Fabozzi Frank, Peterson Pamela. Financial Management and Analysis Workbook

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SolCh12 Page 350 Tuesday, December 16, 2003 9:28 AM

CHAPTER

351

Capital Budgeting Techniques

FILL IN THE BLANKS

Answers

1. cost, pay, ﬁnance; cost, explicit, interest, implicit, price, common,

return, suppliers, capital, value, risk; uncertain, greater

2. payback, length, money; initial, outﬂow, inﬂows, initial, outﬂow;

payback, payoff, recovery

3. discounted payback, pay, original, discounted, payback, longer, dis-

counted, cash, discounted

4. Net present, NPV, expected; net, difference, change; changes, inﬂows,

investment, outﬂows, NPV, difference, inﬂows, outﬂows

5. NPV, future, time value, risk, future; NPV, maximize; NPV, deter-

mine, changes, proﬁtability

6. investment, NPV, NPV, discount; investment, graphical, NPV, dis-

count; NPV, range, discount

7. proﬁtability index, PI, operating, inﬂows, investment, outﬂows; PI,

beneﬁt-cost, beneﬁt, cost; PI

8. internal rate, IRR, discount, future, zero, IRR, discount, NPV, $0;

IRR, yield; mutually exclusive, IRR, not

SolCh13 Page 351 Tuesday, December 16, 2003 9:29 AM

352 SOLUTIONS

SHORT ANSWER QUESTIONS

Answers

1. The six capital budgeting techniques are:

■

Payback period

■

Discounted payback period

■

Net present value (NPV)

■

Proﬁtability index (PI)

■

Internal rate of return (IRR)

■

Modiﬁed internal rate of return (MIRR)

When evaluating investment projects, the ones chosen should

always maximize owner wealth. To determine if they will maximize

shareholder wealth or not, cash ﬂows, and their uncertainty from

each investment should be estimated.

2. Payback and discounted payback periods:

■

The sooner the payback, the better.

Net present value:

■

NPV > 0 indicates the investment increases shareholder wealth—

accept the project.

■

NPV < 0 indicates the investment decreases shareholder wealth—

reject the project.

■

NPV = 0 indicates the investment does nothing to change share-

holder wealth—indifferent about the project.

Proﬁtability index:

■

PI > 1 indicates the investment returns more—accept the project.

■

PI < 1 indicates the investment returns less—reject the project

■

PI = 1 indicates the investment returns nothing extra but loses noth-

ing—indifferent about the project.

Internal rate of return:

■

IRR > cost of capital indicates the investment is expected to return

more—accept the project.

SolCh13 Page 352 Tuesday, December 16, 2003 9:29 AM

Capital Budgeting Techniques 353

■

IRR < cost of capital indicates the investment is expected to return

less—reject the project.

■

IRR = cost of capital indicates the investment is expected to return

what is required—indifferent about the project.

Modiﬁed internal rate of return:

■

MIRR > cost of capital indicates the investment is expected to return

more—accept the project.

■

MIRR < cost of capital indicates the investment is expected to return

less—reject the project.

■

MIRR = cost of capital indicates the investment is expected to return

what is required—indifferent about accepting or rejecting the

project.

3. The proﬁtability index is a good evaluation technique. It considers a

variety of factors such as all cash ﬂows, the time value of money, the

risk associated with these, and capital rationing. However, the PI is

not foolproof. If projects require differing amounts to be invested at

different times, then the PI may not coincide with NPV. Also, mutu-

ally exclusive projects are not comparable using PI.

4. In a sense, the IRR is the discount rate that breaks even. It makes the

present value of all expected future cash ﬂows equal to zero assuming

these cash ﬂows are reinvested at the same IRR each time. The MIRR

technique is much more realistic because it assumes that the rein-

vested rates vary. A drawback to IRR and MIRR is that while they

consider all cash ﬂows and their timing, they do not directly take risk

into account. Risk is indirectly accounted for when using the mea-

sures in the actual act of discounting. Selection of IRR and MIRR

should be taken cautiously as capital rationing and status (depen-

dence, independence, mutual exclusivity) of a project inﬂuence the

selection.

5. When selecting the appropriate techniques, it is important to remem-

ber that discounted cash ﬂows are preferred to the nondiscounted

cash ﬂow techniques although they may not necessarily be appropri-

ate for all situations (although they are appropriate for most). The

goal is to always maximize shareholder wealth.

■

If projects are independent and capital rationing is of no concern,

then any of the discounted cash ﬂow techniques are appropriate.

SolCh13 Page 353 Tuesday, December 16, 2003 9:29 AM

354 SOLUTIONS

■

Recall that for mutually exclusive projects, the NPV method leads to

investing in projects that maximize wealth and if the capital budget

is limited, the NPV and PI methods should be used.

■

If the projects are so constrained that they are mutually exclusive,

cost the same amount to start, and have similar risk, then use either

NPV or MIRR.

■

If projects are mutually exclusive with different risks and scales,

then NPV should be used over MIRR. If capital rationing is neces-

sary, then the NPV or PI are appropriate.

■

Overall, NPV should guide project selection; in particular, NPV of

the entire capital budget is the real concern.

In practice, more than one technique is used in order to give a more

rounded view of the project. As mentioned above, discounted cash

ﬂow techniques (NPV, IRR, PI) are used as a primary method and

payback period is used as a secondary method. IRR with NPV is

being used more frequently.

PROBLEMS

Answers

1. You are the manager and are considering the following two projects for

investment:

a. Project A takes two years in order to regain the initial investment of

$10,000.

Project B takes two years in order to regain the initial investment of

$5,000.

Year 0 Year 1 Year 2 Year 3

Project A ($10,000) $3,000 $7,000 $9,000

Project B ($5,000) $3,000 $4,000 $5,000

SolCh13 Page 354 Tuesday, December 16, 2003 9:29 AM

Capital Budgeting Techniques 355

Project A takes three years in order to regain the initial investment of

$10,000.

Project B takes two years in order to regain the initial investment of

$5,000.

As a manager, you like the fact that the initial outlay for project B

will be paid back quickly, however, this does not necessarily indicate

that project B is the best project. If the required return or cost of cap-

ital was higher than 10%, then the discounted cash ﬂow would have

been a lesser amount and it would take longer to recoup the initial

outlays for both investments.

c. NPV for project A = $2,727 + $5,785 + $6,762 = $15,274

NPV for project B = $2,727 + $3,306 + $3,757 = $9,790

Both projects produce positive NPV, which is desirable of all projects.

d. PI for project A = = 1.5274

PI for project B = = 1.958

The PIs indicate that for project A, for every $1 outﬂow, there is

approximately $1.53 inﬂow and for project B, for every $1 outﬂow,

there is approximately $1.96 inﬂow. It is necessary for cash inﬂow to

be greater than cash outﬂow in order for a project to be considered.

e. IRR for project A =

Discounted Cash Flows

Project A

Year 1 $3,000[1/(1 + 1/10)] = $2,727

Year 2 $7,000[1/(1 + 1/10)

] = $5,785

Year 3 $9,000[1/(1 + 1/10)

] = $6,762

Project B

Year 1 $3,000[1/(1 + 1/10)] = $2,727

Year 2 $4,000[1/(1 + 1/10)

] = $3,306

Year 3 $5,000[1/(1 + 1/10)

] = $3.757

PV cash inflows

PV cash outflows

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

PV cash inflows

PV cash outflows

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

$9,790

$5,000

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

$3,000

1 IRR+()

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

$4,000

1 IRR+()

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

$5,000

1 IRR+()

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

$10,000–++ 0=

SolCh13 Page 355 Tuesday, December 16, 2003 9:29 AM

356 SOLUTIONS

Using a calculator or trial and error, IRR for project A = 33.24%.

IRR for project B =

Using a calculator or trial and error, IRR for project B = 54.05%.

The IRR indicates the discount rate that would generate an NPV

of $0. It also reﬂects the assumption that cash ﬂows are reinvested at

the IRR rate. These rates are not necessarily realistic as investments

that produce those types of returns would have to be very risky.

f. For project A:

PV = $10,000

FV = PV(1 + MIRR)

$20,330 = $10,000(1 + MIRR)

(1 + MIRR)

= 2.033

For project B:

PV = $5,000

FV = PV(1 + MIRR)

$13,330 = $5,000(1 + MIRR)

(1 + MIRR)

= 2.666

$3,000

1 IRR+()

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

$4,000

1 IRR+()

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

$5,000

1 IRR+()

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

$5,000–++ 0=

FV $3,000 1.10()

$7,000 1.10()$9,000 1.10()

++ $20,330==

MIRR 2.033

1– 26.68%==

FV $3,000 1.10()

$4,000 1.10()$5,000 1.10()

++ $13,330==

MIRR 2.666

1– 38.66%==

SolCh13 Page 356 Tuesday, December 16, 2003 9:29 AM

Capital Budgeting Techniques 357

The MIRRs reﬂect a more realistic rate of reinvestment of cash

ﬂows. While these rates are high, they are not as high as IRR. Still, in

today’s market, while these types of investments with these returns

are possible, they would indicate risky investments.

g. If both projects are independent, then both should be undertaken

because they both have positive NPVs. This means they will both

increase the value of the ﬁrm.

h. If the projects are mutually exclusive, then project A should be

undertaken because it increases the value of the ﬁrm more than

project B. In particular, project A increases the value of the ﬁrm by

$5,274 whereas project B only increases the value of the ﬁrm by

$4,790.

SolCh13 Page 357 Tuesday, December 16, 2003 9:29 AM

SolCh13 Page 358 Tuesday, December 16, 2003 9:29 AM

CHAPTER

359

Capital Budgeting and Risk

FILL IN THE BLANKS

Answers

1. investment, industry; economic, market, taxes, interest, international

2. uncertainty, future, evaluating; opportunity, earn, same, risk; return,

capital, additional, compensate, risk

3. risk, projects, total, standalone; assets, standalone, relevant; portfo-

lio, returns, correlated; addition, portfolio, risk, portfolio

4. statistical, risk, project’s, range, standard deviation, coefﬁcient, varia-

tion; dispersion, greater, uncertainty

5. sensitivity, change, reestimating, scenarios; Sensitivity, scenario,

what-if, outcomes, one

6. Simulation, two, more, same; computer, probability, outcomes, prob-

ability, variable, change; simulations, internal rates, frequency, return

7. option pricing, real, real options, ROV, beyond, net present value,

supplemented, options; options, abandon, exercised, expand, defer,

future; strategic, revised, strategic

8. valuation, Black-Scholes; Black-Scholes, ﬁve, valuation; sensitive, dif-

ﬁcult, volatility, two, strategic, volatility, value, cost, capital, static

SolCh14 Page 359 Tuesday, December 16, 2003 9:30 AM