Question 1

What is the equivalent annual cost for a project that requires a $40,000 investment at time-period zero,and a $10,000 annual expense during each of the next 4 years,if the opportunity cost of capital is 10 percent?
A) $20,000.00
B) $21,356.95
C) $22,618.83
D) $25,237.66

Accepted Answer

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Question 2

What is the maximum that should be invested in a project at time zero if the inflows are estimated at $40,000 annually for three years,and the cost of capital is 9 percent?
A) $101,251.79
B) $109,200.00
C) $117,871.97
D) $130,800.00

Accepted Answer

To find the maximum that should be invested in a project at time zero given the inflows and the cost of capital, we use the present value formula for an annuity. The present value (PV) of an annuity formula is PV = PMT × [(1 - (1 + r)^-n) / r], where PMT is the annual payment ($40,000), r is the annual interest rate (9% or 0.09), and n is the number of periods (3 years). Plugging these values into the formula gives the maximum that should be invested today to break even on the project, which calculates to approximately $101,251.79.

Question 3

A currently used machine costs $10,000 annually to run.What is the maximum that should be paid to replace the machine with one that will last three years and cost only $4,000 annually to run? The opportunity cost of capital is 12 percent.
A) $2,000
B) $9,607
C) $14,411
D) $24,018

Accepted Answer

To determine the maximum amount that should be paid to replace the machine, we need to calculate the present value of the cost savings over three years.

The current machine costs $10,000 annually to run, so the total cost over three years is $30,000.

The new machine costs $4,000 annually to run, so the total cost over three years is $12,000.

Therefore, the cost savings over three years is $18,000 ($30,000 - $12,000).

To calculate the present value of this cost savings, we need to use the formula:

PV = CF / (1 + r)^n

where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of periods (in years).

In this case, CF = $18,000, r = 12%, and n = 3.

PV = $18,000 / (1 + 0.12)^3

PV = $14,410.78

Therefore, the maximum that should be paid to replace the machine is $14,410.78.

Since answer choice C is the closest to this amount, it is the best choice.

Question 4

The acceptance of an investment project implies that: Its IRR is greater than 15 percent.
Its NPV is greater than its IRR.
Its NPV is greater than 0.
A) 1
B) 2
C) 3
D) Both 2 and 3

Accepted Answer

The acceptance of an investment project is based on its positive NPV, which means that the project's cash inflows are greater than its cash outflows. Additionally, the project's IRR should be compared to the required rate of return to determine whether it is feasible. However, it is not necessary for the IRR to be greater than 15 percent for the project to be accepted as long as its NPV is greater than 0. Therefore, the correct choice is option 3, which states that the project's NPV must be greater than 0. Both options 2 and 3 are incorrect because there is no relationship between the project's NPV and IRR.

Question 5

Gordon Corporation is considering a 30 year project.The present value of all future cash flows from the project is $825,000.Its initial investment is $475,000.Calculate the Profitability Index on this project.
A) 0.74
B) 0.84
C) 1.14
D) 1.74

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Question 6

The profitability index for a project costing $40,000 and returning $15,000 annually for four years at an opportunity cost of capital of 12 percent is:
A) 0.139
B) 0.320
C) 0.500
D) 0.861

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Question 7

What is the minimum number of years that an investment costing $500,000 must return $65,000 per year at a discount rate of 13 percent in order to be an acceptable investment?
A) 8.69 years
B) 14.00 years
C) 27.51 years
D) An infinite number of years

Accepted Answer

The investment must return at least its cost when discounted at the given rate. The formula for the present value of an annuity (a series of equal annual payments) is PV = PMT * [(1 - (1 + r)^-n) / r], where PV is the present value (initial investment), PMT is the annual payment, r is the discount rate, and n is the number of years. In this case, solving for n with the given values ($500,000 investment, $65,000 annual return, 13% discount rate) would not yield a finite number of years because the annual return does not cover the cost of the investment when discounted at 13%. Therefore, the investment would never be considered acceptable, implying an infinite number of years.

Question 8

Because of its age,your car costs $4,000 annually in maintenance expense.You could replace it with a newer vehicle costing $8,000.Both vehicles would be expected to last four more years.If your opportunity cost is 8 percent,by how much must maintenance expense decrease on the newer vehicle to justify its purchase?
A) $1,250
B) $1,585
C) $2,000
D) $2,415

Accepted Answer

The cost of keeping the older car for four years is 4*$4,000=$16,000.

The cost of buying a new car is $8,000, and the maintenance expense is $x per year for four years, so the total cost is:

$8,000 + 4*$x

To determine the value of x that makes buying a new car a good choice, we need to find the present value of each option and compare them.

For the older car, the present value is:

$16,000/(1+0.08)^4 = $11,313.96

For the new car, the present value is:

$8,000 + ($x/(1+0.08)) + ($x/(1+0.08)^2) + ($x/(1+0.08)^3) + ($x/(1+0.08)^4)

Simplifying the expression, we get:

$8,000 + $x*(3.31213)

Setting the present values equal to each other and solving for x, we get:

$11,313.96 = $8,000 + $x*(3.31213)

$x = $1,585

Therefore, the maintenance expense on the newer vehicle must decrease by $1,585 per year to justify its purchase.

Question 9

What is the approximate maximum amount that a firm should consider paying for a project that will return $15,000 annually for 5 years if the opportunity cost is 10 percent?
A) $33,520
B) $56,862
C) $62,540
D) $75,000

Accepted Answer

To calculate the maximum amount the firm should pay, we need to find the present value of the cash flows at a discount rate of 10%. Using the present value of an annuity formula, we get:

PV = C * [(1 - (1 + r)^-n) / r]

where PV is the present value, C is the annual cash flow, r is the discount rate, and n is the number of years.

Plugging in the values from the problem, we get:

PV = $15,000 * [(1 - (1 + 0.1)^-5) / 0.1] = $56,862

Therefore, the maximum amount the firm should consider paying is $56,862.

Question 10

What is the NPV for the following project cash flows at a discount rate of 15 percent? CF₀ = ($1,000),CF₁ = $700,CF₂ = $700. A) ($308.70) B) ($138.00) C) $138.00 D) $308.70

Accepted Answer

The NPV is calculated as: NPV = CF₀ + CF₁/(1+0.15) + CF₂/(1+0.15)² = -1000 + 700/1.15 + 700/(1.15)² = $138.00.

Question 11

Ajax Corporation is planning a 10 year project that will have an initial cost of $500,000.During the first 2 years,there will be cash outflows of $40,000.Years 3-6 will see cash inflows of $120,000.Years 7-10 will see cash inflows of $200,000.If the company's required rate of return is 9%,determine the NPV of the project.
A) $143,200
B) $225,650
C) $375,800
D) $500,000

Accepted Answer

The NPV (Net Present Value) of the project can be calculated by discounting all cash flows (both inflows and outflows) to their present value using the required rate of return (9% in this case) and then summing those values. The initial cost is an outflow, so it's subtracted. The formula for NPV is: NPV = (Cash Flow / (1 + r)^t) - Initial Investment, where r is the rate of return and t is the time period. Calculating each cash flow's present value and summing them gives an NPV of approximately $143,200.

Question 12

Majestic Corporation is planning a 12 year project that will have an initial cost of $900,000.During the first 3 years,there will be cash inflows of $80,000.Years 4-10 will see cash inflows of $350,000.Years 11-12 will see cash outflows of $20,000.If the company's required rate of return is 11%,determine the NPV of the project.
A) -$175,023
B) -$25,890
C) $227,320
D) $489,366

Accepted Answer

To calculate the NPV of the project, we need to discount all the cash inflows and outflows to their present values using the required rate of return of 11%.

Year 0: Initial cost = -$900,000 (outflow)
Year 1-3: Cash inflows = $80,000 each year, discounted at 11%:
PV = $80,000/(1+11%)^1 + $80,000/(1+11%)^2 +$80,000/(1+11%)^3 = $201,802.69
Year 4-10: Cash inflows = $350,000 each year, discounted at 11%:
PV = $350,000/(1+11%)^4 + $350,000/(1+11%)^5 + ... + $350,000/(1+11%)^10 = $1,654,942.67
Year 11-12: Cash outflows = $20,000 each year, discounted at 11%:
PV = -$20,000/(1+11%)^11 -$20,000/(1+11%)^12 = -$36,409.52

NPV = PV of cash inflows - PV of cash outflows - Initial cost
     = $201,802.69 + $1,654,942.67 - $36,409.52 - $900,000
     = $489,335.84

Therefore, the NPV of the project is $489,335.84. The best choice is D.

Question 13

A polisher costs $10,000 and will cost $20,000 a year to operate and maintain.If the discount rate is 10 percent and the polisher will last for 5 years,what is the equivalent annual cost of the tool?
A) $22,638
B) $85,815
C) $12,638
D) $32,638

Accepted Answer

The equivalent annual cost (EAC) of the tool can be calculated using the formula for the present value of an annuity to find the annual cost equivalent of the initial investment, plus the annual operating and maintenance costs. The formula to calculate the EAC of the initial investment is: EAC = PV / A, where PV is the present value of the initial cost and A is the annuity factor given by [1 - (1 + r)^-n] / r, where r is the discount rate and n is the number of years. For the initial investment of $10,000, the annuity factor at a 10% discount rate over 5 years is 3.7908. So, the EAC of the initial investment is $10,000 / 3.7908 = $2,638 approximately. Adding the annual operating and maintenance costs of $20,000 gives a total EAC of $22,638.

Question 14

What is the minimum cash flow that could be received at the end of year three to make the following project "acceptable?" Initial cost = $100,000; cash flows at end of years one and two = $35,000; opportunity cost of capital = 10 percent.
A) $29,494
B) $30,000
C) $39,256
D) $52,250

Accepted Answer

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Question 15

What is the NPV of a project that costs $100,000 and returns $45,000 annually for three years if the opportunity cost of capital is 14 percent?
A) $3,397.57
B) $4,473.44
C) $16,100.00
D) $35,000.00

Accepted Answer

To calculate the NPV, you need to discount each year's cash flow by the opportunity cost of capital and then subtract the initial cost. 
The formula is:
NPV = -Initial Cost + CF1/(1+r)^1 + CF2/(1+r)^2 + CF3/(1+r)^3
where CF is the cash flow and r is the opportunity cost of capital.
Using the numbers given in the problem:
NPV = -$100,000 + $45,000/(1+0.14)^1 + $45,000/(1+0.14)^2 + $45,000/(1+0.14)^3
NPV = -$100,000 + $39,473.68 + $31,774.59 + $25,786.24
NPV = $-3,965.49
Therefore, the best choice is B because it has the closest value to -$3,965.49, which is the calculated NPV

Question 16

Which of the following projects would you feel safest in accepting? Assume the opportunity cost of capital to be 12 percent for each project.
A) "A" has a small, but negative, NPV
B) "B" has a positive NPV when discounted at 10 percent
C) "C's" cost of capital exceeds its rate of return
D) "D" has a zero NPV when discounted at 14 percent

Accepted Answer

Project D has a zero NPV when discounted at 14 percent, which means it will exactly earn the required rate of return to cover the opportunity cost of capital. Therefore, accepting Project D would be the safest option. Projects A and C have negative NPVs, indicating that they would not generate sufficient returns to cover the cost of capital, and Project B has a positive NPV but only when discounted at 10 percent, which is lower than the opportunity cost of capital.

Question 17

If a Project's IRR is 13 percent and the project provides annual cash flows of $15,000 for four years,how much did the project cost?
A) $44,617
B) $52,200
C) $60,000
D) $72,747

Accepted Answer

The Internal Rate of Return (IRR) is the discount rate that makes the net present value (NPV) of all cash flows from a particular project equal to zero. Given the IRR of 13% and annual cash flows of $15,000 for four years, we can calculate the initial cost of the project by discounting these cash flows back at the IRR. Using the formula for the present value of an annuity: PV = PMT × [(1 - (1 + r)^-n) / r], where PMT is the annual cash flow, r is the discount rate (IRR in this case), and n is the number of periods, we find that the initial cost (or present value of these cash flows) is closest to $44,617.

Question 18

How many IRRs are possible for the following set of cash flows? CF₀ = -1,000,CF₁ = + 500,CF₂ = -300,CF₃ = + 1,000,CF₄ = + 200. A) 1 B) 2 C) 3 D) 4

Accepted Answer

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Question 19

A project's Profitability Index is .85 and its investment value of $250,000.Given this information,determine its NPV.
A) $12,500
B) -$5,000
C) -$12,500
D) -$37,500

Accepted Answer

The Profitability Index (PI) is calculated as the present value of future cash flows divided by the initial investment. A PI of .85 means that for every $1 invested, the project returns 85 cents. To find the NPV, you subtract the initial investment from the present value of future cash flows. Since the PI is .85, the project returns $212,500 ($250,000 * .85) on a $250,000 investment. The NPV is therefore $212,500 - $250,000 = -$37,500.

Question 20

Determine the project's NPV if the Profitability Index is 1.4; and the investment value is $500,000.
A) $25,000
B) $75,000
C) $200,000
D) $250,000

Accepted Answer

The Profitability Index (PI) is calculated as the present value of future cash flows divided by the initial investment. A PI of 1.4 means that for every $1 invested, the project returns $1.40. Therefore, if the investment value is $500,000, the present value of future cash flows would be 1.4 times that amount, which is $700,000. The NPV is the present value of future cash flows minus the initial investment, so $700,000 - $500,000 = $200,000.

Quiz 8: Net Present Value and Other Investment Criteria

What is the equivalent annual cost for a project that requires a $40,000 investment at time-period zero,and a $10,000 annual expense during each of the next 4 years,if the opportunity cost of capital is 10 percent?

What is the maximum that should be invested in a project at time zero if the inflows are estimated at $40,000 annually for three years,and the cost of capital is 9 percent?

A currently used machine costs $10,000 annually to run.What is the maximum that should be paid to replace the machine with one that will last three years and cost only $4,000 annually to run? The opportunity cost of capital is 12 percent.

The acceptance of an investment project implies that: Its IRR is greater than 15 percent. Its NPV is greater than its IRR. Its NPV is greater than 0.

Gordon Corporation is considering a 30 year project.The present value of all future cash flows from the project is $825,000.Its initial investment is $475,000.Calculate the Profitability Index on this project.

The profitability index for a project costing $40,000 and returning $15,000 annually for four years at an opportunity cost of capital of 12 percent is:

What is the minimum number of years that an investment costing $500,000 must return $65,000 per year at a discount rate of 13 percent in order to be an acceptable investment?

What is the approximate maximum amount that a firm should consider paying for a project that will return $15,000 annually for 5 years if the opportunity cost is 10 percent?

What is the NPV for the following project cash flows at a discount rate of 15 percent? CF₀ = ($1,000) ,CF₁ = $700,CF₂ = $700.

A polisher costs $10,000 and will cost $20,000 a year to operate and maintain.If the discount rate is 10 percent and the polisher will last for 5 years,what is the equivalent annual cost of the tool?

What is the minimum cash flow that could be received at the end of year three to make the following project "acceptable?" Initial cost = $100,000; cash flows at end of years one and two = $35,000; opportunity cost of capital = 10 percent.

What is the NPV of a project that costs $100,000 and returns $45,000 annually for three years if the opportunity cost of capital is 14 percent?

Which of the following projects would you feel safest in accepting? Assume the opportunity cost of capital to be 12 percent for each project.

If a Project's IRR is 13 percent and the project provides annual cash flows of $15,000 for four years,how much did the project cost?

How many IRRs are possible for the following set of cash flows? CF₀ = -1,000,CF₁ = + 500,CF₂ = -300,CF₃ = + 1,000,CF₄ = + 200.

A project's Profitability Index is .85 and its investment value of $250,000.Given this information,determine its NPV.

Determine the project's NPV if the Profitability Index is 1.4; and the investment value is $500,000.