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P26-35B Using payback, ARR, NPV, IRR, and profitability index to make capital investment
decisions
Learning Objectives 2, 4
1. Plan A 1.10 profitability index; Plan B $(955,800) NPV
Lolas 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 $8,550,000. Expected annual net cash inflows are
$1,525,000, with zero residual value at the end of 10 years. Under Plan B, Lolas would open three larger
shops at a cost of $8,340,000. This plan is expected to generate net cash inflows of $1,120,000 per year
for 10 years, which is the estimated useful life of the properties. Estimated residual value for Plan B is
$1,300,000. Lolas uses straight-line depreciation and requires an annual return of 10%
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 Lolas 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 depreciation during
operating life of property
=
Cost
−
Residual value
Plan A:
=
$8,550,000
−
$0
=
$8,550,000
Plan B:
=
$8,340,000
−
$1,300,000
=
$7,040,000
P26-35B, cont.
Requirement 1, cont.
ARR
=
Average annual operating income
Average amount invested
Time
Net
Cash
Annuity
PV Factor
(i = 10%,
PV
Factor
(i = 10%,
Present
Plan
Present value of
net cash inflows
/
Initial investment
=
Profitability Index
A
$9,371,125
/
$8,550,000
=
1.10 (rounded)
B
$7,384,200
/
$8,340,000
=
0.89 (rounded)
P26-35B, cont.
Requirement 2
Payback
Accounting Rate
of Return (ARR)
Net Present
Value (NPV)
Profitability
Index
Focus
The time it takes
to recover the
company’s initial
cash investment.
How the
investment will
affect operating
income.
The difference
between the
present value of
the net cash
inflows and the
initial cash
investment.
The number of
dollars returned
for every dollar
invested, with all
calculations in
present value
dollars.
P26-35B, cont.
Requirement 3
Based on the quantitative measures calculated in Requirement 1, Lolas 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.
Requirement 4
Annuity PV Factor
(i = ?%, n = 10)
=
Initial investment
/
Amount of each net cash inflow
=
$8,550,000
/
$1,525,000
=
5.607 (rounded)
P26-36B Using payback, ARR, and NPV with unequal cash flows
Learning Objectives 2, 4
1. Refurbish $(29,750) NPV; Purchase 3.7 years payback
Gaynor 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 $1,600,000. If
refurbished, Gaynor 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 $3,800,000. A new machine would last 10 years and have
no residual value. Gaynor expects the following net cash inflows from the two options:
Gaynor uses straight-line depreciation and requires an annual return of 10%.
Requirements
1. Compute the payback, the ARR, the NPV, and the profitability index of these two options.
2. Which option should Gaynor choose? Why?
SOLUTION
Requirement 1
Refurbish Current Machine:
Net Cash Outflows
Net Cash Inflows
Year
Amount
Invested
Annual
Accumulated
Payback
=
5 years
+
Amount needed to complete
recovery in Year 6
Net cash inflow in Year 6
P26-36B, cont.
Requirement 1
Purchase New Machine:
Net Cash Outflows
Net Cash Inflows
Year
Amount
Invested
Annual
Accumulated
0
$ 3,800,000
1
$ 2,700,000
$ 2,700,000
Amount needed to complete
recovery in Year 4
=
Amount invested
−
Accumulated net cash
inflows at the end of Year 3
=
$3,800,000
−
$3,550,000
=
$250,000
P26-36B, cont.
Requirement 1
Refurbish
Current
Machine
Purchase
New
Machine
Average amount invested
=
Amount invested + Residual value
2
Refurbish Current Machine:
=
$1,600,000 + $0
=
$800,000
2
P26-36B, cont.
Requirement 1
Refurbish Current Machine:
Time
Net
Cash
Inflow
PV Factor
(i = 10%)
Present
Value
PV of each year’s net cash inflow
1
(n = 1)
$ 400,000
0.909
$ 363,600
2
(n = 2)
370,000
0.826
305,620
Purchase New Machine:
Time
Net
Cash
Inflow
PV Factor
(i = 10%)
Present
Value
PV of each year’s net cash inflow
1
(n = 1)
$ 2,700,000
0.909
$ 2,454,300
2
(n = 2)
450,000
0.826
371,700
3
(n = 3)
400,000
0.751
300,400
P26-36B, cont.
Requirement 1
Option
Present value of
net cash inflows
/
Initial investment
=
Profitability Index
Requirement 2
Refurbish
Current Machine
Purchase
New Machine
The profitability index of an investment provides a measure of the number of dollars returned for every
dollar invested, with all calculations performed in present value dollars. Thus, the profitability index
allows valid comparison of alternatives with different initial investment amounts. Based on the
profitability index, Gaynor should choose to purchase a new machine (the option with the higher
profitability index).
Thus, based on both the payback and profitability index, Gaynor should choose to purchase a new
machine.
P26-37B Using Excel to solve for NPV and IRR
Learning Objective 4
1. Plan Beta 11.23% IRR
3. Plan Alpha $115,654 NPV
Whitley Company is considering two capital investments. Both investments have an initial cost of
$5,000,000 and total net cash inflows of $8,000,000 over 10 years.
Whitley requires a 10% 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 $4,800,000. Recalculate
the NPV and IRR. Which plan, if any, should the company pursue?
SOLUTION
Requirement 1
Microsoft Excel Results:
P26-37B, cont.
Requirement 1, cont.
Microsoft Excel Formulas:
Plan Alpha
Plan Beta
Net present value (NPV):
($84,346) (rounded)
$230,895 (rounded)
Internal rate of return (IRR):
9.61% (rounded)
11.23% (rounded)
P26-37B, 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
Requirement 3
Microsoft Excel Results:
P26-37B, cont.
Requirement 3, cont.
Microsoft Excel Formulas:
Plan Alpha
Plan Beta
Net present value (NPV):
$115,654 (rounded)
$430,895 (rounded)
Internal rate of return (IRR):
10.56% (rounded)
12.36% (rounded)
P26-38 Using payback, ARR, NPV, and IRR to make capital investment decisions
This problem continues the Daniels Consulting situation from Problem P25-34 of Chapter 25. Daniels
Consulting is considering purchasing two different types of servers. Server A will generate net cash
inflows of $26,000 per year and have a zero residual value. Server A’s estimated useful life is three
years, and it costs $44,000.
Server B will generate net cash inflows of $28,000 in year 1, $11,000 in year 2, and $5,000 in year 3.
Server B has a $5,000 residual value and an estimated life of three years. Server B also costs $44,000.
Daniels’s required rate of return is 14%.
Requirements
1. Calculate payback, accounting rate of return, net present value, and internal rate of return for both
server investments. Use Microsoft Excel to calculate NPV and IRR.
2. Assuming capital rationing applies, which server should Daniels invest in?
SOLUTION
Requirement 1
Server A:
Payback
=
Amount invested
Expected annual net cash inflow
=
$44,000
=
1.7 years
$26,000
Total net cash inflows during operating life of server:
Server A:
=
$26,000 per year × 3 years
=
$78,000
Server B:
=
$28,000 Yr. 1 + $11,000 Yr. 2 + $5,000 Yr. 3
=
$44,000
