Chapter 8
Today, Sweet Snacks is investing $491,000 in a new oven. As a result, the company expects its cash flows to increase by $64,000 a year for the next two years and by $98,000 a year for the following three years. How long must the firm wait until it recovers all of its initial investment?
The project never pays back.
The payback method of analysis ignores which one of the following?
Time value of money
A project has the following cash flows. What is the internal rate of return? Year/Cash Flow 0/-89300 1/32900 2/64200 3/5800 A. 11.21 percent B. 10.47 percent C. 10.72 percent D. 8.57 percent E. 9.19 percent
D. 8.57 percent NPV = 0 = -$89,300 + $32,900 / (1 + IRR) + $64,200 / (1 + IRR)2 + $5,800 / (1 + IRR)3 IRR = 8.57%
Which one of the following methods of analysis ignores the time value of money? A. Net present value B. Internal rate of return C. Discounted cash flow analysis D. Payback E. Profitability index
D. Payback
China Importers would like to spend $221,000 to expand its warehouse. However, the company has a loan outstanding that must be repaid in 2.5 years and thus will need the $221,000 at that time. The warehouse expansion project is expected to increase the cash inflows by $58,000 in the first year, $139,000 in the second year, and $210,000 a year for the following 2 years. Should the firm expand at this time? Why or why not?
Yes, because the money will be recovered in 2.11 years
the average net income of a project divided by the projects average book value is referred to as the projects
average accounting return
The average net income of a project divided by the project's average book value is referred to as the project's:
average accounting return.
The reinvestment approach to the modified internal rate of return:
compounds all of the cash flows, except for the initial cash flow, to the end of the project.
the reinvestment approach to the modified internal rate of return
compounds all the cash flows except for the initial cash flow to the end of the project
The net present value of an investment represents the difference between the incestment's
cost and its market value
the net present value
decreases as the required rate of return increases
The net present value:
decreases as the required rate of return increases.
which one of the following defines the internal rate of return for a project
discount rate which results in a zero net present value for the project
which one of the following is the primary advantage of payback analysis
ease of use
discounted cash flow valuation is the process of discounting an investments
future cash flow
If a project with conventional cash flows has a profitability index of 1.0, the project will:
have an internal rate of return that equals the required return.
which one of the following statements is correct
if the internal rate of return equals the required return, the net present value will equal zero
The payback period is the length of time it takes an investment to generate sufficient cash flows to enable the project to:
initial
which one of the following is most closely related to the net present value profile
internal rate of return
based on the most recent survey information presented in your textbook CFO's tend to use which 2 methods of investment analysis the most frequently
internal rate of return and net present value
in which one of the following situations would the payback method be the preferred method of analysis
investment funds available only for a limited period of time
payback is best used to evaluate which type of projects
low-cost, short-term
The average accounting return:
measures profitability rather than cash flow.
which one of the following is specifically designed to compute the rate of return on a project that has unconventional cash flows
modified internal rate of return
the possibility that more than one discount rate can cause the net present value of an investment to equal zero is referred to as
multiple rates of return
The possibility that more than one discount rate can cause the net present value of an investment to equal zero is referred to as:
multiple rates of return.
both project A and B are acceptable as independent projects....
mutually exclusive
Mary has just been asked to analyze an investment to determine if it is acceptable....
net present value
Which one of the following defines the internal rate of return for a project?
Discount rate that results in a zero net present value for the project
which one of the following is generally considered to be the best form of analysis if you have to select a single method to analyze a variety of investment opportunities
net present value
which one of the following methods of analysis is most appropriate to use when two investments are mutually exculsive
net present value
which one of the following methods of analysis has the greatest bias towards short term projects
payback
which one of the following methods of analysis ignore the time value of money
payback
which one of the following indicates that a project is expected to create value for its owners
positive net present value
which one of the following inidators offers the best assurance that a project will produce value for its owners
positive npv
which one of the following can be defined as a benefit-cost ratio
profitability index
you were recently hired by a firm as a project analyst, the owner of the firm is unfamiliar with financial analysis
profitability index
which one of the following indicated that a project is definitely acceptable
profitability index greater than 1.0
which one of the following indicates that a project should be rejected
profitability index less than 1.0
the payback period is the length of time it takes an investment to generate sufficient cash flow to enable the project to
recoup its initial cost
which one of the following statements is correct
the payback method is biased towards short term projects
the modified internal rate of return is specifically designed to address the problems associated with which one of the following
unconventional cash flows
If an investment is producing a return that is equal to the required return, the investment's net present value will be:
zero
The payback period is the length of time it takes an investment to generate sufficient cash flows to enable the project to: A. produce a positive annual cash flow. B. produce a positive cash flow from assets. C. offset its fixed expenses. D. offset its total expenses. E. recoup its initial cost.
E. recoup its initial cost.
Which one of the following is the primary advantage of payback analysis?
Ease of use
Which one of the following statements is correct?
If the internal rate of return equals the required return, the net present value will equal zero.
Which one of the following is most closely related to the net present value profile?
Internal rate of return
Based on the most recent survey information presented in your textbook, CFOs tend to use which two methods of investment analysis the most frequently?
Internal rate of return and net present value
Which one of the following is an indicator that an investment is acceptable?
Internal rate of return that exceeds the required return
In which one of the following situations would the payback method be the preferred method of analysis?
Investment funds available only for a limited period of time
Payback is best used to evaluate which type of projects?
Low-cost, short-term
Which one of the following is specifically designed to compute the rate of return on a project that has unconventional cash flows?
Modified internal rate of return
Both Projects A and B are acceptable as independent projects. However, the selection of either one of these projects eliminates the option of selecting the other project. Which one of the following terms best describes the relationship between Project A and Project B?
Mutually exclusive
Mary has just been asked to analyze an investment to determine if it is acceptable. Unfortunately, she is not being given sufficient time to analyze the project using various methods. She must select one method of analysis and provide an answer based solely on that method. Which method do you suggest she use in this situation?
Net present value
Which one of the following is generally considered to be the best form of analysis if you have to select a single method to analyze a variety of investment opportunities?
Net present value
Which one of the following methods of analysis is most appropriate to use when two investments are mutually exclusive?
Net present value
An investment has an initial cost of $3.3 million. This investment will be depreciated by $900,000 a year over the three-year life of the project. Should this project be accepted based on the average accounting rate of return if the required rate is 10.0 percent? Why or why not?
No, because the AAR is less than 10.0 percent
The Flour Baker is considering a project with the following cash flows. Should this project be accepted based on its internal rate of return if the required return is 11 percent?
No, because the project's rate of return is 7.78 percent
Which one of the following indicates that a project should be rejected?
Profitability index less than 1.0
You are considering the following two mutually exclusive projects. The required return on each project is 14 percent. Which project should you accept and what is the best reason for that decision? (-46,000)
Project A, because it has the higher net present value
Jefferson International is trying to choose between the following two mutually exclusive design projects:
Project B; Project A; Project A
You are using a net present value profile to compare Project A and B, which are mutually exclusive. Which one of the following statements correctly applies to the crossover point between these two?
The net present value of Project A equals that of Project B, but generally does not equal zero.
Which one of the following statements is correct?
The payback method is biased toward short-term projects.
Which one of the following statements is correct?
The payback period ignores the time value of money.
The modified internal rate of return is specifically designed to address the problems associated with which one of the following?
Unconventional cash flows
Which one of the following statements is correct?
When the internal rate of return is greater than the required return, the net present value is positive.
An investment has an initial cost of $300,000 and a life of four years. This investment will be depreciated by $60,000 a year and will generate the net income shown below. Should this project be accepted based on the average accounting rate of return (AAR) if the required rate is 9.5 percent? Why or why not?
Yes, because the AAR is greater than 9.5 percent
The Tool Box needs to purchase a new machine costing $1.46 million. Management is estimating the machine will generate cash inflows of $223,000 the first year and $600,000 for the following three years. If management requires a minimum 12 percent rate of return, should the firm purchase this particular machine? Why or why not?
Yes, because the IRR is 12.74 percent
which one of the analytical methods is based on net income
average accounting return
which one of the following methods of analysis ignores cash flows
average accounting return
which one of the following methods of anaylsis is most similar to computing the return on assets
average accounting return
The net present value of an investment represents the difference between the investment's:
cost and its market value.
the net present value profile illustrates how the net present value of an investment is affected by which one of the following
discount rate
Discounted cash flow valuation is the process of discounting an investment's:
future cash flows.
the profitability index reflects the value created per dollar
invested
The profitability index reflects the value created per dollar:
invested.
the average accounting return
measures profitability rather than cash flow
which one of the following statements is correct?
the payback period ignores the time value of money
the payback method of analysis ignores which one of the following
time value of money
if an investment is producing a return that is equal to the required return the investments net present value will be
zero
What is the net present value of the following cash flows if the relevant discount rate is 9.0 percent?
$3,374.11
What is the net present value of a project with the following cash flows if the discount rate is 15 percent?
$39.80
The Greasy Spoon Restaurant is considering a project with an initial cost of $525,000. The project will not produce any cash flows for the first three years. Starting in year 4, the project will produce cash inflows of $721,000 a year for three years. This project is risky, so the firm has assigned it a discount rate of 16 percent. What is the project's net present value?
$512,408.23
Molly is considering a project with cash inflows of $918, $867, $528, and $310 over the next four years, respectively. The relevant discount rate is 10 percent. What is the net present value of this project if it the start-up cost is $2,100?
$59.50
Charles Henri is considering investing $36,000 in a project that is expected to provide him with cash inflows of $12,000 in each of the first two years and $18,000 for the following year. At a discount rate of zero percent this investment has a net present value of ____, but at the relevant discount rate of 17 percent the project's net present value is ____.
$6,000; -$5,739
The net present value of a project's cash inflows is $8,216 at a 14 percent discount rate. The profitability index is 1.03 and the firm's tax rate is 34 percent. What is the initial cost of the project?
$7,976.70
A project has expected cash inflows, starting with year 1, of $2,200, $2,900, $3,500, and finally in year 4, $4,000. The profitability index is 1.14 and the discount rate is 12 percent. What is the initial cost of the project?
$8,166.19
You are making a $120,000 investment and feel that a 20 percent rate of return is reasonable given the nature of the risks involved. You feel you will receive $48,000 in the first year, $54,000 in the second year, and $56,000 in the third year. You expect to pay out $12,000 as an additional investment in the fourth year. What is the net present value of this investment given your expectations?
-$15,879.63
A proposed project requires an initial cash outlay of $849,000 for equipment and an additional cash outlay of $48,500 in year 1 to cover operating costs. During years 2 through 4, the project will generate cash inflows of $354,000 a year. What is the net present value of this project at a discount rate of 13 percent? Round your answer to the nearest whole dollar.
-$152,232
Professional Properties is considering remodeling the office building it leases to Heartland Insurance. The remodeling costs are estimated at $3.4 million. If the building is remodeled, Heartland Insurance has agreed to pay an additional $820,000 a year in rent for the next five years. The discount rate is 15 percent. What is the benefit of the remodeling project to Professional Properties?
-$651,233
The Black Horse is currently considering a project that will produce cash inflows of $12,000 a year for three years followed by $6,500 in year 4. The cost of the project is $38,000. What is the profitability index if the discount rate is 7 percent?
0.96
A firm is reviewing a project that has an initial cost of $71,000. The project will produce annual cash inflows, starting with year 1, of $8,000, $13,400, $18,600, $33,100, and finally in year 5, $37,900. What is the profitability index if the discount rate is 11 percent?
1.07
Miller Brothers is considering a project that will produce cash inflows of $61,500, $72,800, $84,600, and $68,000 a year for the next four years, respectively. What is the internal rate of return if the initial cost of the project is $225,000?
10.22 percent
A project has the following cash flows. What is the internal rate of return?
10.53 percent
Delta Mu Delta is considering purchasing some new equipment costing $400,000. The equipment will be depreciated on a straight-line basis to a zero book value over the four-year life of the project. Projected net income for the four years is $18,900, $21,300, $26,700, and $25,000. What is the average accounting rate of return?
11.49 percent
Textiles Unlimited has gathered projected cash flows for two projects. At what interest rate would the company be indifferent between the two projects? Which project is better if the required return is above this interest rate?
13.15 percent: B
You are considering the following two mutually exclusive projects. The crossover point is _____ and Project _____ should be accepted if the discount rate is 14 percent.
13.28 percent; B
You are considering the following two mutually exclusive projects. The crossover point is _____ and Project _____ should be accepted at a 12 percent discount rate.
14.02 percent; A
A project has the following cash flows. What is the internal rate of return?
14.09 percent
The Nifty Fifty is considering opening a new store at a start-up cost of $720,000. The initial investment will be depreciated straight-line to zero over the 15-year life of the project. What is the average accounting rate of return?
14.35 percent
You are considering an equipment purchase costing $187,000. This equipment will be depreciated straight-line to zero over its three-year life. What is the average accounting return if this equipment produces the following net income?
16.51 percent
Greenbriar Cotton Mill is spending $330,000 to update its facility. The company estimates that this investment will improve its cash inflows by $56,500 a year for 10 years. What is the payback period?
5.84 years
EKG, Inc. is considering a new project that will require an initial cash investment of $398,000. The project will produce no cash flows for the first two years. The projected cash flows for years 3 through 7 are $79,000, $88,000, $102,000, $140,000, and $160,000, respectively. How long will it take the firm to recover its initial investment in this project?
5.92 years
Diamond Enterprises is considering a project that will produce cash inflows of $238,000 a year for three years followed by $149,000 in year 4. What is the internal rate of return if the initial cost of the project is $749,000?
6.32 percent
Chasteen, Inc. is considering an investment with an initial cost of $185,000 that would be depreciated straight-line to a zero book value over the life of the project. The cash inflows generated by the project are estimated at $76,000 for the first two years and $30,000 for the following two years. What is the internal rate of return?
6.94 percent
The Steel Factory is considering a project that will produce annual cash flows of $36,800, $45,500, $56,200, and $21,800 over the next four years, respectively. What is the internal rate of return if the initial cost of the project is $135,000?
7.56 percent
Chestnut Tree Farms has identified the following two mutually exclusive projects:
9.55 percent or less
What is the net present value of a project with the following cash flows if the discount rate is 15 percent? Year/Cash Flow 0/-48100 1/15600 2/28900 3/15200 A. -$2,687.98 B. -$1,618.48 C. $1,044.16 D. $1,035.24 E. $9,593.19
A. -$2,687.98 NPV = - $48,100 + $15,600 / 1.15 + $28,900 / 1.152 + $15,200 / 1.153 NPV = -$2,687.98
The net present value: A. decreases as the required rate of return increases. B. is equal to the initial investment when the internal rate of return is equal to the required return. C. method of analysis cannot be applied to mutually exclusive projects. D. ignores cash flows that are distant in the future. E. is unaffected by the timing of an investment's cash flows.
A. decreases as the required rate of return increases.
What is the net present value of the following cash flows if the relevant discount rate is 8 percent?
$1,587.61
Which one of the following methods of analysis is most similar to computing the return on assets (ROA)?
Average accounting return
Which one of the following is the primary advantage of payback analysis? A. Incorporation of the time value of money concept B. Ease of use C. Research and development bias D. Arbitrary cutoff point E. Long-term bias
B. Ease of use
What is the net present value of a project that has an initial cost of $42,700 and produces cash inflows of $9,250 a year for 9 years if the discount rate is 14.65 percent? A. $798.48 B. $1,240.23 C. $1,992.43 D. $2,111.41 E. $2,470.01
C. $1,992.43 NPV = -$42,700 + $9,250 ×{1 - [1 / (1 + .1465)9]} / .1465 NPV = $1,992.43
13. A project has the following cash flows. What is the payback period? Year/Cash Flow 0/-28000 1/11600 2/11600 3/6500 4/6500 A. 2.38 years B. 2.49 years C. 2.74 years D. 3.01 years E. 3.33 years
C. 2.74 years Payback = 2 + ($28,000 -11,600 -11,600)/$6,500 = 2.74 years
What is the net present value of a project that has an initial cost of $40,000 and produces cash inflows of $8,000 a year for 11 years if the discount rate is 15 percent?
$1,869.69
What is the NPV of the following set of cash flows at a discount rate of zero percent? What if the discount rate is 15 percent?
$2,500; -$8,665.07
Empire Industries is considering adding a new product to its lineup. This product is expected to generate sales for four years after which time the product will be discontinued. What is the project's net present value if the firm wants to earn a 13 percent rate of return?
$4,312.65
What is the net present value of the following set of cash flows at a discount rate of 7 percent? At 20 percent?
$4,518.47; -$321.76
What is the net present value of the following cash flows if the relevant discount rate is 8.0 percent?
$4,529.59
What is the net present value of a project with the following cash flows if the discount rate is 15 percent?
-$5,433.67
What is the IRR of the following set of cash flows? (-26,300)
15.81 percent
You're trying to determine whether or not to expand your business by building a new manufacturing plant. The plant has an installation cost of $26 million, which will be depreciated straight-line to zero over its three-year life. If the plant has projected net income of $2,348,000, $2,680,000, and $1,920,000 over these three years, what is the project's average accounting return (AAR)?
17.82 percent
Which one of the following statements is correct? A. A longer payback period is preferred over a shorter payback period. B. The payback rule states that you should accept a project if the payback period is less than one year. C. The payback period ignores the time value of money. D. The payback rule is biased in favor of long-term projects. E. The payback period considers the timing and amount of all of a project's cash flows.
C. The payback period ignores the time value of money.
A project has the following cash flows. What is the payback period?
2.60 years
Services United is considering a new project that requires an initial cash investment of $78,000. The project will generate cash inflows of $29,500, $32,700, $18,500, and $10,000 over each of the next four years, respectively. How long will it take to recover the initial investment?
2.85 years
You are considering the following two mutually exclusive projects. What is the crossover point?
22.56
Auto Detailers is buying some new equipment at a cost of $228,900. This equipment will be depreciated on a straight-line basis to a zero book value its eight-year life. The equipment is expected to generate net income of $36,000 a year for the first four years and $22,000 a year for the last four years. What is the average accounting rate of return?
25.34 percent
What is the payback period for a project with the following cash flows?
3.17 years
A project has the following cash flows. What is the payback period?
3.21 years
The Flour Baker is considering a project with the following cash flows. Should this project be accepted based on its internal rate of return if the required return is 18 percent? Year/Cash Flow 0/-49000 1/9500 2/26200 3/38700 A. Yes; because the project's rate of return is 7.78 percent B. Yes; because the project's rate of return is 16.08 percent C. Yes; because the project's rate of return is 19.47 percent D. No; because the project's rate of return is 19.47 percent E. No; because the project's rate of return is 16.08 percent
C. Yes; because the project's rate of return is 19.47 percent NPV = 0 = -$49,000 + $9,500 / (1 + IRR) + $26,200 / (1 + IRR)2 + $38,700 / (1 + IRR)3 IRR = 19.47 percent The project should be accepted because its IRR is greater than the required return.
What is the payback period for a $28,500 investment with the following cash flows?
3.65 years
Quattro, Inc. has the following mutually exclusive projects available. The company has historically used a four-year cutoff for projects. The required return is 11 percent.
3.92 years; 3.79 years; $780.85; -$7,945.93; accept Project A only
The Golden Goose is considering a project with an initial cost of $46,700. The project will produce cash inflows of $10,000 a year for the first two years and $12,000 a year for the following three years. What is the payback period?
4.23 years
A project has the following cash flows. What is the internal rate of return?
8.26 percent
Miller and Sons is evaluating a project with the following cash flows:
8.54 percent; 7.38 percent; 8.59 percent
Which one of the following analytical methods is based on net income?
Average accounting return
Which one of the following methods of analysis ignores cash flows?
Average accounting return
Which one of the following statements is correct? A. The net present value is a measure of profits expressed in today's dollars. B. The net present value is positive when the required return exceeds the internal rate of return. C. If the initial cost of a project is increased, the net present value of that project will also increase. D. If the internal rate of return equals the required return, the net present value will equal zero. E. Net present value is equal to an investment's cash inflows discounted to today's dollars.
D. If the internal rate of return equals the required return, the net present value will equal zero.
The internal rate of return is the: A. discount rate that causes a project?s aftertax income to equal zero. B. discount rate that results in a zero net present value for the project. C. discount rate that results in a net present value equal to the project's initial cost. D. rate of return required by the project's investors. E. project's current market rate of return.
B. discount rate that results in a zero net present value for the project.
Consider the following two mutually exclusive projects: Whichever project you choose, if any, you require a 14 percent return on your investment. If you apply the payback criterion, you will choose Project ______; if you apply the NPV criterion, you will choose Project ______; if you apply the IRR criterion, you will choose Project _____; if you choose the profitability index criterion, you will choose Project ___. Based on your first four answers, which project will you finally choose?
B; A; B; A; A
Joe and Rich are both considering investing in a project with the following cash flows. Joe is content earning a 9 percent return, but Rich desires a return of 16 percent. Who, if either, should accept this project?
Both Joe and Rich
Which one of the following indicates that a project should be rejected? Assume the cash flows are normal, i.e., the initial cash flow is negative. A. Average accounting return that exceeds the requirement B. Payback period that is shorter than the requirement period C. Positive net present value D. Profitability index less than 1.0 E. Internal rate of return that exceeds the required return
D. Profitability index less than 1.0
Which one of the following methods of analysis ignores cash flows? A. Profitability index B. Payback C. Average accounting return D. Modified internal rate of return E. Internal rate of return
C. Average accounting return
Based on the most recent survey information presented in your textbook, CFOs tend to use which two methods of investment analysis the most frequently? A. Payback and net present value B. Payback and internal rate of return C. Internal rate of return and net present value D. Net present value and profitability index E. Profitability index and internal rate of return
C. Internal rate of return and net present value
The net present value profile illustrates how the net present value of an investment is affected by which one of the following?
Discount rate
Auto Detailers is buying some new equipment at a cost of $188,900. This equipment will be depreciated on a straight-line basis to a zero book value its eight-year life. The equipment is expected to generate net income of $11,000 a year for the first four years and $24,000 a year for the last four years. What is the average accounting rate of return? A. 15.48 percent B. 17.76 percent C. 18.09 percent D. 22.68 percent E. 18.53 percent
E. 18.53 percent AAR = {[(4 ×$11,000) + (4 ×$24,000)] / 8}/{($188,900 + 0)/2} = .1853, or 18.53 percent
An investment has an initial cost of $420,000 and will generate the net income amounts shown below. This investment will be depreciated straight-line to zero over the four-year life of the project. Should this project be accepted based on the average accounting rate of return if the required rate is 16 percent? Why or why not?
No, because the AAR is less than 16 percent
Woodcrafters requires an average accounting return (AAR) of at least 17 percent on all fixed asset purchases. Currently, it is considering some new equipment costing $178,000. This equipment will have a four-year life over which time it will be depreciated on a straight-line basis to a zero book value. The annual net income from this equipment is estimated at $10,100, $10,300, $17,900, and $19,600 for the four years. Should this purchase occur based on the accounting rate of return? Why or why not?
No, because the AAR is less than 17 percent
You are considering an investment for which you require a 14 percent rate of return. The investment costs $61,900 and will produce cash inflows of $26,000 for three years. Should you accept this project based on its internal rate of return? Why or why not?
No, because the IRR is 12.51 percent
Soft and Cuddly is considering a new toy that will produce the following cash flows. Should the company produce this toy if the firm requires a 15 percent rate of return?
No, because the project's rate of return is 10.21 percent
Which one of the following methods of analysis has the greatest bias toward short-term projects?
Payback
Which one of the following methods of analysis ignores the time value of money?
Payback
Which one of the following indicators offers the best assurance that a project will produce value for its owners?
Positive NPV
Which one of the following indicates that a project is expected to create value for its owners?
Positive net present value
Which one of the following can be defined as a benefit-cost ratio?
Profitability index
You were recently hired by a firm as a project analyst. The owner of the firm is unfamiliar with financial analysis and wants to know only what the expected dollar return is per dollar spent on a given project. Which financial method of analysis will provide the information that the owner requests?
Profitability index
Which one of the following indicates that a project is definitely acceptable?
Profitability index greater than 1.0
You are considering the following two mutually exclusive projects. The required return on each project is 14 percent. Which project should you accept and what is the best reason for that decision? (-24,000)
Project B, because it has the higher net present value
Baker's Supply imposes a payback cutoff of 3.5 years for its international investment projects. If the company has the following two projects available, should it accept either of them?
Reject both Projects A and B
Which one of the following is true if the managers of a firm accept only projects that have a profitability index greater than 1.5?
The firm should increase in value each time the firm accepts a new project.
The internal rate of return is unreliable as an indicator of whether or not an investment should be accepted given which one of the following?
The investment is mutually exclusive with another investment under consideration.
An investment has conventional cash flows and a profitability index of 1.0. Given this, which one of the following must be true?
The net present value is equal to zero.
Which one of the following will occur when the internal rate of return equals the required return?
The profitability index will equal 1.0.
