School of Banking and Finance
FINS5514 Capital Budgeting and Financing Decisions
Tutorial Covering Week 3 – Investment Criteria and Project Cash Flows
Multiple Choice Questions
Use the following information to answer questions 1 to 4.
You are analyzing a proposed project and have compiled the following information:
Year Cash flow
0 -$135,000
1 $ 28,600
2 $ 65,500
3 $ 71,900
The required payback period is 3 years and the required return is 8.50 percent
1. What is the net present value of the proposed project?
a. $3,289.86 b. $3,313.29 c. $4,289.06 d. $4,713.71
Using the NPV formula, we have:
NPV = CF0 +
CF1
1 + r
+ CF2
1 + r
+ ... + CFn
1 + r
NPV = −$135,000 +
Answer: a
$28,600
(1 +.085)1
+ $65,500
(1 +.085)2
+ $71,900
(1 +.085)3
= $3,289.86
2
= +
2. What is the discounted payback period?
a. 2.57 years b. 2.64 years c. 2.87 years d. 2.94 years
The first thing to do is to estimate the discounted value of each of these cash flows:
YearCash flow Discounted cash flow Sum of discounted cash flows
1 $28,600 $26,359.45 $26,359.45
2 $65,500 $55,639.32 $81,998.77
3 $71,900 $56,291.09 $138,289.86
For an investment of $135,000, this project will recover this amount between years 2
and 3. Thus, we estimate the discounted payback period using the formula:
Payback Period = Y + UCF
CF
$135,000 −$26,359.45 −$55,639.32
Discounted payback 2
$56,291.09
= 2.94 years
Answer: d
3. Should the proposed project be accepted based on the IRR?
a. Yes; The project IRR is greater than the required return.
b. Yes; The project IRR is equal to zero.
c. No; The project IRR is greater than the required return.
d. No; The project IRR is greater than zero.
Using a spreadsheet, the IRR can be found as 9.69%. The required rate of return is
given as 8.50% so the project should be accepted.
Answer: a
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4. Should the proposed project be accepted based on the profitability index (PI)?
a. Yes; The PI is less than 1.0
b. Yes; The PI is greater than 1.0.
c. No; The PI is less than 1.0.
d. No; The PI is greater than 1.0.
The formula for the PI is PI = PV of cash flows = PVCF
Investment cost CF0
To estimate the PV of the cash flows, use the discounted values estimated in
question 2. Then we have:
PI = PV of cash flows =
Investment cost
$26,359.45 +$55,639.32 +$56,291.09
$135,000
= 1.024
The PI is greater than 1 so we accept the project.
Answer: b
5. Which of the following statements are correct concerning the internal rate of
return?
I. IRR is used to determine which one of two mutually exclusive projects should
be accepted.
II. IRR is the discount rate that makes the net present value equal to zero.
III. There can be multiple IRRs if the cash flows are unconventional.
IV. You should accept a project when the IRR is less than the required return.
a. I and III only
b. II and IV only
c. II and III only
d. I and II only
I is untrue as is IV, II and III are both correct.
Answer: c
4
Short answer questions
6. You are evaluating projects that are independent and have conventional cash
flows. The analysis methods available to you are Internal Rate of Return, Payback,
Average Accounting Return and Net Present Value. In which order would you use
these approaches?
Net Present Value is the most popular and easy to understand approach and the
Average Accounting return is the least. The IRR is better than Payback from a
financial viewpoint since IRR considers the time value of money and the question
specifies that the projects under evaluation have conventional cash flows and are
independent which means the potential problems with IRR will not arise. So the
order of preference would be: Net Present Value, IRR, Payback, Average Accounting
Return.
7. You own a piece of land, which you purchased ten years ago at a price of
$29,900. Three years ago, you were offered $38,000 for the land but refused the
offer. You are now considering using this land to build a general store to service
the local community. You have just had the land appraised so that you can use it as
collateral for a construction loan. The appraisal value is $36,900. What value
should you place on this land, which is currently debt free, when you conduct your
analysis of the proposed store?
The price you paid for the land is a sunk cost and, therefore, not included in the
analysis. The price you were offered in the past is also irrelevant. The opportunity
cost, is the appraisal value ($36,900) and this should be included in your investment
analysis.
5
= +
Chapter 9 Questions
4. An investment project has annual cash flows of $2,800, $3,700, $5,100 and
$4,300 and a discount rate of 9 percent. What is the discounted payback
period if the initial cost is $5,200? What if it is $6,400? What if it is $10,400?
To use the discounted payback period, we first need to find the present value of
each of the cash flows:
Year Cash Flow Discounted Cash Flow
0 -$5,200
1 $2,800 $2,568.81
2 $3,700 $3,114.22
3 $5,100 $3,938.14
4 $4,300 $3,046.23
If the initial cost is $5,200 then that amount is recovered between years 1 and 2, as
the third column here shows.
So, using the formula, we have:
Payback Period = Y + UCF
CF
($5,200 −$2,568.81)
Payback Period 1
$3,114.22
= 1.84 years
Repeating the same process for the initial cost of $6,400, the discounted payback is
2.18 years
And if the initial cost is $10,400, the discounted payback is 3.26 years
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12. NPV v IRR. Consider two mutually exclusive projects.
Year Cash flow (A) Cash flow (B)
0 -$41,300 -$41,300
1 $19,100 $6,300
2 $17,800 $14,200
3 $15,200 $17,900
4 $8,400 $30,300
(a) What is the IRR for each project? Which should you accept? Reject?
(b) If the required rate of return is 11%, what is the NPV for each project? Which
would you choose?
(c) Over what range of discount rates would you choose project A? Project B? At
what rate would the firm be indifferent? Explain.
a. The IRR is the interest rate that makes the NPV of the project equal to zero. The equation
for the IRR of Project A is:
0 = –$41,300 + $19,100/(1+IRR) + $17,800/(1+IRR)2 + $15,200/(1+IRR)3 + $8,400/(1+IRR)4
Using a spreadsheet, financial calculator, or trial and error to find the root of the
equation, we find that:
IRR = 19.75%
The equation for the IRR of Project B is:
0 = –$41,300 + $6,300/(1+IRR) + $14,200/(1+IRR)2 + $17,900/(1+IRR)3 + $30,300/(1+IRR)4
Using a spreadsheet, financial calculator, or trial and error to find the root of the
equation, we find that:
IRR = 18.75%
Examining the IRRs of the projects, we see that IRRA is greater than IRRB, so the IRR
decision rule implies accepting Project A. This may not be a correct decision
however, because the IRR criterion has a ranking problem for mutually exclusive
projects. To see if the IRR decision rule is correct or not, we need to evaluate the
project NPVs.
b. The NPV of Project A is:
NPVA = –$41,300 + $19,100/1.11+ $17,800/1.112 + $15,200/1.113 + $8,400/1.114
NPVA = $7,001.54
And the NPV of Project B is:
NPVB = –$41,300 + $6,300/1.11 + $14,200/1.112 + $17,900/1.113 + $30,300/1.114
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NPVB = $8,948.59
The NPVB is greater than the NPVA, so we should accept Project B.
c. To find the crossover rate, we subtract the cash flows from one project from the cash
flows of the other project. Here, we will subtract the cash flows for Project B from the
cash flows of Project A.
Year Cash flow (A) Cash flow (B) Differential
1 $19,100 $6,300 $12,800
2 $17,800 $14,200 $3,600
3 $15,200 $17,900 -$2,700
4 $8,400 $30,300 -$21,900
Once we find these differential cash flows, we find the IRR. The equation for the
crossover rate is:
Crossover rate: 0 = $12,800/(1 + R) + $3,600/(1 + R)2 – $2,700/(1 + R)3 – $21,900/(1 +
R)4
Using a spreadsheet, financial calculator, or trial and error to find the root of the
equation, we find that:
R = 16.36%
At discount rates above 16.36 percent choose Project A; for discount rates below
16.36 percent choose Project B; we are indifferent between A and B at a discount
rate of 16.36 percent.
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17. Consider two mutually exclusive projects.
Year Cash flow (A) Cash flow (B)
0 -$291,000 -$41,600
1 37,000 20,000
2 55,000 17,600
3 55,000 17,200
4 366,000 14,000
11% required rate of return on all projects.
a. If you apply payback criterion. Which investment would you choose? Why?
b. If you apply discounted payback criterion. Which investment would you choose?
Why?
c. If you apply NPV criterion. Which investment would you choose? Why?
d. If you apply IRR criterion. Which investment would you choose? Why?
e. If you apply profitability index criterion. Which investment would you choose?
Why?
f. Based on these answers, which project would you choose?
a. The payback period for each project is:
A: 3 + ($144,000/$366,000) = 3.39 years
B: 2 + ($4,000/$17,200) = 2.23 years
The payback criterion implies accepting Project B, because it pays back sooner than
Project A.
b. The discounted payback for each project is:
A: $37,000/1.11 + $55,000/1.112 + $55,000/1.113 = $118,188.09
$366,000/1.114 = $241,095.54
Discounted payback = 3 + ($291,000 – 118,188.09)/$241,095.54
Discounted payback = 3.72 years
B: $20,000/1.11 + $17,600/1.112 = $32,302.57
$17,200/1.113 = $12,576.49
Discounted payback = 2 + ($41,600 – 32,302.57)/$12,576.49
Discounted payback = 2.74 years
The discounted payback criterion implies accepting Project B because it pays back
sooner than A.
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c. The NPV for each project is:
A: NPV = –$291,000 + $37,000/1.11 + $55,000/1.112 + $55,000/1.113 +
$366,000/1.114
NPV = $68,283.63
B: NPV = –$41,600 + $20,000/1.11 + $17,600/1.112 + $17,200/1.113 + $14,000/1.114
NPV = $12,501.30
NPV criterion implies we accept Project A because Project A has a higher NPV than
Project B.
d. The IRR for each project is:
A: $291,000 = $37,000/(1+IRR) + $55,000/(1+IRR)2 + $55,000/(1+IRR)3
+ $366,000/(1+IRR)4
Using a spreadsheet, financial calculator, or trial and error to find the root of the
equation, we find that:
IRR = 18.26%
B: $41,600 = $20,000/(1+IRR) + $17,600/(1+IRR)2 + $17,200/(1+IRR)3
+ $14,000/(1+IRR)4
Using a spreadsheet, financial calculator, or trial and error to find the root of the
equation, we find that:
IRR = 25.29%
IRR decision rule implies we accept Project B because IRR for B is greater than IRR for
A.
e. The profitability index for each project is:
A: PI = ($37,000/1.11 + $55,000/1.112 + $55,000/1.113 + $366,000/1.114)/$291,000
PI = 1.235
B: PI = ($20,000/1.11 + $17,600/1.112 + $17,200/1.113 + $14,000/1.114)/$41,600
PI = 1.301
Profitability index criterion implies we accept Project B because the PI for B is greater
than the PI for A.
f. In this instance, the NPV criteria implies that you should accept Project A, while
profitability index, payback period, discounted payback, and IRR imply that you
should accept Project B. The final decision should be based on the NPV since it does
not have the ranking problem associated with the other capital budgeting
techniques. Therefore, you should accept Project A.