PK10 Notes

CHAPTER 10The Fundamentals of Capital Budgeting

Learning Objectives

1. Discuss why capital budgeting decisions are the most important decisions made by a firm’s

management.

2. Explain the benefits of using the net present value (NPV) method to analyze capital

expenditure decisions, and be able to calculate the NPV for a capital project.

3. Describe the strengths and weaknesses of the payback period as a capital expenditure

decision-making tool, and be able to compute the payback period for a capital project.

4. Explain why the accounting rate of return (ARR) is not recommended for use as a capital

expenditure decision-making tool.

5. Be able to compute the internal rate of return (IRR) for a capital project, and discuss the

conditions under which the IRR technique and the NPV technique produce different

results.

6. Explain the benefits of a postaudit review of a capital project.

I. Chapter Outline

10.1 An Introduction to Capital Budgeting

A. The Importance of Capital Budgeting

Capital budgeting decisions are the most important investment decisions made by

management.

Prepared by Jim Keys 1

The goal of these decisions is to select capital projects that will increase the value of

the firm.

Capital investments are important because they involve substantial cash outlays and,

once made, are not easily reversed.

Capital budgeting techniques help management to systematically analyze potential

business opportunities in order to decide which are worth undertaking.

Imagine you were to start your own business. No matter what type you started, you would have to answer the following three questions in some form or another:

1. What long-term investments should you take on? That is, what lines of business will you be in and what sorts of buildings, machinery, and equipment will you need?

2. Where will you get the long-term financing to pay for your investment? Will you bring in other owners or will you borrow the money?

3. How will you manage your everyday financial activities such as collecting from customers and paying suppliers?

Capital Budgeting The first question concerns the firm's long-term investments. The process of planning and managing a firm's long-term investments is called capital budgeting. In capital budgeting, the financial manager tries to identify investment opportunities that are worth more to the firm than they cost to acquire. Loosely speaking, this means that the value of the cash flow generated by an asset exceeds the cost of that asset. Regardless of the specific investment under consideration, financial managers must be concerned with how much cash they expect to receive, when they expect to receive it, and how likely they are to receive it. Evaluating the size, timing, and risk of future cash flows is the essence of capital budgeting. In fact, whenever we evaluate a business decision, the size, timing, and risk of the cash flows will be, by far, the most important things we will consider.

B. Sources of Information

Most of the information needed to make capital budgeting decisions is generated

internally, beginning likely with the sales force.

Then the production team is involved, followed by the accountants.

All this information is then reviewed by the financial managers, who evaluate the

feasibility of the project.


C. Classification of Investment Projects

Capital budgeting projects can be broadly classified into three types: (1) independent

projects; (2) mutually exclusive projects; and (3) contingent projects.

1. Independent Projects

Projects are independent when their cash flows are unrelated.

If two projects are independent, accepting or rejecting one project has no

bearing on the decision on the other.


2. Mutually Exclusive Projects

When two projects are mutually exclusive, accepting one automatically

precludes the other.

Mutually exclusive projects typically perform the same function.

3. Contingent Projects

Contingent projects are those in which the acceptance of one project is

dependent on another project.

There are two types of contingency situations:

Projects that are mandatory

Projects that are optional

D. Basic Capital Budgeting Terms

The cost of capital is the minimum return that a capital budgeting project must earn

for it to be accepted.

It is an opportunity cost since it reflects the rate of return investors can earn on

financial assets of similar risk.

Capital rationing implies that a firm does not have the resources necessary to fund

all of the available projects.

It implies that funding needs exceed funding resources.

Thus, the available capital will be allocated to the set of projects that will benefit the

firm and its shareholders the most.


Capital budgeting criteria checklist

Does the method account for the time value of money (TVM)?

Are all cash flows included?

Can we adjust for differential project risk?

Is there a decision rule?

Can we measure the effect on the value of the firm?

10.2 Net Present Value

It is a capital budgeting technique that is consistent with the goal of maximizing shareholder

wealth.

The method estimates the amount by which the benefits or cash flows from a project exceeds

the cost of the project in present value terms.

A. Valuation of Real Assets

Valuing real assets calls for the same steps as valuing financial assets.

Estimate future cash flows.

Determine the investor’s cost of capital or required rate of return.

Calculate the present value of the future cash flows.

However, there are some practical difficulties in following the process for real assets.

First, cash flow estimates have to be prepared in-house and are not readily available

as they are for financial assets in legal contracts.

Second, estimates of required rates of return are more difficult than it is for financial

assets because no market data is available for real assets.

B. NPV—The Basic Concept


The present value of a project is the difference between the present value of the expected

future cash flows and the initial cost of the project.

Accepting a positive NPV project leads to an increase in shareholder wealth, while

accepting a negative NPV project leads to a decline in shareholder wealth.

Projects that have an NPV equal to zero imply that management will be indifferent

between accepting and rejecting the project.

The Basic Idea – The NPV measures the increase in firm value, which is also the increase in the value of what the shareholders own. Thus, making decisions with the NPV rule facilitates the achievement of our goal – making decisions that will maximize shareholder wealth.

Estimating Net Present Value: Discounted cash flow (DCF) valuation – finding the market value of assets or their benefits by taking the present value of future cash flows by estimating what the future cash flows would trade for in today’s dollars.

The cost of the project must be determined. Cash flows from the project are estimated. The riskiness of the projected cash flows is determined, so the appropriate rate of

return is used to discount the cash flows. Cash flows are discounted to their present value to obtain an estimate of the

asset’s value to the firm. The present value of the future expected cash flows is compared with the required

outlay, or cost. If the asset’s value exceeds its cost, the project should be accepted; otherwise, it should be rejected. Alternatively, the project’s expected rate of return is compared with the rate of return considered appropriate for the project.

If a firm identifies an investment opportunity with a present value greater than its cost, the firm’s value will increase. There is a very direct link between capital budgeting and stock values. The more effective the firm’s capital budgeting procedures, the higher the price of its stock.

C. Framework for Calculating NPV

The NPV technique uses the discounted cash flow technique.

Our goal is to compute the net cash flow (NCF) for each time period t, where NCFt = (Cash

inflows – Cash outflows) for the period t.


A five-step approach can be utilized to compute the NPV.

1. Determine the cost of the project.

Identify and add up all expenses related to the cost of the project.

While we are mostly looking at projects whose entire cost occurs at the start of the

project, we need to recognize that some projects may have costs occurring beyond

the first year also.

The cash flow in year 0 (NCF0) is negative, indicating a cost.

2. Estimate the project’s future cash flows over its expected life.

Both cash inflows (CIF) and cash outflows are likely in each year of the project.

Estimate the net cash flow (NCFt) = CIFt – COFt for each year of the project.

Remember to recognize any salvage value from the project in its terminal year.

3. Determine the riskiness of the project and the appropriate cost of capital.

The cost of capital is the discount rate used in determining the present value of the

future expected cash flows.

The riskier the project, the higher the cost of capital for the project.

4. Compute the project’s NPV.

Determine the difference between the present value of the expected cash flows from

the project and the cost of the project.

5. Make a decision.

Accept the project if it produces a positive NPV or reject the project if NPV is

negative.

where:


NCFt = Net cash flow cash inflows – cash outflows) in period t, where t =

1, 2, 3,…, n

k = The cost of capital

n = The project’s estimated life

Example - Compute the Net Present Value (NPV) given a required return of 12% and the following net cash flows:

Year NCFt

0 ($20,000)1 $6,0002 $7,0003 $8,0004 $5,0005 $4,000

(Since the NPV>0, the project should be accepted).

Excel Solution (in class)

(note on Excel NPV function)

Calculator Solution (in class)

What is the NPV if the required return is 17%?

(Since the NPV<0, the project should be rejected).Note: It is not the rather mechanical process of discounting the cash flows that is important. Once we have the cash flows and the appropriate discount rate, the required calculations are fairly straightforward. The task of coming up with the cash flows and the discount rate in the first place is much more challenging.

NPV is superior to the other methods of analysis presented in the text because it has no serious flaws.


http://www.tvmcalcs.com/calculators/hp10b/hp10b_page3

http://www.tvmcalcs.com/blog/comments/the_npv_function_doesnt_calculate_net_present_value

http://www.fiu.edu/~keysj/Chapter%208%20-%20Example%201.xls

The method unambiguously ranks mutually exclusive projects, and can differentiate between projects of different scale and time horizon. The only drawback to NPV is that it relies on cash flow and discount rate values that are often estimates and not certain, but this is a problem shared by the other performance criteria as well.

Suppose the firm uses the NPV decision rule. At a required return of 11 percent, should the firm accept this project? What if the required return was 16 percent? What if the required return was 27 percent?

The NPV of a project is the PV of the outflows minus by the PV of the inflows. The equation for the NPV of this project at an 11 percent required return is:

NPV = – $130,000 + $68,000/(1.11)1 + $71,000/(1.11)2 + $54,000/(1.11)3

NPV = $28,730.79

At an 11 percent required return, the NPV is positive, so we would accept the project.

The equation for the NPV of the project at a 16 percent required return is:

NPV = – $130,000 + $68,000/(1.16)1 + $71,000/(1.16)2 + $54,000/(1.16)3

NPV = $15,980.77

At a 16 percent required return, the NPV is positive, so we would accept the project.

The equation for the NPV of the project at a 27 percent required return is:

NPV = – $130,000 + $68,000/(1.27)1 + $71,000/(1.27)2 + $54,000/(1.27)3

NPV = – $6,074.35

At a 27 percent required return, the NPV is negative, so we would reject the project.

D. Concluding Comments on NPV

Beware of optimistic estimates of future cash flows.


Recognize that the estimates going into calculating NPV are estimates and not market

data. Estimates based on informed judgments are considered acceptable.

The NPV method of determining project viability is the recommended approach for

making capital investment decisions.

The NPV decision criteria can be summed up as follows:

Summary of Net Present Value (NPV) Method

Decision Rule: NPV > 0: Accept the project.

NPV < 0: Reject the project.

Key Advantages Key Disadvantages

1. Uses the discounted cash flow

valuation technique.

2. Provides a direct measure of how much

a capital project will increase the value

of the firm.

3. Consistent with the goal of maximizing

shareholder wealth.

1. Difficult to understand without an

accounting and finance background.

10.3 The Payback Period

It is one of the most widely used tools for evaluating capital projects.

The payback period represents the number of years it takes for the cash flows from a

project to recover the project’s initial investment.

A project is accepted if its payback period is below some prespecified threshold.

This technique can serve as a risk indicator—the more quickly you recover the cash, the less

risky is the project.

A. Computing the Payback Period


To compute the payback period, we need to know the project’s cost and to estimate its

future net cash flows.

Equation 10.2 shows how to compute the payback period.

Example: Compute the Payback Period (PB) given a required return of 12% and the following net cash flows:

Year NCFt Cumulative NCF0 ($20,000)1 $6,000 $6,0002 $7,000 $13,0003 $8,000 $21,0004 $5,0005 $4,000

Therefore, payback occurs between two and three years:


Note: The PB period when the cash flows are in the form of an annuity is calculated as:

Year NCFt

0 ($5,000)1 $2,0002 $2,0003 $2,0004 $2,000

There is no economic rationale that links the payback method to shareholder wealth

maximization.

If a firm has a number of projects that are mutually exclusive, the projects are selected in

order of their payback rank: projects with the lowest payback period are selected first.



B. How the Payback Period Performs

The payback period analysis can lead to erroneous decisions because the rule does not

consider cash flows after the payback period.

A rapid payback does not necessarily mean a good investment. See Exhibit 10.6—

Projects D and E.

C. The Discounted Payback Period

One weakness of the ordinary payback period is that it does not take into account the

time value of money.

The discounted payback period calculation calls for the future cash flows to be

discounted by the firm’s cost of capital.

The major advantage of the discounted payback is that it tells management how long it

takes a project to reach a positive NPV.

However, this method still ignores all cash flows after the arbitrary cutoff period, which

is a major flaw.

Example - Compute the Discounted Payback Period (DPB) given a required return of 12% and the following net cash flows:

Year NCFt PVNCFt @12% Cumulative NCF0 ($20,000)1 $6,000 $5,357.14 $5,357.142 $7,000 $5,580.36 $10,937.503 $8,000 $5,694.24 $16,631.744 $5,000 $3,177.59 $19,809.33


5 $4,000 $2,269.71 $22,079.04

D. Evaluating the Payback Rule

The standard payback period is widely used in business.

It provides a simple measure of an investment’s liquidity risk.

The greatest advantage of the payback period is its simplicity.

It ignores the time value of money.

It does not adjust or account for differences in the overall, or total, risk for a project,

which could include operating, financing, and foreign exchange risk.

The biggest weakness of either the standard or discounted payback methods is their

failure to consider cash flows after the payback.

The following table summarizes this capital budgeting technique.

While the payback period is widely used in practice, it is rarely the primary decision criterion. As William Baumol pointed out in the early 1960s, the payback rule serves as a crude “risk screening” device – the longer cash is tied up, the greater the likelihood that it will not be returned. The payback period may be helpful when comparing mutually exclusive projects. Given two similar projects with different paybacks, the project with the shorter payback is often, but not always, the better project.

Redeeming Qualities of the Rule

Despite its shortcomings, the payback period rule is often used by large and sophisticated companies when they are making relatively minor decisions. There are several reasons for this. The primary reason is that many decisions simply do not warrant detailed analysis because the cost of the analysis would exceed the possible loss from a mistake. As a practical matter, an investment that pays back rapidly and has benefits extending beyond the cutoff period probably has a positive NPV.

In addition to its simplicity, the payback rule has two other positive features. First, because it is biased towards short-term projects, it is biased towards liquidity. In other words, a payback rule tends to favor investments that free up cash for other uses more quickly. This could be very important for a small business; it would be less so for a large corporation. Second, the cash flows that are expected to occur later in a project's life are probably more uncertain. Arguably, a payback period rule adjusts for the extra riskiness of later cash flows, but it does so in a rather draconian fashion—by ignoring them altogether.


Summary of Payback Method

Decision Rule: Payback period ≤ Payback cutoff point ] Accept the project.

Payback period > Payback cutoff point ] Reject the project.


1. Easy to calculate and understand for

people without strong finance

backgrounds.

2. A simple measure of a project’s

liquidity.

1. Most common version does not account

for time value of money.

2. Does not consider cash flows past the

payback period

3. Bias against long-term projects such as

research and development and new

product launches.

4. Arbitrary cutoff point.

10.4 The Accounting Rate of Return

It is sometimes called the book rate of return.

This method computes the return on a capital project using accounting numbers—the

project’s net income (NI) and book value (BV) rather than cash flow data.

The most common definition is the one given in Equation 10.3:


Average net income = [$100,000 + 150,000 + 50,000 + 0 + (−50,000)]/5= $50,000

It has a number of major flaws as a tool for evaluating capital expenditure decisions.

First, the ARR is not a true rate of return. ARR simply gives us a number based on

average figures from the income statement and balance sheet. Since it involves

accounting figures rather than cash flows, it is not comparable to returns in capital

markets.

It ignores the time value of money.

There is no economic rationale that links a particular acceptance criterion to the goal of

maximizing shareholders’ wealth.

10.5 Internal Rate of Return

The IRR is an important and legitimate alternative to the NPV method.


The NPV and IRR techniques are similar in that both depend on discounting the cash flows

from a project.

When we use the IRR, we are looking for the rate of return associated with a project so we

can determine whether this rate is higher or lower than the firm’s cost of capital.

The IRR is the discount rate that makes the NPV to equal zero.

A. Calculating the IRR

The IRR is an expected rate of return, much like the yield to maturity calculation that

was made on bonds.

We will need to apply the same trial-and-error method to compute the IRR.

Example - Compute the Internal Rate of Return (IRR) given a required return of 12% and the following cash flows:

Year CFt

0 ($20,000)1 $6,0002 $7,0003 $8,0004 $5,0005 $4,000

o Set the NPV equation equal to zero and solve for the IRR:

o At this point, unless you are using a financial calculator or spreadsheet, solving for the IRR is a trial and error process. That is, we would “plug” in different estimates for the IRR, work through the calculations, and determine if we have found the rate that causes NPV to equal $0. We have already computed the NPV of this project at a 12% discount rate and found the NPV to be positive. In addition, we computed the NPV of the project at a discount rate of 17% and found NPV to be negative.


Therefore, we know that the IRR lies somewhere between 12% and 17% (in fact, we can see that the IRR is much closer to 17%).

o Using a financial calculator, we find the IRR = 16.3757%.

o Since the IRR > k (16.38% > 12%), the project should be accepted.


Calculator Solution (in class)

Note: The calculation of the project’s IRR does not depend upon the required rate of return. The IRR is compared to the required rate of return to determine whether to accept or reject the project. Also, if a project’s NPV is positive, its IRR will exceed the required rate of return. If a project’s NPV is negative, its IRR will be below the required rate of return.

Special cases (IRR)

“Lump Sum” case:


http://www.tvmcalcs.com/calculators/hp10b/hp10b_page3


Year NCFt

0 ($750,000)1 02 03 04 $1,350,000

“Annuity” case: Use the PVIFA tables to estimate the IRR

Year NCFt

0 ($32,000)1 $14,0002 $14,0003 $14,0004 $14,000

NPV = 0 = $14,000(PVIFA 4, IRR) - $32,000

(PVIFA 4, IRR) = $32,000 / $14,000 = 2.285714

Looking down the period column to four periods, we then move to the right to find the interest rate that corresponds to the PVIFA of 2.285714. This occurs somewhere between 24% and 28%. With a financial calculator, we find the exact IRR to be 26.86%..

B. When the IRR and NPV Methods Agree

The two methods will always agree when the projects are independent and the projects’

cash flows are conventional.

After the initial investment is made (cash outflow), all the cash flows in each future year

are positive (inflows).


http://www.fiu.edu/~keysj/PVIFA.xls

Net Present Value ProfileGraphical representation of the relationship between a project’s NPVs and various discount rates:

Discount Rate

0% 5% 10% 13% 14% 15% 20%

NPV $20.0 $11.56 $4.13 $0.09 -$1.20 -$2.46 -$8.33


0

The point at which the project’s NPV profile intersects with the x-axis is by definition the project’s IRR, since the NPV at this point is equal to $0.

C. When the IRR and NPV Methods Disagree

The IRR and NPV methods can produce different accept/reject decisions if a project

either has unconventional cash flows or the projects are mutually exclusive.

1. Unconventional Cash Flows

Unconventional cash flows could follow several different patterns.

A positive initial cash flow followed by negative future cash flows.

Future cash flows from a project could include both positive and negative cash

flows.

A cash flow stream that looks similar to a conventional cash flow stream except

for a final negative cash flow.


In these circumstances, the IRR technique can provide more than one solution. This

makes the result unreliable and should not be used in deciding about accepting or

rejecting a project.

2. Mutually Exclusive Projects

When you are comparing two mutually exclusive projects, the NPVs of the two

projects will equal each other at a certain discount rate. This point at which the NPVs

intersect is called the crossover point. Depending on whether the required rate of

return is above or below this crossover point, the ranking of the projects will be


different. While it is easy to identify the superior project based on the NPV, one

cannot do so based on the IRR. Thus, ranking conflicts can arise.

A second situation arises when you compare projects with different costs. While IRR

gives you a return based on the dollar invested, it does not recognize the difference in

the size of the investments. NPV does!


Example - Calculation of crossover point:

Expected after-tax net cash flows (NCFt)

Cash flow

Year (t) Project S Project L differential0 ($100) ($100) 0 1 50 20 30 2 40 30 10 3 30 50 (20)4 30 65 (35)

IRR = Crossover rate = 14.2978%

Mutually Exclusive Investments Even if there is a single IRR, another problem can arise concerning mutually exclusive investment decisions, a If two investments, X and Y, are mutually exclusive, then taking one of them means that we cannot take the other. Given two or more mutually exclusive investments, which one is the best?

Investment NPV IRR PBA $10,000 22% 2.50 yearsB $11,000 20% 7.00 yearsC $8,000 24% 3.00 years

.

D. Modified Internal Rate of Return (MIRR)

A major weakness of the IRR compared to the NPV method is the reinvestment rate

assumption.

IRR assumes that the cash flows from the project are reinvested at the IRR, while the

NPV assumes that they are invested at the firm’s cost of capital.

This optimistic assumption in the IRR method leads to some projects being accepted

when they should not be.


An alternative technique is the modified internal rate of return (MIRR). Here, each

operating cash flow is reinvested at the firm’s cost of capital.

The compounded values are summed up to get the project’s terminal value.

The MIRR is the interest rate that equates the project’s cost to the terminal value at the

end of the project.

Equation 10.5 shows how to calculate the MIRR.

Modified Internal Rate of Return

1) Using the required rate of return as the compounding rate, find the terminal value (future value) of all of the net cash inflows (positive net cash flows) at the end of the project life.

2) Using the required rate of return as the discounting rate, find the present value at t = 0 of all of the net cash outflows (negative net cash flows).

3) Compute the MIRR.

Where n is equal to the life of the project.

Example - Compute the Modified Internal Rate of Return (MIRR) given a required return of 12% and the following net cash flows:

Year NCFt

0 ($20,000)1 $6,0002 $7,0003 $8,0004 $5,0005 $4,000

1) TVinflows = $6,000(1.12)4 + $7,000(1.12)3 + $8,000(1.12)2 + $5,000(1.12)1 + $4,000(1.12)0

TVinflows = $9,441.12 + $9,834.50 + $10,035.20 + $5,600.00 + $4,000.00 = $38,910.82

2) PVoutflows = $20,000


3)


MIRR example with positive and negative cash flows:Safeway estimates that its required rate of return is 6 percent. The company is considering two mutually exclusive projects whose after-tax cash flows are as follows:

Year Project S Project L0 ($1,255) ($1,060)1 625 (470)2 905 9053 930 7804 (245) 920

For Project S:

TVinflows = $625(1.06)3 + $905(1.06)2 + $930(1.06)1 = $744.39 + $1,016.86 + $985.80 = $2,747.05

PVoutflows = $1,255 + $245(1.06)-4 = $1,255 + $194.06 = $1,449.06

MIRRS = ($2,747.05 / $1,449.06)1/4 – 1.0 = 17.34%

For Project L:

TVinflows = $905(1.06)2 + $780(1.06)1 + $920(1.06)0 = $1,016.86 + $826.80 + $920 = $2,763.66

PVoutflows = $1,060 + $470(1.06)-1 = $1,060 + $443.40 = $1,503.40

MIRRL = ($2,763.66 / $1,503.40)1/4 – 1.0 = 16.44%

Since these projects are mutually exclusive, we would choose Project S.



E. IRR versus NPV: A Final Comment

While the IRR has an intuitive appeal to managers because the output is in the form of a

return, the technique has some critical problems.

On the other hand, decisions made based on the project’s NPV are consistent with the

goal of shareholder wealth maximization. In addition, the result shows management the

dollar amount by which each project is expected to increase the value of the firm.

For these reasons, the NPV method should be used to make capital budgeting decisions.

The following table summarizes the IRR decision-making criteria.

Review of Internal Rate of Return (IRR)

Decision Rule: IRR > Cost of capital ] Accept the project.

IRR < Cost of capital ] Reject the project.


1. Intuitively easy to understand.

2. Based on the discounted cash flow

technique.

1. With nonconventional cash flows, IRR

approach can yield no or multiple answers.

2. A lower IRR can be better if a cash inflow is

followed by cash outflows.

3. With mutually exclusive projects, IRR can

lead to incorrect investment decisions.


The Profitability Index - present value of the future cash flows divided by the initial investment (both numerator and denominator are positive). This definition assumes no negative cash flows after year zero. Technically, PI = PV of inflows / PV of outflows, thus a nonconventional project’s PI will have a PV in the numerator and the denominator.

Decision ruleAn investment should be accepted if the PI > 1.0 and rejected if the PI < 1.0.

Example - Compute the Profitability Index (PI) given a required return of 12% and the following net cash flows:

Year CFt

0 ($20,000)1 $6,0002 $7,0003 $8,0004 $5,0005 $4,000

Therefore, the project should be accepted since the PI > 1.0.

10.6 Capital Budgeting in Practice


A. Practitioners’ Methods of Choice

Exhibit 10.12 summarizes surveys of practitioners on the capital budgeting methods of

choice.

In the late 1950s, less than 20 percent of managers used the NPV or IRR methods.

By 1981, over 65 percent of financial managers surveyed used the IRR, but only 16.5

percent of managers used the NPV.

In a recent study of Fortune 1000 managers, 85 percent of managers used the NPV while

77 percent used the IRR. Surprisingly, over 50 percent of managers used the payback

method.

B. Ongoing and Postaudit Reviews

Management should systematically review the status of all ongoing capital projects and

perform postaudits on all completed capital projects.


In a postaudit review, management compares the actual results of a project with what

was projected in the capital budgeting proposal.

A postaudit examination would determine why the project failed to achieve its

expected financial goals.

Managers should also conduct ongoing reviews of capital projects in progress.

The review should challenge the business plan, including the cash flow projections

and the operating cost assumptions.

Management must also evaluate people responsible for implementing a capital project.


Chapter 10 Sample Problems

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

1. Net present value: Cortez Art Gallery is adding to its existing buildings at a cost of $2 million. The gallery expects to bring in additional cash flows of $520,000, $700,000, and $1,000,000 over the next three years. Given a required rate of return of 10 percent, what is the NPV of this project?

a. $1,802,554b. $197,446c. -$1,802,554d. -$197,446

2. Net present value: Gao Enterprises plans to build a new plant at a cost of $3,250,000. The plant is expected to generate annual cash flows of $1,225,000 for the next five years. If the firm's required rate of return is 18 percent, what is the NPV of this project?

a. $2,875,000b. $3,830,785c. $580,785d. $2,1225,875

3. Payback: Binder Corp. has invested in new machinery at a cost of $1,450,000. This investment is expected to produce cash flows of $640,000, $715,250, $823,330, and $907,125 over the next four years. What is the payback period for this project?

a. 2.12 yearsb. 1.88 yearsc. 4.00 yearsd. 3.00 years.

4. Discounted payback: Roswell Energy Company is installing new equipment at a cost of $10 million. Expected cash flows from this project over the next five years will be $1,045,000, $2,550,000, $4,125,000, $6,326,750, and $7,000,000. The company's discount rate for such projects is 14 percent. What is the project's discounted payback period?

a. 4.2 yearsb. 4.4 yearsc. 4.8 yearsd. 5.0 years

5. Internal rate of return: Modern Federal Bank is setting up a brand new branch. The cost of the project will be $1.2 million. The branch will create additional cash flows of $235,000, $412,300, $665,000 and $875,000 over the next four years. The firm's cost of capital is 12 percent. What is the internal rate of return on this branch expansion? (Round to the nearest percent.)


a. 20%b. 23%c. 25%d. 27%

6. Internal rate of return: Casa Del Sol Property Development Company is refurbishing a 200-unit condominium complex at a cost of $1,875,000. It expects that this will lead to expected annual cash flows of $415,350 for the next seven years. What internal rate of return can the firm earn from this project? (Round to the nearest percent.)

a. 10%b. 12%c. 14%d. 16%

7. Modified internal rate of return: Jamaica Corp. is adding a new assembly line at a cost of $8.5 million. The firm expects the project to generate cash flows of $2 million, $3 million, $4 million, and $5 million over the next four years. Its cost of capital is 16 percent. What is the MIRR on this project?

a. 18.6%b. 19.8%c. 20.2%d. 21.4%


Chapter 10 Sample ProblemsAnswer Section

MULTIPLE CHOICE

1. ANS: DLearning Objective: LO 2Level of Difficulty: MediumFeedback: Initial investment = $2,000,000Length of project = n = 3 yearsRequired rate of return = k = 10%Net present value = NPV

2. ANS: CLearning Objective: LO 2Level of Difficulty: MediumFeedback: Initial investment = $3,250,000Annual cash flows = $1,225,000Length of project = n = 5 yearsRequired rate of return = k = 18%Net present value = NPV

3. ANS: ALearning Objective: LO 3Level of Difficulty: MediumFeedback:

Binder Corp.Year CF Cumulative CF

0 $(1,450,000) $(1,450,000)1 640,000 (810,000)2 715,250 (94,750)3 823,330 728,5804 907,125 1,635,705

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year= 2 + ($94,750 / $823,330)= 2.12 years


4. ANS: ALearning Objective: LO 3Level of Difficulty: MediumFeedback:

Roswell Energyi = 14%

Year CF PVCFCumulative PVCF

0 $(10,000,000) $(10,000,000) $(10,000,0001 1,045,000 916,667 (9,083,333)2 2,550,000 1,962,142 (7,121,191)3 4,125,000 2,784,258 (4,336,934)4 6,326,750 3,745,944 (590,990)5 7,000,000 3,635,581 3,044,591

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year= 4 + ($590,990/ $3,635,581)= 4.16 years

5. ANS: BLearning Objective: LO 5Level of Difficulty: MediumFeedback: Initial investment = $1,200,000Length of project = n = 4 yearsTo determine the IRR, the trial-and-error approach can be used. Set NPV = 0.Try IRR =23.1%.

The IRR of the project is 23.1 percent. Using a financial calculator, we find that the IRR is 23.119 percent.

6. ANS: BLearning Objective: LO 5Level of Difficulty: MediumFeedback: Initial investment = $1,875,000Annual cash flows = $415,350Length of investment = n = 7 yearsTo determine the IRR, the trial-and-error approach can be used. Set NPV = 0.Try IRR =12.3%.


The IRR of the project is 12.3 percent. Using a financial calculator, we find that the IRR is 12.345 percent.

7. ANS: BRefer To: Ref 10-3Learning Objective: LO 5Level of Difficulty: MediumFeedback: Initial investment = $8,500,000Length of investment = n = 4 yearsCost of capital = k = 16%


Documents

PK10 Notes