Chapter 8 Part 1

FINA 361Chapter 8

Net present value

Capital means money

Budgeting means a plan

Capital budgeting

Capital budgeting is the process of planning for major investments in a business

These are usually larger projects, for example: Building a new factory Replacing old equipment Starting a new product line

The big picture

For example:◦ Should your company spend $1 million today to

open a new factory?◦ The answer depends on how much money the

new factory will make for the company This usually requires estimates of what will happen in

the future

Capital budgeting

Is it worth it?

◦ Examples Movies Apple iPod Boeing 777 Smaller projects

Software upgrades Equipment replacement/upgrade New product introduction Etc., etc.

Capital budgeting

MoviesMovies are a good example

They often require large investments to make the movie

How much money the movie will make is uncertain

Suppose you are an executive at GDL Studios.◦ You have to decide on a proposal to spend $100

million on a new movie◦ How would you decide?

Capital budgeting

After extensive research, you expect the movie to make the following profits, in millions of dollars

Capital budgeting

Year 1 Year 2 Year 3 Year 4 Year 5

$75 $15 $20 $4 $1

Is this worth a $100 million investment?

$75 + $15 + $20 +$4 + $1 = $115

This is not a valid argument because:(1)It does not account for the time is takes to earn the profits(2)It does not consider the return investors require

Decisions◦ We use several techniques in finance to make

capital budgeting decisions◦ The best one is Net Present Value

Capital budgeting

NPV = Present value of future cash flows – cost today

Movie example◦ The movie requires a $100 million investment

today It will generate the following profits in the future:

Is it worth it? Suppose investors require a 10% return.

Net present value


$75 $15 $20 $4 $1

𝑃𝑉 𝑓𝑢𝑡𝑢𝑟𝑒 h𝑐𝑎𝑠 𝑓𝑙𝑜𝑤𝑠=$75

1+10%+

$15

(1+10% )2+

$20

(1+10% )3+

$ 4

(1+10% )4+

$1

(1+10% )5

PV future cash flows = $98.96 million

If◦ NPV > 0

◦ NPV < 0

Net present value

Movie Example

PV of future cash flows $98.96 million

Cost to make the movie $100 million

NPV -$1.04

Suppose Ryan Gosling reads the screenplay, and expresses interest in starring in our movie

Could this change our decision?

Net present value

We estimate that with Ryan Gosling in the movie, the cash flows will be:

Assuming the same $100 million budget, does this change our decision?

Net present value


$95 $20 $25 $4 $1

𝑃𝑉 𝑓𝑢𝑡𝑢𝑟𝑒 h𝑐𝑎𝑠 𝑓𝑙𝑜𝑤𝑠=$95

1+10%+

$20

(1+10% )2+

$25

(1+10% )3+

$ 4

(1+10% )4+

$1

(1+10% )5

PV future cash flows = $125.03 million

If Ryan has the same information that we do, how much will his agent ask for as his payment?

Example 8.1, page 231: New computer◦ Cost: $50,000◦ Will last for 4 years◦ Reduce costs by $22,000 per year◦ Required return = 10%

Is it worth it?

Net present value

N I PV PMT FV

4 10 ? 22,000 0

$69,737

NPV = $69,737-$50,00=+$19,737

Using NPV to choose among projects Your studio has two movie proposals for

next summer:◦ Movie 1◦ Action, budget is $100 million

◦ Movie 2◦ Romance, budget is $60 million

NPV

Year1 Year2 Year3 Year4

$85 $25 $10 $2


$55 $20 $5 $1

Which should you choose?

The discount rate is 10%



NPV


$85 $25 $10 $2



Find the NPV of Movie 1

A. -1.82B. 3.25C. 6.81D. 9.19



NPV


$85 $25 $10 $2

CF01 CF02 CF03 CF04



𝑃𝑉 𝑓𝑢𝑡𝑢𝑟𝑒 h𝑐𝑎𝑠 𝑓𝑙𝑜𝑤𝑠=$851+10%

+$25

(1+10% )2+

$10

(1+10% )3+

$2

(1+10% )4

PV = $106.81, NPV = $106.81 - $100 = $6.81


next summer:◦ Movie 2◦ Romance, budget is $60 million

NPV


$55 $20 $5 $1



Find the NPV of Movie 1

A. 4.25B. 7.39C. 8.41D. 10.97


next summer:◦ Movie 2◦ Romance, budget is $60 million

NPV


$55 $20 $5 $1

CF01 CF02 CF03 CF04



NPV = 10.97

Net present value◦ Movie 1

◦ Movie 2

NPV


+$25

(1+10% )2+

$10

(1+10% )3+

$2

(1+10% )4

PV = $106.81, NPV = $106.81 - $100 = $6.81


+$20

(1+10% )2+

$5

(1+10% )3+

$1

(1+10% )4

PV = $70.97, NPV = $70.97 - $60 = $10.97

Net present value◦ Movie 1

◦ Movie 2

NPV

NPV = $6.81

NPV = $10.97

Which one should you choose?

Since both NPVs > 0, make both movies if you can.

If the studio budget < $160 million, then make Movie 2, because it has a higher

present value

Your company is considering buying out a competitor. It will cost $475,000 to buy the competitor. You estimate that this will improve cash flows to your company as follows:

Problem in class

Year Net cash flow

1 $125,000

2 $175,000

3 $113,000

4 $75,000

5 $42,000

The discount rate is 14%. Q1: What is the PV of the future cash flows?

A. $136,088B. $288,203C. $386,797D. $422,118


Problem in class

The discount rate is 14%. Q1: What is the PV of the future cash flows?

Year Net cash flow CF Button

1 $125,000 CF01

2 $175,000 CF02

3 $113,000 CF03

4 $75,000 CF04

5 $42,000 CF05

PV = $386,797


Problem in class

Year Net cash flow CF Button

1 $125,000 CF01

2 $175,000 CF02

3 $113,000 CF03

4 $75,000 CF04

5 $42,000 CF05

The discount rate is 14%. What is the NPV of the project?

A. -$136,088B. -$ 88,203C. $ 44,192D. $109,385

PV = $386,797

You are considering investing in rental property. The property costs $365,000. You estimate that you can make $50,000 per year in rental income (after expenses). You plan to keep the property for 8 years, and you think you can sell the property for about $550,000 8 years from now.

If the discount rate is 9%, what is the NPV of this project?

Problem in class

A. -$144,874B. -$ 26,649C. $ 76,686D. $187,767

You are considering investing in rental property. The property costs $365,000. You estimate that you can make $50,000 per year in rental income (after expenses). You plan to keep the property for 8 years, and you think you can sell the property for about $550,000 8 years from now.

If the discount rate is 9%, what is the NPV of this project?

Problem in class

A. -$144,874B. -$ 26,649C. $ 76,686D. $187,767

N I PV PMT FV

8 9 ? 50,000 550,000

552,767

𝑁𝑃𝑉=552,767−365,000=187,767

Year Project A Project B

0 -200 -200

1 80 100

2 80 100

3 80 100

4 80 0

Homework problem 8-1

The discount rate is 11%.

What is the NPV of project A?

A. -12.18B. - 4.92C. 25.14D. 48.20


0 -200 -200

1 80 100

2 80 100

3 80 100

4 80 0



What is the NPV of project A?

A. -12.18B. - 4.92C. 25.14D. 48.20

𝑁𝑃𝑉=248.20−200=48.20

PV=248.20


0 -200 -200

1 80 100

2 80 100

3 80 100

4 80 0



What is the NPV of project B?

A. 23.22B. 37.88C. 44.37D. 51.53


0 -200 -200

1 80 100

2 80 100

3 80 100

4 80 0



What is the NPV of project B?

A. 23.22B. 37.88C. 44.37D. 51.53

37

PV=244.37


0 -200 -200

1 80 100

2 80 100

3 80 100

4 80 0



Which project is worth pursuing?

A. Project AB. Project BC. This is a trick questionD. Ask the goddess

𝑁𝑃𝑉 𝐴=48.20 𝑁𝑃𝑉 𝐵=44.37


0 -200 -200

1 80 100

2 80 100

3 80 100

4 80 0



Which project is worth pursuing?

A. Project AB. Project BC. This is a trick questionD. Ask the goddess

𝑁𝑃𝑉 𝐴=48.20 𝑁𝑃𝑉 𝐵=44.37

Since both have a positive NPV, both are worth doing.

Payback period How many years until I get the cost of the

investment back? Example:

◦ A machine costs $10,000 per year to operate◦ I can replace it with a new machine that will only

cost $5,000 per year to operate The new machine costs $15,000

◦ What is the payback period for the new machine?

Capital budgeting

3 years

Problems with the payback method:◦ Ignores cash flows that occur after the payback

period Example: Your company only accepts projects with a

payback period < 3 years. You have a project that costs $50,000 and will

provide the following cash flows:

Payback


$10,000 $10,000 $10,000 $10,000 $1,000,0000

The payback > 3, but the NPV is >>0.

Other problems with the payback method:◦ Ignores the time value of money◦ Leads the firm to accept short term project and

ignore long-term projects of value

The payback period is still often used◦ As a rule of thumb◦ Because it is easy to explain and understand

Payback

Perhaps because quick paybacks lead to quick promotions

NPV ReviewYear Cash flow

1 $9,000

2 $9,000

3 $9,000

4 $9,000

5 $9,000

This project will require an initial investment of $35,000.

If the discount rate is 12%, what is the project’s NPV?

a. -$10,000b. -$ 2,557c. +$ 2,557d. +$10,000

Problem #1


1 $9,000

2 $9,000

3 $9,000

4 $9,000

5 $9,000



a. -$10,000b. -$ 2,557c. +$ 2,557d. +$10,000

PV=$32,443

NPV = $32,443 - $35,000 = -$2,577


1 $9,000

2 $9,000

3 $9,000

4 $9,000

5 $9,000



Using the CF button

CF0 -$35,000

CF01 $9,000

F01 5

I = 12% NPV = -$2,557.014

Problem #2

NPV Review

Year Cash flow

1 $19,000

2 $29,000

3 $15,000

4 $4,000

5 $3,000



a. -$7,091b. -$1,566c. +$1,566d. +$7,091

Problem #2

NPV Review

Year Cash flow

1 $19,000

2 $29,000

3 $15,000

4 $4,000

5 $3,000



a. -$7,091b. -$1,566c. +$1,566d. +$7,091

This project costs $5,000. What is the payback period of the project?

Payback review

Year Cash flow

1 $1,000

2 $1,000

3 $1,000

4 $1,000

5 $1,000

6 $1,000

7 $999,950

a. 3 yearsb. 4 yearsc. 5 yearsd. 7 years


Payback review

Year Cash flow

1 $1,000

2 $1,000

3 $1,000

4 $1,000

5 $1,000

6 $1,000

7 $999,950


Chapter 8 1-4, 13-20

◦ Answers on BB

Quiz Wednesday

Problem in class

NPV Review

Year Cash flow

1 $38,000

2 $19,000

3 $26,000

4 $1,000

5 $5,000



a. -$7,292b. -$4,308c. +$4,308d. +$7,292


Payback review

Year Cash flow

1 $2,000

2 $2,000

3 $3,000

4 $1,000

5 $1,000

6 $1,000

7 $999,950


IRR The internal rate of return is the discount

rate that makes the present value of the future cash flows = the cost of the project◦ Meaning, the rate where NPV = 0

Internal rate of return

IRR Example:

◦ A project costs $5,000 will provide cash flows of $3,000 per year for 3 years

◦ What is the IRR of this project?


$5,000=$3,0001+ 𝐼𝑅𝑅

+$3,000

(1+𝐼𝑅𝑅 )2+$3,000

(1+𝐼𝑅𝑅 )3

Solve this equation for the IRR

No easy way to solve this. Trial and error or use a computer/calculator

IRR Example:

◦ A project costs $5,000 and will provide cash flows of $3,000 per year for 3 years

◦ What is the IRR of this project?


$5,000=$3,0001+ 𝐼𝑅𝑅

+$3,000

(1+𝐼𝑅𝑅 )2+$3,000

(1+𝐼𝑅𝑅 )3

Since the cash flows are constant, this is like an annuity, so you can solve it on the calculator

N I PV PMT FV

3 ? -5,000 3,000 0

36.31%

The cash flows are usually not constant, so these are more difficult to solve

Example:◦ A project costs $75,000 today. The future cash

flows are projected to be:

◦ What is the IRR?


Year 1 Year 2 Year 3

$65,000 $25,000 $10,000

$75,000=$ 65 ,0001+𝐼𝑅𝑅

+$ 25 ,000

(1+ 𝐼𝑅𝑅)2+$10 ,000

(1+ 𝐼𝑅𝑅 )3

Use the calculator


$75,000=$ 65 ,0001+𝐼𝑅𝑅

+$ 25 ,000

(1+ 𝐼𝑅𝑅)2+$10 ,000

(1+ 𝐼𝑅𝑅 )3

IRR = 22.69%

Page 245 of your textbook has an example using your calculator

CF0 -75,000

CF01 65,000

F01 1

CF02 25,000

F02 1

CF03 10,000

IRR CPT

The IRR rule IF

◦ IRR > required return

◦ IRR < required return


This rule works as long as we are not considering mutually exclusive projects.

With mutually exclusive projects, the IRR rule sometimes doesn’t work.

Compare NPVs instead.

What is the IRR of the following project?

IRR Problem

Year CF

0 -150,000

1 50,000

2 40,000

3 30,000

4 25,000

5 25,000

a. 5%b. 6%c. 7%d. 9%

What is the IRR of the following project?

IRR Problem

Year CF

0 -150,000

1 50,000

2 40,000

3 30,000

4 25,000

5 25,000

a. 5%b. 6%c. 7%d. 9%

Project costs $3,000 and will provide cash flows of $800 per year for 6 years.

The discount rate is 10%. What is the PV of the future cash flows?


A. $3,484B. $3,529C. $3,699D. $3,702


The discount rate is 10%. What is the PV of the future cash flows?


A. $3,484B. $3,529C. $3,699D. $3,702

N I PV PMT FV

6 10 ? 800 0

$3,484




A. $484B. $529C. $699D. $702




A. $484B. $529C. $699D. $702

𝑁𝑃𝑉=$3,484−$3,000=$ 484

Mutually exclusive projects◦ Different timing and size of cash flows between

mutually exclusive projects may cause the IRR to give you the wrong conclusion

◦ Example, page 245 of your textbook (r=7%)

Problems with IRR

0 1 2 3

Initial -350,000 400,000 0 0

Revised -375,000 25,000 25,000 475,000

The IRR of the Initial project is: 14.29%

What is the IRR of the revised project?

a. 8.76%b. 9.22%c. 12.56%d. 18.22%


mutually exclusive projects may cause the IRR to give you the wrong conclusion


Problems with IRR

0 1 2 3

Initial -350,000 400,000 0 0

Revised -375,000 25,000 25,000 475,000

What is the IRR of the revised project?a. 8.76%b. 9.22%c. 12.56%d. 18.22%

N I PV PMT FV

3 ? -375000 25,000 450,000

12.56%


the projects may cause the IRR to give you the wrong conclusion


Problems with IRR

0 1 2 3 IRR

Initial -350,000 400,000 0 0 14.29%

Revised -375,000 25,000 25,000 475,000 12.56%

The NPV of the initial project is:

What is the NPV of the revised project? a. 57,942b. 60,888c. 68,540d. 70,500




Problems with IRR

0 1 2 3 IRR

Initial -350,000 400,000 0 0 14.29%

Revised -375,000 25,000 25,000 475,000 12.56%

What is the NPV of the revised project?

N I PV PMT FV

3 7 ? 25,000 450,000

432,942 432,942−375,000=57,942




Problems with IRR

0 1 2 3 IRR NPV

Initial -350,000 400,000 0 0 14.29% +23,832

Revised -375,000 25,000 25,000 475,000 12.56% +57,942

The Initial project has a higher IRR, but a smaller NPV

This is because the interest rates are low enough that the large payment received in year 3 still has considerable PV. This is not true at higher rates.

Because the timing and size of those cash flows are so different, the NPV changes a lot as the discount rate changes◦ The initial proposal gets a lot of cash early, so it is

better at high discount rates◦ The revised proposal gets a lot of cash later, so it

is better at lower discount rates

Problems with IRR

0% 5% 10% 15% 20% 25%

-100,000

-50,000

0

50,000

100,000

150,000

NPV Initial

NPV Revised

Remember: When comparing mutually exclusive projects, focus on the NPVs, because the IRR can lead you to the

wrong decision.

It is possible for a project to have more than one solution to the IRR equation◦ This occurs when the project has both inflows and

outflows of cash (the cash flows change sign)◦ Use the NPV

Problems with the IRR

It is OK to make a yes/no decision about a single project with conventional cash flows using IRR◦ If IRR > Discount rate

◦ If IRR < Discount rate

When comparing mutually exclusive projects, however, it isn’t always correct to pick the one with the higher IRR◦ Compare the NPVs

IRR

Project selection

Connect problem

Which mutually exclusive project would you select, if both are priced at $1,000 and your discount rate is 15%: Project A with three annual cash flows of $1,000; or project B, with 3 years of zero cash flow followed by 3 years of $1,500 annually? A. Project A.B. Project B.C. You are indifferent since the NPVs are equal.D. Neither project should be selected.

Find the NPV of each project and choose the one with the higher NPV

Project selection, both cost $1,000

Connect problem

Project A Project B

$1,000 $0

$1,000 $0

$1,000 $0

$1,500

$1,500

$1,500

N I PV PMT FV

3 15% ? $1,000 0

$2,283.23

Project A

NPV = $1,283.23


Connect problem

Project A Project B

$1,000 $0

$1,000 $0

$1,000 $0

$1,500

$1,500

$1,500

N I PV PMT FV

3 15% ? $1,500 0

$3,424.84

Project B

$ 3,424.84

(1+15%)3=$2,251.89

NPV = $1,251.89


Connect problem

Project NPV

A $1,283.23

B $1,251.89

NPVA > NPVB, so choose project A

Example page 236 Your need to buy a new machine. You can

choose between to models:

◦ Rates are 6%. Which is the better deal?◦ We cannot compare NPVs in this case, because

the machines have unequal lives We will have to buy another the Budget model in 2

years, another Deluxe model in 3.

Long vs. short lived equipment

Cost 1 2 3

Deluxe $15,000 4 4 4

Budget $10,000 6 6 -

Equivalent annual annuity◦ Find the annual operating cost of each machine◦ What is the average annual cost of operating

each machine?◦ Machine A costs $15,000 today, then $4,000 per

year for 3 years. This is a total cost today of:

◦ If you were going to spread this cost out equally over 3 years, you would have 3 annual payments with a PV of $25,692

Equivalent annual annuity

𝑃𝑉=15,000+$ 4,0001+6%

+$ 4,000

(1+6% )2+$ 4,000

(1+6%)3=$ 25,692

N I PV PMT FV

3 6 -25,692 ? 0$9,611

Equivalent annual annuity◦ Machine B costs $10,000 today, then $6,000 per

year for 2 years. This is a total cost today of:

◦ If you were going to spread this cost out equally over 2 years, you would have 2 annual payments with a PV of $21,000

Projects with different lives

𝑃𝑉=10,000+$6 ,0001+6%

+$ 6 ,000

(1+6% )2=$ 21,000

N I PV PMT FV

2 6 -21,000 ? 0

$11,454

The Deluxe cost is $9,610 per year, so it is a better deal.

Problem 3, page 238 in the textbook◦ Old machine

Will last 2 more years, costs $12,000 per year◦ New machine

Costs $25,000 now, then $8,000 per year, lasts 5 yrs R = 6%

Replace an old machine

N I PV PMT FV

5 6 ? 8,000 0

$33,699

New machine

What is the equivalent annual cost of the new machine?

This is the PV of the future costs

Should you buy the new machine now, or wait two more years?





N I PV PMT FV

5 6 $58,698 ? 0

$33,699

New machine

This is the PV of the future costs

Equivalent annual annuity will spread the operating costs plus the purchase cost over the life of the machine

$13,935





Machine Annual costs

Old $12,000

New $13,935

The new machine will cost more per year, so keep the old machine

What is the equivalent annual annuity (EAA) for a machine that costs $15,000 to purchase today, costs $4,000 per year to operate, and is expected to last for 6 years?◦ Rates are 9%.

Problem in class

a. $6,588b. $7,012c. $7,344d. $8,122

1. Find the PV of the future costs

2. Add (1) to the cost to purchase to get the total cost today

3. Find the PMT you can get from (2)


Problem in class

a. $6,588b. $7,012c. $7,344d. $8,122

N I PV PMT FV

6 9 ? 4000 0

PV of future payments

$17,943.67


Problem in class

a. $6,588b. $7,012c. $7,344d. $8,122


$17,943.67

$15,000 + $17,943.67 = $32,943.67

Total cost today


Problem in class

a. $6,588b. $7,012c. $7,344d. $8,122

N I PV PMT FV

6 9 32,943.67 ? 0


$17,943.67

EAA of all costs

$15,000 + $17,943.67 = $32,943.67

Total cost today

What is the minimum cash flow that could be received at the end of year 3 to make the following project “acceptable”?◦ Initial cost = $100,000◦ Cash flow end of year 1 = $ 35,000◦ Cash flow end of year 2 = $ 35,000◦ Cash flow end of year 3 = $ ?

◦ The discount rate = 10%.

Connect problem

To make the project acceptable, the NPV > 0.

PV(future cash flows) – Cost today > 0

What is the minimum cash flow that could be received at the end of year 3 to make the following project “acceptable”?◦ Initial cost = $100,000◦ Cash flow end of year 1 = $ 35,000◦ Cash flow end of year 2 = $ 35,000◦ Cash flow end of year 3 = $ ?

◦ The discount rate = 10%.

Connect problem

𝐶𝐹 3

(1+10% )3+ $35,000

(1+10% )2+ $35,0001+10%

−$100,000=0

𝐶𝐹 3

(1+10% )3=$39,265.20→𝐶𝐹 3=$52,250

If a project’s IRR is 13% and the project provides annual cash flows of $15,000 for 4 years, how much did the project cost?◦ Remember that the IRR is the rate when NPV = 0◦ So in the case, when the discount rate = 13%

The cost = PV(4 payments of $15,000)

Connect problem

N I PV PMT FV

4 13 ? 15,000 0

44,617

Your car requires a lot of Maintenance◦ $4,000 per year◦ But it is paid for

◦ You can replace it with a new car that costs $8,000. The new car with require $X in maintenance per year

◦ If you expect both vehicles to last 4 more years, how high can X be and it still be worth buying the new car?

Connect problem

Rates = 8%

Connect problem

$4,000 per year $8,000 today, $X per year

You know the total cost per year of the old car: $4,000

You want to compare that to the cost per year of the new car

The EAA of the new car must be < $4,000

Rates = 8%

Connect problem


The cost of the car today is $8,000. The EAA from this amount is:

N I PV PMT FV

4 8 8,000 ? 0

Rates = 8%

$2,415.37

This is the equivalent cost per year of the new car based only on its purchase price

Connect problem


The cost of the car today is $8,000. The EAA from this amount is:

Rates = 8%

EAA from only the purchase price: $2,415.37

The new car must cost less than $4,000 per year to operate

So the most you could spend on annual maintenance is:

$4,000 - $2,415.37 = $1,584.63Any more, and the new car is not worth it.

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