Capital Budgeting

• Net Present Value (NPV)

• Internal Rate of Return (IRR)

• NPV and IRR compared

• Payback Method

• Accounting Rate of Return

Net Present Value

k = the discount rate (cost of capital)

n = life of the project

NPVn

i = 1

Annual net

Cash Inflows (1+k)i

= Net Investment-

What is the project worth, in today’s dollars?

Net Present Value

k = the discount rate (cost of capital)

n = life of the project

NPVn

i = 1

1 _ (1+k)i

= Net Investment

-

What is the project worth in today’s dollars? Now assume annual cash inflows are constant for the life of the project.

Annual

net cash

Inflows

x

Net Present Value

Table 1Number

of Periods 8% 10% 12%

1 .926 .909 .893

2 .857 .826 .797

3 .794 .751 .712

4 .735 .683 .636

5 .681 .621 .567

Net Present Value

Advantages:

For choosing among projects, this is probably the best method.

Disadvantages:

No significant disadvantages, although NPV assumes cashflows can be reinvested for a return of k.

Net Present Value

Example

Acme Mining Company is considering an investment that will yield an annual cash flow of $8,000 per year for 3 years. The cost of the investment is $15,000. What is the net present value of the investment using a 10% cost of capital.

Net Present Value

Table 1Number

of Periods 8% 10% 12% 10%

1 .926 .909 .893 0.909

2 .857 .826 .797 1.736

3 .794 .751 .712 2.487

2.486

Table 2

Net Present ValueAcme Mining Company is considering an investment that will yield an annual cash flow of $8,000 per year for 3 years. The cost of the investment is $15,000. What is the net present value of the investment using a 10% cost of capital.

$8,000 x 2.487 = 19,896

$19,896 - $15,000 = $4,896

Internal Rate of Return

IRR is the interest rate computed such that the NPV of the project is zero.

Annual net

Cash Inflows (1+k)i

Net Investment-

n

i = 1

0 =

Let:

And solve for k. This is the IRR.

Internal Rate of Return

Advantages:

IRR is a measure of profitability that is independent of the size of the project.

Disadvantages:

Can motivate managers to forego positive net present value projects.

Assumes cash flows can be reinvested at the same internal rate of return.

Internal Rate of Return

Example

Acme Mining Company is considering an investment that will yield an annual cash flow of $8,000 per year for 4 years. The cost of the investment is $25,920. What is the internal rate of return on the investment.

Internal Rate of Return

Example

Acme Mining Company is considering an investment that will yield an annual cash flow of $8,000 per year for 4 years. The cost of the investment is $25,920. What is the internal rate of return on the investment.

$25,920 ÷ $8,000 = 3.24

Net Present Value

Table 2Number

of Periods 8% 10% 12%

1 .926 .909 .893

2 1.78 1.74 1.69

3 2.58 2.49 2.40

4 3.31 3.17 3.04

5 4.00 3.79 3.61

So interpolating, the IRR is approximately 9%

IRR and NPV Compared

If the IRR is less than the discount rate, NPV is negative.

If NPV > 0, IRR is greater than the discount rate.

IRR and NPV ComparedCalculate the NPV and IRR of each project.

EXAMPLE

Year-end

Project Initial Cost Cash Flow

A $1,000 $1,200

B $ 50 $ 100

The project life for both projects is 1 year. Let K = 10%

IRR and NPV Compared

EXAMPLE

Project Initial Cost Cash flow IRR NPV

A $1,000 $1,200 20% $91

B $ 50 $ 100 100% $41

Payback

PAYBACK = NET INVESTMENT AVERAGE EXPECTED CASH FLOWAdvantages:

Easy to Calculate.

Disadvantages:

Fails to account for the time value of money.

Ignores returns after the payback period.

How long will it take to recover the investment?

Accounting Rate of Return

Disadvantage: Ignores the time value of money.

Accounting rate of return =

Average book investmentAverage annual net income

In the simplest scenario, the numerator, net income, is cash flow less depreciation expense; and the denominator, book investment, is the cost of the project, net of accumulated depreciation.

Accounting Rate of ReturnAccounting rate of return =

Average book investmentAverage annual net income

Example: A machine costs $100,000, and has a useful life of 2 years. The machine will generate revenues net of operating expenses of $70,000 per year. The tax rate is 40%. The company uses straight-line depreciation.

Accounting Rate of ReturnA machine costs $100K and has a useful life of 2 years. It will generate annual revenues net of operating expenses of $70K. The tax rate is 40%.

Depreciation expense is $50,000 per year ($100,000/2).

The average book investment is also $50,000.

Accounting Rate of Return

The average of any straight line is the midpoint:

0 21

$100 K

$ 0

$ 50 K

Year 1 Year 2

Zero because the machine has zero salvage value.

Accounting Rate of ReturnAccounting rate of return =

Average book investmentAverage annual net income

Numerator:

Revenues less operating exp.s $70,000

Depreciation expense 50,000

Income before taxes 20,000

Tax Expense (40% of $20K) 8,000

Net Income 12,000

Accounting Rate of ReturnAccounting rate of return =

Average book investmentAverage annual net income

$12,000$50,000

= 24%