Dr. P.V. Viswanath
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## Assignment, Spring 2004

### Chapter 1 Assignment

Practice Problems 16, 19, 22

### Chapter 2 Assignment

Practice Problems 14, 16

### Chapter 3 Assignment

Using the information for Pepsico in the textbook (balance sheet, Table 3-1; income statement, Table 3-2), compute the following quantities as explained in class today: Cash flows from assets, cashflows to equityholders, cashflows to debtholders.

Also, do problems 13, 16, 20, 23, 25.

Compute Cash flows from assets, cashflows to equityholders, cashflows to debtholders for Lifeway Foods, Inc. (LWAY) for 2000, 2001 and 2002.

### Solution to Pepsico Assignment

Net New Equity Raised = Change in Paid-up Capital = +43 - 667 = -624

Cashflow to stockholders = Dividends paid – Net new equity raised = 994 - (-624) = 1618.

Net New borrowing = Change in Long-term Debt = (2651 - 3009) + (5398 - 5349) = -309

Cashflow to debtholders = 152 - (-309) = 461.

Cashflow to stockholders and debtholders = 1618 + 461 = 2079

Operating Cashflow = EBIT + Depreciation – Taxes = 4181 +1082 - 1367 = 3896

Change in NWC = (5853-4998) - (5617-4795) = 33

Net Capital Spending = Change in Net Fixed Assets + Depreciation + Change in intangible and other assets = (6876 - 6558) +1082 + (4841 - 4714) + (4125 - 3868) = 318 + 1082 +127 + 257 = 1784

Cashflow from assets = 3896 - 33 - 1784 = 2079

### Chapter 17 Assignment

Problems 15, 16, 21, 9, 25 from Practice Problems; Problem 1 from Quiz Problems.

#### Chapter 4 Assignment

We are now going to try and price a share of LWAY. Here's what you need to do.

Remembering that in a market, market value = price = present value of future cashflows, we need to get cashflows to stockholders of LWAY, in the future.

Take the cashflow to equityholders for LWAY that you computed in Chapter 3 for 2000, 2001 and 2002. But we need cashflows to LWAY for the future, i.e. 2005 and beyond. Try the following.

Use the cashflows from 2000 to 2002 to forecast future cashflows. You can do this in several ways. A simple way would be to assume that future cashflows will grow annually at the same rate as in the past. Under this assumption, simply take the annual rate of growth from 2000 to 2002. This can be computed by taking (CF2002/CF2000)0.5. Suppose this is g. Then the estimated cashflows in 2005 would be CF2002(1+g)3. You already know from our discussion in class that if the future cashflows are going to increase at a constant growth rate, r, then the PV of that cashflow is CF1/(r-g), where CF1 is the cashflow one year from now, r is the required rate of return on securities with the same risk as this cashflow, and g is the growth rate of the cashflows.

You can also get analyst estimates of the cashflow growth rate from http://finance.yahoo.com/q/ae?s=LWAY. However, if you look at the numbers, there is none for "growth rate for next 5 years." The comparable number for the industry is 8.65%. We could use this as an estimate for LWAY's growth rate. However, it is impossible for LWAY to grow at this rate forever. Hence I would suggest that you assume that this growth rate of 8.65 will continue for the 5 years following 2005. Thereafter, assume a growth rate of 5%. (For more information on this, go to http://webpage.pace.edu/pviswanath/notes/investments/eqval.html.) If you do not assume that the cashflows are increasing at a constant rate forever, then you need a modified formula to compute stock price. You can find an example of this around slide number 18 and 19 from the Stock Valuation slides of Chapter 6.

Now that we have the cashflows, we need a discount rate, which, from our discussion should be the required rate of return on that firm. Recall our discussion of the Capital Asset Pricing Model (CAPM). This model says that:

The required rate of a return on a firm = risk-free rate + beta(market risk premium).

The beta of LWAY can be found by going to http://finance.yahoo.com/q/ks?s=LWAY. For the risk-free rate, use the 30 year T-bond yield or the 10-year T-bond yield. This can be found at http://www.bloomberg.com/markets/index.html or at http://www.bloomberg.com/markets/rates/index.html. Use an estimate of 6% for the market risk premium.

### Solution to the Pricing of LWAY's shares

The cashflow to equityholders for 2002, 2001 and 2000 according to my computations (see excel spreadsheet for details) are \$999, \$811 and \$197 respectively (in thousands).

If we compute the growth rate from 2000 to 2001, we get 312% p.a. and if we compute it from 2001 to 2002, we get 23% per annum. We cannot expect to have the share price for LWAY grow at this rate forever. Considering that the economy as a whole has been growing over the last fifty or so years at a rate of less than 6% p.a., a company that grows at a faster rate would simply be larger than the entire economy, given enough time.

The best thing sumption would be to assume that the higher growth would continue for a limited period of time only, after which it would grow at the same rate of growth as the economy, say at 5.5% per annum. This assumes that once the stock starts growing at this stable rate of growth, it would be a constant percentage of the economy, in terms of market value.

Now, if we go this way, what should we posit as the rate of growth of LWAY's share price for the high-growth period, and how long should this high-growth period be? A rate of 23% is probably too high, except for a very short period. And, of course, this assumes that LWAY's growth rate in the future will be the same as that in the past. If we look at the growth rate for the industry, we see that the five-year growth rate forecast for the industry on Yahoo is 8.61%. (There is no 5-year estimate given for LWAY; note, however, that the growth rate for the next quarter and the next year are negative! Let us ignore this for now.). Let us, then, assume that LWAY's experience will be similar to that of the industry for the next five years, after which it will grow forever at 5.5% p.a.

Using this, we can price LWAY's shares in the following way. First, let us price LWAY, five years from now. In 2002, the cashflow to equity was \$999,000. Since the number of shares outstanding are 8.44m (according to http://finance.yahoo.com), this gives us a per share cashflow to equity in 2002 of \$0.11836. This implies that at a growth rate of 8% per annum for 5 years, the per share cashflow in 2009 (which is five years from now, but seven years from 2002) is 0.11836(1.08)8. = \$0.2191.

Now the 30-year T-bond rate, according to Bloomberg.com on March 23, 2004 is 4.65%; LWAY's beta, according to Yahoo is 0.54; using a market risk premium of 6%, we get a cost of equity of 4.65 + 0.54(6) = 7.89%.

Hence, the share value in 2007 can be computed as (0.2191)/(0.0789 - 0.055) = \$9.1687. The present value of this would be 8.4877/(1.0789)5.= \$5.806. Now the present value of the cashflows from 2005 to 2009 can be computed as a growing annuity, using the formula, PV = C[1-{(1+g)/1+r)}n]/(r-g); in our case, this works out to 0.11836(1.08)3 [1-(1.08/1.0789)5]/(0.0789-0.08) = \$0.6924.

Adding the two quantities, i.e. the present value of cashflows to equity for the next five years, plus cashflows to equity in perpetuity, thereafter, or 0.6924 + 5.806, we get \$6.50.

Now, the current price of LWAY is \$22.91. However, we have to note a few things. First of all, LWAY's shares underwent a 2-1 split. In other words, in 2002, it's shares outstanding totalled about half as much; according to the 2002 10-K, its shares outstanding were 4,268,844. If we use this number, the estimated price approximately doubles to (6.50)(8,440,000/4,268,844) or \$12.85. However, the share has now split 2-1, so each share is now only worth half as much; the per share price then drops to \$6.425. So we still have a big discrepancy between our price and the current market price of \$22.91.

Now, this could be because we were too cautious in estimating growth over the future. If we allow for higher growth, then our price estimate would increase as well. For example, if we allow for 16% for the next 10 years, the price would be 0.234(1.16)3 [1-(1.16/1.0789)10]/(0.0789-0.16) + (0.234)(1.16)13/(0.0789-0.055)(1.0789)-10 = 4.79 + 31.55 = 36.34, or accounting for the 2-for-1 split, a current market price of \$18.17. At this stage, we need to stop playing around with the numbers! Before we leave the issue, take a look at Motley Fool's comments on the share price of LWAY, as of February 18, 2004. (Note that we have, here, changed the per share value of cashflows to equity from 0.11836 to 0.234.) Keep in mind, also that, as late as Mar. 10, the stock was trading at \$15, while at the end of January, it was trading at about \$8!

(If we go ahead and assume a growth rate of 6.5% per annum for ever, then our current price would work out to 0.234(1.065)3/(0.0789-0.065) =\$20.44, which works out to a price of \$10.22 after the split!)

#### Danforth & Donnalley Laundry Products Company

On April 14, 1983, at 3:00 P.M., James Danforth, president of Danforth & Donnalley (D&D) Laundry Products Company, called to order a meeting of the financial directors. The purpose of the meeting was to make a capital budgeting decision with respect to the introduction and production of a new product, a liquid detergent called Blast.

D&D was formed in 1965 with the merger of Danforth Chemical Company, headquartered in Seattle, Washington, producers of Lift-Off detergent, the leading laundry detergent on the West Coast, and Donnalley Home Products Company, headquartered in Detroit, Michigan, maker of Wave detergent, a major midwestern laundry product. As a result of the merger, D&D was producing and marketing two major product lines. Although these products were in direct competition, they not without product differentiation: Lift-Off was a low-suds, concentrated powder, and Wave was a more traditional powder detergent. Each line brought with it considerable brand loyalty, and, by 1983, sales from the two detergent lines had increased tenfold from their 1965 levels with both products now being sold nationally.

In the face of increased competition and technological innovation, D&D spent large amounts of time and money over the past four years researching and developing a new, highly concentrated liquid laundry detergent. D&D's new detergent, which they called Blast, had many obvious advantages over the conventional powdered products. It was felt that with Blast the consumer would benefit in three major areas. Blast was so highly concentrated that only 2 ounces was needed to do an averaged load of laundry as compared with 8 to twelve ounces of powdered detergent. Moreover, being a liquid, it was possible to pour Blast directly on stains and hard-to-wash spots, eliminating the need for a pre-soak and giving it cleaning abilities that powders could not possibly match. And, finally, it would be packaged in a lightweight, unbreakable plastic bottle with a sure-grip handle, making it much easier to use and more convenient to store than the bulky boxes of powdered detergents with which it would compete.

The meeting was attended by James Danforth, president of D&D; Jim Donnalley, director of the board; Guy Rainey, vice president in charge of new products; Urban McDonald, controller; and Steve Gasper, a newcomer to D&D's financial staff, who was invited by McDonald to sit in on the meeting. Danforth called the meeting to order, gave a brief statement of its purpose, and immediately gave the floor to Guy Rainey.

Rainey opened with a presentation of the cost and cash flow analysis for the new product. To keep things clear, he passed out copies of the projected cash flows to those present (see Exhibits 1 and 2). In support of this information, he provided some insight as to how these calculations were determined. Rainey proposed that the initial cost for Blast included \$500,000 for the test marketing, which was conducted in the Detroit area and completed in the previous June, and \$2 million for new specialized equipment and packaging facilities. The estimated life for the facilities was 15 years, after which they would have no salvage value. This 15-year estimated life assumption coincides with company policy set by Donnalley not to consider cash flows occurring more than 15 years into the future, as estimates that far ahead "tend to become little more than blind guesses."

EXHIBIT 1

D&D Laundry Products Company
Annual Cash Flows from the Acceptance of Blast
(including those flows resulting from sales diverted from the existing product lines)

 Year Cash Flows 1 \$280,000 2 280,000 3 280,000 4 280,000 5 280,000 6 350,000 7 350,000 8 350,000 9 350,000 10 350,000 11 250,000 12 250,000 13 250,000 14 250,000 15 250,000

Rainey cautioned against taking the annual cash flows (as shown in Exhibit 1) at face value since portions of these cash flows actually are a result of sales that had been diverted from Lift-Off and Wave. For this reason, Rainey also produced the annual cash flows that had been adjusted to include only those cash flows incremental to the company as a whole (as shown in Exhibit 2).

EXHIBIT 2

D&D Laundry Products Company

Annual Cash Flows From the Acceptance of Blast

(not including those flows resulting from sales diverted from the existing product lines)

 Year Cash Flows 1 \$250,000 2 250,000 3 250,000 4 250,000 5 250,000 6 315,000 7 315,000 8 315,000 9 315,000 10 315,000 11 225,000 12 225,000 13 225,000 14 225,000 15 225,000

At this point, discussion opened between Donnalley and McDonald, and it was concluded that the opportunity cost on funds is 10 percent. Gasper then questioned the fact that no costs were included in the proposed cash budget for plant facilities, which would be needed to produce the new product. Rainey replied that, at the present time, Lift-Off's production facilities were being utilized at only 55 percent of capacity, and since these facilities were suitable for use in the production of Blast, no new plant facilities other than the specialized equipment and packaging facilities previously mentioned need be acquired for the production of the new product line. It was estimated that full production of Blast would only require 10 percent of the plant capacity.

McDonald then asked if there had been any consideration of increased working capital needs to operate the investment project. Rainey answered that there had and that this project would require \$200,000 of additional working capital; however, as this money would never leave the firm and always would be in liquid form it was not considered as outflow and, hence, was not included in the calculations.

Donnalley argued that this project should be charged something for its use of the current excess plant facilities. His reasoning was that, if an outside firm tried to rent this space from D&D, it would be charged somewhere in the neighborhood of \$2 million, and since this project would compete with the current projects, it should be treated as an outside project and charged as such; however he went on to acknowledge that D&D has a strict policy that forbids the renting or leasing out of any of its production facilities. If they didn't charge for facilities, he concluded, the firm might end up accepting projects that under normal circumstances would be rejected.

From here, the discussion continued, centering on the questions of what to do about the "lost contribution from other projects," the test marketing costs, and the working capital.

We see that the answer to the original question that we posed is none too clear, at first blush. What decision should Danforth take? How is he to take into account the detailed cash flow analyses that have been prepared by Rainey? What about the marketing implications of the new product introduction? How important is market share retention? What about corporate strategy? If shareholder wealth is important, how is Danforth to know what his shareholders want? Should he send out a questionnaire?

### Chapter 5 Assignment

Problems 16, 19, 23, 25

### Chapter 6 Assignment

Problems 11, 16, 20, 23, 28

### Chapter 7 Assignment

Problems 9, 17, 19, 22

### Chapter 8 Assignment

Problems 15, 21, 25

### Chapter 10 Assignment

Problems 10, 13, 14, 15, 17, 20, 21, 23

### Chapter 11 Assignment

Problems 2, 3, 6, 7, 8, 9, 15, 17, 21, 27