Financial Management

Please help me with the highlighted questions

Mini Case

perience as an equities analyst, was recently brought in as assistant to the chairman of the board of Computron Industries, a manufacturer of computer components.

president plus its major stockholders (who were all local businesspeople),was most upset when directors learned how the expansion was going. Suppliers were being paid late and were unhappy, and the bank was complaining about the deteriorating situation and threatening to cut off credit. As a result, Robert Edwards, Computron’s president, was informed that changes would have to be made—and quickly—or he would be fired. At the board’s insistence, Jenny Cochran was given the job of assistant to Gary Meissner, a retired banker who was Computron’s chairman and largest stockholder. Meissner agreed to give up a few of his golfing days and to help nurse the company back to health, with Cochran’s assistance.

14

)

)

40% 40%

2014 2015

20,000

460,000

$ 1,468,800 $ 2,886,592

2015

$ (95,136)

116,960

9,000

$ 7,282

)? What are operating current assets? What are operating current liabilities? How much net operating working capital and total net operating capital does Computron have?

2015

EBIT x

x

2014 NOPAT = EBIT x ( 1 – T )

x 60%

=

2015

=

–

=

–

=

2014 NOWC = Operating current assets – Operating current liabilities
=

–

=

2015

NOWC

= $1,317,842 +

=

2014 TOC = NOWC + Fixed assets
= $793,800 +

=

2015

NOPAT –

=

–

=

2015

$11,000

-$1,108,568

cost of capital (

). Do you think Computron’s growth added value?

2014 2015

10% 10%

2015

NOPAT

Operating Capital

= $10,464.0 $2,257,632
=

2014 ROIC = NOPAT ÷ Operating Capital
=

$1,138,600

=

2015

NOPAT –

WACC

= $10,464 – $2,257,632 x 10%
= $10,464 –

=

2014

NOPAT – Operating Capital x WACC

= $125,460 – $1,138,600 x 10%
= $125,460 –

=

100,000

2015

x

–

= $6.00 x 100,000 –

=

– $557,632

=

2014

MVA = Stock price x # of shares – Total common equity

= $8.50 x 100,000 –

=

– $663,768

=

of taxable income from operations plus

of interest income and

of dividend income. What is the company’s tax liability?

$100,000

$5,000

$10,000

s for

$0

$0

$50,000

$75,000 $100,000

$100,000

$335,000

34.0%

$10,000,000

$15,000,000

$18,333,333

35.0%

39.0%

$5,000

10%

7%

Tax Rate 25.0%

–

ExxonMobil =

Yield * (Investment) – 0

California =

1/6/15
Chapter 6 Mini Case
Situation
Jenny Cochran, a graduate of the University of Tennessee with 4 years of e										x
The company doubled its plant capacity, opened new sales offices outside its home territory, and launched an expensive advertising campaign. Computron’s results were not satisfactory, to put it mildly. Its board of directors, which consisted of its president and vice																				–
Cochrane began by gathering financial statements and other data.
Assume that you are Cochrane’s assistant and that you must help her answer the following questions for Meissner.
Computron’s Income Statement
								2	0
											2015
INCOME STATEMENT
Net sales	$ 3,432,000	$ 5,834,400
Cost of Goods Sold Except Depr.	2,864,000	4,980,000
Depreciation and amortization	18,900		116,960
Other Operating Expenses	340,000	7 Save Time On Research and Writing Hire a Pro to Write You a 100% Plagiarism-Free Paper. Get My Paper	20,000
Total Operating Costs	$ 3,222,900	$ 5,816,960
Earnings before interest and taxes (		EBIT	$ 209,100	$ 17,440
Less interest	62,500	176,000
Pre-tax earnings	$ 146,600	$ (158,560)
Taxes (		40%	58,640	(63,424)
Net Income	$ 87,960		$ (95,136)
Dividends	$22,000		$11,000
Tax rate
a. (1.) What effect did the expansion have on sales and net income?
Computron’s Balance Sheets
Assets
Cash and equivalents	$	9,000		$ 7,282
Short-term investments	48,600
Accounts receivable	351,200	632,160
Inventories	715,200	1,287,360
Total current assets	$ 1,124,000	$ 1,946,802
Gross fixed assets	$ 491,000	$ 1,202,950
Less: Accumulated depreciation	146,200	263,160
Net plant and equipment	$ 344,800	$ 939,790 Bart Kreps: Property, Plant and Equipment minus Depreciation
Total assets		$ 1,468,800		$ 2,886,592
Liabilities and equity
Accounts payable	$ 145,600	$ 324,000
Notes payable	200,000	720,000
Accruals	136,000	284,960
Total current liabilities	$ 481,600	$ 1,328,960
Long-term bonds	$ 323,432	$ 1,000,000
Common Stock		460,000
Retained Earnings	203,768	97,632
Total Equity	$ 663,768	$ 557,632
Total Liabilites and Equity
a. (2.) What effect did the expansion have on the asset side of the balance sheet?
Computron’s Statement of Cash Flows Bart Kreps: The statement of cash flows provides information about cash inflows and outflows during an accounting period.
Operating Activities
Net Income before preferred dividends
Noncash adjustments
Depreciation and amortization
Due to changes in working capital
Change in accounts receivable	(280,960) Bart Kreps: Change is negative because accounts receivable went up in 2001. This means that more sales revenue has been reflected in net income than has been collected in cash.
Change in inventories	(572,160) Bart Kreps: Inventories went up meaning that Computron used cash to purchase inventories.
Change in accounts payable	178,400 Bart Kreps: This is positive because accounts payable went up. Computron bought on credit from suppliers and did not dispense cash.
Change in accruals	148,960 Bart Kreps: Accruals increased in 2001. Cash flow is positive because it recognizes an increased expense prior to the payment of cash.
Net cash provided by operating activities	$ (503,936)
Investing activities
Cash used to acquire fixed assets	$ (711,950) Bart Kreps: Make sure to add back annual Depreciation to Net PP&E.
Change in short-term investments	28,600 Bart Kreps: Short term investments went down in 2001. Computron received cash through the sale or maturity of these assets.
Net cash provided by investing activities	$ (683,350)
Financing Activities
Change in notes payable	$ 520,000 Bart Kreps: Notes payable went up in 2001. Computron received cash from creditors.
Change in long-term debt	676,568 Bart Kreps: Long term debt went up in 2001. Computron received cash from creditors.
Payment of cash dividends	(11,000) Bart Kreps: Computron used cash to pay dividends to shareholders.
Net cash provided by financing activities	$ 1,185,568
Net change in cash and equivilents	$ (1,718)
Cash and securities at beginning of the year
Cash and securities at end of the year
b. What do you conclude from the statement of cash flows?
c. What is free cash flow? Why is it important? What are the five uses of FCF?
d. What is Computron’s net operating profit after taxes (					NOPAT
Net Operating Profit After Taxes
NOPAT is the amount of profit Computron would generate if it had no debt and held no financial assets.
	NOPAT =		( 1 – T )
																=	$17,440		60%
						=			$10,464
					=	$209,100
		$125,460
Net Operating Working Capital
Those current assets used in operations are called operating current assets, and the current liabilities that result from operations are called operating current liabilities. Net operating working capital is equal to operating current assets minus operating current liabilities.
			NOWC		Operating current assets		Operating current liabilities
$1,926,802	$608,960
	$1,317,842
$1,075,400	$281,600
	$793,800
Total Net		Operating Capital
The Total OperatingCapital is Net Operating Working Capital plus any fixed assets.
	TOC =				+		Fixed assets
$939,790
		$2,257,632
$344,800
		$1,138,600
e. What is Computron’s free cash flow (FCF)? What are Computron’s “net uses” of its FCF?
Free Cash Flow
Computron’s Free Cash Flow caluclation is the cash flow actually availabe for distribution to investors after the company has made all necessary investments in fixed assets and working capital to sustain ongoing operations.
FCF =	Net Investment in Operating Capital
	$10,464.0	$1,119,032
	-$1,108,568
Uses of FCF:
After-tax interest payment =	$105,600
Reduction (increase) in debt =	-$1,196,568
Payment of dividends =
Repurchase (Issue) stock =			$0
Purchase (Sale) of short-term investments =	-$28,600
Total uses of FCF =
f. Calculate Computron’s return on invested capital. Computron has a					10%		WACC
Cost of Capital (WACC)
Return on Invested Capital
The Return on Invested Capital tells us the amount of NOPAT per dollar of operating capital.
	ROIC =		÷
0.5%
$125,460.0
11.0%
g. What is Computron’s EVA? The after-tax cost of capital was 10 percent in both years.
Economic Value Added
Economic Value Added represents Computron’s residual income that remains after the cost of all capital, including equity capital, has been deducted.
EVA =		Operating Capital x
$225,763.2
-$215,299
EVA =
$113,860.0
$11,600
h. What happened to Computron’s market value added (MVA)?
Year-end common stock price		$8.50		$6.00
Year-end shares outstanding (in millions)				100,000
Earnings per share (EPS)	Bart Kreps: An increase in Earnings Per Share either means the company is generating more net income or they are reducing the amount of common shares outstanding. Shares that are repurchased by the company are called Treasury stocks.	($0.95)	$0.88
Dividends per share (DPS)	Bart Kreps: The same rational holds for interpreting Dividends Per Share data. If the company increases their dividend payout policies or reduces shares outstanding, DPS will increase.	$0.11	$0.22
Market Value Added
Assume that the market value of debt is equal to the book value of debt. In this case, Market Value Added (MVA) is the difference between the market value of Computron’s stock and the amount of equity capital supplied by shareholders.
	MVA =		Stock price		# of shares		Total common equity
	$557,632
$600,000
$42,368
	$663,768
$850,000
$186,232
i. Assume that a corporation has			$100,000		$5,000	$10,000
Operating income =
Interest income =
Dividends =
Taxable dividends=	$3,000
Taxable Income:	$108,000
Corporate	Tax Rate	2013
If a corporation’s taxable income is between:	It pays this amount on the base of the bracket:	Plus this percentage on the excess over the base
(1)	(2)	(3)	(4)
	$50,000	15.0%
	$75,000	$7,500		25.0%
$13,750		34.0%
	$335,000	$22,250		39.0%
	$10,000,000	$113,900
	$15,000,000	$3,400,000		35.0%
	$18,333,333	$5,150,000	38.0%
and up	$6,416,667
Base amount of tax	$ 22,250
Marginal tax rate in bracket
Income above base of bracket	$ 8,000
Tax on income above base	$ 3,120
Total tax liability:	$25,370
j. Assume that you are in the 25 percent marginal tax bracket and that you have $5,000 to invest. You have narrowed your investment choices down to California bonds with a yield of 7 percent or equally risky ExxonMobil bonds with a yield of 10 percent. Which one should you choose and why? At what marginal tax rate would you be indifferent to the choice between California and ExxonMobil bonds?
Taxable vs. Tax Exempt bonds
ExxonMobil bonds at 10% vs. California muni bonds at	7%
Amount to invest
ExxonMobil Yield
California Yield
	ExxonMobil =		Yield * (Investment)	Yield * (Investment) * (Tax Rate)
$375.00
	California =
$350.00
Tax rate which you would be indifferent
Solve for T
Muni Yield =	Corp Yield *(1-Tax rate)
Tax Rate =	30.00%

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C

hapter23

.

Mini Case for Other Topics in Working Capital Management

Andria Mullins

,

financial manager of Webster Eelectronics, has been asked by the firm’s CEO,

F

red Weygandt, to evaluate the company’s inventory control techniques and to lead a discussion of the subject with the senior executives. Andria plans to use as an example one of Webster’s “big ticket” items, a customized computer microchip which the firm uses in its laptop computer. Each chip

cost

s Webster $2

0

0, and in addition it must pay its supplier a $1,

000

setup fee on each order. Further, the minimum order size is 2

5

0

units

; Webster’s annual usage forecast is

5,000

units; and the annual carrying cost of this item is estimated to be 20 percent of the average inventory value.
Andria plans to begin her session with the senior executives by reviewing some basic inventory concepts, after which she will apply the EO

Q

model to Webster’s microchip inventory. As her assistant, you have been asked to help her by answering the following questions:

a. Why is inventory management vital to the health of most firms? Inventory management is critical to the financial success of most firms. If insufficient inventories are carried, a firm will lose sales. Conversely, if excess inventories are carried, a firm will incur higher costs than necessary. Worst of all, if a firm carries large inventories, but of the wrong items, it will incur high costs and still lose sales.

b. What assumptions underlie the

EOQ

Model

?

The standard form of the EOQ model requires the following assumptions: · All values are known with certainty and constant over time. · Inventory usage is uniform over time. For example, a retailer would sell the same number of units each day. · All carrying costs are variable, so carrying costs change proportionally with changes in inventory levels · All ordering costs are fixed per order; that is, the company pays a fixed amount to order and receive each shipment of inventory, regardless of the number of units ordered. These assumed conditions are not met in the real world, and, as a result, safety stocks are carried, and these stocks raise average inventory holdings above the amounts that result from the “pure” EOQ model. c. Write out the formula for the total costs of carrying and ordering inventory, and then use the formula to derive the EOQ model.

TIC

=

total carrying costs + total ordering costs = C

P

(

Q/2

)

+ F(

S

/Q)

C =

annual carrying cost as a percentage of inventory value. P =

purchase price per unit. Q = number of units in each order. F =

fixed costs per order. S =

annual usage in units. Note that S/Q is the number of orders placed each year, and, if no safety stocks are carried, Q/2 is the average number of units carried in inventory during the year. The economic (optimal) order quantity (EOQ) is that order quantity which minimizes total inventory costs. Thus, we have a standard optimization problem, and the solution is to take the first derivative of the TIC with respect to quantity and set it equal to zero: Solving for Q gives us: d. What is the EOQ for custom microchips? What are total inventory costs if the EOQ is ordered? TIC =

CP(Q/2) + F(S/Q)

= 0.2

($

200

)(

50

0

/2) + $1,000(5,000/500)

= $40(250) + $1,000(

10

) = $10,000 + $10,000 = $20,000. C =

20% P =

$ 200 F =

$ 1,000 S = 5,000
EOQ =

500
TIC =

$ 20,000 e. What is Webster’s added cost if it orders 400 units at a time rather than the EOQ quantity? What if it orders

600

per order?

C = 20%
P = $ 200

F = $ 1,000

@400, TIC = 20,500 S = 5,000

@600, TIC = 20,333 Order quantity =

600

plug in 400 and 600 TIC =

$ 20,333

f. Suppose it takes 2 weeks for Webster’s supplier to set up production, make and test the chips, and deliver them to Webster’s plant. Assuming certainty in delivery times and usage, at what inventory level should Webster reorder? (assume a 52

–

week year, and assume that Webster orders the EOQ amount.

With an annual usage of 5,000 units, Webster’s weekly usage rate is 5,000/52 ~ 96 units. If the order lead time is 2 weeks, then Webster must reorder each time its inventory reaches 2(96) = 192 units. Then, after 2 weeks, as it uses its last microchip, the new order of 500 chips arrives. g. Of course, there is uncertainty in Webster’s usage rate as well as in delivery times, so the company must carry a safety stock to avoid running out of chips and having to halt production. If a 200-unit safety stock is carried, what effect would this have on total inventory costs? What is the new reorder point? What protection does the safety stock provide if usage increases, or if delivery is delayed? There are two ways to view the impact of safety stocks on total inventory costs. Webster’s total cost of carrying the operating inventory is $20,000 (see part d). Now the cost of carrying an additional 200 units is CP(safety stock) = 0.2($200)(200) = $8,000. Thus, total inventory costs are increased by $8,000, for a total of $20,000 + $8,000 = $28,000. Another approach is to recognize that, with a 200-unit safety stock, Webster’s average inventory is now (500/2) + 200 = 450 units. Thus, its total inventory cost, including safety stock, is $28,000: TIC = CP(average inventory) + F(S/Q) = 0.2($200)(450) + $1,000(5,000/500) = $18,000 + $10,000 = $28,000. Webster must still reorder when the operating inventory reaches 192 units. However, with a safety stock of 200 units in addition to the operating inventory, the reorder point becomes 200 + 192 = 392 units. Since Webster will reorder when its microchip inventory reaches 392 units, and since the expected delivery time is 2 weeks, Webster’s normal 96 unit usage could rise to 392/2 = 196 units per week over the 2-week delivery period without causing a stockout. Similarly, if usage remains at the expected 96 units per week, Webster could operate for 392/96 » 4 weeks versus the normal two weeks while awaiting delivery of an order. h. Now suppose Webster’s supplier offers a discount of 1 percent on orders of 1,000 or more. Should Webster take the discount? Why or why not? First, note that since the discount will only affect the orders for the operating inventory, the discount decision need not take account of the safety stock. Webster’s current total cost of its operating inventory is $20,000 (see part d). If Webster increases its order quantity to 1,000 units, then its total costs for the operating inventory would be $24,800: TIC = CP(Q/2) + F(S/Q) = 0.2($198)(1,000/2) + $1,000(5,000/1,000) = $19,800 + $5,000 = $24,800. Note that we have reduced the unit price by the amount of the discount. Since total costs are $24,800 if Webster orders 1,000 chips at a time, the incremental annual cost of taking the discount is $24,800 – $20,000 = $4,800. However, Webster would save 1 percent on each chip, for a total annual savings of 0.01($200)(5,000) = $10,000. Thus, the net effect is that Webster would save $10,000 – $4,800 = $5,200 if it takes the discount, and hence it should do so. i. For many firms, inventory usage is not uniform throughout the year, but, rather, follows some seasonal pattern. Can the EOQ model be used in this situation? If so, how? The EOQ model can still be used if there are seasonal variations in usage, but it must be applied to shorter periods during which usage is approximately constant. For example, assume that the usage rate is constant, but different, during the summer and winter periods. The EOQ model could be applied separately, using the appropriate annual usage rate, to each period, and during the transitional fall and spring seasons inventories would be either run down or built up with special seasonal orders. j. How would these factors affect an EOQ analysis? (1.) The use of just-in-time procedures. Just-in-time procedures are designed specifically to reduce inventories. If a just in time system were put in place, it would largely obviate the need for using the EOQ model. (2.) The use of air freight for deliveries. Air freight would presumably shorten delivery times and reduce the need for safety stocks. It might or might not affect the EOQ. (3.) The use of a computerized inventory control system, wherein as units were removed from stock, an electronic system automatically reduced the inventory account and, when the order point was hit, automatically sent an electronic message to the supplier placing an order. The electronic system ensures that inventory records are accurate, and that orders are placed promptly. Computerized control systems would, generally, enable the company to keep better track of its existing inventory. This would probably reduce safety stocks, and it might or might not affect the EOQ. (4.) The manufacturing plant is redesigned and automated. Computerized process equipment and state-of-the-art robotics are installed, making the plant highly flexible in the sense that the company can switch from the production of one item to another at a minimum cost and quite quickly. This makes short production runs more feasible than under the old plant setup. The trend in manufacturing is toward flexibly designed plants, which permit small production runs without high setup costs. This reduces inventory holdings of final goods. Applying this to cash management: Monthly cash deficit (cash needs) 100,000.00 Opportunity cost for cash 7% Brokerage costs for each transaction 32 Total cash needs per year 1,200,000.00 EOQ = Optimal cash transfer 33,123 Number of times to liquidate per year 36.2 Number of weeks between liquidations 1.435 Optimal cash transfer size for various order costs and carrying costs carrying–or opportunity–cost 33,123

3% 5%

7%

9% 11% 10

28,284 21,

90

9 18,516 16,330 14,771 32

50,596 39,192

33,123

29,212 26,423 order/transaction

50

63,246 48,990 41,404 36,515 33,029 cost

70 74,833 57,966

48,990

43,205 39,080 90

84,853 65,727 55,549

48,990

44,313 110 93,808 72,664 61,412 54,160

48,990
k. Webster runs a $100,000 per month cash deficit, requiring periodic transfers from its portfolio of marketable securities. Broker fees are $32 per transaction, and Webster earns 7% on its investment portfolio. How can Andria use the EOQ model to determine how Webster should liquidate part of its portfolio to provide cash?

0
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EOQ

Real Op

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Chapter 1

4

.

Real Option

s

Assume that you have just been hired as a financial analyst by Tropical Sweets Inc., a mid-sized California company that specializes in creating exotic candies from tropical fruits such as mangoes, papayas, and dates. The firm’s CEO, George Yamaguchi, recently returned from an industry corporate executive conference in San Francisco, and one of the sessions he attended was on real options. Since no one at Tropical Sweets is familiar with the basics of real options, Yamaguchi has asked you to prepare a brief report that the firm’s executives could use to gain at least a cursory understanding of the topics. a. What are some types of real options? b. What are the five steps for analyzing a real option? c. Tropical Sweets is considering a project that will cost $7

0

million and will generate expected cash flows of

$

3

0

per year for three years. The cost of capital for this type of project is 10 percent and the risk-free rate is

6

percent. After discussions with the marketing department, you learn that there is a 30 percent chance of high demand, with future cash flows of

$4

5

million per year. There is a 40 percent chance of average demand, with cash flows of

$30

million per year. If demand is low (a 30 percent chance), cash flows will be only

$15

per year. What is the expected NPV? REAL OPTIONS: THE INVESTMENT TIMING OPTION Cost = ($70) WACC= 10% Risk-free rate= 6% Demand Prob. Annual

Cash Flow Prob. x (CF) High 0.3 $45 $13.50 Average 0.4

$30

$12.00 Low

0.3 $15

$4.50 Expected CF

= $3

0.00 Procedure 1: DCF Only Year

1 2 3
Expected CF $30.00 $30.00 $30.00
NPV= $4.61 d. Now suppose this project has an investment timing option, since it can be delayed for a year. The cost will still be $70 million at the end of the year, and the cash flows for the scenarios will still last three years. However, Tropical Sweets will know the level of demand, and will implement the project only if it adds value to the company. Perform a qualitative assessment of the investment timing option’s value. e. Use decision tree analysis to calculate the NPV of the project with the investment timing option. Procedure 3: Decision Tree Analysis a.

Scenario

Analysis: Proceed with Project Today Cost

Future Cash Flows NPV this

Prob.

Data for Year 0

Prob. 1 2 3 Scenario

x NPV Std Deviation $45 $45 $45

$41.91 $12.57 417 30% -$70 40%

$30 $30 $30 $4.61

$1.84

0

30%

$15 $15 $15

-$32.70 -$9.81

417
Expected NPV of Future CFs =

$4.61

835 =Variance of PV Standard Deviation= $28.89 Coefficient of Variation = 6.27 b. Decision Tree Analysis: Implement in One Year Only if Optimal Cost Future Cash Flows NPV this Prob. Data for
Year 0 Prob. 1 2 3 4

Scenarioa

x NPV Std Deviation
-$70 $45 $45 $45

$35.70 $10.71 177

30%

$0

40% -$70 $30 $30 $30

$1.79 $0.71 37

30%

$0 $0 $0 $0

$0.00

$0.00

39 Expected NPV of Future CFs =

$11.42 253

=Variance of PV
Standard Deviation=

$15.91 Coefficient of Variation =

1.39 Notes: a Discount the cost of the project at the risk-free rate, since the cost is known. Discount the operating cash flows at the WACC. f. Use a financial option pricing model to estimate the value of the investment timing option. Procedure 4: Analysis with a

Financial Option The option to defer the project is like a call option. The company has until

Year 1

to decide whether or not to implement the project, so the time to maturity of the option is one year. If the company exercises the option, it must pay a strike price equal to the cost of implementing the project. If the company does implement the project, it gains the value of the project. If you exercise a call option, you will own a stock that is worth whatever its price is. If the company implements the project, it will gain a project, whose value is equal to the present value of its cash flows. Therefore, the present value of a project’s future cash flows is analogous to the current value of a stock. The rate of return on the project is equal to its cost of capital. To find the value of a call option, we need the standard deviation of its rate of return; to find the value of this real option, we need the standard deviation of the projects expected rate of return. The first step is to find the value of the project’s future cash flows, as of the time the option must be exercised. We also need the standard deviation of the project’s value as of the date it must be exercised. Finally, we need the present value of the project’s future cash flows. Find the

Year 1 Value

and Risk of Future Cash Flows If Project is Deferred Future Cash Flows

PV at

Prob. Data for
Year 0 Prob. 1 2 3 4 Year 1

x Value

Std Deviation
$45 $45 $45

$111.91 $33.57

417

30%

40% $30 $30 $30

$74.61 $29.84

0

30%

$15 $15 $15

$37.30 $11.19

417
Expected Year 1 Value of Future CFs =

$74.61 835 =Variance of PV
Standard Deviation of value at Year 1=

$28.89
Coefficient of Variation at Year 1 = 0.39 Find the current value of future cash flows if project is deferred (note: this is the estimate of P). Current Value =

Year 1 Value = $74.61 =

$67.82

(1

+

WACC)

1.10 P =

$67.82
Use the direct approach to estimate the variance of the project’s rate of return. Probability

Data for
PVYear 0 PVYear 1 Return

Probability

x ReturnYear 1

Std Deviation
$111.91

65.00% 0.30 19.5% 9.1% High
$67.82 Average $74.61

1

0.0% 0.40 4.0%

0.0%
Low
$37.30

-45.0%

0.30

-13.5%

9.1%
1.00 Expected return = 10.0% 18.2%

=Variance of PV
Standard deviation of return = 42.6% Direct estimate of

s2 =

Variance of return =

18.2%

Use the indirect approach to estimate the variance of the project’s rate of return. Start by estimating the coefficient of variation,

CV

, of the project’s value at the time the option expires. This was done in an earlier step.

CV =Coefficient of Variation = 0.39
Michael C. Ehrhardt: Note: we rounded this to make it consistent with the PowerPoint Show. Now use the following formula to estimate the variance of the project’s rate of return. t =

time until the option expires =

1
Indirect estimate of s2 = 14.2% Find the Value of a Call Option Using the Black-Scholes Model Financial Option Real Option
rRF = Risk-free interest rate

= Risk-free interest rate
t =

Time until the option expires

= Time until the option expires
X = Strike price

=

Cost to implement the project P =

Current price of the underlying stock

=

Current value of the project s2 =

Variance of the stock’s rate of return

=

Variance of the project’s rate of return rRF = 6%
t = 1
X =

$70.00

P = $67.82

s2 = 14.2%
d1 =

{ ln (P/X) + rRF + s2 /2)

]

t } / (s t1/2 ) =

0.2637 d2 = d1 – s (t 1 / 2)

=

-0.1131 N(d1)=

=

0.6040 Note: use the NORMSDIST function. N(d2)=

=

0.4550 V = P[ N (d1) ] – Xe-rRF t [ N (d2) ]

=

$ 10.97 REAL OPTIONS: THE GROWTH OPTION g. Now suppose the cost of the project is

$75

million and the project cannot be delayed. But if Tropical Sweets implements the project, then Tropical Sweets will have a growth option. It will have the opportunity to replicate the original project at the end of its life. What is total expected NPV of the two projects if both are implemented? Cost=

$75
WACC= 10%
Risk-free rate =

6%
Original Project Cost Future Cash Flows NPV this Prob. Data for
Year 0 Prob. 1 2 3 Scenario x NPV Std Deviation
$45 $45 $45

$36.91 $11.07 417.45

30%

-$75

40% $30 $30 $30

-$0.39 -$0.16

0.00

30%

$15 $15 $15

-$37.70 -$11.31

417.45
Expected

NPV =

-$0.39

834.90

=Variance of PV
Standard Deviation= $28.89
Coefficient of Variation =

(73.25) NPV without growth option: NPV = -$0.39
Expected NPV is you simply repeat project at time 3: NPV =

NPV of project 1 + PV of repeated project NPV =

NPV1

+ NPV1 /

(1+WACC)

3
NPV = -$0.39 +

-$0.30
Michael C. Ehrhardt: The NPV would be even lower if we separately discounted the $75 million cost of Replication at the risk-free rate. NPV =

-$0.69 h. Tropical Sweets will replicate the original project only if demand is high. Using decision tree analysis, estimate the value of the project with the growth option. Decision Tree: Implement the repeated project only if demand is high.

Data for
Cost Future Cash Flows NPV this Prob. Std Deviation
Year 0 Prob. 1 2 3 4 5 6

Scenario
Michael C. Ehrhardt: The operating cash flows are discounted at the project cost of capital. The cost to implement the repeated project is discounted at the risk-free rate, since the cost is known.

x NPV
$45 $45

-$30

$45 $45 $45

$58.02 $17.40 1,010

30%

-$75 40% $30 $30 $30 $0 $0 $0 -$0.39 -$0.16 0

30%

$15 $15 $15 $0 $0 $0 -$37.70 -$11.31

– 0 Expected NPV = $5.94 1,010 =Variance of PV
Standard Deviation=

$31.78 Coefficient of Variation =

5.35 Notes:

1. The CF in

Year 3

includes the cost to implement the second project if it is optimal to do so. 2. When finding the NPV, the cost to implement the second project is discounted at the risk-free rate; other cash flows are discounted at the cost of capital. i. Use a financial option model to estimate the value of the growth option. Financial Option Approach Find the value and risk of the future cash flows as of the time the option expires. Data for
Cost Future Cash Flows

PV at

Prob. Std Deviation
Year 0 Prob. 1 2 3 4 5 6 Year 3 x NPV
$45 $45 $45 $111.91 $33.57 417

30%

40% $30 $30 $30 $74.61 $29.84 – 0

30%

$15 $15 $15 $37.30 $11.19 417
Expected value at Year 3 =

$74.61
835 =Variance of PV
Standard Deviation of value at Year 3=

$28.89
Coefficient of Variation at Year 3=

0.39

Find the current value of future cash flows if project is deferred (note: this is the estimate of P).

Current Value =

Year 3 Value

= $74.61 =

$56.05 (1+WACC)3 1.33 P = $56.05

Use the direct approach to estimate the variance of the project’s rate of return.

Annual Data for
PVYear 0 1 2

PVYear 3

Return Probability

x Return2005

Std Deviation
$111.91

25.9%

0.30

7.8% 1.0%

High

$56.05 Average $74.61 10.0% 0.40 4.0% 0.0%

Low

$37.30

-12.7%

0.30

-3.8% 1.3% 1.00
Expected return =

7.968% 2.3%

=Variance of PV
Standard deviation of return =

15.0% Direct estimate of s2 = Variance of return =

2.3%
Use the indirect approach to estimate the variance of the project’s rate of return. Start by estimating the coefficient of variation, CV, of the project’s value at the time the option expires. This was done in an earlier step.

CV =Coefficient of Variation = 0.39
Michael C. Ehrhardt: Note: we rounded this to make it consistent with the PowerPoint Show.

Michael C. Ehrhardt: The NPV would be even lower if we separately discounted the $75 million cost of Replication at the risk-free rate.

Now use the following formula to estimate the variance of the project’s rate of return.
t = time until the option expires =

3
Indirect estimate of s2 =

4.7%
Michael C. Ehrhardt: Note: we rounded to make it consistent with PowerPoint show. j. What happens to the value of the growth option if the variance of the project’s return is 14.2 percent? What if it is 50 percent? How might this explain the high valuations of many dot.com companies?

Find the Value of a Call Option Using the Black-Scholes Model

Sensitivity Analysis Base Case Case 1 Case 2 rRF = 6% 6% 6%
t = 3 3 3
X =

$75.00

$75.00 $75.00
P = $56.05 $56.05 $56.05
s2 =

4.70% 14.20% 50.00% d1 =

{ ln (P/X) + [rRF + s2 /2) ] t }
(s t1/2 )

=

-0.1085 0.1559 0.5215 d2 = d1 – s (t 1 / 2) =

-0.4840 -0.4968 -0.7032 N(d1)= =

0.4568 0.5619 0.6990 Note: we used the NORMSDIST function. N(d2)= =

0.3142 0.3097 0.2410 V = P[ N (d1) ] – Xe-rRF t [ N (d2) ] =

$ 5.92 $ 12.10 $ 24.08 Total Value = Value of Project 1 + Value of growth option Total Value = -$0.39 +

$5.92 Total Value =

$ 5.53

t
]
1
CV

ln[

2
2
+
=
s
t

]1CVln[

2
2