Chapter 5 Exercises

Step-by-Step Exercises

Net Present Value

First, calculate the net initial investment, the annual cash flows, and the terminal cash flows of the project.

Question 1

Dama, Inc., is considering purchasing a new machine costing $1,200,000 to replace their current machine, which has a book value of $350,000 and could be sold for $75,000. The new machine would last 10 years and would have a salvage value of $200,000. Each year, the new machine would save $300,000 in operating expenses. Dama has a tax rate of 30%, and a required rate of return of 9%.

Calculate the net initial investment, the annual cash flows, and the terminal cash flows of the project.

Question 2

Palles Company is considering a new investment that would cost $700,000 for new assets that would have a salvage value of $100,000. The project would last for 6 years and would bring in $200,000 in additional income each year. To free up capacity for the new project, Palles would have to sell off assets with a book value of $100,000 and sales value of $250,000. Palles has a tax rate of 20% and a required rate of return of 11%.

Calculate the net initial investment, the annual cash flows, and the terminal cash flows of the project.

Next, discount the annual cash flows and terminal cash flows to present value.

Question 3

A project requires a $100,000 net initial investment, has a terminal cash flows of $12,000, and increases cash flows by $25,000 each year over its 5-year life. The required rate of return is 8%.

• Review Present Value Tables

Discount the annual cash flows and terminal cash flows to present value.

Question 4

A project requiring a net initial investment of $800,000 yields annual cash flows of $120,000 and has a terminal cash flows of $50,000 at the end of its 10-year life. The required rate of return is 10%.

• Review Present Value Tables

Discount the annual cash flows and terminal cash flows to present value.

Next, calculate the net present value.

Question 5

A proposed project requires a net initial investment of $1,000,000. The present value of annual cash flows is $1,137,236.03, and the present value of the terminal cash flows is $31,046.07.

Calculate the net present value.

Question 6

A proposed project requires a net initial investment of $600,000. The present value of annual cash flows is $565,022.30, and the present value of the terminal cash flows is $13,392.86.

Calculate the net present value.

Finally, indicate whether accepting the project would be financially beneficial.

Question 7

A project’s net present value is $1,200,000.

Indicate whether it would be financially beneficial to accept or reject the project.

Question 8

A proposed project has a net present value of $(20,000).

Indicate whether it would be financially beneficial to accept or reject the project.

Internal Rate Of Return

Solve for the present value factor of an annuity by dividing the net initial investment by annual cash flows.

Question 9

The net initial investment of a 7-year project is $235,610. Annual cash flows for the project are $50,000.

Solve for the present value factor of an annuity.

Question 10

A project that requires a net initial investment of $1,500,000 will save the company $265,450 each year for ten years.

Solve for the present value factor of an annuity.

Next, find the range for the internal rate of return by looking in the row corresponding to the number of years in the life of the project on the annuity table.

Question 11

The net initial investment divided by annual cash flows for an 8-year investment is 4.7.

• Review Present Value Tables

Find the range for the internal rate of return.

Question 12

The net initial investment of a 5-year project is 4 times its annual cash flows.

• Review Present Value Tables

Find the range for the internal rate of return.

Finally, indicate whether accepting the project would be financially beneficial.

Question 13

The internal rate of return of a project is 12%. The required rate of return is 15%.

Indicate whether it would be financially beneficial to accept or reject the project.

Question 14

The internal rate of return of a project is 8%. The required rate of return is 6%.

Indicate whether it would be financially beneficial to accept or reject the project.

Payback Period

For a project with even cash flows, find the payback period by dividing the net initial investment by annual cash flows.

Question 15

The net initial investment of a project is $540,000. Annual cash flows are $144,000.

Find the payback period.

Question 16

The net initial investment of a project is $2,630,000, and it will earn $620,000 per year over the life of the project.

Find the payback period.

For a project with uneven cash flows, first calculate the cumulative cash flows each year.

Question 17

A project is expected to save a company $80,000 the first year it is in operation, but the benefit will reduce by 5% each year afterwards for five more years.

Calculate the cumulative cash flows for each year of the project.

Question 18

An investment will produce net cash inflows of $200,000 the first year and $300,000 the following year, but then will reduce by $50,000 per year for the remaining five years of its life.

Calculate the cumulative cash flows for each year of the project.

For a project with uneven cash flows, finally, find the payback period by finding the first year in which cumulative cash flows are larger than the net initial investment and subtracting the proportion of cash flows occurring during that year since payoff.

Question 19

A project that required a net initial investment of $1,300,000 had the following annual and cumulative cash flows:

Find the payback period.

Question 20

After 15 years, the cumulative cash flows of an investment project exceeded the $20,000,000 net initial investment in the project for the first time. Cash flows that year were $850,000, for a cumulative total of $20,100,000.

Find the payback period.

Complete Problems

Question 21

Baja Company is considering replacing one of their machines with a new one that costs $2,000,000 and has a projected salvage value of $500,000. The old machine has a book value of $500,000 and could be sold for $300,000. Replacing the machine would allow Baja to save $300,000 a year over the 10-year life of the new machine. Baja has a tax rate of 25%, and a required rate of return of 10%.

Review Present Value Tables

1. Calculate the net present value of the machine replacement.
2. From a financial perspective, should Baja replace the machine?
3. What is the payback period of the machine replacement?
4. Now assume the net initial investment and annual cash flows you calculated are the same, but the terminal value of the investment is zero. What range would the internal rate of return of the investment fall into?

Question 22

Billman Corporation has an investment opportunity that would require an up-front investment of $7,000,000 in assets and would bring in additional revenues of $3,000,000 each year for 4 years. The assets could be sold at the end of 4 years for $400,000. Billman has a tax rate of 30% and a required rate of return of 14%.

Review Present Value Tables

1. Calculate the net present value of the investment opportunity.
2. From a financial perspective, should Billman accept or reject the opportunity?
3. What is the payback period of the investment opportunity?
4. Now assume the net initial investment and annual cash flows you calculated are the same, but the terminal value of the investment is zero. What range would the internal rate of return of the investment fall into?

Question 23

Perry Corporation has an opportunity to purchase entirely new machinery for their factory for $6,000,000. This machinery would provide substantial increases in productivity, allowing Perry to sell enough additional product to add revenues of $2,500,000 and incur variable costs of $1,200,000 each year until the machinery is obsolete, which is projected to happen in 5 years. At that point, the machinery could only be sold for $100,000. Perry will need to sell equipment carried on the books at $1,000,000 to make way for the new machinery; they estimate the old equipment will sell for $800,000. Perry has a tax rate of 15% and a required rate of return of 9%.

Review Present Value Tables

1. Calculate the net present value of the investment in the new machinery.
2. From a financial perspective, should Perry accept or reject the opportunity?
3. What is the payback period of the investment?
4. Now assume the net initial investment and annual cash flows you calculated are the same, but the terminal value of the investment is zero. What range would the internal rate of return of the investment fall into?

Question 24

Scootch Company is considering whether it would be worth it to invest $50,000 to improve the company website. They could amortize the costs over four years, at which point the website will probably need another overhaul. An improved website would make it easier for customers to purchase Scootch’s goods, bringing in an estimated additional $20,000 per year. Website maintenance will cost an additional $2,000 per year. Scootch has a required rate of return of 11% and a tax rate of 20%.

Review Present Value Tables

1. Calculate the net present value of the website upgrade.
2. From a financial perspective, should Scootch upgrade their website (yes/no)?
3. What is the payback period of the website upgrade?
4. What range does the internal rate of return for the website upgrade fall into?

Question 25

Portnoy, Inc. has decided to sell some aging equipment; although the book value of the equipment is $0, it should bring in $20,000. To replace the equipment, Portnoy wants to purchase more sophisticated machinery that will save Portnoy $50,000 in operating expenses every year for the next 7 years. The equipment will cost $300,000, and its estimated salvage value is $40,000. Portnoy’s tax rate is 25%, and their required rate of return is 8%.

Review Present Value Tables

1. Calculate the net present value of the investment opportunity.
2. From a financial perspective, should Portnoy accept or reject the opportunity?
3. What is the payback period of the investment opportunity?
4. Now assume the net initial investment and annual cash flows you calculated are the same, but the terminal value of the investment is zero. What range would the internal rate of return of the investment fall into?

Question 26

Marders, Inc. is considering replacing an old machine (which has a book value of $10,000 but could be sold for $40,000) with a new one that would cost $450,000. The new machine would have a useful life of seven years, at which time Marders could expect to sell it for $16,000. Marders estimates that the new machine will save them $100,000 per year due to efficiency gains and fewer maintenance costs. Marders’ tax rate is 30%, and Marauders has a required rate of return of 13%.

Review Present Value Tables

1. Calculate the net present value of the machine replacement.
2. From a financial perspective, should Marders replace the machine?
3. What is the payback period of the machine replacement?
4. Now assume the net initial investment and annual cash flows you calculated are the same, but the terminal value of the investment is zero. What range would the internal rate of return of the investment fall into?

Assignment Problem

Note: Check figures are not provided for assignment problems so your instructor may use them for homework.

Question 27

Melloni, Inc., is considering replacing a piece of equipment with a book value of $8,000 with one that costs $5,000,000. The current machinery can be sold for $50,000. The new machine will improve efficiency, resulting in cost savings of $1,000,000 each year for the 10-year life of the equipment, which is expected to have no salvage value at the end of its life. Melloni has a tax rate of 35% and a required rate of return of 11%.

Review Present Value Tables

1. Calculate the net present value of the equipment replacement.
2. From a financial perspective, should Melloni replace the equipment?
3. What is the payback period of the equipment replacement?
4. What range does the internal rate of return for the project fall into?

Challenge Problem

Question 28

Maximilian Company is considering making enhancements to their product. Doing so would require an additional investment in production machinery of $1,500,000, which would have a salvage value of $200,000 at the end of the product lifecycle 8 years from now. The new machinery would require a maintenance overhaul every 2 years, costing $100,000 for each overhaul. Maximilian could sell their old production machinery, which has a book value of $200,000, for $150,000.

Currently, per-unit product costs are as follows:

 

Direct materials	13
Direct labor	25
Variable overhead	15
Total	53

Maximilian currently charges $75 per unit and sells 40,000 units per year. The product enhancements would cause a 20% increase in direct materials costs and a 40% increase in direct labor costs. The enhancements will allow Maximilian to increase the price they charge by 25%. In addition, unit sales are projected to increase 15%.

Maximilian has a tax rate of 25% and a required rate of return of 12%.

Review Present Value Tables

Calculate the net present value of making the product enhancements. 

 

Pre-Assessment Problem

Use this problem to check whether you are fully prepared for the assessment. Work the problem under assessment conditions – don’t use any notes or other materials!

Question 29

Carrack Company is trying to decide whether to launch a new product line, which would require an initial investment of $3,500,000. Each year, the new product should bring in $1,100,000 in revenues but would cost $450,000 to manufacture. The product should have a 10-year life, after which the equipment associated with it could be sold for $150,000. To make room for the new production line, Carrack would sell a piece of equipment with a book value of $40,000 for $25,000. Carrack has an effective tax rate of 25%, and a required rate of return of 10%.

Review Present Value Tables

1. Calculate the net present value of the investment opportunity.
2. From a financial perspective, should Carrack accept or reject the opportunity?
3. What is the payback period of the investment opportunity?
4. Now assume the net initial investment and annual cash flows you calculated are the same, but the terminal value of the investment is zero. What range would the internal rate of return of the investment fall into?