S26-14 Using NPV to make capital investment decisions
Learning Objective 4
Castle is considering an investment opportunity with the following expected net cash inflows: Year 1,
$230,000; Year 2, $170,000; Year 3, $110,000. The company uses a discount rate of 9%, and the initial
investment is $345,000. Calculate the NPV of the investment. Should the company invest in the project?
Why or why not?
SOLUTION
Time
Net
Cash
Inflow
PV Factor
(i = 9%)
Present
Value
PV of each year’s net cash inflow
1
(n = 1)
$ 230,000
0.917
$ 210,910
2
(n = 2)
0.842
(n = 3)
0.772
Total present value of net cash inflows
Initial investment
Net present value of the investment
Exercises
E26-15 Defining capital investments and the capital budgeting process
Learning Objectives 1, 2, 4
Match each definition with its capital budgeting method.
METHODS
1. Accounting rate of return
2. Internal rate of return
3. Net present value
4. Payback
DEFINITIONS
a. Is only concerned with the time it takes to get cash outflows returned.
b. Considers operating income but not the time value of money in its analyses.
c. Compares the present value of cash outflows to the present value of cash inflows to determine
investment worthiness.
d. The true rate of return an investment earns.
SOLUTION
Methods
Definitions
1.
b.
2.
d.
4.
E26-16 Defining capital investment terms
Learning Objectives 1, 2, 4
Fill in each statement with the appropriate capital investment analysis method: Payback, ARR, NPV, or
IRR. Some statements may have more than one answer.
a. —–— is (are) more appropriate for long-term investments.
b. —–— highlights risky investments.
c. —–— shows the effect of the investment on the company’s accrual-based income.
d. —–— is the interest rate that makes the NPV of an investment equal to zero.
e. —–— requires management to identify the discount rate when used.
f. —–— provides management with information on how fast the cash invested will be recouped.
g. —–— is the rate of return, using discounted cash flows, a company can expect to earn by investing
in the asset.
h. —–— does not consider the asset’s profitability.
i. —–— uses accrual accounting rather than net cash inflows in its computation.
SOLUTION
a.
NPV and IRR
b.
Payback
c.
ARR
d.
IRR
e.
NPV
Payback
g.
IRR
h.
Payback
ARR
E26-17 Using payback to make capital investment decisions
Learning Objective 2
Consider the following three projects. All three have an initial investment of $500,000.
Requirements
1. Determine the payback period of each project. Rank the projects from most desirable to least
desirable based on payback.
2. Are there other factors that should be considered in addition to the payback period?
SOLUTION
Requirement 1
The payback period of each project, ranked from most desirable (shortest) to least desirable (longest) is:
Project
Payback
Period
N
2 years
4 years
L
5 years
Requirement 2
The company should also consider the cash inflows that occur after the payback period. For example,
Project N has the shortest payback period, but does not generate any cash flows after that point.
Therefore, the project only recoups the initial cash investment but does not provide any profits. Projects
E26-18 Using payback to make capital investment decisions
Learning Objective 2
4.1 yrs.
White Co. is considering acquiring a manufacturing plant. The purchase price is $1,350,000. The owners
believe the plant will generate net cash inflows of $329,000 annually. It will have to be replaced in six
years. Use the payback method to determine whether White should purchase this plant. Round to one
decimal place.
SOLUTION
Payback
=
Amount invested
Expected annual net cash inflow
=
E26-19 Using payback to make capital investment decisions
Learning Objective 2
5.3 yrs.
Rapp Hardware is adding a new product line that will require an investment of $1,418,000. Managers
estimate that this investment will have a 10-year life and generate net cash inflows of $310,000 the first
year, $290,000 the second year, and $250,000 each year thereafter for eight years. Compute the payback
period. Round to one decimal place.
SOLUTION
Net Cash Outflows
Net Cash Inflows
Year
Amount
Invested
Annual
Accumulated
0
$ 1,418,000
1
$ 310,000
$ 310,000
2
290,000
600,000
3
250,000
850,000
4
250,000
5
250,000
6
250,000
7
250,000
8
250,000
9
250,000
250,000
Amount needed to complete
recovery in Year 6
=
Amount invested
−
Accumulated net cash
inflows at the end of Year 5
=
$1,418,000
−
$1,350,000
=
$68,000
Amount needed to complete recovery in Year 6
=
5 years
+
=
5.3 years
Note: Exercise S26-19 must be completed before attempting Exercise S26-20.
E26-20 Using ARR to make capital investment decisions
Learning Objective 2
16.67%
Refer to the Rapp Hardware information in Exercise E26-19. Assume the project has no residual value.
Compute the ARR for the investment. Round to two places.
SOLUTION
Total net cash inflows
during
operating life of project
=
Sum of net cash inflows during operating
life of project
=
=
$2,600,000
=
$1,418,000
=
$1,418,000
Total net cash inflows during operating life of project
$ 2,600,000
Less: Total depreciation during operating life of project
1,418,000
Total operating income during operating life
1,182,000
Average annual operating income from project
$ 118,200
Average amount invested
=
Amount invested + Residual value
2
=
=
E26-21 Using the time value of money
Learning Objective 3
2. $143,208
Requirements
1. How much money does Sharon need now to fund her travels?
SOLUTION
Requirement 1
Present value
=
Amount of each
net cash inflow
×
Annuity PV Factor for i = 8%, n = 5
Requirement 2
Present value
=
Amount of each
net cash inflow
×
Annuity PV Factor for i = 6%, n = 5
E26-22 Using the time value of money
Learning Objective 3
Option #2 $7,582,000
Congratulations! You have won a state lottery. The state lottery offers you the following (after-tax)
payout options:
Assuming you can earn 10% on your funds, which option would you prefer?
SOLUTION
Option #1:
Present value
=
Net cash inflow
×
PV Factor for i = 10%, n = 5
=
×
=
$6,831,000
Option #2:
Present value
=
Amount of each
net cash inflow
×
Annuity PV Factor for i = 10%, n = 5
=
×
=
Option #3:
Present value
=
Net cash inflow
×
PV Factor for i = 10%, n = 3
=
×
=
$7,510,000
Option
Present Value
#1
$ 6,831,000
#2
#3
E26-23 Using NPV to make capital investment decisions
Learning Objective 4
2. Equip. with refurb. $(74,219) NPV
Eon Industries is deciding whether to automate one phase of its production process. The manufacturing
equipment has a six-year life and will cost $920,000. Projected net cash inflows are as follows:
Requirements
1. Compute this project’s NPV using Eon’s 16% hurdle rate. Should Eon invest in the equipment?
2. Eon could refurbish the equipment at the end of six years for $104,000. The refurbished equipment
could be used one more year, providing $77,000 of net cash inflows in year 7. Additionally, the
refurbished equipment would have a $51,000 residual value at the end of year 7. Should Eon invest
in the equipment and refurbish it after six years? (Hint: In addition to your answer to Requirement 1,
discount the additional cash outflow and inflows back to the present value.)
SOLUTION
Requirement 1
Time
Net
Cash
Inflow
PV Factor
(i = 16%)
Present
Value
PV of each year’s net cash inflow
1
(n = 1)
$ 261,000
0.862
$224,982
2
(n = 2)
254,000
0.743
188,722
3
(n = 3)
227,000
0.641
145,507
4
(n = 4)
211,000
0.552
116,472
5
(n = 5)
201,000
0.476
6
(n = 6)
175,000
0.410
Total PV of net cash inflows
843,109
0
Initial investment
(920,000)
$ (76,891)
E26-23, cont.
Requirement 2
Time
Net
Cash
Inflow (Outflow)
PV Factor
(i = 16%)
Present
Value
PV of each year’s net cash inflow
7
(n = 7)
$ 77,000
0.354
$ 27,258
7
(n = 7)
0.354
18,054
Total PV of net cash inflows
45,312
6
Cost to refurbish the equipment (n = 6)
0.410
Net present value
of the equipment with
refurbishment
=
Net present value
of the equipment prior to
refurbishment
+
Net present value
of the
refurbishment
Based on net present value (NPV), Eon should not invest in the equipment and refurbish it after six
E26-24 Using NPV and profitability index to make capital investment decisions
Learning Objective 4
1. Project B $500 NPV
Use the NPV method to determine whether Juda Products should invest in the following projects:
• Project A: Costs $290,000 and offers seven annual net cash inflows of $57,000. Juda Products
requires an annual return of 14% on investments of this nature.
• Project B: Costs $395,000 and offers 10 annual net cash inflows of $70,000. Juda Products demands
an annual return of 12% on investments of this nature.
Requirements
1. What is the NPV of each project? Assume neither project has a residual value. Round to two decimal
places.
2. What is the maximum acceptable price to pay for each project?
3. What is the profitability index of each project? Round to two decimal places.
SOLUTION
Requirement 1
Time
Net
Cash
Inflow
Annuity
PV Factor
Present
Value
(i = 14%,
n = 7)
(i = 12%,
n = 10)
Project A:
1 – 7 years
PV of annuity
$ 57,000
4.288
$ 244,416
Initial investment
$ (45,584)
Project B:
1 – 10 years
PV of annuity
$ 70,000
5.650
$ 395,500
Initial investment
Requirement 2
Requirement 3
Project
Present value of
net cash inflows
/
Initial investment
=
Profitability Index
/
=
/
=
E26-25 Using IRR to make capital investment decisions
Learning Objective 4
Project A 8%–9% IRR
Refer to the data regarding Juda Products in Exercise E26-24. Compute the IRR of each project, and use
this information to identify the better investment.
SOLUTION
Project A:
Annuity PV Factor
(i = ?%, n = 7)
=
Initial investment
/
Amount of each net cash inflow
=
$290,000
/
$57,000
=
5.088 (rounded)
Annuity PV Factor
(i = 8%,n = 7)
(i = 9%,n = 7)
Because 5.088 is between 5.206 and 5.033, the IRR is between 8% and 9%.
Note: Using a business calculator or Microsoft Excel, the IRR is 8.68% (rounded).
Project B:
Annuity PV Factor
(i = ?%, n = 10)
=
Initial investment
/
Amount of each net cash inflow
=
$395,000
/
$70,000
=
Annuity PV Factor
(i = 12%,n = 10)
(i = 14%,n = 10)
Because 5.643 is between 5.650 and 5.216, the IRR is between 12% and 14%.
Note: Using a business calculator or Microsoft Excel, the IRR is 12.03% (rounded).
Project A’s internal rate of return (IRR) is between 8% and 9%, which is less than the 14% required rate
of return on projects like A. Project B’s IRR is between 12% and 14%, which is greater than the 12%
E26-26 Using capital rationing to make capital investment decisions
Learning Objective 4
Back Manufacturing is considering three capital investment proposals. At this time, Back only has funds
available to pursue one of the three investments.
Which investment should Back pursue at this time? Why?
SOLUTION
Equipment
Present value of
net cash inflows
/
Initial investment
=
Profitability Index
A
$1,695,378
/
$ 1,356,302
=
1.25
B
$1,969,888
/
=
1.23
C
$2,169,724
/
=
1.14
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. The profitability
index of each investment should be computed, and the investment with the highest profitability index
E26-27 Using capital rationing to make capital investment decisions
Learning Objective 4
Mountain Manufacturing is considering the following capital investment proposals. Mountain’s
requirement criteria include a maximum payback period of five years and a required rate of return of
12.5%. Determine if each investment is acceptable or should be rejected (ignore qualitative factors).
Rank the acceptable investments in order from most desirable to least desirable.
SOLUTION
The acceptability of each project based on each criterion:
Project
Payback
Period
(Acceptable if
< or = 5 years)
NPV
(Acceptable if
positive)
IRR
(Acceptable if
> or = 12.5%)
Profitability
Index
(Acceptable if
> or = 1.0)
A
Acceptable
Acceptable
Acceptable
Acceptable
B
Acceptable
Acceptable
Acceptable
Acceptable
C
Acceptable
D
Acceptable
Acceptable
Acceptable
Acceptable
Acceptable
Acceptable
Acceptable
Acceptable
The ranking (most desirable to least desirable) of each acceptable project based on each criterion:
Payback Period
NPV
IRR
Profitability Index
Ranking
The lower the
payback period,
the more desirable
the project, all
else being equal.
The higher the
NPV, the more
desirable the
project (if the
initial investment
is the same for all
projects).
The higher the
IRR, the more
desirable the
project.
The higher the
profitability index,
the more desirable
the project.
#1
Project A
Project B
Project B
Project D
#2
Project D
Project D
Project D
Project B
#3
Project B
Project A
Project A
Project A
#4
Project E
Project E
Project E
Project E
Problems (Group A)
P26-28A Using the time value of money
Learning Objective 3
1. $2,026,805
You are planning for a very early retirement. You would like to retire at age 40 and have enough money
saved to be able to withdraw $215,000 per year for the next 30 years (based on family history, you think
you will live to age 70). 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 70 years old.
Requirements
1. How much money must you accumulate by retirement to make your plan work? (Hint: Find the
present value of the $215,000 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 = 30
=
$215,000
×
9.427
=
$2,026,805
Requirement 2
Total withdrawn
during retirement
=
Amount withdrawn each year
×
Total number of years
=
×
=
P26-29A Using payback, ARR, NPV, IRR, and profitability index to make capital investment
decisions
Learning Objectives 2, 4
1. 26.35% ARR; 1.28 profitability index
Water Country is considering purchasing a water park in Atlanta, Georgia, for $1,850,000. The new
facility will generate annual net cash inflows of $475,000 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 12% 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
=
=
3.9 years (rounded)
Total net cash inflows during
operating life of facility
=
Average annual
net cash inflow
×
Operating life
of facility
=
$475,000
×
=
$3,800,000
Total depreciation during
operating life of facility
=
Cost
−
Residual value
=
$1,850,000
=
$1,850,000
Total net cash inflows during operating life of facility
$ 3,800,000
Less: Total depreciation during operating life of facility
1,850,000
Average annual operating income from facility
Average amount invested
=
Amount invested + Residual value
2
=
2
ARR
=
Average annual operating income
Average amount invested
=
P26-29A, cont.
Requirement 1, cont.
Time
Net
Cash
Inflow
Annuity
PV Factor
(i = 12%,n = 8)
Present
Value
1 – 8 years
PV of annuity
$ 475,000
Initial investment
(1,850,000)
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 3.895 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 19.50% (rounded).
Profitability Index
=
Present value of
net cash inflows
/
Initial investment
=
/
=
1.28 (rounded)
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
profitability index is greater than one, and both the accounting rate of return and internal rate of return
are greater than the company’s required rate of return.