Question 1

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.

Accepted Answer

The answer of Gordon Corporation is considering a 30 year...

Question 2

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.

Accepted Answer

The acceptance of an investment project is based on the NPV. If the NPV is positive, then the investment is accepted. The IRR is used to determine the profitability of the investment, but it is not the sole basis for acceptance. Therefore, choices A and B are incorrect. Choice C is correct because a positive NPV indicates that the investment will generate more value than the initial investment and is therefore worth pursuing.

Question 3

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

Accepted Answer

The NPV (Net Present Value) is calculated using the formula: NPV = $\sum \frac{CF_t}{(1+r)^t}$ where $CF_t$ is the cash flow at time t, and r is the discount rate. For this project: NPV = $\frac{-1000}{(1+0.15)^0} + \frac{700}{(1+0.15)^1} + \frac{700}{(1+0.15)^2}$ = -$1000 + $608.70 + $529.30 = $138.00.

Question 4

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.

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 5

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?

Accepted Answer

The equivalent annual cost (EAC) is calculated by finding the present value of all costs and then converting this present value into an annuity over the project's life. The present value of the $40,000 investment and the $10,000 annual expenses over 4 years at a 10% discount rate is calculated, and then this total present value is converted into an annuity over 4 years at the same discount rate, resulting in an EAC of $22,618.83.

Question 6

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?

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 7

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

Accepted Answer

The number of possible IRRs for a set of cash flows corresponds to the number of times the cash flow changes sign. In this sequence, the cash flows change sign three times: from negative to positive between CF0 and CF1, back to negative between CF1 and CF2, and then back to positive between CF2 and CF3. According to the Descartes' Rule of Signs, each sign change represents a potential IRR, so there can be up to 3 IRRs for this set of cash flows.

Question 8

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?

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 9

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:

Accepted Answer

The profitability index is calculated as the present value of the future cash flows divided by the initial investment. In this case, the present value of the future cash flows is $40,000 * (1 - 1 / (1 + 0.12)^4) / 0.12 = $32,000. Therefore, the profitability index is $32,000 / $40,000 = 0.8.

Question 10

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?

Accepted Answer

The maximum amount a firm should consider paying can be calculated using present value formula:
PV = (Annual Return / Discount Rate) x [1 - 1 / (1 + Discount Rate)^n]
Where, 
Annual Return = $15,000
Discount Rate = 10% or 0.1
n = 5 years

Putting the values in the formula, we get:
PV = (15,000 / 0.1) x [1 - 1 / (1+ 0.1)^5]
    = 150,000 x [1 - 0.6209]
    = $56,862

Therefore, the firm should pay a maximum of $56,862 for the project. The closest option is B, which is the answer.

Question 11

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

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 12

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?

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 13

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?

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 14

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

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 15

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?

Accepted Answer

The cost of keeping the current car for four more years would be:
4 years x $4,000/year = $16,000

The cost of buying the newer car and keeping it for four years would be:
$8,000 + 4 years x (maintenance cost - depreciation) = $8,000 + 4 years x (maintenance cost - $8,000/4) = $8,000 + 4 years x (maintenance cost - $2,000) = $8,000 + 4(maintenance cost - $2,000)

In order to justify purchasing the newer car, the cost of owning it for four years must be less than the cost of keeping the current car for four years:
$8,000 + 4(maintenance cost - $2,000) < $16,000
4(maintenance cost - $2,000) < $8,000
maintenance cost - $2,000 < $2,000
maintenance cost < $4,000

Therefore, the maintenance expense on the newer vehicle must be less than $4,000 per year to justify its purchase. The decrease in maintenance expense required is:
$4,000 - maintenance cost = $4,000 - $2,415 = $1,585

So, the best choice is (B), a decrease in maintenance expense of $1,585.

Question 16

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

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.

Question 17

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?

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 18

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.

Accepted Answer

The maximum that should be paid to replace the machine can be calculated using the Net Present Value (NPV) of the cost savings. The annual savings from the new machine would be $10,000 - $4,000 = $6,000. Over three years, at a 12% discount rate, the NPV of these savings is calculated as: NPV = $6,000 / (1+0.12)^1 + $6,000 / (1+0.12)^2 + $6,000 / (1+0.12)^3 = $5,357.14 + $4,783.93 + $4,270.30 = $14,411.37. Therefore, up to $14,411 could be paid to replace the machine and still break even on the investment.

Question 19

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.

Accepted Answer

The answer of What is the minimum cash flow that...

Question 20

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.

Accepted Answer

The answer of Majestic Corporation is planning a 12 year...

Quiz 8: Net Present Value and Other Investment Criteria