Fabozzi Frank, Peterson Pamela. Financial Management and Analysis Workbook

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340 SOLUTIONS

b. The correlation coefﬁcient = = = 0.9395.

c. Because the covariance is positive, the investment’s returns covary

together in the same direction. The correlation coefﬁcient, which is

positive and close to 1, means that the two investments tend to go in

the same direction at the same time together.

σ x()

Inv2

0.15 0.15 0.3375–()

0.30 0.45 0.3375–()

0.55 0.30 0.3375–()++=

0.0992=

Covariance 0.15 0.18 0.397–()0.15 0.3375–()=

0.30 0.50 0.397–()0.45 0.3375–()+

0.55 0.40 0.397–()0.30 0.3375–()+

0.0095=

12,

------------ -

0.0095

0.1012()0.0992()

----------------------------------------------

SolCh10 Page 340 Tuesday, December 16, 2003 9:27 AM

CHAPTER

341

The Cost of Capital

FILL IN THE BLANKS

Answers

1. cost, capital, funds; borrowed, cost, interest; equity, cost, return, appre-

ciation, dividends; capital, required, return

2. structure, debt, preferred, common; optimum proportions, capital

3. cost, debt, dollar, marginal, rate, tax, taxable; interest, taxable, effec-

tive, lower

4. debt, stock, ﬂotation; payments, lawyers, accountants, bankers; all-

in-cost, up

5. cost, preferred, dollar, issuing, preferred; Preferred, maturity; matu-

rity, perpetual preferred

6. cost, common, common, internally, externally; Internally, retained,

externally, shares, common

7. Dividend Valuation, DVM, common, price, stock, present, future,

dividends, discounted, required, return, equity; dividends, constant,

future

8. Capital Asset Pricing, CAPM, diversiﬁed, market; compensated, time,

money, risk; compensation, time, money, risk premium, market, beta.

SolCh11 Page 341 Tuesday, December 16, 2003 9:28 AM

342 SOLUTIONS

9. optimal capital, maximize, investment, marginal, capital, equal, bene-

ﬁt; optimal capital budget, expenditure, marginal, capital, internal,

efﬁciency

SHORT ANSWER QUESTIONS

Answers

1. The cost of capital and the required rate of return are similar. The dif-

ference comes in from the perspective. Cost of capital is from the

ﬁrm’s perspective as it is the amount the ﬁrm has to compensate

investors in order to receive their money. Required rate of return is

from the investor’s perspective as it represents the personal return

rate they require in order to temporarily part with their money and

invest it in the company. These are marginal concepts because they

represent the incremental cost or return associated with raising or

investing an additional dollar.

2. The cost of capital is determined in three steps:

■

Calculate the proportions of each source of capital to be used.

■

Calculate the cost of each source of capital.

■

Calculate the weighted average cost of capital using these two mea-

sures.

3. It is appropriate to use the DVM when companies have stable divi-

dend policies. The CAPM relies on historical values for stock returns

and market returns and should be reserved for only publicly traded

ﬁrms. A pitfall of this model is often the lack of data and even if data

is available, the past is not indicative of future earnings.

SolCh11 Page 342 Tuesday, December 16, 2003 9:28 AM

The Cost of Capital 343

PROBLEMS

Answers

1. Yield on current debt:

r = 4.7813%

Effective annual yield = (1 + 0.047813)

– 1 = 9.79%

After-tax effective yield:

2. Without ﬂotation costs:

With ﬂotation costs:

3. Given:

4. Given:

= $3.12

P = $65

g =5%

=4%

= 11%

B = 1.35

$900

$35

1 r+()

------------------

t 1=

∑

$1,000

1 r+()

----------------------

9.79% 1 0.30–()6.85%==

$1.05

$35

-------------- -

3.00%==

$1.05

$35 1 0.01–()

------------------------------------

$1.05

$34.65

------------------

==3.03%=

$3.12 1 0.05+()

$65

----------------------------------------- -

5%+=

5.04% 5%+ 10.04%==

SolCh11 Page 343 Tuesday, December 16, 2003 9:28 AM

344 SOLUTIONS

5. Estimation of the cost of capital for Sutton, Inc.:

Given:

Solve: Cost of capital (r

) for alternative ﬁnancing proportions

Calculation of costs of sources of funds:

Financing arrangement #1:

Financing arrangement #2:

=8%

= $2.00

= $30

P = $25

= $1.50

g =5%

t = 40%

Cost of debt

Cost of preferred equity

Cost of common equity

4% 1.35 11% 4%–()+=

4% 9.45%+ 13.45%==

0.08 1 0.40–()0.08 0.6()0.048===

$2.00

$30.00

------------------

0.0667==

$1.50

$25.00

------------------





0.05+=

0.06 0.05+ 0.11==

0.30 0.048()[]0.10 0.0667()[]0.60 0.11()[]++=

0.0144 0.00667 0.066++=

0.087 or 8.7%=

0.50 0.048()[]0.25 0.0667()[]0.25 0.11()[]++=

0.024 0.016675 0.0275++=

0.0682 or 6.82%=

SolCh11 Page 344 Tuesday, December 16, 2003 9:28 AM

CHAPTER

345

Capital Budgeting: Cash Flows

FILL IN THE BLANKS

Answers

1. objective, wealth; investment, value; invest, tangible, intangible,

income, cash, reinvest, pay

2. Capital, assets, notes, bonds, stock, short-term; capital, projects; fac-

tors, estimate, future, change, uncertainty, future

3. risk, sales, operating; Sales, uncertainty, sold, price, operating, uncer-

tainty, operating, mix, operating; business, discount, return, capital,

required, cost

4. budgeting, identifying, selecting, long, beneﬁts, one; budgeting, ongoing;

budgeting, strategy, objectives

5. length, risk, dependence; economic, useful, length, beneﬁts; risk,

nature; dependence, independent, mutually exclusive, contingent,

complementary

6. difference, with, without, incremental; change, components, operat-

ing, investment, expenditures, acquire, disposing

7. simplest, outﬂow, acquired, inﬂow, outﬂow, economic; revenues,

expenditures, taxes, working; operating

SolCh12 Page 345 Tuesday, December 16, 2003 9:28 AM

346 SOLUTIONS

8. depreciation, depreciation tax-shield; outﬂow, inﬂow; accelerated,

straight-line; accelerated, larger, sooner, straight-line

9. Salvage, not, depreciation; guess, asset, worth, useful; Salvage, dis-

pose

SHORT ANSWER QUESTIONS

Answers

1. The ﬁve stages of the capital budgeting process are:

■

Stage 1: Investment screening and selection. A project’s cash ﬂows

are screened and selected according to their ability to fulﬁll corpo-

rate strategy.

■

Stage 2: Capital budget proposal. A capital budget is proposed for

the selected projects.

■

Stage 3: Budgeting approval and authorization. Projects that are

approved are included in the capital budget. More analysis is con-

ducted prior to making expenditures.

■

Stage 4: Project tracking. Projects that are approved are tracked dur-

ing the life of the project.

■

Stage 5: Postcompletion audit. Projects that are approved are

audited from time to time in order to review if they still comply with

corporate strategy.

2. The use of current assets are usually the focus of short-term invest-

ment decisions and don’t necessarily entail long-term cash ﬂow pro-

jections. Current assets are cash, marketable securities, accounts

receivable, and inventory. With long-term investment decisions, cash

ﬂow projections are necessary as there is a concern for the time value

of money and the day-to-day operating needs of the ﬁrm. A ﬁrm

needs both current and long-term assets in order to function even

during down times.

3. A ﬁrm must consider future cash ﬂows and how these cash ﬂows

inﬂuence the assets already utilized by the ﬁrm. New projects may or

may not adversely affect the current assets in place. Often, ﬁrms can

take on additional projects if they already have the necessary assets in

place. When decisions are made, capital rationing is a concern as a

SolCh12 Page 346 Tuesday, December 16, 2003 9:28 AM

Capital Budgeting: Cash Flows 347

company may not be able to ﬁnancially take on all the projects it

wants.

■

An independent project is as the name implies, a project that does

not rely on another project. Hence their cash ﬂows are unrelated.

■

Mutually exclusive projects are projects in which the cash ﬂows

affect each other. In other words, the ﬁrm can either do one project

or the other, but not both.

■

Contingent projects rely on the acceptance of another project.

■

Complementary projects are projects that positively inﬂuence other

projects.

4. Cash ﬂows from investments come from asset acquisition, asset dis-

position, taxes, and operations. All these cash ﬂows include costs of

assets, expenditures in the utilization and disposal of the assets, and

the effect of taxes.

PROBLEMS

Answers

1. Asset acquisition cash ﬂow for Year 0 = ($10,000) for the cost of the

asset.

Operating Cash Flows for Year 1 through Year 5 = $5,500 each year.

Asset disposition cash ﬂow = $0 as there is no salvage value.

Operating Cash Flows

Change in revenues $15,000

Less change in expenses –8,000

Change in before-tax cash ﬂow $7,000

Less change in depreciation –2,000

Change in taxable income $5,000

Less change in taxes –1,500



G30% of $5,000

Change in net income $3,500

Plus change in depreciation +2,000

Change in after-tax cash ﬂow $5,500

SolCh12 Page 347 Tuesday, December 16, 2003 9:28 AM

348 SOLUTIONS

2. Asset acquisition cash ﬂow for Year 0 = ($49,000) for the cost of the asset.

Operating Cash Flows for Year 1 through Year 7 = $5,500 each year.

Asset disposition cash ﬂow = $7,500.

Operating Cash Flows

Asset Disposition

3. Asset acquisition cash ﬂow for Year 0 = ($30,000) for the asset.

Operating Cash Flows for Year 1 through Year 7 = $3,300 each year.

Asset disposition cash ﬂow = $5,500.

Asset Acquisition

Operating Cash Flows

Change in revenues $18,000

Less change in expenses –5,000

Change in before-tax cash ﬂow $13,000

Less change in depreciation –7,000

Change in taxable income $6,000

Less change in taxes –1,500



G25% of $6,000

Change in net income $4,500

Plus change in depreciation +7,000

Change in after-tax cash ﬂow $11,500

Cash inﬂow from sale of cookie press $10,000

Tax on sale of press –2,500

Net cash ﬂow form asset disposition $7,500

Cost of equipment $(20,000)

Installation (8,000)

Spare parts inventory (2,000)

Initial investment outlay $(30,000)

Change in revenues $0

Less change in expenses –3,000

Change in before-tax cash ﬂow $3,000

Less change in depreciation –4,000



G$28,000/7

Change in taxable income $(1,000)

Less change in taxes –300



G tax savings

Change in net income $(700)

Plus change in depreciation +4,000

Change in after-tax cash ﬂow $3,300

SolCh12 Page 348 Tuesday, December 16, 2003 9:28 AM

Capital Budgeting: Cash Flows 349

Asset Disposition

Salvage value $5,000

Tax on salvage value –1,500

Net cash ﬂow form asset disposition $5,500

SolCh12 Page 349 Tuesday, December 16, 2003 9:28 AM