Capital Budgeting Techniques

Investment B

Investment C

Probability

After Tax  Cash Flow

0.25

$20,000

0.30

$22,000

0.50

  32,000

  40,000

0.20

  50,000

Assignment 1 Grading Criteria

Maximum Points

Correctly calculated the cost of new equity and explained the calculations, as well as the advantages and disadvantages of using this type of financing for the firm. (CO4)

20

Correctly calculated the cost of new debt and explained the calculations, as well as the advantages and disadvantages of using this type of financing for the firm. (CO4)

Correctly calculated the weighted average cost of capital and explained how and why it is used in the capital budgeting process. (CO4)

Correctly calculated the annual cash flows for the projects and explained the methods used in the calculations. (CO1)

44

Evaluated the projects using the NPV method and came to the correct conclusions based on the decision rules for the NPV. (CO2)

Evaluated the projects using the IRR method and came to the correct conclusion based on the decision rules for the IRR. Identified any conflicts between the IRR and the NPV and explained why these conflicts may occur. (CO 3)

Correctly introduced risk into the evaluation by using the expected values as the cash flows and evaluated these cash flows using risk adjusted discounted rates. (CO 5)

Written in a clear, concise, and organized manner; demonstrated ethical scholarship in accurate representation and attribution of sources; displayed accurate spelling, grammar, and punctuation.

64

Total:

300

 Capital Budgeting Techniques (3 of 5)

Discounted Cash Flow Methods

In the discounted cash flow analysis decisions are based on the calculation of NPVs of future cash flows.
The Net Present Value (NPV) Method: According to this method a dollar that is received immediately is preferable to a dollar received at some future date. The method discounts the cash flow based on the time value of money concept. You calculate the present value of expected net cash flows of an investment discounted at the cost of capital and subtract the initial cash outlay of the project. If the NPV is positive, the project is acceptable, and if the NPV is negative, the project should be rejected. When the projects are mutually exclusive the project with the highest NPV should be accepted.

Example

Given the cash flows for projects A and B, calculate the NPV for each using a discount rate of 10%. Calculate the NPV for each using a discount rate of 14%.

Year 0

Year 1

Year 2

Year 3

Year 4

Project A Cash Flow

(100)

30

30

40

30

Project B Cash Flow

(100)

50

50

20

10

Solution

Project A: NPV at 10% = + 2.61; NPV at 14% = – 5.8
Project B: NPV at 10% = + 8.63; NPV at 14% = + 1.75

At 10% discount rate:
If the projects are independent both are acceptable.
If they are mutually exclusive Project B is acceptable.

At 14% discount rate:
If the projects are independent Project B is acceptable. 
If they are mutually exclusive Project B is acceptable.

Using a Financial Calculator

Enter all the cash flows in CF register; NPV; I = 10% 
Compute; NPV = 2.61

 Capital Budgeting Techniques (4 of 5)

Advantages of NPV method

· It indicates the increase in the value of the firm by taking the project. This is in line with the goal of the firm.

· It adjusts for the timing of the project’s expected cash flows.

· It adjusts for the risk of the project’s cash flow through the discount rate.

· It is additive. According to the value additive property if one project has an NPV of $50,000 and another project has an NPV of $150,000, and the projects are independent, the projects have a combined NPV of $200,000.

Disadvantages of the NPV method

· It is difficult to explain to non-finance people.

· The solution is in dollars not percentage rates of return.

Internal Rate of Return (IRR) Method: IRR is the discount rate at which the NPV of a project is equal to zero.

Example: Given the following cash flows for projects A and B, calculate the IRR for each project.

Year 0

Year 1

Year 2

Year 3

Year 4

Project A Cash Flow

(100)

30

30

40

30

Project B Cash Flow

(100)

50

50

20

10

Calculating the IRR is similar to calculating the yield to maturity of a bond.

Using a Financial Calculator

Enter cash flows in CF register; IRR 
Compute: IRR = 11.2% (Project A)
IRR = 15.1 (Project B)

IRR Decision Rules

Independent projects: Accept all as long as the IRR > = hurdle rate.
Hurdle rate: Refers to the cost of capital compared to the investment’s IRR.

Using the navigation on the left, please proceed to the next page.

 Capital Budgeting Techniques (5 of 5)

Advantages of the IRR Method

The advantages of the IRR method are:

· It considers all cash flows.

· It considers time value of money.

· It is comparable with hurdle rate.

Disadvantages of the IRR Method

The disadvantages of the IRR method are:

· It does not show dollar increases or decreases in the value of the firm if a project is accepted.

· Multiple IRRs may exist.

NPV and IRR Methods: Possible Decision Conflicts

An accept/reject conflict occurs when NPV indicates that the firm should accept, and IRR indicates that the firm should reject the project, and vice versa.

Ranking conflicts arise as a result of:

· Timing differences in incremental cash flows.

· Magnitude differences in incremental cash flows.

When a conflict arises it is a good idea to use the NPV method.

 Estimating Project Cash Flows and Risk Analysis (1 of 3)

We’ll now discuss how to estimate the cash flows for a project. A project’s cash flow generally comprises: initial investment or cash outflow, operating cash flows or cash inflows for each period, and terminal cash flows such as salvage value. Incremental after-tax cash flows are the only relevant cash flows in capital budgeting, which are directly attributable to the project. Incremental cash flows represent the change in the firm’s total cash flows that occur as a result of accepting the project. The risk of the project is ascertained by using the discount rate. Usually a higher discount rate is used for projects with high risk, and a lower discount rate is used for projects with low risk.

A project’s cash flows are estimated as shown:

Initial investment in t = 0 includes investment in machinery and building. During the course of the project operating cash flows are generated. Terminal cash flows are generated as a result of disposing machinery and building, among other things, when the project is terminated.

Estimating cash outflows involves estimating the price of machinery. In other words depreciable assets, any shipping costs and installation costs, and investment in working capital. Working capital comprises investment in inventory and other short-term assets that are required for day-to-day project activities. Estimating operating cash inflows involves estimating after-tax operating cash flows — which is the addition of net income and depreciation — during the estimated life of the project.

Operating cash flows typically occur over several years, where the amount in each year may vary as a result of varying sales, costs, and depreciation. Terminal cash flows are cash flows associated with project termination as a result of selling depreciable assets and recapturing working capital.

 Estimating Project Cash Flows and Risk Analysis (2 of 3)

Operating cash flows are estimated on a periodical basis as shown:

Example

A project with a 3-year life requires an initial investment of $1,500. The project is expected to generate revenues of $1,000 each year for 3 years. The costs are $300 per year. If there is no salvage value, calculate the cash flows for the project assuming a tax rate of 35%. Calculate the NPV of the project with the cost of capital as 10%. Use straight-line depreciation. 
(Depreciation each year = 1500/3 = $500)

Solution

Year

0

1

2

3

Initial Investment

-1500

Revenues

1000

1000

1000

-Costs

-300

-300

-300

-Depreciation

-500

-500

-500

Earnings Before Taxes

200

200

200

-Taxes (35%)

-70

-70

-70

Net Income

130

130

130

+Depreciation

500

500

500

Operating Cash Flows from the Project

630

630

630

Total Cash Flows

-1500

630

630

630

NPV at 10%

=

-1500 + 630/(1.1) + 630/(1.1)2 + 630/(1.1)3

=

+ 66.72

The project is acceptable because the NPV is positive.

Note: If the working capital requirement is $500, which is invested in Year 0 and recovered at the end of the project, and if the after-tax salvage value at the end of the project is $200, the cash flows for the project will be:

Year

0

1

2

3

Total Cash Flows

-(1500 + 500)

+630

+630

(630 + 500 + 200)

Total Cash Flows

-2000

+630

+630

+1330

NPV at 10% = + 92.

The project is acceptable because the NPV is positive.

 Estimating Project Cash Flows and Risk Analysis (3 of 3)

Project Risk Considerations

So far you estimated a project’s cash flows to evaluate and decide whether or not to accept the project. In reality cash flow values cannot be calculated with certainty because there are several risks. The Risk-Adjusted Discount Rate (RADR) method adjusts the discount rate used for calculating the NPV of a project. Projects with higher risks are discounted at higher rates because their required rates of return are higher.

Projects can be categorized depending on the following types of project:

· Low risk or below-average risk projects: Projects that do not require any changes or very minor changes.

· Average risk projects: Project replacement decisions that require changes in technology or plant layout, including expansion of product lines and markets.

· Above-average risk projects: Expansion projects in a new product or market and research and development projects.

· High-risk projects: Expansion into less developed countries and introduction of products unrelated to existing product lines, which require high rates of return.

Discount rate adjustments for projects with varying risk levels are shown below:

· Below-average risk: Discount rate = Cost of capital – 2%

· Average risk: Discount rate = Cost of capital

· Above-average risk: Discount rate = Cost of capital + 2%

· High-risk: Discount rate = Cost of capital + 5%

 Risk (1 of 2)

Risk Definition

Risk can be defined as the different possible outcomes given an investment. If we put money into a one-year CD account at the local bank, the outcome is known. Hence, there is no risk. Especially because banks are insured by the FDIC. If we invest in a startup company, the risk is potentially great. Risk is measured in loss and uncertainty. It is assumed that most investors are risk averse. This means they prefer to know the possible results of investing rather than not. Most people are willing to take some risk. However, the higher the risk the higher the expected return.

Measurement of Risk

Risk may be measured using a number of statistical devices. An easy way to ascertain risk is through experience, use of industry ratios, trends, research into company management, and simulation techniques.

Standard deviation is a measure of how far an outcome may fall from an expected value. The further the value is away from the expected value, the higher the risk.

Rates of Return

The investor return is a measure of the growth in wealth as a result of the investment. This growth is expressed in percentage over a specific time interval, usually for one year, for purposes of comparison. For example the purchase of a share of stock at time t, represented as Pt, will yield P  t+1 in one year’s time, assuming that no dividends are paid. The return is calculated as:

R t = [ P  t+1 – Pt]/ Pt

Note its algebraic expression as: Rt= [P t+1/ Pt] -1

When dividends are paid the calculation includes the intermediate dividend payment:

Rt = [ P t+1 – Pt + Dt]/ Pt

Standard Deviation (s) as a Measure of Risk

Stock returns may be riskier or more volatile. This concept is expressed by using a statistical measure called standard deviation, which is the square root of the variance. Standard deviation is a summary measure of the average spread of observations. The higher the standard deviation the higher the risk. The variance (σ2) is calculated as:

 Risk (2 of 2)

(The graphic on the page provides the arithmetic mean and standard deviation of returns for various investments over 1926-2002.)

Example

Given the following data for Stock A and Stock B:

Year

2000

2001

2002

2003

Rate of Return A

90%

– 20%

50%

20%

Rate of Return B

110 %

60%

-60%

50%

Calculate the arithmetic return and the standard deviation of returns.

Solution

Stock A:

Stock A has a lower return and lower risk than Stock B. Usually investors prefer high returns and low standard deviation or risk. In this way you can meaningfully summarize stock return data using the arithmetic mean and standard deviation measures in terms of average returns and risk.
The coefficient of variation (V) is simply dividing the standard deviation of an investment (σ) by the expected value (D). The larger the coefficient of variation, the greater the risk. The formula for the coefficient of variation is

coefficient of variation (V)

=

s
D

Beta (β) is another risk measure. Beta is used with portfolios of common stock. It describes the relation of returns with that of the financial market. A stock with a beta of one means that its price is correlated with the market. This is considered a positive beta. The stock would move with the market. A negative beta is not correlated with the market. It is said to follow the market inversely. This stock would move opposite with the market.