Capital Budgeting

Plus some stocks and bonds

Review question

A bond has a coupon rate of 8%. It sells today at par, that is, for $1000. What is the yield? 8% Prove it. Calculate value at 8%. Maturity can be anything.

Growing perpetuity

Time 0 1 2 3 …Cash flow 0 1 (1+g) (1+g) 2̂ …

grgrPVGPF

1),(

Example: share of stock

The market expects a dividend of $4 in one year.

It expects the dividend to grow by 5% per year

The discount rate for such firms is 16%. What is the price of a share?

Solution

P=4*(1/(.16-.05)) =36.3636...

Decomposition of value

Absent growth, as a cash cow,value = 4*(1/.16)

= 25. Remaining value of 36.3636… - 25 is

net present value of growth opportunities (NPVGO).

=11.3636...

Example: whole firm

The market expects $30M in one year and growth of 2% thereafter. Discount rate = 17%. Value of the firm is $200M. That is 30M*(1/(.17-.02))

continued

A new line of business for the firm is discovered.

The market expects $20M in a year, with growth at 7% thereafter. Value of the new growth opportunity is

$200M (at r = 17%).

Whole value:400M = 200M + 200M

Note that the value is gross, not net. Share price? Divide by the number of shares.

Arguing for your project

Capital budgeting CFO receives proposals from divisions Projects described by cash flows

Arguing means applying measures

Net present value is the right measure. Many smart people use the wrong

ones. Alternative ways to the same end.

Uses of measures

Project acceptance Mutually exclusive alternatives.

Capital Budgeting Techniques

Kim, Crick, and Kim, Management Accounting

Nov. 1986, p. 49-52

Survey of use of measures by corporations

Measure Primary Secondary

Internal rate of return 49% 15%Accounting rate of return 8% 19%Net present value 21% 24%Payback period 19% 35%Other 17% 7%

Total responses 587 469

Make no mistake

NPV is the right measure always. Others work sometimes. NPV measures value to owners, their

wealth.

Objectives of a good measure

Value cash flows. Respond to the market.

NPV’s merits

Values cash flows as the market does. Responsive because the discount rate

is the current market rate. Measures increase in shareholder

value.

Payback period is

The time required for undiscounted cash flows to add up to the initial investment.

e.g., build a Wendy’s if it “pays for itself” in two years or less.

Payback merits

Based on cash flows

Payback defects

No market response. When r is high, the satisfactory payback

period should be shorter. Subtracts time-t dollars from time-0

dollars, a cardinal sin. Ignores cash flow after payback. Ignores timing during payback.

Defects are not necessarily fatal

Repeated, similar investments. Stable financial conditions.

The well-informed capital budgeter knows

When to accept payback period as a measure.

When it is likely to fail.

Accounting rate of return

Doesn’t value cash flows No market response Ignores market values Scaling problems: melons or malls

Merits of accounting r.o.r.

Easily understood. Sometimes okay in stable markets. Smart application can overcome

defects.

Internal rate of return

Definition: IRR is the discount rate that makes NPV = 0

CFCF

r

CF

r

CF

rTT0

1 221 1 1

0

( )

. . .( )

That is, IRR is the r such that

Internal rate of return

Definition: IRR is the discount rate that makes NPV(r) = 0.

NPV(r) is a function. RWJ Figures 6.4 and 6.5.

IRR is almost the same as bond yield

Bond yield is r such that

0)2

1(

1000...

)2

1(2

1 22

Trc

rc

rc

P

Project

Time 0 1 2 3Cash flow -200 100 100 100

Figure 6.4: NPV(r)=0 at r=23.37%

NPV

r

100

NPV(r)

NPV(.1) = 48.68520

.1

IRR =23.3748.685

Figure 6.4

NPV (r) = 0 at r = 23.37%

Applications of IRR measure

Hurdle rate = market rate Project acceptance: Accept a project if

IRR > hurdle rate. Mutually exclusive projects: Take the

one with the highest IRR (> hurdle rate)????? Don’t rely on it.

Project acceptance:

NPV and IRR give the same conclusion when ...

Cash flows have one sign change. In the example: IRR = 23.37% > hurdle

= 10% for an investment project. IRR = 23.37% < hurdle rate = 30% for a

financing or “borrowing from nature” project.

Merits

Uses cash flows. Responds to the market when the

hurdle rate changes

Objective

Learn to recognize the times when NPV and IRR are the same.

and also the problems with IRR

Defects of IRR -- project acceptance

Lending to nature or borrowing from her?

Multiple IRR's may occur.

Financing (borrowing from nature)

Seek IRR < hurdle rate Same as NPV > 0

Multiple IRR's

Time in decades 0 1 2Cash flows -1 5 -6

IRR’s at r = 1 and r = 2

100% per decade = 7.17735% per year. 200% per decade = 11.61232% per

year.

IRR’s at r=1 and r=2.

NPV

r

100% 200%

Descartes’ Rule

The number of internal rates of return is no more than the number of sign changes.

The number of positive roots of a polynomial with real coefficients is at most equal to the number of sign changes in the coefficients.

Interest rates are more than -100%

Defects of IRR -- mutually exclusive projects

Ignores market values. Scale problems -- melons or malls.

Typical hour exam question

What is the scale problem in using IRR to choose between mutually exclusive projects?

Scale problem in IRR

Time 0 1 IRR NPV(r=.1)Little dam -100 200 1 81.8181…Big dam -1000 1500 0.5 363.6363…

One canyon, one dam.

Sketch of answer

The smaller dam has the higher IRR. The big dam has higher value. The big dam extends consumption

possibility of owners more than the little dam does.

It is wrong to take the higher IRR in this case.

Capital Budgeting Jiu Jitsu

Consider the project of replacing the little dam by the big dam.

Cash flows are -900, +1300. IRR of the project is 4/9 = .4444 > .1 NPV is 281.8181… So replace the little dam. Capital budgeting jiu jitsu.

Scale problems in IRR

Time 0 1 IRR NPV(r=.1)

Littledam

-100 200 1 81.8181...

Bigdam

-1000 1500 .5 363.63...

r

NPV

50% 100%

100

500

Big dam

Little dam

IRR IRR

Big dam, little dam

NPV

NPV of the big dam

NPV of the small dam

500

100

.51

r

r*

For hurdle rates below r*,the big dam is preferred.

r* = .4444...