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```									Lesson 17
Example

Should we make the building more energy efficient?
At a cost of \$300,000, an office building can be made more energy efficient. It is estimated that the company owning the building will save \$20,000 per year in energy costs. The building will last for 20 more years.

Lesson 17
CAPITAL BUDGETING

1. Payback period
\$300,000 cost / \$20,000 annual savings = 15 years to recover the initial cost

2. Unadjusted rate of return (or accounting rate of return)
Net income increase of \$20,000 from energy cost savings. Net income decrease of \$15,000 (\$300,000 / 20 years) from depreciation. \$20,000 - \$15,000 = net income increase of \$5,000 per year. Unadjusted rate of return \$5,000 annual net income increase/\$300,000 initial investment = 1.7%

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2

Should we make the building more energy efficient?
At a cost of \$300,000, an office building can be made more energy efficient. It is estimated that the company owning the building will save \$20,000 per year in energy costs. The building will last for 20 more years.

Example

N

I

PV

PMT

FV

where
N

3. What is the present value of the energy savings? Assume that the interest rate is 10%.
A \$20,000 energy savings this year is worth more, in terms of the time value of money, than a \$20,000 energy savings to occur 20 years from now. It is incorrect to say that the energy efficiency investment of \$300,000 will ultimately save \$400,000. (\$20,000 per year × 20 years) Compute the present value of the \$20,000 savings each year for 20 years.

is the number of periods involved. is the interest rate per period. is the present value of the cash flows. is the amount of a series of equal payments made each period. is the future value of the cash flows.

I

PV

PMT

FV

3

4

Should we make the building more energy efficient?
At a cost of \$300,000, an office building can be made more energy efficient. It is estimated that the company owning the building will save \$20,000 per year in energy costs. The building will last for 20 more years.

Example

Example

Should we make the building more energy efficient?
At a cost of \$300,000, an office building can be made more energy efficient. It is estimated that the company owning the building will save \$20,000 per year in energy costs. The building will last for 20 more years.

3. What is the present value of the energy savings? Assume that the interest rate is 10%.
Clear memory:
C ALL

3. What is the present value of the energy savings? Assume that the interest rate is 10%.

20 10 20,000 0

N

: 20 because the length of the cash savings interval is 20 years. : 10% which was given as the appropriate interest rate. : \$20,000 which is the amount of the annual cash savings. : \$0 because there is no additional cash savings at the end of the project. : For the answer.

I
PMT FV PV

Net Present Value = Present value of the cash inflows minus (or NPV) present value of the cash outflows. = \$170,271 - \$300,000 = negative \$129,729

\$170,271

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17-1

Example

Should we make the building more energy efficient?
At a cost of \$300,000, an office building can be made more energy efficient. It is estimated that the company owning the building will save \$20,000 per year in energy costs. The building will last for 20 more years.

Four different capital budgeting techniques:

1. Payback period 2. Unadjusted rate of return 3. Net present value, or NPV 4. Internal rate of return, or IRR

4. After adjusting for the time value of money, what rate of return will be earned on the \$300,000 investment in energy efficiency equipment? C ALL Clear memory:

300,000 +/20,000 20 0

PV

: Negative \$300,000 to represent the initial cash outflow.

PMT : Positive \$20,000 which is the amount of the annual cash inflow. N FV

: 20 because the length of the cash savings interval is 20 years. : \$0 because there is no additional cash savings at the end of the project. : For the answer.

I

2.91%

INTERNAL RATE OF RETURN (or IRR)

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Example

Example

Buying a Weekend Car in Hong Kong
A few years ago my family and I lived in Hong Kong. When we arrived, we considered buying a car. We didn't really want a good car; we just intended to use it for family trips on weekends. We found that the cost of a cheap weekend car was HK\$40,000.
Note: There are about 7.7 Hong Kong dollars to one U.S. dollar, so HK\$40,000 is the equivalent of \$5,195.

Buying a Weekend Car in Hong Kong
A few years ago my family and I lived in Hong Kong. When we arrived, we considered buying a car. We didn't really want a good car; we just intended to use it for family trips on weekends. We found that the cost of a cheap weekend car was HK\$40,000.
Note: There are about 7.7 Hong Kong dollars to one U.S. dollar, so HK\$40,000 is the equivalent of \$5,195.

We estimated that our family of seven could save HK\$10,000 per year in bus, taxi, and MTR (subway) costs by buying the weekend car. The car was expected to last for 5 years. Should we have purchased the car?

We estimated that our family of seven could save HK\$10,000 per year in bus, taxi, and MTR (subway) costs by buying the weekend car. The car was expected to last for 5 years. Should we have purchased the car?

1. Payback period
HK\$40,000 cost / HK\$10,000 annual savings = 4 years to recover the cost of the car

3. Net Present Value (NPV)

Clear memory:

C ALL

2. Unadjusted rate of return (or accounting rate of return)
Net income increase of HK\$10,000 from energy cost savings. Net income decrease of HK\$8,000 (HK\$40,000 / 5 years) from depreciation. HK\$10,000 - HK\$8,000 = net income increase of HK\$2,000 per year. Unadjusted rate of return: \$HK\$2,000 annual net income increase/HK\$40,000 initial investment = 5.0%

5 10 10,000 0

N

: 5 years : 10% : HK\$10,000 which is the amount of the annual cash savings. : \$0 because there is no additional cash savings at the end of the project. : For the answer.

I
PMT FV PV

HK\$37,908

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Example

Buying a Weekend Car in Hong Kong
A few years ago my family and I lived in Hong Kong. When we arrived, we considered buying a car. We didn't really want a good car; we just intended to use it for family trips on weekends. We found that the cost of a cheap weekend car was HK\$40,000.
Note: There are about 7.7 Hong Kong dollars to one U.S. dollar, so HK\$40,000 is the equivalent of \$5,195.

Example

Buying a Weekend Car in Hong Kong
A few years ago my family and I lived in Hong Kong. When we arrived, we considered buying a car. We didn't really want a good car; we just intended to use it for family trips on weekends. We found that the cost of a cheap weekend car was HK\$40,000.
Note: There are about 7.7 Hong Kong dollars to one U.S. dollar, so HK\$40,000 is the equivalent of \$5,195.

We estimated that our family of seven could save HK\$10,000 per year in bus, taxi, and MTR (subway) costs by buying the weekend car. The car was expected to last for 5 years. Should we have purchased the car?

We estimated that our family of seven could save HK\$10,000 per year in bus, taxi, and MTR (subway) costs by buying the weekend car. The car was expected to last for 5 years. Should we have purchased the car?

3. Net Present Value (NPV)

4. Internal Rate of Return (IRR)

Clear memory:

C ALL

Net Present Value = Present value of the cash inflows minus (or NPV) present value of the cash outflows. = HK\$37,908 - HK\$40,000 = negative HK\$2,092

40,000 10,000 5 0

+/-

PV

: Negative HK\$40,000 to represent the initial cash outflow. inflow.

PMT : Positive HK\$10,000 which is the amount of the annual cash N FV

: 5 because the expected life of the car is 5 years. : \$0 because there is no additional cash savings at the end of the project. : For the answer.

I

7.93%

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17-2

Example

Buying a Weekend Car in Hong Kong
A few years ago my family and I lived in Hong Kong. When we arrived, we considered buying a car. We didn't really want a good car; we just intended to use it for family trips on weekends. We found that the cost of a cheap weekend car was HK\$40,000.
Note: There are about 7.7 Hong Kong dollars to one U.S. dollar, so HK\$40,000 is the equivalent of \$5,195.

Review of time value of money calculations
The essence of the concept of the time value of money is as follows:
A dollar received now is worth more than a dollar to be received in the future because the dollar received now can be invested and will grow in value. For example, if the interest rate is 10%, receiving a dollar now is the same as receiving \$1.10 one year from now; the dollar received now can be invested and will have grown in value to \$1.10 by the end of the year.

We estimated that our family of seven could save HK\$10,000 per year in bus, taxi, and MTR (subway) costs by buying the weekend car. The car was expected to last for 5 years. Should we have purchased the car?

1. Payback period: 4 years to recover the cost of the car. 2. Unadjusted rate of return (or accounting rate of return): 5.0% 3. Net Present Value (NPV):

\$1.00 Now

\$1.10 One Year

Negative HK\$2,092
4. Internal Rate of Return (IRR): 7.93%

Present Value = \$1.00 Interest Rate = 10%

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Computing the present value of a single amount
1. What is the present value of \$10,000 to be received 4 years from now if the interest rate is 12%?
??? Now Year 1 Year 2 Year 3 \$10,000 Year 4

Examples

Examples

Computing the present value of a single amount
2. What is the present value of \$100,000 to be received 25 years from now if the interest rate is 14%?
??? Now Year 1 Year 2 Year 3 \$100,000 Year 25

To compute the present value, we input the following into the calculator:
Clear memory:
C ALL

To compute the present value, we input the following into the calculator:
Clear memory:
C ALL

4 12 0 10,000

N

: 4 because the time until we receive the cash is 4 years. : 12% which was given as the appropriate interest rate. : \$0 because this is a one-time cash flow, not a series of equal cash flows. : \$10,000 because this is the amount of cash we will receive in the future. : For the answer.

I
PMT FV PV

25 14 0 100,000

N

: 25 because the time until we receive the cash is 25 years. : 14% which was given as the appropriate interest rate. : \$0 because this is a one-time cash flow, not a series of equal cash flows. : \$100,000 because this is the amount of cash we will receive in the future. : For the answer.

I
PMT FV PV

\$6,355

\$3,779

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Examples

Examples

Computing the present value of an annuity, or series of equal payments
1. What is the present value of \$10,000 to be received at the end of each year for the next 4 years? The interest rate is 7%.
??? Now \$10,000 Year 1 \$10,000 Year 2 \$10,000 Year 3 \$10,000 Year 4

Computing the present value of an annuity, or series of equal payments
2. You expect to receive \$8,000 at the end of each year for the next 4 years. In addition, you expect to receive an additional payment of \$25,000 at the end of 4 years. What is the present value of these payments? The interest rate is 11%.
??? Now \$8,000 Year 1 \$8,000 Year 2 \$8,000 Year 3 \$25,000 \$8,000 Year 4

To compute the present value, we input the following into the calculator:
Clear memory:
C ALL

To compute the present value, we input the following into the calculator:
Clear memory:
C ALL

4 7 10,000 0

N

: 4 because four equal payments are expected in the future. : 7% which was given as the appropriate interest rate. : \$10,000 which is the amount of each equal cash flow. : \$0 because no extra amount is received at the end of 4 years when the final annuity payment of \$10,000 is received. : For the answer.

I
PMT FV PV

4 11 8,000 25,000

N

: 4 because four equal payments are expected in the future, and the additional payment occurs at the end of 4 years. : 11% which was given as the appropriate interest rate. : \$8,000 which is the amount of each equal cash flow. : \$25,000 which is the amount of the extra payment at the end of 4 years. : For the answer.

I
PMT FV PV

\$33,872

\$41,288

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17-3

Examples

Examples

Computing the internal rate of return
1. You have \$10,000 you wish to invest in an account. You want to be able to withdraw \$15,000 from the account at the end of 5 years. What rate of return on the account would make this possible?
\$10,000 Now Year 1 Year 2 Year 3 Year 4 \$15,000 Year 5

Computing the internal rate of return
2. You have \$100,000 you wish to invest in one of two business projects. Project 1 will pay you a lump sum of \$220,000 at the end of 10 years. Project 2 will pay you \$17,000 at the end of each year for 10 years. Which project offers the higher internal rate of return?
\$100,000 \$220,000 Year 1 Year 2 Year 3 Year 10

Project 1:
Now

To compute the internal rate of return, we input the following into the calculator:
Clear memory:
C ALL

To compute the internal rate of return on Project 1, we input the following into the calculator:
Clear memory:
C ALL

10,000

+/-

PV

: Negative \$10,000 to represent the initial cash outflow.

0 5 15,000

PMT : \$0 because we are not expecting yearly withdrawals. N FV

100,000

+/-

PV

: Negative \$100,000 to represent the initial cash outflow.

: 5 because we want to be able to withdraw the \$15,000 at the end of 5 years. : \$15,000 because this is the amount of the cash inflow at the end of 5 years. : For the answer.

0 10 220,000

PMT : \$0 because we are not expecting yearly cash flows. N FV

: 10 because we expect the \$220,000 cash flow at the end of 10 years. : \$220,000 because this is the amount of the cash inflow at the end of 10 years. : For the answer.

I

8.45%

8.20%

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Computing the internal rate of return
2. You have \$100,000 you wish to invest in one of two business projects. Project 1 will pay you a lump sum of \$220,000 at the end of 10 years. Project 2 will pay you \$17,000 at the end of each year for 10 years. Which project offers the higher internal rate of return?
\$100,000 \$17,000 Year 1 \$17,000 Year 2 \$17,000 Year 3 \$17,000 Year 10

Examples

Examples

Computing the internal rate of return
2. You have \$100,000 you wish to invest in one of two business projects. Project 1 will pay you a lump sum of \$220,000 at the end of 10 years. Project 2 will pay you \$17,000 at the end of each year for 10 years. Which project offers the higher internal rate of return?

Project 2:
Now

Project 2
IRR = 11.03% Total Cash Inflow = \$170,000 (\$17,000 x 10 years)

To compute the internal rate of return on Project 2, we input the following into the calculator:
Clear memory:
C ALL

100,000 +/17,000 10 0

PV

: Negative \$100,000 to represent the initial cash outflow.

PMT : \$17,000 because this is the amount of the yearly cash inflows. N FV

: 10 because we expect the \$17,000 yearly cash inflows for 10 years. : \$0 because there is no extra cash inflow at the end of 10 years. : For the answer.

Project 1
IRR = 8.20% Total Cash Inflow = \$220,000

I

11.03%

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Problem 17-1

Review of present value calculations
Compute the following: 1. The present value of \$40,000 to be received 8 years from now if the interest rate is 15%. 2. The present value of \$40,000 to be received 8 years from now if the interest rate is 9%. 3. The present value of \$21,000 to be received at the end of each year for the next 50 years if the interest rate is 18%. 4. The present value of \$21,000 to be received at the end of each year for the next 60 years if the interest rate is 18%. 5. The internal rate of return on a business project that requires an initial investment of \$600,000. The project will generate cash flows of \$75,000 at the end of each year for the next 14 years. 6. The internal rate of return on a business project that requires an initial investment of \$600,000. The project will generate cash flows of \$105,000 at the end of each year for the next 10 years.

Review of present value calculations
1. The present value of \$40,000 to be received 8 years from now if the interest rate is 15%.
??? Now Year 1 Year 2 Year 3 \$40,000 Year 8

To compute the present value, we input the following into the calculator:
Clear memory:
C ALL

8 15 0 40,000

N

: 8 because the time until we receive the cash is 8 years. : 15% which was given as the appropriate interest rate. : \$0 because this is a one-time cash flow, not a series of equal cash flows. : \$40,000 because this is the amount of cash we will receive in the future. : For the answer.

I
PMT FV PV

\$13,076

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17-4

Review of present value calculations
2. The present value of \$40,000 to be received 8 years from now if the interest rate is 9%.
??? Now Year 1 Year 2 Year 3 \$40,000 Year 8

Review of present value calculations
3. The present value of \$21,000 to be received at the end of each year for the next 50 years if the interest rate is 18%.
??? Now \$21,000 Year 1 \$21,000 Year 2 \$21,000 Year 3 \$21,000 Year 50

To compute the present value, we input the following into the calculator:
Clear memory:
C ALL

To compute the present value, we input the following into the calculator:
Clear memory:
C ALL

8 9 0 40,000

N

: 8 because the time until we receive the cash is 8 years. : 9% which was given as the appropriate interest rate. : \$0 because this is a one-time cash flow, not a series of equal cash flows. : \$40,000 because this is the amount of cash we will receive in the future. : For the answer.

I
PMT FV PV

50 18 21,000 0

N

: 50 because fifty equal payments are expected in the future. : 18% which was given as the appropriate interest rate. : \$21,000 which is the amount of each equal cash flow. : \$0 because no extra amount is received at the end of 50 years when the final annuity payment of \$21,000 is received. : For the answer.

I
PMT FV PV

\$20,075

\$116,637

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Review of present value calculations
4. The present value of \$21,000 to be received at the end of each year for the next 60 years if the interest rate is 18%.
??? Now \$21,000 Year 1 \$21,000 Year 2 \$21,000 Year 3 \$21,000 Year 60 Now

Review of present value calculations
5. The internal rate of return on a business project that requires an initial investment of \$600,000. The project will generate cash flows of \$75,000 at the end of each year for the next 14 years.
\$600,000 \$75,000 Year 1 \$75,000 Year 2 \$75,000 Year 3 \$75,000 Year 14

To compute the present value, we input the following into the calculator:
Clear memory:
C ALL

To compute the internal rate of return on the project, we input the following into the calculator:
Clear memory:
C ALL

60 18 21,000 0

N

: 60 because fifty equal payments are expected in the future. : 18% which was given as the appropriate interest rate. : \$21,000 which is the amount of each equal cash flow. : \$0 because no extra amount is received at the end of 60 years when the final annuity payment of \$21,000 is received. : For the answer.

I
PMT FV PV

600,000 +/75,000 14 0

PV

: Negative \$600,000 to represent the initial cash outflow.

PMT : \$75,000 because this is the amount of the yearly cash inflows. N FV

: 14 because we expect the \$75,000 yearly cash flows for 14 years. : \$0 because there is no extra cash inflow at the end of 14 years. : For the answer.

\$116,661

8.52%

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Review of present value calculations
6. The internal rate of return on a business project that requires an initial investment of \$600,000. The project will generate cash flows of \$105,000 at the end of each year for the next 10 years.
\$600,000 Now \$105,000 Year 1 \$105,000 Year 2 \$105,000 Year 3 \$105,000 Year 10

Payback Period and Unadjusted Rate of Return
Capital Budgeting Technique Computation Decision Rule

Payback Period

Compute the length of time until total net cash inflow equals the initial investment cost. Compute the additional yearly accounting earnings, divided by the initial investment cost.

Accept the project if the computed payback period is less than a predetermined length of time. Accept the project if the computed unadjusted rate of return is greater than a predetermined percentage.

To compute the internal rate of return on the project, we input the following into the calculator:
Clear memory:
C ALL

600,000 +/105,000 14 0

PV

: Negative \$600,000 to represent the initial cash outflow.

PMT : \$105,000 because this is the amount of the yearly cash inflows. N FV

: 10 because we expect the \$105,000 yearly cash flows for 10 years. : \$0 because there is no extra cash inflow at the end of 10 years. : For the answer.

Advantages: Easy to understand and easy to compute. Disadvantage: Do not take into account the time value of money.

Net Present Value
and

11.73%

Internal Rate of Return

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17-5

Payback Period
Project A costs \$50,000 and will provide net cash inflows each year of \$10,000. Is Project A a good project?
\$50,000 cost = 5 years to recover the initial cost \$10,000 annual net cash inflow

Example: You are considering purchasing a new machine to increase your production. The machine costs \$80,000. Operation of the machine will generate cash revenues of \$40,000 per year and cash expenses of \$12,000. The machine is expected to last for 10 years. The estimated impact of this machine on annual net income is computed as follows. Net income increase of \$28,000 (\$40,000 - \$12,000) from the cash revenues and expenses. Net income decrease of \$8,000 (\$80,000 / 10 years) from depreciation. \$28,000 - \$8,000 = net income increase of \$20,000 per year.

Is 5 years a sufficiently quick payback period? Well, that depends on the nature of the project. Consider the following two scenarios.
Scenario 1: Project A is an investment in an office building. The cash inflows will come from annual rent payments to be received. Scenario 2: Project A is an investment in a Web-based order tracking system that is expected to save \$10,000 each year in order tracking costs.

\$20,000 annual net income increase = 25% \$80,000 initial investment

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Problem 17-2

Computation of payback period and unadjusted rate of return For each of the following long-term projects, compute: (a) the payback period and (b) the unadjusted rate of return. Also, for each project state whether you think that the company should or should not undertake the project:
Annual Cash Revenues Annual Cash Expenses

Computation of payback period and unadjusted rate of return
a. Computation of payback period:
Initial Cost Annual Cash Revenues Annual Cash Expenses Annual Net Cash Inflow Payback Period [Cost / Inflow]

Project 1 Project 2 Project 3 Project 4

\$100,000 400,000 700,000 800,000

\$45,000 50,000 110,000 205,000

\$30,000 5,000 40,000 15,000

\$15,000 45,000 70,000 190,000

6.7 years 8.9 years 10.0 years 4.2 years

Initial Cost

Project Life

b. Computation of unadjusted rate of return:
Initial Cost Annual Net Cash Inflow Project Life Annual Depreciation [Cost/Life] Increase in Annual Net Income

Project 1 Project 2 Project 3 Project 4

\$100,000 400,000 700,000 800,000

\$45,000 50,000 110,000 205,000

\$30,000 5,000 40,000 15,000

8 years 10 years 10 years 20 years
Project 1 Project 2 Project 3 Project 4

\$100,000 400,000 700,000 800,000

\$15,000 45,000 70,000 190,000

8 years 10 years 10 years 20 years

\$12,500 40,000 70,000 40,000

\$2,500 5,000 0 150,000

2.50% 1.30% 0.00% 18.80%

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Computation of payback period and unadjusted rate of return
For each project state whether you think that the company should or should not undertake the project:
Answer: Project 1 and Project 2 both have relatively long payback periods compared to the total expected life of the projects. This is confirmed by the low unadjusted rates of return for both projects (2.5% and 1.3%). Project 3 is even worse; the payback period is exactly the same length of time as the expected project life, so even if the projects lasts as long as it is expected to last, you still will have just barely recovered your initial investment in the project. This bad news is confirmed with an unadjusted rate of return of 0.0%. So these numbers suggest that you should reject Project 1, Project 2, and Project 3. Project 4 has a quick payback period of just 4.2 years, especially compared to the 20-year expected life of the project. Project 4 also has a relatively high unadjusted rate of return of 18.8%. These numbers suggest that it is a good idea to go ahead with Project 4.

Net Present Value
Capital Budgeting Technique Computation Decision Rule

Net Present Value (NPV)

Compute the present value of all cash inflows and outflows and add them together.

Accept the project if the net present value (NPV) is greater than zero.

There are five general steps associated with Net Present Value (NPV) analysis. 1. Estimate the amount and timing of all cash inflows and outflows associated with the project. 2. Evaluate the riskiness of the project in order to select an appropriate required rate of return. 3. Use time value of money calculations to adjust all cash flows to a common point in time in order to make the cash flows comparable. "Now" is the point in time traditionally used. 4. Add up the discounted cash flows. 5. Make a decision. If the total of the discounted cash flows is positive, the project is a good one, meaning that it generates an above-normal return and thus adds value to the company.

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17-6

1. Estimate the amount and timing of all cash inflows and outflows associated with the project.
Since we can't tell the future the best we can do is estimate the amount and timing of all future cash flows. This requires a very thorough understanding of: the project. the market for my products. the markets for my raw materials. my workers. other important inputs into my production process.

2. Evaluate the riskiness of the project in order to select an appropriate required rate of return.
High Risk: A project that could result in very good cash flows or very bad cash flows.
Example: Developing commercial spacecraft to cater to space tourists.

Evaluated using: High Intrest Rates. Low Risk: A project that will result in about the same cash flows no matter whether things turn out very well or very poorly is said to have .
Example: Building a McDonald's location in a high-traffic area.

Evaluated using: Low Intrest Rates. We will usually just assume a certain interest rate, although we will briefly discuss one technique (the weighted-average cost of capital) that is used in computing an interest rate that can be used in an NPV analysis.

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3. Use time value of money calculations to adjust all cash flows to a common point in time in order to make the cash flows comparable.
"Now" is the point in time traditionally used.
The reason we compute the present value of the cash flows is that we need to line up all of the cash flows at the same point in time for them to be comparable. Remember that the key insight of the concept of the time value of money is that a dollar in cash flow today is not the same as a dollar in cash flow next year, and is certainly not the same as a dollar in cash flow 20 years from now. By using time value of money computations to adjust all of the cash flows to a common point in time, we can then be comfortable about comparing them. When first doing an NPV analysis, many students grasp the importance of the time value of money computations, but they want to compute the value of all of the cash flows as of the END of the project rather than as of the beginning of the project. NFV (or Net Future Value) Analysis The reason that we do an NPV, or present value, analysis rather than an NFV, or future value, analysis, is twofold:
1. The tradition for NPV analysis is deeply ingrained. 2. An NPV analysis makes sense because it involves computing the value of all of the project's cash flows in terms of "right now" dollars.

4. Add up the discounted cash flows.
We learned how to do this years ago in second grade.

We just add up the numbers.
Be careful to treat:

The cash outflows as negative numbers. and The cash inflows as positive numbers.

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5. Make a decision. If the total of the discounted cash flows is positive, the project is a good one, meaning that it generates an above-normal return and thus adds value to the company.
A positive NPV project; is one that we should do. The project earns a normal rate of return, as represented by the interest rate used in the present value calculations, plus some extra. A negative NPV project; is one that we should not do because it earns less than a normal rate of return. A NPV of exactly zero; should we do it or not? For a zero NPV project, it doesn't matter whether the company does it or not; the project earns a normal rate of return, but we could get that same return from any number of other "normal" projects. Another way to interpret the amount of a project's NPV is that this is the amount by which the value of the entire company changes the instant that the decision is made to go forward with the project. The theoretical value of a company is the present value of the future cash flows expected to be generated by the company. The instant that a company decides to undertake a positive NPV project, the present value of the future cash flows to be generated by that company have increased, so the value of the company itself increases.

Purchase of equipment
Ryan Company is considering whether to invest in a piece of equipment that requires an investment of \$500,000 today. The project will provide net operating cash inflows of \$150,000 at the end of each year for five years, and it will have a salvage value of \$0 at the end of five years. Ryan Company uses straight-line depreciation. The appropriate interest rate is 10%.
(\$500,000) Now \$150,000 Year 1 \$150,000 Year 2 \$150,000 Year 3 \$150,000 Year 4 \$150,000 Year 5

Example

The present value of the annuity of \$150,000 for 5 years is computed as follows. Clear memory:
C ALL

5 10 150,000 0

N

: 5 because five equal payments are expected in the future. : 10% which was given as the appropriate interest rate.

I

PMT : \$150,000 which is the amount of each equal cash flow. FV PV

: \$0 because no extra amount is received at the end of 5 years when the final annual cash inflow of \$150,000 is generated. : For the answer.

\$568,618

41

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17-7

Example

Example

Purchase of equipment
Ryan Company is considering whether to invest in a piece of equipment that requires an investment of \$500,000 today. The project will provide net operating cash inflows of \$150,000 at the end of each year for five years, and it will have a salvage value of \$0 at the end of five years. Ryan Company uses straight-line depreciation. The appropriate interest rate is 10%.
(\$500,000) Now \$150,000 Year 1 \$150,000 Year 2 \$150,000 Year 3 \$150,000 Year 4 \$150,000 Year 5 Now

Purchase of a doughnut-making machine
Franklin Bakery is considering buying a new doughnut-making machine. The cost of the machine is \$10,000. The machine will last for ten years and is expected to be worth \$1,000 as scrap at that time. The new machine will reduce operating costs by \$700 per year. In addition, the new machine will allow for an increase in production of 10,000 doughnuts per year. Franklin makes 10 cents in contribution margin on each doughnut it sells. The required rate of return on this project is 16 percent.
(\$10,000) \$1,000 \$700 Year 1 \$1,000 \$700 Year 2 \$1,000 \$700 Year 3 Salvage value of \$1,000 \$1,000 \$700 Year 10

The present value calculations with respect to this piece of equipment are summarized in this table.
Interest rate is 10% Amount Present Value

\$700 Annual Cost Savings:

Clear memory:

C ALL

Original Cost (\$500,000 now) Net cash inflows (\$150,000 per year) Net Present Value (or NPV)

(500,000) \$150,000 × 5 yrs

(500,000) 568,618 68,618

10 16 700 0

N

: 10 because ten equal payments are expected in the future. : 16% which was given as the appropriate interest rate.

I

PMT : \$700 which is the amount of each equal cost savings cash inflow. FV PV

: \$0 because no extra cost savings is realized at the end of 10 years when the final cost savings amount of \$700 is generated. : For the answer.

Depreciation expense each year is \$100,000 (\$500,000 cost / 5-year life).

\$3,383

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44

Purchase of a doughnut-making machine
Franklin Bakery is considering buying a new doughnut-making machine. The cost of the machine is \$10,000. The machine will last for ten years and is expected to be worth \$1,000 as scrap at that time. The new machine will reduce operating costs by \$700 per year. In addition, the new machine will allow for an increase in production of 10,000 doughnuts per year. Franklin makes 10 cents in contribution margin on each doughnut it sells. The required rate of return on this project is 16 percent.
(\$10,000) Now \$1,000 \$700 Year 1 \$1,000 \$700 Year 2 \$1,000 \$700 Year 3 Salvage value of \$1,000 \$1,000 \$700 Year 10

Example

Example

Purchase of a doughnut-making machine
Franklin Bakery is considering buying a new doughnut-making machine. The cost of the machine is \$10,000. The machine will last for ten years and is expected to be worth \$1,000 as scrap at that time. The new machine will reduce operating costs by \$700 per year. In addition, the new machine will allow for an increase in production of 10,000 doughnuts per year. Franklin makes 10 cents in contribution margin on each doughnut it sells. The required rate of return on this project is 16 percent.
(\$10,000) Now \$1,000 \$700 Year 1 \$1,000 \$700 Year 2 \$1,000 \$700 Year 3 Salvage value of \$1,000 \$1,000 \$700 Year 10

\$1,000 Annual Contribution Margin Increase:

Clear memory:

C ALL

The \$1,000 salvage value at the end of 10 years is a one-time cash inflow. The present value of this cash inflow is computed as follows.

10 16 1,000 0

N

: 10 because ten equal payments are expected in the future. : 16% which was given as the appropriate interest rate.

Clear memory:

C ALL

I

PMT : \$1,000 which is the amount of each annual increase in contribution margin. FV PV

: \$0 because no extra contribution margin is realized at the end of 10 years when the final increased contribution margin amount of \$1,000 is generated. : For the answer.

10 16 0 1,000

N

: 10 because the time until we receive the salvage value is 10 years. : 16% which was given as the appropriate interest rate.

I

PMT : \$0 because this is a one-time cash flow, not a series of equal cash flows. FV

: \$1,000 because this is the amount of cash we will receive in the future. : For the answer.

\$4,833

\$227

45

46

Example

Purchase of a doughnut-making machine
Franklin Bakery is considering buying a new doughnut-making machine. The cost of the machine is \$10,000. The machine will last for ten years and is expected to be worth \$1,000 as scrap at that time. The new machine will reduce operating costs by \$700 per year. In addition, the new machine will allow for an increase in production of 10,000 doughnuts per year. Franklin makes 10 cents in contribution margin on each doughnut it sells. The required rate of return on this project is 16 percent.
(\$10,000) Now \$1,000 \$700 Year 1 \$1,000 \$700 Year 2 \$1,000 \$700 Year 3 Salvage value of \$1,000 \$1,000 \$700 Year 10

Computation of the Weighted-Average Cost of Capital
There are two ways to think of this choice of the correct interest rate.
1. Use the interest rate that can be earned on comparable investments. This is an OPPORTUNITY COST approach. 2. Use the weighted-average cost of acquiring the funds to finance the project. This is an OUT-OF-POCKET COST approach.
Cost of debt. The cost of borrowing is reflected in the interest rate that must be paid on the debt. Cost of new equity. In order to induce investors to purchase newly-issued shares of stock, the investors must expect a return on their investment. Accordingly, the issuance price of the shares must be low enough so that investors can expect the share price to rise over time, on average, to give them a return on their investment. This return that investors expect can be thought of as the implicit cost associated with capital raised through issuance of new shares of stock. Cost of retained earnings. A very convenient way for a company to raise new capital is to simply retain some or all of the company's profits. At first glance, this may seem like a costless way to raise financing. However, the shareholders, to whom all of the profits belong, expect some return on the profits that are retained in the business. This expected return can be thought of as the implicit cost of financing obtained through retaining earnings.

The present value calculations with respect to the doughnut machine are summarized in this table.
Interest rate is 16% Amount Present Value

Original Cost (\$10,000 now) Scrap Value (\$1,000 after 10 years) Operating Cost Savings (\$700 per year for 10 years) Increased Profits from Sales (10,000 units @ \$.10) Net Present Value (or NPV)

(10,000) 1,000 \$700 × 10 yrs \$1,000 × 10 yrs

(10,000) 227 3,383 4,833 (1,557)

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17-8

Example

Problem 17-3

Computation of the weighted-average cost of capital (WACC)
Twenty percent of a company's total capital is debt, 35 percent is from the issuance of stock, and 45 percent is equity from retained earnings. The company has determined that the cost of its debt capital is 8 percent and the cost of its equity capital is 20 percent from stock and 15 percent from retained earnings. Compute the company's weighted-average COST OF CAPITAL.
Cost of Capital Average Cost of Capital

Computation of NPV MaScare Company is considering whether to purchase a new store. The store will cost \$2,500,000. The store will generate net cash inflows of \$400,000 at the end of each year for the next 20 years. At the end of 20 years, it is expected that the store can be sold for \$700,000. The appropriate interest rate is 14%. Compute the net present value (NPV) of the store purchase and state whether you think MaScare Company should purchase the store.

Type

Weight

Debt . . . . . . . . . . . . . . . . . . . . Equity (retained earnings) . . . WACC

8% 15%

x x x

20% 35% 45% 100%

= = =

1.60% 7.00% 6.75% 15.35%

Equity (stocks) . . . . . . . . . . . . 20%

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50

Computation of NPV
A timeline of the cash flows associated with this store is as follows. Note that the initial purchase price of \$2,500,000 is shown on the timeline as a negative amount representing a cash outflow.
(2,500,000) Now \$400,000 Year 1 \$400,000 Year 2 \$400,000 Year 3 Salvage value of \$700,000 \$400,000 Year 20

Computation of NPV
Clear memory:
C ALL

20 14 400,000 700,000

N

: 20 because the length of the operating life of the store is 20 years. : 14% which was given as the appropriate interest rate. : \$400,000 which is the amount of each equal net cash inflow. : \$700,000 because this additional cash inflow is to be received at the end of 20 years when the store is sold. : For the answer.

I
PMT FV PV

Three cash flows are associated with the store - the immediate \$2,500,000 cash outflow to purchase the store, the \$400,000 net cash inflow per year for 20 years that will be generated by the store, and the \$700,000 cash inflow at the end of 20 years from the sale of the store. Of course, computation of the present value of the immediate \$2,500,000 cash outflow is easy - the present value of \$2,500,000 out right now is just \$2,500,000. The combined present value of the annuity of \$400,000 for 20 years as well as the \$700,000 selling price of the store at the end of 20 years is computed as follows.

\$2,700,185
Note that we took a little shortcut here and computed the present value of the \$400,000 annual cash inflows and the present value of the \$700,000 to be received at the end of 20 years all in one step. This works because the length of the annuity is 20 years and the time until the store is sold is also 20 years. If the store were to be sold at, say, the end of 21 years, then we would have to compute these two present values in separate steps.

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Problem 17-4

Computation of NPV
The present value calculations with respect to this piece of equipment are summarized in this table.
Interest rate is 14% Amount Present Value

Computation of WACC
Harold Company receives its financing from four different sources in various proportions, as follows.
Proportion of Total Financing

Original Cost (\$2,500,000 now) Net cash inflows

(2,500,000) \$400,000 × 20 yrs \$700,000 at end of 20 yrs

(2,500,000) 2,700,185 \$200,185

Short-term debt Long-term debt New stock issues Retained earnings Total

10% 45% 15% 30% 100%

Net Present Value (or NPV)

Because the present value of the cash inflows (\$2,700,185) is greater than the present value of the cash outflows (\$2,500,000), the project has a positive NPV and should be undertaken.

The cost of short-term debt is 6 percent; the cost of long-term debt is 9 percent. In addition, Harold Company has estimated the cost of its equity capital to be 22 percent from stock and 16 percent from retained earnings. Compute Harold Company's weighted-average COST OF CAPITAL (WACC).

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17-9

Problem 17-5

Computation of WACC
Harold Company's weighted-average cost of capital (WACC) is 12.75%, as shown below.
Cost of Capital Average Cost of Capital

NPV and a Least-Cost Decision Kamili Company is required to install a new piece of safety equipment. The company has two alternatives for the equipment. One alternative would cost \$260,000 immediately but would not add to operating costs over the five-year life of the equipment. The second alternative costs \$75,000 immediately but would add \$45,000 to annual operating costs for five years. Kamili Company uses an 8 percent interest rate in evaluating long-term projects. Which alternative should Kamili Company purchase?

Type

Weight

Short-term debt . . . . . . . . . . . . Long-term debt . . . . . . . . . . . . Equity (retained earnings) . . . WACC

6% 9% 16%

x x x

10% 45% 15% 30% 100%

= = =

0.60% 4.05% 3.30% 4.80% 12.75%

Equity (stocks) . . . . . . . . . . . . 22%

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NPV and a Least-Cost Decision
Kamili Company should choose the second alternative because it has a lower outlay cost, in present value terms, as shown below.
Clear memory:
C ALL

Internal rate of return
Capital Budgeting Technique Computation Decision Rule

Internal Rate of Return (IRR)

5 8 45,000 0

N

: 5 because operating costs are increased in each year for 5 years. : 8% which was given as the appropriate interest rate. costs.

Compute the interest rate that makes the present value of the cash inflows equal to the present value of the cash outflows.

Accept the project if the internal rate of return (IRR) is greater than a predetermined hurdle rate.

I

PMT : \$45,000 which is the amount of the increase in annual operating FV PV

: \$0 because no extra cost exists at the end of 5 years. : For the answer.

Internal rate of return, or IRR, is the interest rate that makes the present value of the cash inflows equal to the present value of the cash outflows. In other words, the IRR is the interest rate that causes the NPV to be equal to zero.

Savings Account: 0.5% Intrest Certificate of Deposit: 3.5% Intrest
The internal rate of return, or IRR, is the measure of what rate of return you can earn on a long-term project.

\$179,672
The first alternative costs \$260,000. The second alternative costs just \$254,672 (\$75,000 + \$179,672) in present value terms.

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Purchase of equipment
Ryan Company is considering whether to invest in a piece of equipment that requires an investment of \$500,000 today. The project will provide net operating cash inflows of \$150,000 at the end of each year for five years, and it will have a salvage value of \$0 at the end of five years. The appropriate interest rate is 10%.

Example

Example

Purchase of equipment
Ryan Company is considering whether to invest in a piece of equipment that requires an investment of \$500,000 today. The project will provide net operating cash inflows of \$150,000 at the end of each year for five years, and it will have a salvage value of \$0 at the end of five years. The appropriate interest rate is 10%.

NPV = \$68,618
To compute the NPV of this project with an interest rate of 20%, we compute the present value of the annuity of \$150,000 each year for 5 years, as follows.
Clear memory:
C ALL

NPV = \$68,618
The present value calculations with respect to this piece of equipment are summarized in this table.

5 20 150,000 0

N

: 5 because five equal payments are expected in the future. : 20% which is the interest rate that we are trying.

Interest rate is 20% Amount

I

Present Value

PMT : \$150,000 which is the amount of each equal cash flow. FV PV

Original Cost (\$500,000 now) Net cash inflows (\$150,000 per year) Net Present Value (or NPV)

(500,000) \$150,000 × 5 yrs

(500,000) 448,592 (51,408)

: \$0 because no extra amount is received at the end of 5 years when the final annual cash inflow of \$150,000 is generated. : For the answer.

\$448,592

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17-10

Example

Example

Purchase of equipment
Ryan Company is considering whether to invest in a piece of equipment that requires an investment of \$500,000 today. The project will provide net operating cash inflows of \$150,000 at the end of each year for five years, and it will have a salvage value of \$0 at the end of five years. The appropriate interest rate is 10%.

Purchase of equipment
Ryan Company is considering whether to invest in a piece of equipment that requires an investment of \$500,000 today. The project will provide net operating cash inflows of \$150,000 at the end of each year for five years, and it will have a salvage value of \$0 at the end of five years. The appropriate interest rate is 10%.

NPV with a return of 10% = \$68,618 NPV with a return of 20% = (\$51,408)
It looks like the return that will result in an NPV of exactly zero will be somewhere around 15%, but we can compute this return exactly, as follows.
Clear memory:
C ALL

NPV with a return of 10% = \$68,618 NPV with a return of 20% = (\$51,408)
Let's verify this by computing the present value of the \$150,000 annuity using an interest rate of 15.2382%.
Clear memory:
C ALL

500,000 +/150,000 5 0

PV PMT N FV

: Negative \$500,000 to represent the initial cash cost of the project. : Positive \$150,000 which is the amount of the annual cash inflow. : 5 because the length of the project is 5 years. : \$0 because there is no additional cash inflow at the end of the project. : For the answer.

5 15.2382 150,000 0

N

: 5 because five equal payments are expected in the future. : 15.2382% which is the interest rate that we are trying.

I

PMT : \$150,000 which is the amount of each equal cash flow. FV

: \$0 because no extra amount is received at the end of 5 years when the final annual cash inflow of \$150,000 is generated. : For the answer.

I

15.2382%

\$500,000

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Example

Example

Purchase of equipment
Ryan Company is considering whether to invest in a piece of equipment that requires an investment of \$500,000 today. The project will provide net operating cash inflows of \$150,000 at the end of each year for five years, and it will have a salvage value of \$0 at the end of five years. The appropriate interest rate is 10%.

Computing the IRR of a business project
A business project requires the initial outlay of \$200,000 in cash. The project will generate cash inflows of \$40,000 at the end of each year for the next 15 years. What is the internal rate of return of this project? The following inputs into our business calculator will allow us to compute the IRR.
Clear memory:
C ALL

NPV with a return of 10% = \$68,618 NPV with a return of 20% = (\$51,408)
The present value calculations with respect to this piece of equipment, with an interest rate of 15.2382%, are summarized in this table.
Interest rate is 15.2382% Amount Present Value

200,000

+/-

PV PMT N FV

: Negative \$200,000 to represent the initial cash cost of the project. : Positive \$40,000 which is the amount of the annual cash inflow. : 15 because the length of the project is 15 years. : \$0 because there is no additional cash inflow at the end of the project. : For the answer.

40,000 15 0

Original Cost (\$500,000 now) Net cash inflows (\$150,000 per year) Net Present Value (or NPV)

(500,000) \$150,000 × 5 yrs

(500,000) 500,000 -0-

I

18.41546%

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Computing the IRR of a business project
A business project requires the initial outlay of \$200,000 in cash. The project will generate cash inflows of \$40,000 at the end of each year for the next 15 years. What is the internal rate of return of this project? Let's check this answer to see whether the interest rate 18.41546% does indeed yield an NPV of zero. We compute the present value of the annuity of \$40,000 per year as follows.
Clear memory:
C ALL

Example

Computing the IRR of a business project
A business project requires the initial outlay of \$200,000 in cash. The project will generate cash inflows of \$40,000 at the end of each year for the next 15 years. What is the internal rate of return of this project? The present value calculations with respect to this piece of equipment, with an interest rate of 18.41546%, are summarized in this table.
Interest rate is 18.41546% Amount Present Value

Example

15 18.41546 40,000 0

N

: 15 because fifteen equal cash flows are expected in the future. : 18.41546% which is the interest rate that we are trying.

Original Cost (\$200,000 now) Net cash inflows (\$40,000 per year for 15 years) Net Present Value (or NPV)

(200,000) \$40,000 × 15 yrs

(200,000) 200,000 -0-

I

PMT : \$40,000 which is the amount of each equal cash flow. FV PV

: \$0 because no extra amount is received at the end of 15 years when the final annual cash inflow of \$40,000 is generated. : For the answer.

\$200,000

If the minimum rate of return is 15%, then we should undertake this project. If the minimum rate of return is 20%, then we should reject this project.

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17-11

Example

Problem 17-6

Computing the IRR of a piece of equipment
Aina Company is considering whether to invest in a piece of equipment that requires an investment of \$250,000 today. The project will provide net cash inflows of \$50,000 per year for eight years, and it will have a salvage value of \$51,509 at the end of eight years. Calculate the INTERNAL RATE OF RETURN. The following inputs into our business calculator will allow us to compute the IRR.
Clear memory:
C ALL

Computation of IRR MaScare Company is considering whether to purchase a new store. The store will cost \$2,500,000. The store will generate net cash inflows of \$400,000 at the end of each year for the next 20 years. At the end of 20 years, it is expected that the store can be sold for \$700,000. The minimum required rate of return on projects such as this is 14%. Compute the internal rate of return (IRR) of the store purchase and state whether you think MaScare Company should purchase the store.

250,000 +/50,000 8 51,509

PV PMT N FV

: Negative \$250,000 to represent the initial cash cost of the project. : Positive \$50,000 which is the amount of the annual cash inflow. : 8 because the life of the equipment is 8 years. : Positive \$51,509 because this is an additional cash inflow at the end of 8 years. : For the answer.

I

14.0%

If the minimum rate of return is 15%, then we should buy this equipment. If the minimum rate of return is 20%, then we should we should not buy the equipment.

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Computation of IRR
The following business calculator inputs will allow us to compute the IRR.

Capital Rationing (ranking projects)

Clear memory:

C ALL

2,500,000 +/400,000 20 700,000

PV PMT N FV

: Negative \$2,500,000 to represent the initial cash cost of the store. : Positive \$400,000 which is the amount of the annual cash inflow. : 20 because the life of the store is 20 years. : Positive \$700,000 because this is the amount for which the store can be sold at the end of 20 years. : For the answer.

Screening
Identifying which projects are good and which are bad.

I

15.3%

The internal rate of return, or IRR, for this project is 15.3%; this is the interest rate that yields an NPV of exactly zero. Because the minimum rate of return on a project such as this is 14%, then these IRR calculations suggest that we should buy the store. You may recall that this is exactly the same capital budgeting decision that we examined in Walkthrough Problem 17-3. In that problem we computed the NPV of the store purchase; the NPV, with an interest rate of 14%, is positive \$200,185 indicating that we should buy the store. In this problem we computed the IRR of the store purchase to be 15.3%; when compared to the minimum rate of return of 14%, we see that the decision is again that we should buy the store. The NPV and the IRR calculations will always identify the same projects as being attractive and the same projects as being ones that we should reject.

Ranking
Choosing the best among a set of good projects.

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The Good News
We don't have to learn any new time value of money tools in order to rank projects.
Internal Rate of Return (IRR) - excellent tool for ranking projects.
The one with the highest IRR is the best.

Ranking Capital Budgeting Projects
Mimi Company is considering three projects. Mimi has already determined that each of the projects has a positive NPV. However, Mimi can only undertake one of the projects, so she would like to identify which one of the projects is the best. Each of the projects involves an initial investment and results in an annuity of cash inflows in the future. The details for each of the three projects are as follows.
Initial Investment Annual Cash Inflow Length of Project

Example

Net Present Value (NPV) - not a good measure to use for ranking.
The biggest project, or the project with the largest initial investment. Always gives preference to LARGE projects, when a series of small projects could yield a higher overall NPV.

Profitability Index
Easier to compute the NPV of a project than it is to compute the project's IRR. The project evaluation systems of many companies are designed around the computation of NPV. It is often the case that we know the NPV of a project but we don't know the project's IRR.
In these cases, we can easily compute the project's Profitability Index from the NPV.

Project 1 Project 2 Project 3

\$200,000 300,000 170,000

\$35,000 60,000 27,000

8 years 7 years 10 years

Which one of the projects should Mimi Company undertake?
Note: Mimi Company has established a minimum required rate of return of 8%.
Initial Investment IRR NPV Profitability Index

Project 1 Project 2 Project 3

\$200,000 300,000 170,000

8.15% 9.20% 9.44%

\$1,132 12,382 11,172

1.006 1.041 1.066

Profitability Index = (NPV / Initial Investment) + 1

Profitability Index = (NPV / Initial Investment) + 1

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17-12

Screening
Which projects have a positive NPV. Which projects have a negative NPV. Which projects have IRR above or below the required rate of return.

Problem 17-7

Ranking Long-term Projects A real estate company is considering four different investments. Each of the investments involves an initial cash outflow now with a single cash inflow a number of years in the future. The company's required rate of return is 12%. Your job is to rank the investments. To do so, compute both the IRR and the Profitability Index for each of the four investments.
Initial Investment Single Cash Inflow Years Until Cash Inflow

Ranking
Rank projects to pick the best one using either: IRR Profitability Index
Investment 1 Investment 2 Investment 3 Investment 4

\$10,000 10,000 100,000 100,000

\$37,000 90,000 400,000 700,000

10 15 10 15

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Ranking Long-term Projects
We can use our business calculators to calculate the NPV and the IRR of each of the projects.
Initial Investment NPV IRR

Ranking Long-term Projects
Profitability Index computations for each of the four investments reveal the following.
Initial Investment NPV Profitability Index

Investment 1 Investment 2 Investment 3 Investment 4

\$10,000 10,000 100,000 100,000

\$1,913 6,443 28,789 27,887

13.98% 15.78% 14.87% 13.85%

Investment 1 Investment 2 Investment 3 Investment 4

\$10,000 10,000 100,000 100,000

\$1,913 6,443 28,789 27,887

1.1913 1.6443 1.2879 1.2789

Using the IRR numbers, we see that Investment 2, with an IRR of 15.78%, is the best of the four investments and is the one investment that we should choose if we can only choose one of the four investments. Note again that all of the investments are good in that they all have a positive NPV and an IRR above the minimum required rate of return of 12%, but Investment 2 is the best of the four.

Again we see that Investment 2 is the best of the four investments because it has the highest Profitability Index. So whether we use the IRR or the Profitability Index, Investment 2 is shown to be the best.

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The impact of income taxes on NPV and IRR analysis
The two primary impacts of income taxes:
After-tax cash flow = Before-tax cash flow × (1 - Tax Rate) Depreciation tax shield = Depreciation Deduction × (Tax Rate)

Impact of Income Taxes on Cash Revenues and Cash Expenses
The existence of income taxes makes good news not so good and bad news not so bad. Example: Assume that you have earned \$1,000. Assume that the income tax rate is 40%.
Your before-tax earnings Income tax (40%) After-tax earnings \$1,000 (400) \$600

We can express this in a formula: After-tax earnings = Before-tax earnings × (1 - Tax Rate) After-tax earnings = \$1,000 × (1 - 0.40) After-tax earnings = \$600

After-Tax Cash Flows 77 78

17-13

Example

After-tax earnings
You earn \$100. The income tax rate is 99%.

Impact of Income Taxes on Cash Revenues and Cash Expenses
The existence of income taxes makes good news not so good and bad news not so bad. Example: You pay \$1,000 for advertising. The income tax rate is 40%. What is the after-tax cost of the advertising?
Before-tax cost Reduction in taxes After-tax cost \$1,000 (400) \$600

After-tax earnings = Before-tax earnings × (1 - Tax Rate) After-tax earnings = \$100 × (1 - 0.99) After-tax earnings = \$1

In doing a capital budgeting analysis, the only relevant number is the after-tax earnings which is what you get to keep.

We can express this in a formula: After-tax cost = Before-tax cost × (1 - Tax Rate) After-tax cost = \$1,000 × (1 - 0.40) After-tax cost = \$600

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Example

After-tax cost
You pay \$100 for advertising. The income tax rate is 99%.

What is the after-tax cost of the advertising?
After-tax cost = Before-tax cost × (1 - Tax Rate) After-tax cost = \$100 × (1 - 0.99) After-tax cost = \$1

The existence of income taxes means that you don't get to keep all of the cash inflows that you generate, but you also get a tax subsidy (in essence) for all of your tax-deductible business expenses.

In doing a capital budgeting analysis, the only relevant number is the after-tax cost which is what you end up paying.

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Depreciation Tax Shield
Example: Assume that you report a \$1,000 depreciation deduction on your tax form. The income tax rate is 40%. How much does this depreciation deduction save you in income taxes? By lowering your taxable income by \$1,000, the depreciation deduction will save you \$400 (\$1,000 × 0.40) in income taxes. A formula to compute the amount of the depreciation tax savings is as follows.

Remember, depreciation is a non-cash expense.
Thus, in doing time value of money calculations, we ignore depreciation because it doesn't involve any cash flow. Except when we are considering the impact of income taxes. When you write down the amount of the non-cash depreciation expense on your income tax form, you reduce your taxable income and therefore reduce the amount of income tax that you pay. So in the specific context of income taxes, depreciation does result in a cash inflow in the form of an income tax savings.

Depreciation tax savings = Depreciation Deduction × (Tax Rate)
= \$1,000 × 0.40 = \$400
Example: You report a \$100 depreciation deduction on your tax form. The income tax rate is 99%. How much does this depreciation deduction save you in income taxes?

Depreciation tax savings = Depreciation Deduction × (Tax Rate) Depreciation tax savings = \$100 × 0.99 Depreciation tax savings = \$99

83

84

17-14

Example

Example

Computing NPV in a setting with income taxes
Ryan Company is considering whether to invest in a piece of equipment that requires an investment of \$500,000 today. The project will provide net before-tax operating cash inflows of \$150,000 at the end of each year for five years, and it will have a salvage value of \$0 at the end of five years. Ryan Company uses straight-line depreciation. The interest rate is 10%. The income tax rate is 30%. Calculate the NET PRESENT VALUE of the piece of equipment and state whether the equipment should be purchased. 1. Cash outflow of \$500,000 today for the purchase of the equipment.
The existence of income taxes does not change this amount. The deduction does not occur immediately. The \$500,000 cost of the equipment is deducted as depreciation expense over the 5-year life of the equipment.

Computing NPV in a setting with income taxes
Ryan Company is considering whether to invest in a piece of equipment that requires an investment of \$500,000 today. The project will provide net before-tax operating cash inflows of \$150,000 at the end of each year for five years, and it will have a salvage value of \$0 at the end of five years. Ryan Company uses straight-line depreciation. The interest rate is 10%. The income tax rate is 30%. Calculate the NET PRESENT VALUE of the piece of equipment and state whether the equipment should be purchased. The after-tax operating cash inflow of \$105,000 is an annuity with a present value of \$398,033 computed as follows.

Clear memory:

C ALL

2. After-tax operating cash inflow of \$105,000 at the end of each year for five years. After-tax operating cash inflow = Before-tax operating cash inflow × (1 - Tax Rate) After-tax operating cash inflow = \$150,000 × (1 - 0.30) After-tax operating cash inflow = \$150,000 × 0.70 After-tax operating cash inflow = \$105,000 3. Annual depreciation tax shield of \$30,000 at the end of each year for five years. The anual amount of depreciation is \$100,000 (\$500,000/5 years). Depreciation tax savings = Depreciation Deduction × (Tax Rate) Depreciation tax savings = \$100,000 × 0.30 Depreciation tax savings = \$30,000

5 10 105,000 0

N

: 5 because five equal cash inflows are expected in the future. : 10% which is given as the appropriate interest rate.

I

PMT : \$105,000 which is the amount of each after-tax cash inflow. FV PV

: \$0 because no extra amount is received at the end of 5 years when the final annual after-tax cash inflow of \$105,000 is generated. : For the answer.

\$398,033

85

86

Example

Example

Computing NPV in a setting with income taxes
Ryan Company is considering whether to invest in a piece of equipment that requires an investment of \$500,000 today. The project will provide net before-tax operating cash inflows of \$150,000 at the end of each year for five years, and it will have a salvage value of \$0 at the end of five years. Ryan Company uses straight-line depreciation. The interest rate is 10%. The income tax rate is 30%. Calculate the NET PRESENT VALUE of the piece of equipment and state whether the equipment should be purchased. The depreciation tax shield of \$30,000 is also an annuity with a present value of \$113,724 computed as follows.

Computing NPV in a setting with income taxes
Ryan Company is considering whether to invest in a piece of equipment that requires an investment of \$500,000 today. The project will provide net before-tax operating cash inflows of \$150,000 at the end of each year for five years, and it will have a salvage value of \$0 at the end of five years. Ryan Company uses straight-line depreciation. The interest rate is 10%. The income tax rate is 30%. Calculate the NET PRESENT VALUE of the piece of equipment and state whether the equipment should be purchased. These present value calculations are summarized in this table.
Interest rate is 10% Amount Present Value

Clear memory:

C ALL

5 10 30,000 0

N

: 5 because five equal cash inflows (from tax savings) are expected in the future. : 10% which is given as the appropriate interest rate.

Original Cost (\$500,000 now) Depreciation tax shield (\$100,000 depreciation × 0.30)

(500,000) \$30,000 × 5 yrs

(500,000) 113,724 398,033 11,757

I

PMT : \$30,000 which is the amount of each depreciation tax savings. FV PV

Net cash inflows (\$150,000 × [1 – 0.30]) \$105,000 × 5 yrs Net Present Value (or NPV)

: \$0 because no extra depreciation tax savings is generated at the end of 5 years. : For the answer.

\$113,724

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Example

Computing NPV in a setting with income taxes
1. In the absence of income taxes, this same project has a net present value of \$68,618. Introduction of income taxes has lowered the NPV of this project. With an income tax rate of 40% the NPV for this project would be negative. It is an important fact of business to remember that higher income tax rates can transform attractive projects into unattractive projects. 2. In this problem, note that without the income tax savings generated by the depreciation tax shield, this project would have a negative NPV rather than a positive NPV. The depreciation tax shield is an important part of the cash inflows associated with many projects. In recognition of this fact, government bodies all over the world often allow companies to depreciate the cost of their capital projects very quickly in order to increase the present value of the depreciation tax savings.
In the United States, Congress allows companies to use double-declining-balance depreciation in computing their depreciation deductions for income tax purposes. By allowing more rapid depreciation, the present value of the depreciation tax savings is increased, even though the total amount of depreciation tax savings is the same.

Example

Computing IRR in a setting with income taxes
Lorien Company is considering whether to invest in a piece of equipment that requires an investment of \$600,000 today. The project will provide net before-tax operating cash inflows of \$150,000 at the end of each year for 10 years, and it will have a salvage value of \$0 at the end of 10 years. Lorien Company uses straight-line depreciation. The minimum required rate of return is 12%. The income tax rate is 60%. Calculate the INTERNAL RATE OF RETURN of the piece of equipment and state whether the equipment should be purchased.
1. Cash outflow of \$600,000 today for the purchase of the equipment. 2. After-tax operating cash inflow of \$60,000 at the end of each year for 10 years. With an income tax rate of 60%, the after-tax operating cash inflow is computed as follows. After-tax operating cash inflow = Before-tax operating cash inflow × (1 - Tax Rate) After-tax operating cash inflow = \$150,000 × (1 - 0.60) After-tax operating cash inflow = \$60,000 3. Annual depreciation tax shield of \$36,000 at the end of each year for 10 years. The annual amount of straight-line depreciation is \$60,000 (\$600,000 / 10 years). With an income tax rate of 60%, the amount of the depreciation tax shield is computed as follows. Depreciation tax savings = Depreciation Deduction × (Tax Rate) Depreciation tax savings = \$60,000 × 0.60 Depreciation tax savings = \$36,000

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17-15

Example

Problem 17-8

Computing IRR in a setting with income taxes
Lorien Company is considering whether to invest in a piece of equipment that requires an investment of \$600,000 today. The project will provide net before-tax operating cash inflows of \$150,000 at the end of each year for 10 years, and it will have a salvage value of \$0 at the end of 10 years. Lorien Company uses straight-line depreciation. The minimum required rate of return is 12%. The income tax rate is 60%. Calculate the INTERNAL RATE OF RETURN of the piece of equipment and state whether the equipment should be purchased. The following inputs into our business calculator will allow us to compute the IRR. Clear memory:
C ALL

Computing NPV and IRR with income taxes
Lily Company is considering purchasing a machine. The associated cash inflows and outflows are as follows: a. Cost of the machine is \$100,000. b. Net before-tax cash inflows from the output from the machine are expected to be \$40,000 per year for 5 years. c. The required rate of return on this project is 10%. d. All cash flows occur at the end of the appropriate year, except for the \$100,000 initial cost. e. The machine will be depreciated for tax purposes on a straight-line basis with an assumed salvage value of \$0. f. The tax rate is 40%. COMPUTE: 1. The net present value (NPV) of this machine. 2. The internal rate of return (IRR) of this machine.

600,000 +/96,000 10 0

PV PMT N FV

: Negative \$600,000 to represent the initial cash cost of the project. : Positive \$96,000 which is the sum of the \$60,000 after-tax operating cash inflow and the \$36,000 depreciation tax savings. : 10 because the life of the equipment is 10 years. : \$0 because there is no additional cash inflow at the end of 10 years. : For the answer.

I

9.61%

91

92

Computing NPV and IRR with income taxes
First, let's calculate the amount of each of the three types of cash flow associated with this equipment.
a. Cash outflow of \$100,000 today for the purchase of the machine. b. After-tax operating cash inflow of \$24,000 at the end of each year for five years. The amount of the before-tax operating cash inflow is \$40,000 per year. With an income tax rate of 40%, the after-tax operating cash inflow is computed as follows. After-tax operating cash inflow = Before-tax operating cash inflow × (1 - Tax Rate) After-tax operating cash inflow = \$40,000 × (1 - 0.40) After-tax operating cash inflow = \$24,000 c. Annual depreciation tax shield of \$8,000 at the end of each year for five years. The annual amount of straight-line depreciation is \$20,000 (\$100,000 / 5 years). With an income tax rate of 40%, the amount of the depreciation tax shield is computed as follows. Depreciation tax savings = Depreciation Deduction × (Tax Rate) Depreciation tax savings = \$20,000 × 0.40 Depreciation tax savings = \$8,000

Computing NPV and IRR with income taxes
1. Compute the net present value (NPV) of this machine. Now that we have computed the amount of the cash flows, we can compute their present values. The present value of the \$100,000 purchase price is just \$100,000. The after-tax operating cash inflow of \$24,000 is an annuity with a present value of \$90,979 computed as follows.
Clear memory:
C ALL

5 10 24,000 0

N

: 5 because five equal cash inflows are expected in the future. : 10% which is given as the appropriate interest rate : \$24,000 which is the amount of each after-tax cash inflow. : \$0 because no extra amount is received at the end of 5 years when the final annual after-tax cash inflow of \$24,000 is generated. : For the answer.

I
PMT FV

PV

\$90,979

93

94

Computing NPV and IRR with income taxes
1. Compute the net present value (NPV) of this machine. The depreciation tax shield of \$8,000 is also an annuity with a present value of \$30,326 computed as follows.
Clear memory:
C ALL

Computing NPV and IRR with income taxes
1. Compute the net present value (NPV) of this machine. These present value calculations are summarized in this table.
Interest rate is 10% Amount Present Value

5 10 8,000 0

N

: 5 because five equal cash inflows (from tax savings) are expected in the future. : 10% which is given as the appropriate interest rate. : \$8,000 which is the amount of each depreciation tax savings. : \$0 because no extra depreciation tax savings is generated at the end of 5 years. : For the answer.

Original Cost(\$100,000 now) Depreciation tax shield(\$20,000 depreciation × 0.40) Net cash inflows(\$40,000 × [1 – 0.40]) Net Present Value (or NPV)

(100,000) \$8,000 × 5 yrs \$24,000 × 5 yrs

(100,000) 30,326 90,979 21,305

I
PMT FV PV

We see that this project has a positive NPV so we should undertake it.

\$30,326

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17-16

Problem 17-9

Computing NPV and IRR with income taxes
2. Compute the internal rate of return (IRR) of this machine. The following inputs into our business calculator will allow us to compute the IRR.
Clear memory:
C ALL

Impact of depreciation rules on NPV
Hilly Pice Company is considering whether to invest in a piece of equipment that requires an investment of \$600,000 today. The project will provide net before-tax operating cash inflows of \$120,000 at the end of each year for 10 years, and it will have a salvage value of \$0 at the end of 10 years. The minimum required rate of return is 12%. The income tax rate is 30%. Calculate the NET PRESENT VALUE of the piece of equipment and state whether the equipment should be purchased under each of the following two assumptions about depreciation. 1. Hilly Pice Company uses straight-line depreciation for income tax purposes. 2. Instead of using straight-line depreciation, Hilly Pice Company is able to deduct the entire cost of the equipment as an expense in the year the equipment is purchased. The equipment is paid for at the beginning of the first year, but the tax savings from being able to deduct the cost of the equipment don't occur until the end of the first year.

100,000

+/-

PV

: Negative \$100,000 to represent the initial cash cost of the project operating cash inflow and the \$8,000 depreciation tax savings.

32,000 5 0

PMT : Positive \$32,000 which is the sum of the \$24,000 after-tax N FV

: 5 because the life of the machine is 5 years. : \$0 because there is no additional cash inflow at the end of 5 years. : For the answer.

I

18.03%

The internal rate of return, or IRR, for this project is 18.03%. Because the minimum rate of return on a project such as this is 10%, these IRR calculations suggest that we should buy this equipment.

97

98

Impact of depreciation rules on NPV
1. Straight-line depreciation Let's start by computing the amount of the three cash flows associated with the purchase of this equipment.
a. Cash outflow of \$600,000 today for the purchase of the equipment. b. After-tax operating cash inflow of \$84,000 at the end of each year for 10 years. With an income tax rate of 30%, the after-tax operating cash inflow is computed as follows. After-tax operating cash inflow = Before-tax operating cash inflow × (1 - Tax Rate) After-tax operating cash inflow = \$120,000 × (1 - 0.30) After-tax operating cash inflow = \$84,000 c. Annual depreciation tax shield of \$18,000 at the end of each year for 10 years. The annual amount of straight-line depreciation is \$60,000 (\$600,000 / 10 years). With an income tax rate of 30%, the amount of the depreciation tax shield is computed as follows. Depreciation tax savings = Depreciation Deduction × (Tax Rate) Depreciation tax savings = \$60,000 × 0.30 Depreciation tax savings = \$18,000

Impact of depreciation rules on NPV
1. Straight-line depreciation Now that we have computed the amount of the cash flows, we can compute their present values. The present value of the \$600,000 purchase price is just \$600,000. The after-tax operating cash inflow of \$84,000 is an annuity with a present value of \$474,619 computed as follows.
Clear memory:
C ALL

10 12 84,000 0

N

: 10 because ten equal cash inflows are expected in the future. : 12% which is given as the appropriate interest rate. : \$84,000 which is the amount of each after-tax cash inflow. : \$0 because no extra amount is received at the end of 10 years when the final annual after-tax cash inflow of \$84,000 is generated. : For the answer.

I
PMT FV

PV

\$474,619

99

100

Impact of depreciation rules on NPV
1. Straight-line depreciation The depreciation tax shield of \$18,000 is also an annuity with a present value of \$101,704 computed as follows.
Clear memory:
C ALL

Impact of depreciation rules on NPV
1. Straight-line depreciation These present value calculations are summarized in this table.
Interest rate is 12% Amount Present Value

10 12 18,000 0

N

: 10 because ten equal cash inflows (from tax savings) are expected in the future. : 12% which is given as the appropriate interest rate. : \$18,000 which is the amount of each depreciation tax savings. : \$0 because no extra depreciation tax savings is generated at the end of 10 years. : For the answer.

Original Cost (\$600,000 now)

(600,000)

(600,000) 101,704 474,619 (23,677)

Depreciation tax shield (\$60,000 depreciation × 0.30) \$18,000 × 10 yrs Net cash inflows (\$120,000 × [1 – 0.30]) \$84,000 × 10 yrs Net Present Value (or NPV)

I
PMT FV PV

We see that this project has a negative NPV so we should reject it.

\$101,704

101

102

17-17

Impact of depreciation rules on NPV
2. Immediate depreciation of equipment cost instead of straight-line depreciation. Again, let's start by computing the amount of the three cash flows associated with the purchase of this equipment.
a. Cash outflow of \$600,000 today for the purchase of the equipment. b. After-tax operating cash inflow of \$84,000 at the end of each year for 10 years. With an income tax rate of 30%, the after-tax operating cash inflow is computed as follows. After-tax operating cash inflow = Before-tax operating cash inflow × (1 - Tax Rate) After-tax operating cash inflow = \$120,000 × (1 - 0.30) After-tax operating cash inflow = \$84,000 c. Immediate depreciation tax shield of \$180,000 at the end of the first year. With this special tax arrangement, Hilly Pice Company is allowed to deduct the entire \$600,000 cost of the equipment in the year that it is purchased. You can think of this as immediate depreciation. With an income tax rate of 30%, the amount of this first-year depreciation tax shield is computed as follows.. Depreciation tax savings = Depreciation Deduction × (Tax Rate) Depreciation tax savings = \$600,000 × 0.30 Depreciation tax savings = \$180,000

Impact of depreciation rules on NPV
2. Immediate depreciation of equipment cost instead of straight-line depreciation. Now that we have computed the amount of the cash flows, we can compute their present values. The present value of the \$600,000 purchase price is just \$600,000. The after-tax operating cash inflow of \$84,000 is an annuity with a present value of \$474,619 computed as follows.
Clear memory:
C ALL

10 12 84,000 0

N

: 10 because ten equal cash inflows are expected in the future. : 12% which is given as the appropriate interest rate. : \$84,000 which is the amount of each after-tax cash inflow. : \$0 because no extra amount is received at the end of 10 years when the final annual after-tax cash inflow of \$84,000 is generated. : For the answer.

I
PMT FV

PV

\$474,619

103

104

Impact of depreciation rules on NPV
2. Immediate depreciation of equipment cost instead of straight-line depreciation. The first-year depreciation tax shield of \$180,000 is a one-time cash flow with a present value of \$160,714 computed as follows.
Clear memory:
C ALL

Impact of depreciation rules on NPV
2. Immediate depreciation of equipment cost instead of straight-line depreciation. These present value calculations are summarized in this table.
Interest rate is 12% Amount Present Value

1 12 0 180,000

N

: 1 because with this special immediate depreciation deduction the tax savings all occur at the end of the first year. : 12% which is given as the appropriate interest rate. : \$0 because this is a one-time cash flow. : \$180,000 because the depreciation tax savings is generated in one lump at the end of the first year. : For the answer.

Original Cost (\$600,000 now) Depreciation tax shield (\$600,000 depreciation × 0.30) Net cash inflows (\$120,000 × [1 – 0.30]) Net Present Value (or NPV)

(600,000) \$180,000 at end of first year \$84,000 × 10 yrs

(600,000) 160,714 474,619 35,333

I
PMT FV PV

\$160,714

We see that this project has a positive NPV so we should undertake it. The only difference between (1), when the project had a negative NPV, and (2), when the project had a positive NPV, is depreciation policy. You can see that allowing companies to rapidly depreciate the cost of their capital equipment increases the NPV of the equipment. Governments all over the world allow rapid depreciation (although not usually as rapid as this example) in order to increase the NPVs of capital projects, causing companies to undertake more projects and thus stimulating the economy.

105

106

Summary
Capital Budgeting Technique Computation Decision Rule

Summary
Accept the project if the computed payback period is less than a predetermined length of time. Accept the project if the computed unadjusted rate of return is greater than a predetermined percentage. Accept the project if the net present value (NPV) is greater than zero. Accept the project if the internal rate of return (IRR) is greater than a predetermined hurdle rate.

Payback Period

Compute the length of time until total net cash inflow equals the initial investment cost. Compute the additional yearly accounting earnings, divided by the initial investment cost. Compute the present value of all cash inflows and outflows and add them together. Compute the interest rate that makes the present value of the cash inflows equal to the present value of the cash outflows.

Both Net Present Value (NPV) and Internal Rate of Return (IRR) involve present value calculations, so this lesson involved an extensive review of how to use our business calculators. Screening capital budgeting projects involves separating the good projects from the bad projects. Ranking those projects involves identifying the best among a set of good projects.
Both IRR and Profitability Index can be used to identify the best project.

Net Present Value (NPV)

In this lesson we learned how income taxes impact the cash flows associated with a long-term project. We learned how to compute after-tax cash flows and also how to compute the amount of the depreciation tax shield. Capital budgeting involves making decisions with respect to long-term decisions. By definition, the consequences of a capital budgeting decision will be with a company for many years. For this reason, these decisions must be made only after careful analysis. This lesson has given you an introduction to the common techniques for doing this analysis.

Internal Rate of Return (IRR)

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