FNAN 303
Solutions to test bank problems – capital budgeting criteria
Some answers may be slightly different than provided solutions due to rounding
1. Central Concrete is evaluating a project that would last for 4 years. The project’s cost of
capital is 12.26 percent and the expected cash flows are presented in the table. What is the net
present value of the project?
Years from today
0
1
2
3
4
Expected cash flow (in $)
-1,100
9,400
7,000
-7,600
9,000
A. An amount equal to or greater than $1,000 but less than $2,000
B. An amount equal to or greater than $2,000 but less than $3,000
C. An amount equal to or greater than $3,000 but less than $4,000
D. An amount less than $1,000 or an amount equal to or greater than $4,000
E. The amount can not be determined or does not exist because the cash flows are not
conventional
NPV = [-1,100] + [9,400/1.1226] + [7,000/1.12262] + [-7,600/1.12263] + [-9,000/1.12264] = 1,789
npv(12.26,-1100,{9400,7000,-7600,-9000})  $1,789
Answer: A
$1,789 is an amount equal to or greater than $1,000 but less than $2,000
1
FNAN 303
Solutions to test bank problems – capital budgeting criteria
2. Area Forests is evaluating a project that would cost $137,000 today. The project is expected to
produce annual cash flows of $8,920 forever with the first annual cash flow expected in 1 year.
The cost of capital associated with the project is 8.47 percent and the project’s internal rate of
return is 6.51 percent. What is the net present value of the project?
(Fall 2017, test 3, question 1)
Step 1: expected cash flows are given
C0 = -137,000
C1 = C2 = C3 = … = 8,920
Step 2: cost of capital is given as 8.47%
The IRR is not relevant for computing NPV
Step 3: compute NPV
Can not use npv function with financial calculator – there are an infinite number of cash flows
NPV = C0 + [C1 / (1+r)] + [C2 / (1+r)2] + ...
C1, C2, C3, … represent a fixed perpetuity with annual cash flows of $8,920 and r = .0847
So [C1 / (1+r)] + [C2 / (1+r)2] + ...
= (C / r)
= ($8,920 / .0847)
NPV = -137,000 + (8,920 / .0847)
= -137,000 + 105,313
= -31,687
2
FNAN 303
Solutions to test bank problems – capital budgeting criteria
3. Wooden Forests is evaluating a project that would require an initial investment of $900,000
today. The project is then expected to produce annual cash flows that grow by 1.80 percent per
year forever. The first annual cash flow is expected in 1 year and is expected to be $65,000. The
project’s internal rate of return is 9.02 percent and its cost of capital is 9.32 percent. What is the
net present value (NPV) of the project?
(Fall 2012, test 3, question 7)
Step 1: expected cash flows are given
C0 = -900,000
C1 = 65,000
g = .0180
Step 2: cost of capital is given as 9.32%
The IRR is not relevant for computing NPV
Step 3: compute NPV
Can not use npv function with financial calculator – there are an infinite number of cash flows
NPV = C0 + [C1 / (1+r)] + [C2 / (1+r)2] + ...
C1, C2, C3, … represent a growing perpetuity with C1 = $65,000, r = .0932, and g = .0180
So [C1 / (1+r)] + [C2 / (1+r)2] + ...
= [C / (r – g)]
= [$65,000 / (.0932 – .0180)]
= [$65,000 / .0752]
NPV = -900,000 + [65,000 / .0752]
= -900,000 + 864,362
= -35,638
3
FNAN 303
Solutions to test bank problems – capital budgeting criteria
4. Karim’s Kabobs is evaluating a project that would last for 3 years. The project’s cost of
capital is 9.7 percent; its NPV is $6,700; and the expected cash flows are presented in the table.
What is X?
Years from today
0
1
2
3
Expected cash flow (in $)
-65,000
52,000
-12,000
X
A. An amount equal to or greater than $28,000 but less than $36,000
B. An amount equal to or greater than $36,000 but less than $44,000
C. An amount equal to or greater than $44,000 but less than $52,000
D. An amount less than $36,000 or an amount equal to or greater than $52,000
E. The amount can not be determined or does not exist because the cash flows are not
conventional
(Spring 2011, test 3, question 7)
(Fall 2011, test 3, question 8)
(Fall 2012, final, question 13)
(Spring 2013, test 3, question 7)
(Spring 2014, test 3, question 7)
(Spring 2017, test 3, question 4)
NPV = [C0] + [C1 / (1 + r)] + [C2 / (1 + r)2] + [C3 / (1 + r)3]
NPV = 6,700
C0 = -65,000
C1 = 52,000
C2 = -12,000
C3 = X
r = .097
6,700 = [-65,000] + [52,000 / 1.097] + [-12,000 / 1.0972] + [X / 1.0973]
 6,700 = [-65,000] + [47,402] + [-9,972] + [X / 1.0973]
 6,700 = -27,570 + [X / 1.0973]
 6,700 + 27,570 = [X / 1.0973]
 34,270 = [X / 1.0973]
 X = C3 = 34,270 × 1.0973 = 45,241
Answers may differ slightly due to rounding
Answer: C
$45,241 is an amount equal to or greater than $44,000 but less than $52,000
4
FNAN 303
Solutions to test bank problems – capital budgeting criteria
5. Graphco Rackets is considering a project that is expected to cost $5,800 today; produce a cash
flow of $8,900 in 4 years, and have an NPV of $300. What is the cost of capital for the project?
(Fall 2015, test 3, question 3)
(Fall 2016, test 3, question 3)
NPV = [C0] + [C1 / (1+r)] + [C2 / (1+r)2] + [C3 / (1+r)3] + [C4 / (1+r)4]
In this case,
300 = [-5,800] + [0 / (1+r)] + [0 / (1+r)2] + [0 / (1+r)3] + [8,900 / (1+r)4]
= [-5,800] + [8,900 / (1+r)4]
So 300 + 5,800 = 8,900 / (1+r)4
= 6,100
So (1 + r)4 = 8,900 / 6,100
And 1 + r = [(8,900 / 6,100)(1/4)] = 1.0990
So r = .0990 = 9.90%
5
FNAN 303
Solutions to test bank problems – capital budgeting criteria
6. Viny Jungles is evaluating a project that would cost $765,100 today. The project is expected to
produce annual cash flows of $59,100 forever with the first annual cash flow expected in 1 year.
The NPV of the project is $5,200. What is the cost of capital of the project?
Can not use the npv function with financial calculator – there are an infinite number of CFs
NPV = C0 + [C1 / (1+r)] + [C2 / (1+r)2] + ...
r is the cost of capital by definition, as the sum of the present values of all expected cash
flows is NPV when the discount rate is the cost of capital
In this case,
NPV = 5,200
C0 = -765,100
C1 = C2 = C3 = … = 59,100
C1, C2, C3, … represent a fixed perpetuity with annual cash flows of $59,100
So [C1 / (1+r)] + [C2 / (1+r)2] + ... = (C / r) = ($59,100 / r)
So 5,200 = -765,100 + (59,100 / r)
So 5,200 + 765,100 = 59,100 / r
So 770,300 = 59,100 / r
So r = 59,100 / 770,300 = 0.0767 = 7.67%
6
FNAN 303
Solutions to test bank problems – capital budgeting criteria
7. Which of the following assertions is true if we define a “good” project as creating value, a
“bad” project as destroying value, the “right” decision as accepting a “good” project or rejecting a
“bad” project, and the “wrong” decision as rejecting a “good” project or accepting a “bad”
project?
A. Using net present value (NPV) always leads to the “right” decision for “good” projects when
projects have conventional cash flows and using NPV always leads to the “right” decision
for “bad” projects when projects have conventional cash flows
B. Using net present value (NPV) always leads to the “right” decision for “good” projects when
projects have conventional cash flows and using NPV can lead to the “wrong” decision for
“bad” projects when projects have conventional cash flows
C. Using net present value (NPV) can lead to the “wrong” decision for “good” projects when
projects have conventional cash flows and using NPV always leads to the “right” decision
for “bad” projects when projects have conventional cash flows
D. Using net present value (NPV) can lead to the “wrong” decision for “good” projects when
projects have conventional cash flows and using NPV can lead to the “wrong” decision for
“bad” projects when projects have conventional cash flows
Using net present value (NPV) always leads to the “right” decision for “good” projects when
projects have conventional cash flows
Regardless of the pattern of expected cash flows, net present value and the NPV rule always
lead to the “right” decision for both “good” and “bad” projects, which means that “good”
projects are accepted and “bad” projects are rejected
Using NPV always leads to the “right” decision for “bad” projects when projects have
conventional cash flows
Regardless of the pattern of expected cash flows, net present value and the NPV rule always
lead to the “right” decision for both “good” and “bad” projects, which means that “good”
projects are accepted and “bad” projects are rejected
Answer: A. Using net present value (NPV) always leads to the “right” decision for “good”
projects when projects have conventional cash flows and using NPV always leads to the
“right” decision for “bad” projects when projects have conventional cash flows
7
FNAN 303
Solutions to test bank problems – capital budgeting criteria
8. Which of the following assertions is true if we define a “good” project as creating value, a
“bad” project as destroying value, the “right” decision as accepting a “good” project or rejecting a
“bad” project, and the “wrong” decision as rejecting a “good” project or accepting a “bad”
project?
A. Using net present value (NPV) can lead to the “wrong” decision for “good” projects when
projects do not have conventional cash flows and using NPV can lead to the “wrong”
decision for “bad” projects when projects do not have conventional cash flows
B. Using net present value (NPV) can lead to the “wrong” decision for “good” projects when
projects do not have conventional cash flows and using NPV always leads to the “right”
decision for “bad” projects when projects do not have conventional cash flows
C. Using net present value (NPV) always leads to the “right” decision for “good” projects when
projects do not have conventional cash flows and using NPV can lead to the “wrong”
decision for “bad” projects when projects do not have conventional cash flows
D. Using net present value (NPV) always leads to the “right” decision for “good” projects when
projects do not have conventional cash flows and using NPV always leads to the “right”
decision for “bad” projects when projects do not have conventional cash flows
(Spring 2016, test 3, question 4)
Using net present value (NPV) always leads to the “right” decision for “good” projects when
projects do not have conventional cash flows
Regardless of the pattern of expected cash flows, net present value and the NPV rule always
lead to the “right” decision for both “good” and “bad” projects, which means that “good”
projects are accepted and “bad” projects are rejected
Using NPV always leads to the “right” decision for “bad” projects when projects do not have
conventional cash flows
Regardless of the pattern of expected cash flows, net present value and the NPV rule always
lead to the “right” decision for both “good” and “bad” projects, which means that “good”
projects are accepted and “bad” projects are rejected
Answer: D. Using net present value (NPV) always leads to the “right” decision for “good”
projects when projects do not have conventional cash flows and using NPV always leads to the
“right” decision for “bad” projects when projects do not have conventional cash flows
8
FNAN 303
Solutions to test bank problems – capital budgeting criteria
9. What is the internal rate of return for a project that is expected to cost $1,410 today; produce a
cash flow of $1,620 in 3 years; and have a net present value of $100?
(Spring 2014, test 3, question 8)
(Fall 2014, test 3, question 7)
0 = C0 + [C1/(1+IRR)] + [C2/(1+IRR)2] + [C3/(1+IRR)3]
In this case,
0 = -1,410 + [0/(1+IRR)] + [0/(1+IRR)2] + [1,620 / (1 + IRR)3]
So 0 + 1,410 = 1,620 / (1 + IRR)3
And 1,410 = 1,620 / (1 + IRR)3
So (1,620 / 1,410) = (1 + IRR)3
So [(1 + IRR)3](1/3) = (1 + IRR) = (1,620 / 1,410)(1/3)
So IRR = [(1,620 / 1,410)(1/3)] – 1
= .0474 = 4.74%
Note: irr (-1410,{0,0,1620}  4.74%
9
FNAN 303
Solutions to test bank problems – capital budgeting criteria
10. Wooden Forests is evaluating a project that would require an initial investment of $54,300
today. The project is expected to produce annual cash flows of $6,200 each year forever with the
first annual cash flow expected in 1 year. The NPV of the project is $3,700. What is the IRR of
the project?
(Fall 2013, test 3, question 9)
(Spring 2015, test 2, question 10)
(Spring 2016, test 3, question 5)
Can not use the irr function with financial calculator – there are an infinite number of cash flows
By definition of IRR: 0 = C0 + [C1 / (1+IRR)] + [C2 / (1+IRR)2] + ...
In this case,
C0 = -54,300
C1 = C2 = C3 = … = 6,200
C1, C2, C3, … represent a fixed perpetuity with annual cash flows of $6,200
So [C1 / (1+IRR)] + [C2 / (1+IRR)2] + ... = (C / IRR) = ($6,200 / IRR)
So 0 = -54,300 + (6,200 / IRR)
So 54,300 = 6,200 / IRR
So IRR = 6,200 / 54,300 = 0.1142 = 11.42%
Note that the NPV is not relevant to finding IRR, since IRR is the discount rate at which the
present value of the expected cash flows is 0.
10
FNAN 303
Solutions to test bank problems – capital budgeting criteria
11. FiberTech is evaluating a project that would last for 3 years. The project’s internal rate of
return is 9.71 percent; its NPV is $6,700; and the expected cash flows are presented in the table.
What is X?
Years from today
0
1
2
3
Expected cash flow (in $)
-65,000
52,000
13,000
X
(Fall 2017, test 3, question 2)
Since we know the IRR, but not the cost of capital, the NPV is irrelevant to finding X.
0 = [C0] + [C1 / (1 + IRR)] + [C2 / (1 + IRR)2] + [C3 / (1 + IRR)3]
C0 = -65,000
C1 = 52,000
C2 = 13,000
C3 = X
IRR = .0971
0 = [-65,000] + [52,000 / 1.0971] + [13,000 / 1.09712] + [X / 1.09713]
 0 = [-65,000] + [47,398] + [10,801] + [X / 1.09713]
 0 = -6,801 + [X / 1.09713]
 6,801 = [X / 1.09713]
 X = C3 = 6,801 × 1.09713 = 8,981
Answers may differ slightly due to rounding
11
FNAN 303
Solutions to test bank problems – capital budgeting criteria
12. Which of the following assertions is true if we define a “good” project as creating value, a
“bad” project as destroying value, the “right” decision as accepting a “good” project or rejecting
a “bad” project, and the “wrong” decision as rejecting a “good” project or accepting a “bad”
project?
A. Using internal rate of return (IRR) and the IRR rule always leads to the “right” decision
when projects have conventional cash flows and using IRR always leads to the “right”
decision when projects have non-conventional cash flows
B. Using internal rate of return (IRR) and the IRR rule always leads to the “right” decision
when projects have conventional cash flows and using IRR can lead to the “wrong” decision
when projects have non-conventional cash flows
C. Using internal rate of return (IRR) and the IRR rule can lead to the “wrong” decision when
projects have conventional cash flows and using IRR always leads to the “right” decision
when projects have non-conventional cash flows
D. Using internal rate of return (IRR) and the IRR rule can lead to the “wrong” decision when
projects have conventional cash flows and using IRR can lead to the “wrong” decision when
projects have non-conventional cash flows
(Fall 2013, test 3, question 8)
Answer:
B. Using internal rate of return (IRR) and the IRR rule always leads to the “right” decision
when projects have conventional cash flows and using IRR can lead to the “wrong” decision
when projects have non-conventional cash flows
When cash flows are conventional, IRR always leads to the “right” decision for both “good”
and “bad” projects, which means that “good” projects are accepted and “bad” projects are
rejected
When cash flows are not conventional, IRR can lead to the “wrong” decision for both “good”
and “bad” projects, which means that “good” projects can be rejected and “bad” projects can
be accepted
12
FNAN 303
Solutions to test bank problems – capital budgeting criteria
13. Mulberry is analyzing a project with conventional cash flows that is expected to last for 3
years. The cost of capital for the project is 5.8 percent. The internal rate of return (IRR) of the
project is between 7.1 percent and 7.5 percent. The initial investment today is $10,200; the
expected cash flow in 1 year is $4,700; the expected cash flow in 2 years is $3,600; and the
expected cash flow in 3 years is X. Which of the following statements is true?
A. The NPV of the project is a positive number
B. The NPV of the project is equal to zero
C. The NPV of the project is a negative number
D. Without knowing X, it is not clear whether the NPV of the project is a positive number,
zero, or a negative number
E. Without knowing the IRR, it is not clear whether the NPV of the project is a positive
number, zero, or a negative number
(Spring 2011, test 3, question 8)
(Fall 2014, test 3, question 8)
(Spring 2017, test 3, question 5)
Answer: A. The NPV of the project is a positive number
Recall that for projects with conventional cash flows, IRR rule (which states that if IRR >
cost of capital, then project should be accepted, IRR < cost of capital, then project should
be rejected, and if IRR = cost of capital, then firm should be indifferent) always leads to
acceptance of projects that create value and always leads to rejection of projects that
destroy value. The IRR rule produces same results as NPV rule for these types of projects.
In this case, the project has conventional cash flows and IRR, which is at least 7.1 percent,
is greater than the cost of capital for the project, which is 5.8 percent, so NPV > 0.
We do not need to know what X is to answer this question
13
FNAN 303
Solutions to test bank problems – capital budgeting criteria
14. Yumberry is analyzing a project with conventional cash flows that is expected to last for 3
years. The cost of capital for the project is 5.8 percent. The internal rate of return (IRR) of the
project is between 4.1 percent and 4.5 percent. The initial investment today is $10,200; the
expected cash flow in 1 year is $4,700; the expected cash flow in 2 years is $3,600; and the
expected cash flow in 3 years is X. Which of the following statements is true?
A. The NPV of the project is a positive number
B. The NPV of the project is equal to zero
C. The NPV of the project is a negative number
D. Without knowing X, it is not clear whether the NPV of the project is a positive number,
zero, or a negative number
E. Without knowing the IRR, it is not clear whether the NPV of the project is a positive
number, zero, or a negative number
(Spring 2011, test 3, question 8)
(Fall 2014, test 3, question 8)
(Spring 2017, test 3, question 5)
Answer: C. The NPV of the project is a negative number
Recall that for projects with conventional cash flows, IRR rule (which states that if IRR >
cost of capital, then project should be accepted, IRR < cost of capital, then project should
be rejected, and if IRR = 0, then firm should be indifferent) always leads to acceptance of
projects that create value and always leads to rejection of projects that destroy value. The
IRR rule produces same results as NPV rule for these types of projects.
In this case, the project has conventional cash flows and IRR, which is at most 4.5 percent,
is less than the cost of capital for the project, which is 5.8 percent, so NPV < 0.
We do not need to know what X is to answer this question
14
FNAN 303
Solutions to test bank problems – capital budgeting criteria
15. For how many of the projects described in the table is it appropriate to use the internal rate of
return (IRR) rule to analyze whether the project should be accepted or rejected?
Expected cash flows (number of years from today)
Project
0
1
2
3
Cost of capital
A
-34
13
13
13
6.3%
B
-57
7
8
9
9.6%
C
-29
3
3
41
4.7%
D
41
19
19
-4
5.2%
E
-51
35
35
-12
8.1%
F
-64
64
0
0
7.0%
Answer: 4
The IRR rule can be used when cash flows are conventional. The IRR can not be used
when cash flows are not conventional.
Conventional cash flows involve a negative cash flow at time 0 followed by all non0negative
cash flows with at least on positive cash flow.
These projects have conventional cash flows, so IRR can be used: A, B, C, & F
These projects do not have conventional cash flows, so IRR can not be used: D & E
15
FNAN 303
Solutions to test bank problems – capital budgeting criteria
16. The following table presents information on a potential project currently being evaluated by
Erie Shipping. Which assertion about statement 1 and statement 2 is true?
Expected cash flows (number of years from today)
Cost of capital
0
1
2
3
4
-76,000
38,000
29,000
7,000
11,000
8.2%
Statement 1: Erie Shipping would accept the project based on the project’s net present value
(NPV) and the NPV rule
Statement 2: Erie Shipping would accept the project based on the project’s payback period and
the payback rule if the payback threshold is 3.25 years
A. Statement 1 is true and statement 2 is true
B. Statement 1 is true and statement 2 is false
C. Statement 1 is false and statement 2 is true
D. Statement 1 is false and statement 2 is false
(Spring 2012, final, question 12)
(Spring 2014, test 3, question 9)
(Fall 2014, test 3, question 9)
(Spring 2015, test 2, question 11)
(Spring 2016, test 3, question 6)
Answer: C. statement 1 is false and statement 2 is true
NPV - Statement 1 is false
NPV = [-76,000] + [38,000 / 1.082] + [29,000 / 1.0822] + [7,000 / 1.0823] + [11,000 / 1.0824] = -$2,557
npv(8.2,-76000,{38000,29000,7000,11000})  -$2,557
Reject the project, because it has a negative NPV
Payback - Statement 2 is true
Assume expected cash flows occur uniformly throughout the year
Year
Expected CF Expected CF needed after year-end
0
-76,000
76,000
1
38,000
76,000 – 38,000 = 38,000
2
29,000
38,000 – 29,000 = 9,000
3
7,000
9,000 – 7,000 = 2,000
4
11,000
2,000 – 11,000 = -9,000
Payback occurs between 3 and 4 years
After 3 years, 2,000 in expected cash flows are needed
In year 4, the expected cash flow is $11,000
Therefore, it would take ($2,000 / $11,000) = 0.18 of year 4 to reach payback
So payback = 3 + 0.18 = 3.18 years
Accept the project, because its payback period is 3.18 years, which is less than the
threshold of 3.25 years
16
FNAN 303
Solutions to test bank problems – capital budgeting criteria
17. The following table presents information on a potential project currently being evaluated by
Macklemore Thrift Shops. Which of the assertions about statement 1 and statement 2 is true?
Expected cash flows (number of years from today)
Cost of capital
0
1
2
3
4
-$98,000
$56,000
$25,000
$27,000
$3,000
7.20%
Statement 1: Macklemore Thrift Shops would accept the project based on the project’s internal
rate of return (IRR) and the IRR rule
Statement 2: Macklemore Thrift Shops would accept the project based on the project’s payback
period and the payback rule if the payback threshold is 2.50 years
A. Statement 1 is true and statement 2 is true
B. Statement 1 is true and statement 2 is false
C. Statement 1 is false and statement 2 is true
D. Statement 1 is false and statement 2 is false
(Spring 2013, final, question 13)
(Fall 2015, test 3, question 5)
(Fall 2015, final, question 10)
(Spring 2017, final, question 10)
Answer: B. Statement 1 is true and statement 2 is false
IRR - Statement 1 is true
irr(-98000,{56000,25000,27000,3000})  7.31 percent > 7.20 percent = cost of capital
Accept the project, because IRR > cost of capital
Payback - Statement 2 is false
Assume expected cash flows occur uniformly throughout the year
Year
Expected CF Expected CF needed after year-end
0
-98,000
98,000
1
56,000
98,000 – 56,000 = 42,000
2
25,000
42,000 – 25,000 = 17,000
3
27,000
17,000 – 27,000 = -10,000
4
3,000
Payback occurs between 2 and 3 years
After 2 years, $17,000 in expected cash flows are needed
In year 3, the expected cash flow is $27,000
Therefore, it would take ($17,000 / $27,000) = 0.63 of year 3 to reach payback
So payback = 2 + 0.63 = 2.63 years
Reject the project, because its payback period is 2.63 years, which is greater than the
threshold of 2.50 years
17
FNAN 303
Solutions to test bank problems – capital budgeting criteria
18. The following table presents information on a potential project currently being evaluated by
Book Jacket. Which one of the assertions about statement 1 and statement 2 is true?
Expected cash flows (number of years from today)
Cost of capital
0
1
2
3
4
-90,000
44,000
50,000
18,000
5,000
10.2%
Statement 1: Book Jacket would accept the project based on the project’s net present value
(NPV) and the NPV rule
Statement 2: Book Jacket would accept the project based on the project’s discounted payback
period and the discounted payback rule if the discounted payback threshold is 2.55 years
A. Statement 1 is true and statement 2 is true
B. Statement 1 is true and statement 2 is false
C. Statement 1 is false and statement 2 is true
D. Statement 1 is false and statement 2 is false
(Fall 2010, test 3, question 9)
(Spring 2017, test 3, question 6)
Answer: B. Statement 1 is true and statement 2 is false
NPV - Statement 1 is true
NPV = -90,000 + [44,000/1.102] + [50,000/1.1022] + [18,000/1.1023] + [5,000/1.1024] = 7,940
npv(10.2,-90000,{44000,50000,18000,5000})  $7,940
Accept the project, because it has a positive NPV
Discounted payback - Statement 2 is false
Assume discounted expected cash flows occur uniformly throughout the year. However,
discount expected cash flows as if they occur at end of year. Also, discounted expected cash
flows are rounded to the nearest dollar for simplicity and convenience.
Year
Expected CF Expected DCF = PV
Expected DCF needed after year-end
(expected CF) @ 10.2%
0
-90,000
-90,000
90,000
1
44,000
44,000 / 1.102 = 39,927
90,000 – 39,927 = 50,073
2
50,000
50,000 / 1.1022 = 41,172 50,073 – 41,172 = 8,901
3
18,000
18,000 / 1.1023 = 13,450 8,901 – 13,450 = -4,549
4
5,000
5,000 / 1.1024 = 3,390
Discounted payback occurs between 2 and 3 years
After 2 years, 8,901 in discounted expected cash flows are needed
In year 3, the expected discounted cash flow is $13,450
Therefore, it would take ($8,901 / $13,450) = 0.66 of year 3 to reach discounted payback
So discounted payback = 2 + 0.66 = 2.66 years
Reject the project, because its discounted payback period is 2.66 years, which is greater
than the threshold of 2.55 years
18
FNAN 303
Solutions to test bank problems – capital budgeting criteria
19. The following table presents information on a potential project currently being evaluated by
Kasual Kat. Which one of the assertions about statement 1 and statement 2 is true?
Expected cash flows (number of years from today)
Cost of capital
0
1
2
3
4
-95,000
11,000
84,000
34,000
1,000
11.60%
Statement 1: Kasual Kat would accept the project based on the project’s internal rate of return
(IRR) and the IRR rule
Statement 2: Kasual Kat would accept the project based on the project’s discounted payback
period and the discounted payback rule if the discounted payback threshold is 2.65 years
A. Statement 1 is true and statement 2 is true
B. Statement 1 is true and statement 2 is false
C. Statement 1 is false and statement 2 is true
D. Statement 1 is false and statement 2 is false
(Fall 2011, test 3, question 9)
(Spring 2012, test 3, question 9)
(Fall 2016, test 3, question 4)
Answer: B. Statement 1 is true and statement 2 is false
IRR - Statement 1 is true
irr(-95000,{11000,84000,34000,1000})  15.57 percent > 11.60 percent = cost of capital
Accept the project, because IRR > cost of capital
Discounted payback - Statement 2 is false
Assume discounted expected cash flows occur uniformly throughout the year. However,
discount expected cash flows as if they occur at end of year. Also, discounted expected cash
flows are rounded to the nearest dollar for simplicity and convenience.
Year
Expected CF Expected DCF = PV
Expected DCF needed after year-end
(expected CF) @ 11.60%
0
-95,000
-95,000
95,000
1
11,000
11,000 / 1.1160 = 9,857
95,000 – 9,857 = 85,143
2
84,000
84,000 / 1.11602 = 67,445
85,143 – 67,445 = 17,698
3
3
34,000
34,000 / 1.1160 = 24,462
17,698 – 24,462 = -6,764
4
1,000
Not relevant
Discounted payback occurs between 2 and 3 years
After 2 years, 17,698 in discounted expected cash flows are needed
In year 3, the expected discounted cash flow is $24,462
Therefore, it would take ($17,698 / $24,462) = 0.72 of year 3 to reach discounted payback
So discounted payback = 2 + 0.72 = 2.72 years
Reject the project using discounted payback, because its discounted payback period is 2.72
years, which is greater than the threshold of 2.65 years
19
FNAN 303
Solutions to test bank problems – capital budgeting criteria
20. The following table presents information on a potential project currently being evaluated by Snow
Day Amusements. Which one of the assertions about statement 1 and statement 2 is true?
Expected cash flows (number of years from today)
Cost of capital
0
1
2
3
4
-50,000
33,000
11,000
35,000
9,000
14.3%
Statement 1: Snow Day Amusements would accept the project based on the project’s payback period and
the payback rule if the payback threshold is 2.25 years
Statement 2: Snow Day Amusements would accept the project based on the project’s discounted payback
period and the discounted payback rule if the discounted payback threshold is 2.60 years
A. Statement 1 is true and statement 2 is true
B. Statement 1 is true and statement 2 is false
C. Statement 1 is false and statement 2 is true
D. Statement 1 is false and statement 2 is false
(Spring 2011, test 3, question 9)
(Fall 2012, test 3, question 9) (Spring 2013, test 3, question 9)
(Fall 2013, test 3, question 10)
(Spring 2015, final, question 14)
(Spring 2016, final, question 7)
(Fall 2017, test 3, question 3)
Answer: A. Statement 1 is true and statement 2 is true
Payback - Statement 1 is true
Year
Expected CF
0
-50,000
1
33,000
2
11,000
3
35,000
4
9,000
Expected CF needed after year-end
50,000
50,000 – 33,000 = 17,000
17,000 – 11,000 = 6,000
6,000 – 35,000 = -29,000
Payback occurs between 2 and 3 years
After 2 years, 6,000 in expected cash flows are needed
In year 3, the expected cash flow is $35,000
Therefore, it would take ($6,000 / $35,000) = 0.17 of year 3 to reach payback
So payback = 2 + 0.17 = 2.17 years
Accept the project using payback, because its payback period is 2.17 years, which is less than the threshold of
2.25 years
Discounted payback - Statement 2 is true
Assume discounted expected CFs occur uniformly throughout the year. However, discount expected CFs as if
they occur at end of year. Also, discounted expected CFs are rounded to the nearest dollar for simplicity and
convenience.
Year
Expected CF
Expected DCF = PV
Expected DCF needed after year-end
(expected CF) @ 14.3%
0
-50,000
-50,000
50,000
1
33,000
33,000 / 1.143 = 28,871
50,000 – 28,871 = 21,129
2
11,000
11,000 / 1.1432 = 8,420
21,129 – 8,420 = 12,709
3
35,000
35,000 / 1.1433 = 23,438
12,709 – 23,438 = -10,729
4
9,000
Not relevant
Discounted payback occurs between 2 and 3 years
After 2 years, 12,709 in discounted expected cash flows are needed
In year 3, the expected discounted cash flow is $23,438
Therefore, it would take ($12,709 / $23,438) = 0.54 of year 3 to reach discounted payback
So discounted payback = 2 + 0.54 = 2.54 years
Accept the project using discounted payback, because its discounted payback period is 2.54 years, which is
less than the threshold of 2.60 years
20
FNAN 303
Solutions to test bank problems – capital budgeting criteria
21. Indicate whether each of the following 8 statements is true or false.
Statement 1: 1A Tech would accept project A based on the project’s net present value and the net
present value rule if project A has a net present value of $912
Statement 2: 2B Tech would accept project B based on the project’s net present value and the net
present value rule if project B has a net present value of -$3,257
Statement 3: 3C Tech would accept project C, which has conventional cash flows, based on the
project’s internal rate of return and the internal rate of return rule if project C has an internal rate of
return of 12.32 percent and a cost of capital of 13.65 percent
Statement 4: 4D Tech would accept project D, which has conventional cash flows, based on the
project’s internal rate of return and the internal rate of return rule if project D has an internal rate of
return of 14.67 percent and a cost of capital of 11.72 percent
Statement 5: 5E Tech would accept project E, which has conventional cash flows, based on the
project’s payback period and the payback rule if project E has a payback period of 2.82 years and the
payback threshold is 2.86 years
Statement 6: 6F Tech would accept project F, which has conventional cash flows, based on the
project’s payback period and the payback rule if project F has a payback period of 4.56 years and the
payback threshold is 4.53 years
Statement 7: 7G Tech would accept project G, which has conventional cash flows, based on the
project’s discounted payback period and the discounted payback rule if project G has a discounted
payback period of 3.71 years and the discounted payback threshold is 3.67 years
Statement 8: 8H Tech would accept project H, which has conventional cash flows, based on the
project’s discounted payback period and the discounted payback rule if project H has a discounted
payback period of 2.43 years and the discounted payback threshold is 2.48 years
Statement 1 is true
Accept project A, because it has a positive NPV
Statement 2 is false
Reject project B, because it has a negative NPV
Statement 3 is false
Reject project C, because its IRR is less than its cost of capital
Statement 4 is true
Accept project D, because its IRR is greater than its cost of capital
Statement 5 is true
Accept project E, because its payback period is less than the payback threshold
Statement 6 is false
Reject project F, because its payback period is greater than the payback threshold
Statement 7 is false
Reject project G, because its discounted payback period is greater than the discounted payback threshold
Statement 8 is true
Accept project H, because its discounted payback period is less than the discounted payback threshold
21
FNAN 303
Solutions to test bank problems – capital budgeting criteria
22. Which of the following assertions is true if all payback and discounted payback thresholds
are a finite, positive number of years (such as 0.6 years or 3.9 years, but not -4.5 years or
infinity), and all projects have conventional cash flows?
A. Projects with negative NPV can sometimes be accepted using the payback rule and
projects with negative NPV can sometimes be accepted using the discounted payback
rule
B. Projects with negative NPV can sometimes be accepted using the payback rule and
projects with negative NPV are never accepted using the discounted payback rule
C. Projects with negative NPV are never accepted using the payback rule and projects with
negative NPV can sometimes be accepted using the discounted payback rule
D. Projects with negative NPV are never accepted using the payback rule and projects with
negative NPV are never accepted using the discounted payback rule
E. None of the above assertions is true
(Spring 2010, test 4, question 3)
(Spring 2011, final, question 12)
Answer: B. Projects with negative NPV can sometimes be accepted using the payback rule
and projects with negative NPV are never accepted using the discounted payback rule
If NPV < 0, then discounted payback is infinite, and it is therefore not possible to accept
negative-NPV projects using the discounted payback approach if all discounted payback
thresholds are a finite, positive number of years
If NPV < 0, the payback period can still be a finite, positive number of years, so it is
therefore possible to accept negative-NPV projects using the payback approach
For example, a project that requires an investment of $110, pays $110 in 1 year, and has a
cost of capital of 10%, would have a negative NPV (-110 + 110/1.10 = -10), but payback
would be 1 year, and would therefore be accepted if the payback threshold was 1 year or
greater.
22
FNAN 303
Solutions to test bank problems – capital budgeting criteria
23. Which of the following assertions is true if all payback and discounted payback thresholds
are a finite, positive number of years (such as 0.6 years or 3.9 years, but not -4.5 years or
infinity), and all projects have conventional cash flows?
A. Projects with positive NPV are never rejected using the payback rule and projects with
positive NPV are never rejected using the discounted payback rule
B. Projects with positive NPV are never rejected using the payback rule and projects with
positive NPV can sometimes be rejected using the discounted payback rule
C. Projects with positive NPV can sometimes be rejected using the payback rule and
projects with positive NPV are never rejected using the discounted payback rule
D. Projects with positive NPV can sometimes be rejected using the payback rule and
projects with positive NPV can sometimes be rejected using the discounted payback rule
E. None of the above assertions is true
(Spring 2014, test 3, question 10)
(Fall 2016, test 3, question 5)
Answer: D. Projects with positive NPV can sometimes be rejected using the payback rule and
projects with positive NPV can sometimes be rejected using the discounted payback rule
If a project with positive NPV has substantial expected cash flows that occur after the
payback threshold, then it could be rejected. For example, a firm with a payback threshold
of 1 year would reject a project with a cost of capital of 10%, an investment of $100 today,
and an expected cash flow to the firm of $1 million in 3 years, despite having a positive and
relatively large NPV.
If a project with positive NPV has substantial expected cash flows that occur after the
discounted payback threshold, then it could be rejected. For example, a firm with a
discounted payback threshold of 1 year would reject a project with a cost of capital of 10%,
an investment of $100 today, and an expected cash flow to the firm of $1 million in 3 years,
despite having a positive and relatively large NPV.
23
FNAN 303
Solutions to test bank problems – capital budgeting criteria
24. The managers of Logical Balance Financial have evaluated five potential projects. Each
project has conventional cash flows. Based on the information in the table and this paragraph,
which one of the projects is the riskiest?
Cost of
Net present
Payback
Discounted
Internal rate
capital
value
period
payback period
of return
Project
(in %)
(in $ millions)
(in years)
(in years)
(in %)
A
11.0
0.2
7.6
8.1
11.1
B
7.1
53.3
5.6
8.7
13.5
C
13.2
12.6
2.4
3.2
13.4
D
6.7
8.9
5.8
8.2
14.3
E
9.2
-1.5
2.1
∞
8.6
(Fall 2009, final, question 10)
(Spring 2010, final, question 17)
(Fall 2010, final, question 10)
(Fall 2011, test 3, question 10)
(Spring 2012, test 3, question 10)
(Spring 2015, test 2, question 12)
(Fall 2017, final, question 10)
Project C is the riskiest. Project C has the highest cost of capital, which is the only relevant
piece of information for answering this question. Higher cost of capital  higher risk.
24
FNAN 303
Solutions to test bank problems – capital budgeting criteria
25. The managers of Logical Balance Financial have evaluated five potential projects. Each
project has conventional cash flows. Based on the information in the table and this paragraph,
which one of the projects is the safest?
Cost of
Net present
Payback
Discounted
Internal rate
capital
value
period
payback period
of return
Project
(in %)
(in $ millions)
(in years)
(in years)
(in %)
A
11.0
0.2
7.6
8.1
11.1
B
7.1
53.3
5.6
8.7
13.5
C
13.2
12.6
2.4
3.2
13.4
D
6.7
8.9
5.8
8.2
14.3
E
9.2
-1.5
2.1
∞
8.6
(Fall 2012, test 3, question 10)
(Spring 2013, test 3, question 10)
(Spring 2014, final, question 10)
(Fall 2014, final, question 12)
(Fall 2016, final, question 10)
Project D is the safest. Project D has the lowest cost of capital, which is the only relevant
piece of information for answering this question. Lower cost of capital  lower risk.
25