P26-30A Using payback, ARR, NPV, IRR, and profitability index to make capital investment
decisions
Learning Objectives 2, 4
1. Plan A 1.19 profitability index; Plan B $(755,780) NPV
Lados operates a chain of sandwich shops. The company is considering two possible expansion plans.
Plan A would open eight smaller shops at a cost of $8,600,000. Expected annual net cash inflows are
$1,600,000, with zero residual value at the end of 10 years. Under Plan B, Lados would open three
larger shops at a cost of $8,300,000. This plan is expected to generate net cash inflows of $1,090,000 per
year for 10 years, the estimated useful life of the properties. Estimated residual value for Plan B is
$1,300,000. Lados uses straight-line depreciation and requires an annual return of 9%.
Requirements
1. Compute the payback, the ARR, the NPV, and the profitability index of these two plans.
2. What are the strengths and weaknesses of these capital budgeting methods?
3. Which expansion plan should Lados choose? Why?
4. Estimate Plan A’s IRR. How does the IRR compare with the company’s required rate of return?
SOLUTION
Requirement 1
Payback
=
Amount invested
Expected annual net cash
inflow
Total net cash inflows during
operating life of property
=
×
Operating life
of property
Plan A:
=
×
=
$16,000,000
Plan B:
=
×
=
$10,900,000
Total depreciation during
operating life of property
=
Cost
−
Residual value
Plan A:
=
$8,600,000
=
$8,600,000
Plan B:
=
$8,300,000
=
$7,000,000
Plan A
Plan B
Total net cash inflows during operating life of property
$ 16,000,000
$ 10,900,000
Less: Total depreciation during operating life of property
8,600,000
7,000,000
Total operating income during operating life
7,400,000
3,900,000
Average annual operating income from plan
Average amount invested
=
Amount invested + Residual value
2
Plan A:
=
=
$4,300,000
2
P26-30A, cont.
Requirement 1, cont.
ARR
=
Average annual operating income
Average amount invested
=
Plan A:
1 – 10 years
PV of annuity
$ 1,600,000
6.418
$ 10,268,800
0
Initial investment
(8,600,000)
NPV of Plan A
$ 1,668,800
Plan B:
1 – 10 years
PV of annuity
$ 1,090,000
6.418
$ 6,995,620
10
PV of residual value
0.422
Total PV of net cash inflows
0
Initial investment
(8,300,000)
NPV of Plan B
Plan
net cash inflows
A
/
=
P26-30A, cont.
Requirement 2
Payback
Accounting Rate
of Return (ARR)
Net Present
Value (NPV)
Profitability
Index
• Highlights
risks of
investments
with longer
accounting
figures.
• Measures the
• Considers the
asset’s net cash
flows over its
• Considers the
asset’s net cash
flows over its
• No additional
steps needed
for capital
rationing
decisions when
occurring after
the payback
period,
rationing
decisions when
assets require
net cash
inflows and the
initial
P26-30A, cont.
Requirement 3
Based on the quantitative measures calculated in Requirement 1, Lados should choose Plan A, rather
than Plan B. Plan A has a positive net present value (NPV), whereas Plan B has a negative NPV. Plan A
also has the lower payback period and the higher accounting rate of return and profitability index.
Note: Decisions about which investments to pursue and which ones to delay or reject should not be
based on quantitative factors only. Qualitative factors should also be considered. A project that is
acceptable based on quantitative factors might be rejected after considering qualitative factors (and a
project that would be rejected based on quantitative factors might be accepted after considering
qualitative factors).
Requirement 4
Annuity PV Factor
(i = ?%, n = 10)
=
Initial investment
/
Amount of each net cash inflow
Annuity PV Factor
Because 5.375 is between 5.216 and 5.650, the IRR is between 12% and 14%.
P26-31A Using payback, ARR, and NPV with unequal cash flows
Learning Objectives 2, 4
1. Refurbish $116,260 NPV; Purchase 4.2 years payback
Mandel Manufacturing, Inc. has a manufacturing machine that needs attention. The company is
considering two options. Option 1 is to refurbish the current machine at a cost of $1,100,000. If
refurbished, Mandel expects the machine to last another eight years and then have no residual value.
Option 2 is to replace the machine at a cost of $2,200,000. A new machine would last 10 years and have
no residual value. Mandel expects the following net cash inflows from the two options:
Mandel uses straight-line depreciation and requires an annual return of 16%.
Requirements
1. Compute the payback, the ARR, the NPV, and the profitability index of these two options.
2. Which option should Mandel choose? Why?
SOLUTION
Requirement 1
Refurbish Current Machine:
Net Cash Outflows
Net Cash Inflows
Year
Amount
Invested
Annual
Accumulated
0
$ 1,100,000
1
$280,000
$ 280,000
2
500,000
780,000
3
380,000
4
260,000
1,420,000
5
140,000
1,560,000
6
140,000
1,700,000
7
140,000
1,840,000
8
140,000
1,980,000
Amount needed to complete
recovery in Year 3
=
Amount invested
−
Accumulated net cash
inflows at the end of Year 2
=
=
Payback
=
2 years
+
Amount needed to complete
recovery in Year 3
Net cash inflow in Year 3
$320,000
$380,000
=
+
=
2.8 years (rounded)
P26-31A, cont.
Requirement 1, cont.
Purchase New Machine:
Net Cash Outflows
Net Cash Inflows
Year
Amount
Invested
Annual
Accumulated
0
$ 2,200,000
1
$ 260,000
$ 260,000
2
740,000
1,000,000
3
620,000
1,620,000
4
500,000
5
380,000
6
380,000
2,880,000
7
380,000
3,260,000
8
380,000
3,640,000
9
380,000
4,020,000
380,000
4,400,000
Amount needed to complete
recovery in Year 5
=
Amount invested
−
Accumulated net cash
inflows at the end of Year 4
=
=
Payback
=
4 years
+
Amount needed to complete
recovery in Year 5
Net cash inflow in Year 5
$380,000
=
+
=
4.2 years
P26-31A, cont.
Requirement 1, cont.
Total depreciation during
operating life of machine
=
Cost
−
Residual value
Refurbish Current Machine:
=
$1,100,000
−
$0
=
$1,100,000
=
$2,200,000
−
$0
=
$2,200,000
Amount invested + Residual value
Refurbish Current Machine:
=
=
$1,100,000
Refurbish Current
Machine
Purchase New
Machine
Total net cash inflows during operating life of machine
$ 1,980,000
$ 4,400,000
Less: Total depreciation during operating life of machine
1,100,000
2,200,000
Total operating income during operating life
2,200,000
Average annual operating income from machine
$ 110,000
$ 220,000
P26-31A, cont.
Requirement 1, cont.
Refurbish Current Machine:
Inflow
PV of each year’s net cash inflow
1
(n = 1)
$280,000
0.862
$ 241,360
2
(n = 2)
500,000
0.743
3
(n = 3)
380,000
0.641
4
(n = 4)
260,000
0.552
5
(n = 5)
140,000
0.476
66,640
6
(n = 6)
140,000
0.410
57,400
7
(n = 7)
140,000
0.354
49,560
Net
PV Factor
Present
8
(n = 8)
140,000
0.305
42,700
Total PV of net cash inflows
1,216,260
0
Initial investment
(1,100,000)
NPV of refurbishing current machine
$ 116,260
Purchase New Machine:
PV of each year’s net cash inflow
1
(n = 1)
$ 260,000
0.862
$ 224,120
2
(n = 2)
740,000
0.743
549,820
3
(n = 3)
620,000
0.641
397,420
4
(n = 4)
500,000
0.552
276,000
5
(n = 5)
380,000
0.476
180,880
6
(n = 6)
380,000
0.410
155,800
7
(n = 7)
380,000
0.354
134,520
8
(n = 8)
380,000
0.305
115,900
9
(n = 9)
380,000
0.263
99,940
10
(n = 10)
380,000
0.227
86,260
Total PV of net cash inflows
2,220,660
0
Initial investment
NPV of purchasing new machine
$ 20,660
P26-31A, cont.
Requirement 1, cont.
Option
Present value of
net cash inflows
/
Initial investment
=
Profitability Index
Current Machine
New Machine
/
=
Refurbish
=
Requirement 2
Refurbish
Current Machine
Purchase
New Machine
Payback period:
2.8 years (rounded)
4.2 years
Accounting rate of return (ARR):
20%
Net present value (NPV):
Profitability index:
1.01 (rounded)
Based on payback Mandel should choose to refurbish the current machine (the option with the shorter
payback period).
Because the accounting rate of return (ARR) of the two options is the same, ARR doesn’t help choose
between the two options.
Because each of the two options requires a different initial investment (cost), comparing the net present
value (NPV) of the two options is not valid.
P26-32A Using Excel to solve for NPV and IRR
Learning Objective 4
1. Plan Beta 20.58% IRR
3. Plan Alpha $369,461 NPV
Langley Company is considering two capital investments. Both investments have an initial cost of
$6,000,000 and total net cash inflows of $14,000,000 over 10 years. Langley requires a 20% rate of
return on this type of investment. Expected net cash inflows are as follows:
Requirements
1. Use Excel to compute the NPV and IRR of the two plans. Which plan, if any, should the company
pursue?
2. Explain the relationship between NPV and IRR. Based on this relationship and the company’s
required rate of return, are your answers as expected in Requirement 1? Why or why not?
3. After further negotiating, the company can now invest with an initial cost of $5,500,000. Recalculate
the NPV and IRR. Which plan, if any, should the company pursue?
SOLUTION
Requirement 1
Microsoft Excel Results:
P26-32A, cont.
Requirement 1, cont.
Microsoft Excel Formulas:
Plan Alpha
Plan Beta
Net present value (NPV):
$(130,539) (rounded)
$111,172 (rounded)
Internal rate of return (IRR):
Based on the foregoing, the company should pursue Plan Beta because the NPV is positive and the IRR
is greater than the company’s required rate of return. The company should not pursue Plan Alpha
P26-32A, cont.
Requirement 2
The internal rate of return is the actual rate of return, based on discounted cash flows, of an investment.
The net present value of an investment measures the difference between the present value of the
investment’s net cash inflows and the investment’s cost (cash outflows), calculated using the required
Requirement 3
Microsoft Excel Results:
P26-32A, cont.
Requirement 3, cont.
Microsoft Excel Formulas:
Plan Alpha
Plan Beta
Net present value (NPV):
$369,461 (rounded)
$611,172 (rounded)
Internal rate of return (IRR):
Based on the foregoing, if the company has sufficient resources and the plans are not mutually
exclusive, it should pursue both plans because the NPV is positive and the IRR is greater than the
Problems (Group B)
P21-33B Using the time value of money
Learning Objective 3
1. $2,249,170
You are planning for an early retirement. You would like to retire at age 40 and have enough money
saved to be able to withdraw $230,000 per year for the next 40 years (based on family history, you think
you will live to age 80). You plan to save by making 10 equal annual installments (from age 30 to age
40) into a fairly risky investment fund that you expect will earn 10% per year. You will leave the money
in this fund until it is completely depleted when you are 80 years old.
Requirements
1. How much money must you accumulate by retirement to make your plan work? (Hint: Find the
present value of the $230,000 withdrawals.)
2. How does this amount compare to the total amount you will withdraw from the investment during
retirement? How can these numbers be so different?
SOLUTION
Requirement 1
Present value
=
Amount of each
net cash inflow
(investment withdrawal)
×
Annuity PV Factor
for i = 10%, n = 40
=
×
=
Requirement 2
Total withdrawn
during retirement
=
Amount withdrawn each year
×
Total number of years
=
×
=
P26-34B Using payback, ARR, NPV, IRR, and profitability index to make capital investment
decisions
Learning Objectives 2, 4
1. 25.99% ARR; 1.36 profitability index
Splash City is considering purchasing a water park in Omaha, Nebraska, for $1,910,000. The new
facility will generate annual net cash inflows of $487,000 for eight years. Engineers estimate that the
facility will remain useful for eight years and have no residual value. The company uses straight-line
depreciation, and its stockholders demand an annual return of 10% on investments of this nature.
Requirements
1. Compute the payback, the ARR, the NPV, the IRR, and the profitability index of this investment.
2. Recommend whether the company should invest in this project.
SOLUTION
Requirement 1
Payback
=
Amount invested
Expected annual net cash inflow
=
=
Total net cash inflows during
operating life of facility
=
×
Operating life
of facility
=
×
=
$3,896,000
Total depreciation during
operating life of facility
=
Cost
−
Residual value
=
$1,910,000
=
$1,910,000
Total net cash inflows during operating life of facility
$ 3,896,000
Less: Total depreciation during operating life of facility
1,910,000
Total operating income during operating life
1,986,000
Average annual operating income from facility
$ 248,250
Average amount invested
=
Amount invested + Residual value
2
=
$1,910,000 + $0
=
$955,000
2
ARR
=
Average annual operating income
Average amount invested
=
25.99% (rounded)
P26-34B, cont.
Requirement 1, cont.
Time
Net
Cash
Inflow
Annuity
PV Factor
(i = 10%,n = 8)
Present
Value
1 – 8 years
PV of annuity
$ 487,000
2,598,145
Initial investment
(1,910,000)
$ 688,145
Annuity PV Factor
(i = ?%, n = 8)
=
Initial investment
/
Amount of each net cash inflow
=
/
=
Annuity PV Factor
(i = 18%,n = 8)
(i = 20%,n = 8)
Because 3.922 is between 3.837 and 4.078, the IRR is between 18% and 20%.
Note: Using a business calculator or Microsoft Excel, the IRR is 19.27% (rounded).
Profitability Index
=
Present value of
net cash inflows
/
Initial investment
=
/
=
Requirement 2
Based on the quantitative measures calculated in Requirement 1, the company should invest in the
project because the payback period is less than the operating life, the net present value is positive, the