# Lecture _16

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```					Lecture 16                                                                      FIN 625: Class Notes

THE BASICS OF CAPITAL BUDGETING
   What is the Capital Investment Decision?
   Project Evaluation Models
Focus on:          Payback Period
NPV
IRR
MIRR
   Comparing Payback Period, IRR, and NPV

What is Capital Budgeting and Why is it Important?

capital investments:

Why are these important decisions?

1. scarce financial resources for assets which cannot be liquidated easily

2. they define the firm’s line of business

3. they affect the firm’s cash flows for many years

4. bad decisions can cause the firm’s downfall

capital budgeting :

 - Richard T. Bliss, Babson University
and Terry D. Nixon, Miami University
Lecture 16                                                                        FIN 625: Class Notes

Steps in the Capital Budgeting Process

1.       Identify and estimate current and expected future cash flows.
2.       Establish a decision rule (NPV, IRR, etc.)
3.       Evaluate and rank the proposed projects.
4.       Make a decision and monitor results.

Project Types
Mutually exclusive - a project whose selection depends on whether or not another project
is selected

Independent - a project whose selection does not depend on whether or not another
project is selected

Project Evaluation Models

1. Payback period or PBP
2. Net Present Value or NPV
3. Internal Rate of Return or IRR
4. Modified Internal Rate of Return or MIRR

As always, only cash flow matters!

Payback Period - the expected number of years it takes to recover a project’s initial
investment.

 - Richard T. Bliss, Babson University
and Terry D. Nixon, Miami University
Lecture 16                                                                     FIN 625: Class Notes

Example: You have a project with the following forecasted cash flows:
Year           Cash Flow
0              -\$40,000
1               \$20,000
2               \$15,000
3               \$10,000
4               \$ 5,000

What is the project’s payback period?

Example: As the Chief Financial Analyst at D/A Industries, you are presented with the
following possible projects for investment. Compute the payback period for each project.
Year         Proj. A          Proj. B             Proj. C                Proj. D
0            -\$90,000         -\$90,000            -\$90,000               -\$90,000
1            \$90,000          \$65,000             \$45,000                \$30,000
2                             \$45,000             \$35,000                \$30,000
3                                                 \$25,000                \$30,000
4                                                 \$25,000                \$30,000

 - Richard T. Bliss, Babson University
and Terry D. Nixon, Miami University
Lecture 16                                                                         FIN 625: Class Notes

Deficiencies of the Payback Period method
   ignores the time value of money
   no consideration of cash flows occurring after the payback period
   no economic rationale for target payback periods

 - Calculate the Payback Period for Example 3, Example 4, and the Practice
problems from the previous Lecture

Net Present Value - the most theoretically correct model for evaluating investment
opportunities; the measure of value a project adds to the firm.

NPV = PV{cash inflows} - PV{cash outflows}

CFt

n
NPV               t 0
(1  r ) t
or,
CFt

n
NPV               t 0
(1  WACC ) t

CFt = forecasted after-tax operating Cash Flow (CF) at the end of year t
r = the required risk-adjusted rate of return
n = the economic life of the project
WACC = the appropriate weighted average cost of capital for the project

 - Richard T. Bliss, Babson University
and Terry D. Nixon, Miami University
Lecture 16                                                                       FIN 625: Class Notes

The decision rules associated with NPV analysis:
NPV > \$0  accept project
NPV < \$0  reject project
NPV = \$0  indifferent to project

Example: Gamma Industries is analyzing a new project with the following information:
Initial investment = \$306,000
Annual after-tax operating cash flows:          Year                  CF
1-3                   \$80,000
4-6                   \$90,000
In addition, the equipment being purchased will have an after-tax salvage value of
\$25,000 at the end of the project. If the firm’s weighted average cost of capital is 15%,
should Gamma undertake the project?

Timeline:

CFt
t 0 (1  WACC ) t
n
NPV          

 - Richard T. Bliss, Babson University
and Terry D. Nixon, Miami University
Lecture 16                                                                           FIN 625: Class Notes

Note that we used Gamma’s existing weighted average cost of capital (WACC) as the
appropriate discount rate. What does this assume about the project and its financing?

How can we compute the NPV of risk-changing investments?

     CAPM approach

rproject = rRF + ( rM – rRF) βproject

Important: The CAPM approach gives us the cost of common stock for a company. If
we use rproject as the firm's WACC, we are assuming an all equity financed firm. If the
firm has debt in its capital structure, you will need to recalculate the firm's WACC using
rproject in place of the company's usual rS.

Question: Where could we obtain a βproject?

 - Richard T. Bliss, Babson University
and Terry D. Nixon, Miami University
Lecture 16                                                                     FIN 625: Class Notes

Example: The CFO of Henderson-Cincinnati Corp. is evaluating the following projects:
Project             beta       Forecast Return
A                   1.9               17.5%
B                   1.2               14.0%
C                   0.8               12.0%

The risk-free rate is 5% and the market return is 12%. If the firm’s overall WACC is 13%
(assuming an all equity financed firm), which projects should be accepted?

rproject = rRF + (rM – rRF) βproject

Question: What part does the company’s overall WACC of 13% play in this problem?

 - Calculate the NPV for Example 3 (assume 12% WACC), Example 4 (assume
12% WACC), and the Practice problems from the previous Lecture.

 - Richard T. Bliss, Babson University
and Terry D. Nixon, Miami University
Lecture 16                                                                      FIN 625: Class Notes

Internal Rate of Return (IRR) - the annualized rate of return a project generates
on the funds invested in it.

The IRR is the interest rate that equates the PV of cash inflows with the PV of cash
outflows for any project or investment. IRR is conceptually the same as YTM.

What is the NPV if PV{inflows} = PV{outflows}?

Thus,

CFt

n
NPV                             0
t 0
(1  IRR) t

or,

CFt
Initial Investment Outlay  t 1
n

(1  IRR) t

How can we solve for IRR?

Example: You can buy a truck today for \$5,200. You will use it in a delivery business
for one year and earn an after-tax Cash Flow (CF) of \$3,800. At the end of the year, the
after-tax cash flow from the sale of the truck is \$2,000. What is the IRR of this
investment?
TIMELINE:

 - Richard T. Bliss, Babson University
and Terry D. Nixon, Miami University
Lecture 16                                                                    FIN 625: Class Notes

Example: DCH Machine Tools is considering a new stamping machine. The machine
costs \$340,000 today and generates after-tax CFs of \$65,000 at the end of each of the
next 6 years. What is the IRR of this investment?

CFt
Initial Investment Outlay  t 1
n

(1  IRR) t

 Practice: You are analyzing a project with the following cash flows. What is the
project’s IRR?
Time Period         Cashflow
0          -\$550,000
1          \$200,000
2          \$400,000
3          \$250,000
4          \$ 50,000
5          \$ 10,000

What is the project’s IRR?

CFt
Initial Investment Outlay  t 1
n

(1  IRR) t

 - Richard T. Bliss, Babson University
and Terry D. Nixon, Miami University
Lecture 16                                                                          FIN 625: Class Notes

Example: Sallinger’s Inc. is considering a new refrigerated truck that costs \$25,000. It
increases the firm’s after-tax cash flow by \$4,000 in years 1-3, and by \$10,000 in years
4-6. What is the NPV of buying the truck if the appropriate discount rate (WACC) is 9%?

What is the investment’s IRR?

IRR Decision Rule:
   if the project’s IRR > WACC, the required risk-adjusted return, accept the project
   if the project’s IRR < WACC, reject the project
   if the project’s IRR = WACC, we are indifferent to the project

 - Richard T. Bliss, Babson University
and Terry D. Nixon, Miami University
Lecture 16                                                                        FIN 625: Class Notes

 Potential problems with IRR:

    multiple IRRs

    assumes reinvestment at the IRR

 - Calculate the IRR for Example 3, Example 4, and the
Practice problems from the previous Lecture.

Modified Internal Rate of Return (MIRR) – the discount rate at which the
present value of a project’s cost is equal to the present value of its terminal value, where
the terminal value is found as the sum of the future values of the cash inflows,
compounded at the firm’s cost of capital.

MIRRs main advantage over IRR is that it no longer assume reinvestment at the IRR.
Funds are now assumed to be reinvested at the firm’s WACC (this is generally a more
reasonable assumption).

N

 CIFt 1  r 
N t

COFt                                              TV
t 0 1  r t  t 01  MIRRN
N

1  MIRRN
where,

COF = Cash outflows
CIF = Cash inflows
TV  = terminal value (the compounded value of the inflows assuming
reinvestment at the WACC.

 - Richard T. Bliss, Babson University
and Terry D. Nixon, Miami University
Lecture 16                                                                    FIN 625: Class Notes

Calculate the MIRR for the previous problem (Sallinger’s).

 - Calculate the MIRR for Example 3, Example 4, and the
Practice problems from the previous Lecture.

 - Richard T. Bliss, Babson University
and Terry D. Nixon, Miami University
Lecture 16                                                                       FIN 625: Class Notes

 Practice: You are the financial manager for a large and highly profitable
manufacturing company. You are currently evaluating a project proposal involving the
construction of a new product line. The proposed project will have a 5-year life and will
require the purchase of new capital equipment with a total purchase price of \$175,000.
In addition, the project will require an initial \$15,000 investment in supplies and spare
parts for the equipment, with 40% of this amount financed with accounts payable. The
new product line is expected to increase annual cash sales by \$80,000 and increase
annual cash operating expenses by \$10,000. The new equipment will have a 3-year
MACRS class life. At the end of five years, you expect to terminate the project, liquidate
the supplies and parts, and sell the equipment for \$10,000. Assume the marginal tax
rate is 34 percent. Calculate the IRR and MIRR (assume a WACC of 10%) for this
project.

 - Richard T. Bliss, Babson University
and Terry D. Nixon, Miami University
Lecture 16                                                                    FIN 625: Class Notes

Comparing NPV and IRR

Under the following assumptions, NPV and IRR will accept and reject the same projects:

1. independent projects

2. no capital rationing

Under the following assumptions, NPV and IRR may disagree regarding the ordering of
projects:

1. mutually exclusive projects

2. capital rationing

 - Richard T. Bliss, Babson University
and Terry D. Nixon, Miami University
Lecture 16                                                                     FIN 625: Class Notes

Causes of potential disagreement between NPV and IRR:

    project size (scale) differences

    timing differences

(Note: A comparison of MIRR with NPV yields similar conclusions to IRRs comparison
relative to NPV.)

 - Richard T. Bliss, Babson University
and Terry D. Nixon, Miami University

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