(1,169.4)

Exercise 2. Challenging the Level of the S&P 500 Index with Analysts’ Forecasts

The required return = risk free rate + risk premium

= 5% + 5%

= 10%

To develop the pro forma for the implied growth rate, first apply the forward P/E ratio to get an earnings forecast for 2006, then convert the PEG ratio to an earnings forecast for 2007:

Forward P/E = Price/Earnings2006

Treat the 1271 as dollars to get earnings in dollars:

$1,271/Earnings2006 = 15

Thus Earnings2006 = $84.73

PEG = [pic]= 1.47

Thus, for a forward P/E of 15, the 2007 growth rate for 2007 earnings is 10.2%.

Thus, 2007 earnings forecasted is $84.73 × 1.102 = $93.37

a. The pro forma to calculate abnormal earnings growth (AEG) is as follows:

2003. 2004

Earnings 84.73 93.37

Dividends (payout = 27%) 22.88

Reinvested dividends (at 10%) 2.288

Cum-dividend earnings 95.658

Normal earnings ($84.73 x 1.10) 93.203

AEG 2.455

b. If cum-dividend earnings are expected to grow at the required rate of return, 10%, after 2006, the P/E should be normal:

P/E = [pic]= 10

At this P/E, the index should be $84.73 × 10 = 847.3

The normal P/E is appropriate if (cum-dividend) earnings are expected to grow at a rate equal to the required return, 10%. The P/E based on analysts forecast (15) is higher than this because the market sees earnings growing at a higher rate. Is this assessment reasonable?

c. Applying the abnormal earnings growth (AEG) pricing model with the long-term growth rate for AEG of 4%:

[pic]

= 1256

d. The S&P 500 index is appropriately priced (approximately) at 1271. This will not always be the case. The estimated level can different from the actual level for a number of reasons:

1. Analysts’ forecasts are too optimistic relative to how the rest of the market sees it.

2. The market agrees with analysts’ forecasts for 2006 and 2007, but sees the long-term growth rate at less than 4%.

3. The market requires a higher or lower required return than 10%.

4. The market is mispriced.

With respect to point 1, sell-side analysts’ forecasts are often overly optimistic, particularly two-year ahead forecasts on which the AEG is calculated.

This exercise is dangerous when both the market and analysts are too optimistic (as in the bubble). Then you have to challenge the price with your own forecasts. Notice that the next exercise works with actual earnings numbers, not analysts’ forecasts.

Exercise 3. Reverse Engineering the S&P 500 Index Using Book Rates of Return

(a)

With a P/B ratio is 2.5, investors are paying $2.50 for every dollar of book value in the S&P 500 companies. With an ROCE of 18%, the current residual earnings on a dollar of book value is:

RE0 = (0.18 – 0.10) ( 1.0

= 0.08

That is, 8 cents per dollar of book value. The value of an asset (with a constant growth rate is mind) is calculated as:

[pic]

(One always capitalizes the one-year-ahead amount, which is the current residual earnings, RE0, growing one year at 10%.) So, for every dollar of book value worth $2.50,

[pic]

Solving for g,

g = 1.044 (a 4.4% growth rate)

A good benchmark growth rate for the market as a whole is the GDP growth rate. This has historically been an average of about 4.0%. So, if history is an indication of the future, a 4.4 % implied growth rate suggests that the S&P 500 stocks, as a portfolio, are a little overpriced.

What does a growth rate of 4.4% for residual earnings mean? If the S&P 500 firms can maintain an ROCE of 18%, then investment in net assets must grow by 4.4%. Alternatively, if ROCE were to improve, a growth in residual earnings of 4.4% can be maintained with a lower growth rate. Is a 4.4% growth rate for residual earnings reasonable? What is the prospect for ROCE for the market as a whole? Is the market appropriately priced?

(Analysis in Module II of the course will help answer these questions.)

(b)

See the last paragraph. With a constant ROCE, the growth in residual earnings is determined by the growth in net assets (book value). Remember, residual earnings is driven by two factors:

1. Profitability of net assets: ROCE

2. Growth in net assets

(c)

For all U.S. listed firms, the historical (arithmetic) average ROCE (since 1960) has been 10.3% and the median ROCE has been 12.5%. Since 1977, the average ROCE for the S&P 500 (a weighted average of the 500 stocks in the index) has been about 17%, but it was 14% in 1983 and again in 1987, and 20% in 1999.

(d)

See Figure 2.2 on page 44 of the text. Since 1977, the P/B ratio for the S&P 500 (a weighted average of the 500 stocks in the index) has been about 2.8, but it was 1.2 in 1981 and 5.1 in early 2000.

Exercise 4. Forecasting from market prices: Cisco Systems

a. Book value of shareholders’ equity (from the 2003 balance sheet) = $28,029 million

Shares outstanding = 6,998 million

Book value per share = $4.005

Forward P/E = 31.25

Forward earnings = 0.64

Current price = 31.25 x 0.64 = $20.00

Price-to-book ratio = 4.99

b. Prepare the pro forma and calculate residual earnings by charging prior book value at 9%:

2003 2004 2005

Eps 0.640 0.740

Dps 0.0 0.0

Bps 4.005 4.645 5.385

Residual earnings 0.2796 0.3220

c. Reverse engineer the residual earnings model:

[pic]

Setting [pic] = $20.00, then g = 1.0713 ( a 7.13% growth rate)

(You may have calculated 1.0712 with rounding in an Excel spreadsheet)

d. Eps2006 = (Bps2005 x 0.09) + RE2006

RE2006 is RE2005 growing at 7.13% = 0.322 x 1.0713 = 0.3449

So, Eps2006 = (5.385 x 0.09) + 0.3449

= 0.8296 (83 cents)

e. Set up the pro forma. Normal eps is prior year’s eps x 1.09.

2003 2004 2005 2006

Eps 0.640 0.740 0.8296

Dps 0.0 0.0 0.0

Cum-dividend eps (no divs) 0.7400 0.8296

Normal eps 0.6976 0.8066

Abnormal eps growth (AEG) 0.0424 0.0230

f. Reverse engineer the AEG model:

[pic]

Setting [pic], then g = 1.0713 (a 7.13% growth rate)

(You may have calculated 1.0712 with rounding)

g. Complete the pro forma above to include residual earnings (charging prior book value at 9%):

2003 2004 2005 2006

Eps 0.640 0.740 0.8296

Dps 0.0 0.0 0.0

Bps 4.005 4.645 5.385 6.2363

Residual earnings 0.2796 0.3220 0.3450

Change is RE 0.0424 0.0230

The last line is equal to abnormal earnings growth (AEG).

h. From the pro forma in part e, eps growth rates for each year are:

2004 2005 2006

Eps 0.64 0.74 0.8296

Growth rates 15.63% 12.11%

These growth rates are cum-dividend growth rates because the firm pays no

dividends.

i. A long-term growth rate of 7.13% is high against a benchmark of 4% for GDP.

With the telecom sector less vibrant than it was, the market for routers may not sustain such a growth rate. Does Cisco have other strategies for growth?

Exercise 5. Inferring Implied Eps Growth Rate: Kimberly Clark Corporation

Price, March 2005 $64.81

a.

[pic]

[pic]

[pic]

[pic]

b.

Calculate AEG for 2006:

2004 2005 2006

Eps 3.64 3.81 4.14

Dps 1.60 1.80 1.96

Dividends reinvested at 8.9% 0.1602

Cum-dividend earnings 4.3002

Normal eps (3.81 x 1.089) 4.1491

Abnormal earnings growth (AEG)

0.1511

[pic]

[pic]

c.

2005 2006 2007 2008 2009 2010

Eps 3.81 4.14

Dps 1.80 1.96 2.14 2.33 2.54 2.77

AEG 0.1511 0.1529 0.1547 0.1566 0.1585

(growing at 1.2%)

Reinvested dividends (0.1744) (0.1905) (0.2074) (0.2261)

(at 8.9%)

Normal earnings 4.5085 4.8863 5.2822 5.6970

Eps 4.4870 4.8505 5.2314 5.6294

Eps growth rate 8.66% 8.38% 8.10% 7.85% 7.61%

Note: Normal earnings are the earnings in the prior year growing at 8.9%. So, for 2008, normal earnings = $4.487 x 1.089 = 4.8863.

d.

The market was pricing approximately the same growth rates as forecasted by analysts. Put another way, the market was pricing KMB based on consensus analysts’ forecasts.

e.

Yes, as analysts were forecasting the same growth rates as those implied in the market price, they are saying that the market price is reasonable. The 2.6 rating – a HOLD – has integrity.

(If you are following the Continuing Case in the text, some of this material will be familiar to you.)

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