Question 1

Based on the profitability index (PI) rule, should a project with the following cash flows be accepted if the discount rate is 8%? Why or why not? $$\begin{array} { c c } 
\underline{\text { Year }} &\underline{ \text { Cash Flow }} \
 0 & - \$ 18,600 \
1 & \$ 10,000 \
2 & \$ 7,300 \
3 & \$3,700
\end{array}$$
A)yes; because the PI is 1.008.
B)yes; because the PI is .992.
C)yes; because the PI is .999.
D)no; because the PI is 1.008.
E)no; because the PI is .992.

Accepted Answer

To calculate the profitability index (PI) we divide the present value of future cash flows by the initial investment.

The present value of cash flows can be calculated using the following formula:

PV = CF1 / (1+r)^1 + CF2 / (1+r)^2 + CF3 / (1+r)^3

PV = 10,000 / (1+0.08)^1 + 7,300 / (1+0.08)^2 + 3,700 / (1+0.08)^3

PV = 10,000 / 1.08 + 7,300 / 1.1664 + 3,700 / 1.2597

PV = 9,259.26

Therefore, the PI = PV / Initial Investment = 9,259.26 / 18,600 = 0.497.

Since the PI is less than 1, the project should not be accepted. Thus, the correct answer is E.

Question 2

What is the internal rate of return on an investment with the following cash flows? $$\begin{array} { c c } 
\underline{\text { Year }}  & \underline{\text { Cash Flow }}  \
0 & - \$ 123,400 \
1&\$ 36,200 \
2 & \$ 54,800 \
3 & \$ 48,100
\end{array}$$
A)5.93%
B)5.96%
C)6.04%
D)6.09%
E)6.13%

Accepted Answer

The answer of What is the internal rate of return...

Question 3

You are considering two mutually exclusive projects with the following cash flows.Will your choice between the two projects differ if the required rate of return is 8% rather than 11%? If so, what should you do? $\begin{array}{cccl}
\underline{\text { Year } }&\underline{\text { Project A }}& & \underline{\text { Project B }} \
0 &-\$ 240,000 & & -\$ 198,900 \
1 &\$ 0 & & \$110,800 \
2 &  \$ 0 & & \$ 82,500\
3 & \$ 325,000 & & \$ 45,000\

\end{array}$

A)yes; Select A at 8% and B at 11%.
B)yes; Select B at 8% and A at 11%.
C)yes; Select A at 8% and select neither at 11%.
D)no; Regardless of the required rate, project A always has the higher NPV.
E)no; Regardless of the required rate, project B always has the higher NPV.

Accepted Answer

The choice between the projects will differ. At an 8% discount rate, Project A has a higher NPV, while at an 11% discount rate, Project B has a higher NPV.

Question 4

A project has an initial cost of $8,500 and produces cash inflows of $2,600, $4,900, and $1,500 over the next three years, respectively.What is the discounted payback period if the required rate of return is 7%?
A)2.13 years
B)2.33 years
C)2.67 years
D)2.91 years
E)never

Accepted Answer

The answer of A project has an initial cost of...

Question 5

You are considering a project with an initial cost of $4,300.What is the payback period for this project if the cash inflows are $550, $970, $2,600, and $500 a year over the next four years?
A)2.04 years
B)2.36 years
C)2.89 years
D)3.04 years
E)3.36 years

Accepted Answer

The answer of You are considering a project with an...

Question 6

Ginny Trueblood is considering an investment which will cost her $120,000.The investment produces no cash flows for the first year.In the second year the cash inflow is $35,000.This inflow will increase to $55,000 and then $75,000 for the following two years before ceasing permanently.Ginny requires a 10% rate of return and has a required discounted payback period of three years.Ginny should _____ this project because the discounted payback period is ____.
A)accept; 2.03 years
B)accept; 2.97 years
C)accept; 3.97 years
D)reject; 3.03 years
E)reject; 3.97 years

Accepted Answer

The answer of Ginny Trueblood is considering an investment which...

Question 7

You would like to invest in the following project. $$\begin{array} { c c } 
\underline{\text { Year }} &\underline{ \text { Cash Flow }} \
 0 & - \$ 55,000 \
1 & \$ 30,000 \
2 & \$37,000 \

\end{array}$$ Victoria, your boss, insists that only projects that can return at least $1.10 in today's dollars for every $1 invested can be accepted.She also insists on applying a 10% discount rate to all cash flows.Based on these criteria, you should:
A)accept the project because it returns almost $1.22 for every $1 invested.
B)accept the project because it has a positive PI.
C)accept the project because the NPV is $2,851.
D)reject the project because the PI is 1.05.
E)reject the project because the IRR exceeds 10%.

Accepted Answer

The profitability index (PI) is calculated as the present value of future cash flows divided by the initial investment. Using a 10% discount rate, the present value of cash flows is approximately $57,750, leading to a PI of 1.05, which is below the required 1.10.

Question 8

Jack is considering adding toys to his general store.He estimates that the cost of inventory will be $4,200.The remodeling and shelving costs are estimated at $1,500.Toy sales are expected to produce net cash inflows of $1,200, $1,500, $1,600, and $1,750 over the next four years, respectively.Should Jack add toys to his store if he assigns a three-year payback period to this project?
A)yes; because the payback period is 2.94 years.
B)yes; because the payback period is 2.02 years.
C)yes; because the payback period is 3.80 years.
D)no; because the payback period is 2.02 years.
E)no; because the payback period is 3.80 years.

Accepted Answer

The total initial investment is $5,700 ($4,200 for inventory + $1,500 for remodeling). The cumulative cash inflows over the first three years are $4,300 ($1,200 + $1,500 + $1,600), which is less than the initial investment. The payback period extends into the fourth year, making it 3.80 years, which exceeds the three-year requirement.

Question 9

What is the profitability index for an investment with the following cash flows given a 9% required return? $$\begin{array} { c c } 
\underline{\text { Year }} &\underline{ \text { Cash Flow }} \
 0 & - \$ 21,500 \
1 & \$ 7,400 \
2 & \$ 9,800 \
3 & \$ 8,900
\end{array}$$
A).96
B).98
C)1.00
D)1.02
E)1.04

Accepted Answer

The answer of What is the profitability index for an...

Question 10

Yancy is considering a project which will produce cash inflows of $900 a year for 4 years.The project has a 9% required rate of return and an initial cost of $2,800.What is the discounted payback period?
A)3.11 years
B)3.18 years
C)3.82 years
D)4.18 years
E)never

Accepted Answer

The answer of Yancy is considering a project which will...

Question 11

You are considering two independent projects with the following cash flows.The required return for both projects is 10%.Given this information, which one of the following statements is correct? $\begin{array}{lll}
\underline{\text { Year} } & \underline{\text { Project A }} &\underline{ \text { Project B }} \
 0 & -\$ 950,000 & -\$ 125,000 \
1 & \$ 330,000 & \$ 55,000 \
2 & \$ 400,000 & \$ 50,000 \
3 & \$ 450,000 & \$ 50,000
\end{array}$
A)You should accept project B since it has the higher IRR and reject project A because you can not accept both projects.
B)You should accept project A because it has the lower NPV and reject project B.
C)You should accept project A because it has the higher NPV and you can not accept both projects.
D)You should accept project B because it has the higher IRR and reject project A.
E)You should accept both projects if the funds are available to do so since both NPV's are > 0.

Accepted Answer

Both projects have positive NPVs at a 10% discount rate, indicating they are both expected to generate returns above the required rate. Therefore, if funds are available, both projects should be accepted.

Question 12

A project will produce cash inflows of $1,750 a year for four years.The project initially costs $10,600 to get started.In year five, the project will be closed and as a result should produce a cash inflow of $8,500.What is the net present value of this project if the required rate of return is 13.75%?
A)-$5,474.76
B)-$1,011.40
C)-$935.56
D)$1,011.40
E)$5,474.76

Accepted Answer

To calculate the net present value (NPV), we need to find the present value of all the cash inflows and outflows of the project using a discount rate of 13.75%.

Year 0: -$10,600 (initial cost)
Year 1: $1,750 ÷ (1+0.1375) = $1,537.39
Year 2: $1,750 ÷ (1+0.1375)² = $1,350.70
Year 3: $1,750 ÷ (1+0.1375)³ = $1,178.19
Year 4: $1,750 ÷ (1+0.1375)⁴ = $1,018.06
Year 5: $8,500 ÷ (1+0.1375)⁵ = $4,145.09

NPV = Present value of cash inflows - Present value of cash outflows
NPV = $1,537.39 + $1,350.70 + $1,178.19 + $1,018.06 + $4,145.09 - $10,600
NPV = -$935.56

Therefore, the net present value of this project is -$935.56, which means the project is not worth pursuing as it will result in a loss. Option B is the correct answer.

Question 13

What is the net present value of a project that has an initial cash outflow of $12,670 and the following cash inflows? The required return is 11.5%. $$\begin{array} { c l } 
\text { Year } & \text { Cash Inflows } \
\hline 1 & \$ 4,375 \
2 & \$ \quad 0 \
3 & \$ 8,750 \
4 & \$ 4,100
\end{array}$$
A)$218.68
B)$370.16
C)$768.20
D)$1,249.65
E)$1,371.02

Accepted Answer

The net present value (NPV) is calculated by discounting each cash inflow at the required return rate and subtracting the initial investment. The NPV is $218.68.

Question 14

It will cost $2,600 to acquire a small ice cream cart.Cart sales are expected to be $1,400 a year for three years.After the three years, the cart is expected to be worthless as that is the expected remaining life of the cooling system.What is the payback period of the ice cream cart?
A).86 years
B)1.46 years
C)1.86 years
D)2.46 years
E)2.86 years

Accepted Answer

To find the payback period, we need to divide the initial cost ($2,600) by the annual cash flows ($1,400).
Payback period = $2,600 ÷ $1,400 per year = 1.86 years
Therefore, the best choice is C.

Question 15

What is the net present value of a project with the following cash flows and a required return of 12%? $$\begin{array} { c c } 
\text { Year } & \text { Cash Flow } \
\hline 0 & - \$ 28,900 \
1 & \$ 12,450 \
2 & \$ 19,630 \
3 & \$ 2,750
\end{array}$$
A)-$287.22
B)-$177.62
C)$177.62
D)$204.36
E)$287.22

Accepted Answer

The answer of What is the net present value of...

Question 16

You are considering two independent projects both of which have been assigned a discount rate of 8%.Based on the profitability index, what is your recommendation concerning these projects? 
A)You should accept both projects since both of their PIs are positive.
B)You should accept project A since it has the higher PI.
C)You should accept both projects since both of their PIs are greater than 1.
D)You should only accept project B since it has the largest PI and the PI exceeds 1.
E)Neither project is acceptable.

Accepted Answer

The answer of You are considering two independent projects both...

Question 17

You are considering the following two mutually exclusive projects that will not be repeated.The required rate of return is 11.25% for project A and 10.75% for project B.Which project should you accept and why? $\begin{array}{cccl}
\underline{\text { Year } }&\underline{\text { Project A }}& & \underline{\text { Project B }} \
0 &-\$ 48,000 & & -\$ 126,900 \
1 &\$ 18,400 & & \$ 69,700 \
2 &  \$ 31,300 & & \$ 80,900\
3 & \$ 11,700 & & \$ 0\

\end{array}$

A)project A; because its NPV is about $335 more than the NPV of project B.
B)project A; because it has the higher required rate of return.
C)project B; because it has the largest total cash inflow.
D)project B; because it returns all its cash flows within two years.
E)project B; because it is the largest sized project.

Accepted Answer

To determine which project should be accepted, we need to calculate the net present value for each project using their respective required rates of return.

For project A: 
NPV(A) = -$48,000 + $\frac{18,400}{(1+0.1125)} + \frac{31,300}{(1+0.1125)^2} + \frac{11,700}{(1+0.1125)^3} = $12,327.34

For project B: 
NPV(B) = -$126,900 + $\frac{69,700}{(1+0.1075)} + \frac{80,900}{(1+0.1075)^2} + \frac{0}{(1+0.1075)^3} = $11,992.76

Since project A has a higher NPV, it is the best choice.

Question 18

An investment has the following cash flows.Should the project be accepted if it has been assigned a required return of 9.5%? Why or why not? $$\begin{array} { c c } 
 \underline{\text { Year }} & \underline{\text { Cash Flow }} \
0&-\$24,000\
1 & \$ 8,000 \
2 & \$ 12,000 \
3 & \$ 9,000
\end{array}$$
A)yes; because the IRR exceeds the required return by about 0.39%.
B)yes; because the IRR is less than the required return by about 3.9%.
C)yes; because the IRR is positive.
D)no; because the IRR exceeds the required return by about 3.9%.
E)no; because the IRR is 9.89%.

Accepted Answer

We can calculate the IRR (Internal Rate of Return) of the project using a financial calculator or Excel. The IRR for this project is approximately 9.89%. Since the IRR exceeds the required return of 9.5% by about 0.39%, the project should be accepted. A higher IRR means that the project is generating a higher return than the required return, making it a good investment.

Question 19

A project has an initial cost of $1,900.The cash inflows are $0, $500, $900, and $700 over the next four years, respectively.What is the payback period?
A)2.71 years
B)2.98 years
C)3.11 years
D)3.71 years
E)never

Accepted Answer

The answer of A project has an initial cost of...

Question 20

You are considering an investment with the following cash flows.If the required rate of return for this investment is 13.5%, should you accept it based solely on the internal rate of return rule? Why or why not? $\begin{array}{ll}
\underline{\text { Year }} & \underline{\text { Cash Flow} } \
0& -\$ 12,000 \
1 & \$ 5,500 \
2 & \$ 8,000 \
3 & -\$ 1,500
\end{array}$
A)Yes; because the IRR exceeds the required return.
B)Yes; because the IRR is a positive rate of return.
C)No; because the IRR is less than the required return.
D)No; because the IRR is a negative rate of return.
E)You can not apply the IRR rule in this case because there are multiple IRRs.

Accepted Answer

The cash flows have more than one sign change, indicating the possibility of multiple IRRs, making the IRR rule unreliable.

Quiz 5: Net Present Value and Other Investment Rules

What is the internal rate of return on an investment with the following cash flows? $\begin{array} { c c } \underline{\text { Year }} & \underline{\text { Cash Flow }} \\0 & - \$ 123,400 \\1&\$ 36,200 \\2 & \$ 54,800 \\3 & \$ 48,100\end{array}$

A project has an initial cost of $8,500 and produces cash inflows of $2,600, $4,900, and $1,500 over the next three years, respectively.What is the discounted payback period if the required rate of return is 7%?

You are considering a project with an initial cost of $4,300.What is the payback period for this project if the cash inflows are $550, $970, $2,600, and $500 a year over the next four years?

What is the profitability index for an investment with the following cash flows given a 9% required return? $\begin{array} { c c } \underline{\text { Year }} &\underline{ \text { Cash Flow }} \\ 0 & - \$ 21,500 \\1 & \$ 7,400 \\2 & \$ 9,800 \\3 & \$ 8,900\end{array}$

Yancy is considering a project which will produce cash inflows of $900 a year for 4 years.The project has a 9% required rate of return and an initial cost of $2,800.What is the discounted payback period?

What is the net present value of a project that has an initial cash outflow of $12,670 and the following cash inflows? The required return is 11.5%. $\begin{array} { c l } \text { Year } & \text { Cash Inflows } \\\hline 1 & \$ 4,375 \\2 & \$ \quad 0 \\3 & \$ 8,750 \\4 & \$ 4,100\end{array}$

It will cost $2,600 to acquire a small ice cream cart.Cart sales are expected to be $1,400 a year for three years.After the three years, the cart is expected to be worthless as that is the expected remaining life of the cooling system.What is the payback period of the ice cream cart?

What is the net present value of a project with the following cash flows and a required return of 12%? $\begin{array} { c c } \text { Year } & \text { Cash Flow } \\\hline 0 & - \$ 28,900 \\1 & \$ 12,450 \\2 & \$ 19,630 \\3 & \$ 2,750\end{array}$

You are considering two independent projects both of which have been assigned a discount rate of 8%.Based on the profitability index, what is your recommendation concerning these projects?

An investment has the following cash flows.Should the project be accepted if it has been assigned a required return of 9.5%? Why or why not? $\begin{array} { c c } \underline{\text { Year }} & \underline{\text { Cash Flow }} \\0&-\$24,000\\1 & \$ 8,000 \\2 & \$ 12,000 \\3 & \$ 9,000\end{array}$

A project has an initial cost of $1,900.The cash inflows are $0, $500, $900, and $700 over the next four years, respectively.What is the payback period?