Download Chapter 11 - - Capital Budgeting Techniques: Certainty and Risk

Chapter 11 - - The Basics of Capital Budgeting
I.
II.
Project Classifications
A.
Replacement projects = expenditures to replace worn-out or damaged equipment
required in the production of profitable products
B.
Replacement: cost reduction = expenditures to replace serviceable but obsolete
equipment and lower costs
C.
Expansion of existing products or markets = expenditures to increase output of
existing products or to expand retail outlets or distribution facilities in markets now
being served
D.
Expansion of new products or markets = expenditures to produce new products or
to expand into new markets
E.
Safety and/or environmental products = expenditures necessary to comply with
government orders, labor agreements, or insurance policy terms
F.
Other = expenditures on office buildings, parking lots, and executive aircraft
Capital Budgeting Techniques
A.
Three ways to determine appropriate project, be it either an expansion or
replacement project, independent projects or mutually exclusive projects
1.
Payback period
2.
Net present value (NPV)
3.
Internal rate of return (IRR)
4.
Modified internal rate of return (MIRR)
B.
Example: After-tax, incremental cash flows of two projects
Year
Project A
Project B
0
-$42,000
-$45,000
1
14,000
28,000
2
14,000
12,000
3
14,000
10,000
4
14,000
10,000
5
14,000
10,000
C.
Payback period
1.
Def’n: amount of time required for a firm to recover its initial investment in
a project, as calculated from cash flows
Payback period = number of years prior to full recovery + (unrecovered cost
at start of last year)/(cash flow during full recovery year)
2.
Viewed as unsophisticated capital budgeting technique
Chapter 11: The Basics of Capital Budgeting.
Page 1
3.
4.
Decision rule: Let N* years = firm’s maximum acceptable payback period
a.
Independent projects: Accept all projects whose payback periods <
N*
b.
Mutually exclusive projects: Among those projects whose payback
periods are < N*, choose the project with the shortest payback period
The example:
a.
Project A: The cash inflow of every year = $14,000.
$42,000/14,000= 3 = => Project A’s payback period is 3 years
Year
Cash flow
Cumulative cash flow
0
-$42,000
-$42,000
1
$14,000
-$28,000
2
$14,000
-$14,000
3
$14,000
$0
4
$14,000
$14,000
5
$14,000
$28,000
Payback period = 3 years
b.
Project B: To get $45,000 = => Need all the $28,000 of the 1st year
($17,000 left to go), need all the $12,000 of the second year ($5,000 left
to go), need only $5,000 of the $10,000 earned during third year. To
prorate the time need after the second year : $5,000/$10,000 = .5 year
= => Project B’s payback period = 2.5 years
Year
Cash flow
Cumulative cash flow
0
-$45,000
-$45,000
1
$28,000
-$17,000
2
$12,000
-$5,000
3
$10,000
$5,000
4
$10,000
$14,000
5
$10,000
$28,000
Payback period = 2 years + $5,000/$10,000 years = 2.5 years
c.
d.
5.
Let N* = 3.5 years
If independent projects: accept both projects because 3 < 3.5 and 2.5 <
3.5
e.
If projects mutually exclusive: pick project B as 2.5 < 3 < 3.5
Pros and cons of the payback method
a.
The pros:
i.
Widely used
ii.
Computationally simple
iii.
Intuitive appeal
iv.
Since it measures how quick firm recovers initial investment,
gives implicit consideration to time value of money
v.
By picking projects with payback < N* = => approach is may
reduce risk and payback period has some relation to risk
exposure
b.
The con:
a.
N* a subjective predetermined measure
b.
Payback period not linked to goal of shareholder wealth
maximization
c.
Approach doesn’t fully take the time value of money into
account (cash flows aren’t discounted to present value)
d.
Payback period approach ignores cash flows received after the
payback period.
Chapter 11: The Basics of Capital Budgeting.
Page 2
6.
One possible modification: Discounted payback at 10% cost of capital
a.
Length of time required for investment’s cash flows, discounted at the
cost of capital to cover its cost
b.
Project A:
Year
Cash flow
Discounted cash flow
Cumulative discounted cash flow
0
-$45,000
-$45,000
-$45,000
1
$14,000
$12,727
-$32,273
2
$14,000
$11,570
-$20,702
3
$14,000
$10,518
-$10,184
4
$14,000
$9,562
-$622
5
$14,000
$8,693
$8,071
Payback period = 4 + 622/8693 = 4 + .07 = 4.07
c.
Project B
Year
Cash flow
Discounted cash flow
Cumulative discounted cash flow
0
-$45,000
-$45,000
-$45,000
1
$28,000
$25,455
-$19,545
2
$12,000
$9,917
-$9,628
3
$10,000
$7,513
-$2,115
4
$10,000
$6,830
$4,715
5
$10,000
$6,209
$10,924
Payback period = 3 + 2115/6830 = 3 + 0.31 = 3.031
d.
D.
If N* = 4:
i.
If projects are independent: Accept Project B and reject
project A. 3.031 < 4 < 4.07
ii.
If projects are mutually exclusive: Accept Project B and reject
project A. 3.031 < 4 < 4.07
Net present value (NPV)
1.
Def’n: sophisticated capital budgeting technique found by subtracting
project’s initial investment from present value of future cash flows (which
where discounted at rate equal to firm’s cost of capital)
2.
Let CFt be the firm’s cash flow in year t. Let k be the firm’s cost of capital.
N
CFt
CFN-1
CFN
CF1
CF2
NPV = е
- CF0 =
+
+ +
+
- CF0
t
1
2
N-1
(1+r) (1+r)
(1+r)
(1+r)N
t=1 (1 + r)
3.
r = discount rate = required return = cost of capital = opportunity cost =
minimum return that must be earned on project to leave firm’s market value
unchanged
4.
Decision rule:
a.
Independent projects: Accept all projects with NPV > 0
b.
Mutually exclusive projects: choose project with largest positive NPV
5.
The example: Let r = 10%
a.
Excel formula: NPV(discount rate, CF1, . . . , CFN) – CF0
b.
Project A:
$14,000 $14,000 $14,000 $14,000 $14,000
NPVA =-$42,000+
+
+
+
+
=$11,071
(1.10)1 (1.10)2 (1.10)3 (1.10)4 (1.10)5
c.
Project B
$28,000 $12,000 $10,000 $10,000 $10,000
NPVB =-$45,000+
+
+
+
+
=$10,924
(1.10)1
(1.10)2
(1.10)3 (1.10)4
(1.10)5
Chapter 11: The Basics of Capital Budgeting.
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d.
E.
Decision rule:
i.
If A and B are independent projects: pick both projects.
$11,091 > 0 and $10,024 > 0
ii.
If Projects A and B are mutually exclusive: Pick project A
because $11,091 > $10,924 > 0
Internal Rate of Return (IRR)
1.
Def’n: Sophisticated capital budgeting technique. It is that discount rate
where the net present value of the project is equal to zero. It is the discount
rate that equates the present value of the future cash flows with the initial
investment.
2.
Let IRR = the internal rate of return. IRR is the discount rate that solves the
following equation:
N
CFt
CFN-1
CFN
CF1
CF2
- CF0 =
+
+ +
+
- CF0 = $0

t
1
2
N-1
(1 + IRR) (1 + IRR)
(1 + IRR)
(1 + IRR)N
t=1 (1 + IRR)
Decision rule: let r = the firm’s cost of capital
a.
Independent projects: Accept any project whose IRR > r.
b.
Mutually exclusive projects: Among those projects with an IRR > r,
choose the project with the largest IRR.
4.
Excel formula: IRR(beginning cell:last cell, guess)
Enter yearly cash flows in order from initial investment to terminal cash
flow. The beginning cell of the array contains the initial investment, while
the last cell contains cash flows of the last year of the project. Guess is a
fraction to initiate the convergence to the solution.
5.
Example:
a.
Project A - - IRR = 19.86%
$14,000
$14,000
$14,000
$14,000
$14,000
-$42,000 +
+
+
+
+
=$0
2
3
4
(1.1986) (1.1986)
(1.1986)
(1.1986)
(1.1986)5
3.
b.
Project B - - IRR = 21.65%
$28,000
$12,000
$10,000
$10,000
$10,000
-$45,000 +
+
+
+
+
=$0
2
3
4
(1.2165) (1.2165)
(1.2165)
(1.2165)
(1.2165)5
c.
Decision rules: Let r = 10%
i.
Independent projects: Since IRRA = 19.86% > 10.00% and
IRRB = 21.65% > 10.00% → accept both projects A and B
ii.
Mutually exclusive projects: Pick project B because IRRB >
IRRA > r or 21.65% > 19.86% > 10.00%. In this case, there is
a conflict in the choices recommended by NPV and IRR.
According to NPV, project A should be accepted, while
according to IRR, project B is preferred.
III.
The possibilities of conflicting rankings using NPV and IRR
A.
Examine the net present value profiles
1.
Net present value profile = graph depicting project’s NPV for various
discount rates
2.
Figure 1 is the NPV profiles for the example
Chapter 11: The Basics of Capital Budgeting.
Page 4
Figure 1
NPV Profiles
20.0
15.0
Project A
Project B
NPV ($000)
10.0
5.0
0.0
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
30.00%
-5.0
-10.0
Discount Rate (%)
3.
Conflicting decisions: Independent vs mutually exclusive projects
a.
Refer to figure : IRRA = k4 , IRRB = k6
Cross over rate where NPVA = NPVB = k2
b.
Refer to Figure 2 on next page. Assume projects A and B are
independent.
Cost of Capital
NPV Approach
IRR Approach
NPV and IRR Agree?
k1
Accept A; Accept B
Accept A; Accept B
Yes
k2
Accept A; Accept B
Accept A; Accept B
Yes
k3
Accept A; Accept B
Accept A; Accept B
Yes
k4
Reject A; Accept B
Reject A; Accept B
Yes
k5
Reject A; Accept B
Reject A; Accept B
Yes
k6
Reject A; Reject B
Reject A; Reject B
Yes
k7
Reject A; Reject B
Reject A; Reject B
Yes
Conclude: When projects are independent, NPV and IRR approach
always agree.
c.
Refer to Figure 2 on next page. Now assume projects A and B are
mutually exclusive.
Cost of Capital
NPV Approach
IRR Approach
NPV and IRR Agree?
k1
Accept A; Reject B
Reject A; Accept B
No
k2
Accept either A or B Reject A; Accept B
No
k3
Reject A; Accept B
Reject A; Accept B
Yes
k4
Reject A; Accept B
Reject A; Accept B
Yes
k5
Reject A; Accept B
Reject A; Accept B
Yes
k6
Reject A; Reject B
Reject A; Reject B
Yes
k7
Reject A; Reject B
Reject A; Reject B
Yes
Conclude: For mutually exclusive projects, if k < the crossover rate,
then the recommendations of the NPV and IRR approaches will
disagree. If k > the crossover rate then the recommendations of the
two approaches agree.
Chapter 11: The Basics of Capital Budgeting.
Page 5
Figure 2
d.
Which approach is better?
i.
NPV approach is theoretically correct. The NPV approach
assumes cash flows are reinvested at the firm’s cost of capital.
However, the IRR assumes the firm’s cash flows are
reinvested at the IRR which is greater than the firm’s cost of
capital. Because the cost of capital is a more realistic estimate
of the rate at which the firm could reinvest intermediate cash
flows, use of the NPV is theoretically preferable with its more
conservative and realistic reinvestment rate of the cost of
capital.
ii.
Surveys show financial managers prefer IRR. Managers tend
to talk more about rates of return than actual dollar returns.
Managers comfortable with return data, they express interest
rates and profitability in percentage rates. NPV seems less
intuitive as it doesn’t measure benefits relative to amount
invested.
Chapter 11: The Basics of Capital Budgeting.
Page 6
B.
Multiple IRR
1.
Normal cash flows
a.
A project has normal cash flows if it has one or more outflows (costs)
followed by a series of cash inflows
b.
Examples:
i.
-+++++
ii.
---+++++
2.
Nonnormal cash flows
a.
A project has nonnormal cash flows if a cash outflow occurs
sometime after the inflows have commenced.
b.
Examples:
i.
-++++ii.
-+++-+++
3.
Key result: If a project has nonnormal cash flows, it can have multiple IRRs.
a.
A project has nonnormal cash flows if a cash outflow occurs
sometime after the inflows have commenced.
b.
Example: Assume r = 12%
Year
Cash flow
Discounted cash flow (r=12%)
Cumulative discounted cash flow
i.
ii.
0
-$400,000
-$400,000
-$400,000
1
$960,000
$857,143
$457,143
2
-$572,000
-$455,995
$1,148
PV = $1,148 → Accept project
Find IRR. Solve following equation
-$400,000 +
$960,000
-$572,000
+
=0
1
(1 + IRR)
(1 + IRR)2
400(1+IRR)2 -960(1+IRR)+572=0
400[IRR2 + 2(IRR) + 1] -960(1 + IRR) + 572 = 0
400(IRR2)-160(IRR)+12 =0
100(IRR2)-40IRR+3 = 0 → IRR =
iii.
-(-40) ± (-40)2 - 4(100)(3)
2(100)
Find two IRR: 10% and 30%
See Table 1 and Figure 3 on next page
Chapter 11: The Basics of Capital Budgeting.
Page 7
Table 1
r
PV
0.00 -$12,000.00
0.02 -$8,612.07
0.04 -$5,769.23
0.06 -$3,417.59
0.08 -$1,508.92
0.10
$0.00
0.12 $1,147.96
0.14 $1,969.84
0.16 $2,497.03
0.18 $2,757.83
0.20 $2,777.78
0.22 $2,579.95
0.24 $2,185.22
0.26 $1,612.50
0.28
$878.91
0.30
$0.00
0.32 -$1,010.10
0.34 -$2,138.56
0.36 -$3,373.70
0.38 -$4,704.89
0.40 -$6,122.45
0.42 -$7,617.54
0.44 -$9,182.10
0.46 -$10,808.78
0.48 -$12,490.87
0.50 -$14,222.22
0.52 -$15,997.23
0.54 -$17,810.76
0.56 -$19,658.12
Figure 1
Multiple IRR
$0.00
0
0.1
0.2
0.3
0.4
0.5
-$5,000.00
PV
PV
-$10,000.00
-$15,000.00
-$20,000.00
r
Chapter 11: The Basics of Capital Budgeting.
Page 8
0.6
C.
Modified internal rate of return = MIRR
1.
MIRR = discount rate at which the present value of a project’s cost is equal
to the present 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
2.
Notation
a.
COFt = cash outflow in year t
b.
CIFt = cash inflow in year t
c.
MIRR = modified internal rate of return
d.
MIRR equates present value of terminal value to present value of costs
N
terminal value = TV =
е
CIFt (1+r)N-t
t=0
N
COFt
t
t=0 (1+r)
MIRR is that interest rate that solves the following equation:
PV cost =
е
N
еt=0 CIFt (1 + r)N-t
COFt
еt=0 (1 + r)t = (1 + MIRR)N
Decision rule: Accept project if MIRR > cost of capital = r
Example: Return to previous example of Projects A and B
N
e.
f.
Year
0
1
2
3
4
5
i.
Project A
-$42,000
14,000
14,000
14,000
14,000
14,000
Project B
-$45,000
28,000
12,000
10,000
10,000
10,000
Project A
TV=$14,000(1.10)4 +$14,000(1.10)3 +$14,000(1.10)2 +$14,000(1.10)+$14,000=$85,471.40
PV of costs = $42,000
$85,471.40
$42,000 =
→ 15.27%
(1 + MIRR)5
ii.
Project B
TV=$28,000(1.10)4 +$12,000(1.10)3 +$10,000(1.10)2 +$10,000(1.10) +$10,000=$90,066.80
PV of costs = $45,000
Chapter 11: The Basics of Capital Budgeting.
Page 9
$90,066.80
→ 14.89%
(1 + MIRR)5
Decision: If projects are independent → Accept both since
MIRR > r
$45,000 =
iii.
4.
Note
a.
b.
MIRR solves multiple IRR problem, can never be more than one
MIRR. Compare it to cost of capital.
Is MIRR good for choosing between mutually exclusive projects?
i.
In general, no.
ii.
Conflicts may occur if projects differ in length → In this case
use NPV
Chapter 11: The Basics of Capital Budgeting.
Page 10