Seminar 2
Problem #1
An art collector has the opportunity to invest in paintings. The paintings cost $3 million and are
expected to be worth $3,829 million in five years. He also has the opportunity to invest in 5-year
bank certificates of deposit, which guarantee a return of 6% per year.
1) What is the future value of $3 million invested for five years in bank certificates of deposit?
2) Which has the highest return?
a. The paintings.
b. The bank CDS.
3) What is the rate of return for an investment in these paintings?
4) Assuming you would be satisfied with a 6% return from holding these paintings, what is the
maximum you would be willing to pay for them today (again assuming they will be worth $3.829
million in 5 years)?
Answers
1.
FV = PV (1+r)t = $3,000,000 (1.06)5 = $3,000,000 (1.3382) = $4,014,677
2.
Paintings
$3,000,000
will be worth $3,829,000
Bank CDs
$3,000,000
will be worth $4,014,677
Bank CDs have a higher return.
3.
FV = PV (1+r)t
$3,829,000 = $3,000,000 (1+r)5
(1+r)5 = $3,829,000 / $3,000,000 = 1.2763
(1+r) = (1.2763).2 = 1.05
r = .05
or 5%
4.
PV = FV/(1+r)t = $3,829,000 / (1.06)5 = $3,829,000 (.74726) = $2,861,252
in 5 years
in 5 years
Problem 2
Investment A pays $100 per year for three years. Investment B pays $80 per year for four years.
Which of these investments has the higher present value if the discount rate is
a. 10%?
b. 25%?
Answers:
PVA = C [ 1 - 1/(1+r)t ]/r
a)
PVAA =
PVAB =
$100 [ 1 - 1/(1.10)3 ]/ .10 = 100 (2.4868) = $248.68
$80 [ 1 - 1/(1.10)4]/.10 =
80 (3.1699) = $253.59
b)
PVAA =
PVAB =
$100 [ 1 - 1/(1.25)3]/ .25 = 100 (2.30811) = $195.20
$80 [ 1 - 1/(1.25)4]/ .25 = 80 (2.36160) = $188.93
Problem 3
Consider the following cash flows on two mutually exclusive projects that require an annual return
of 15%.
Year
0
1
2
3
Project A
-$600,000
270,000
350,000
300,000
Project B
-$1,800,000
1,000,000
700,000
900,000
a) Based on the discounted payback period rule, which project should be chosen?
b) If your decision rule is to accept the project with a greater IRR, which project should you
choose?
c) Since you are fully aware of the IRR rule’s scale problem, you calculate the incremental IRR.
Based on your computations, which project should you choose?
d) To be prudent, you compute the NPV for both projects. Which project should you choose? Is
it consistent with the incremental IRR rule?
Solution:
a) Project A
Year
0
1
2
3
Discounted CF
-$600,000
234,783
264,650
197,255
Cumulative CF
-$600 ,000
-365,217
-100,576
DPP for A = 2 + 100,576/197,255 = 2.51 years
Analogously one can compute DPP for B = 2.68 years.
Hence, project A should be chosen.
b) IRR of A solves -600,000 + 270,000/(1+r) + 350/(1+r)2 + 300/(1+r)3 = 0. We obtain IRR =
24.3%
Analogously, IRR of B = 21.46%.
Hence, project A should be chosen
c) Incremental cash flows
Year
0
1
2
3
B-A
-$1,200,000
730,000
350,000
600,000
Doing similarly to b), we get incremental IRR = 19.92%. Since it is > 15%, project B should be
chosen.
d) NPV of A = -600,000 + 270,000/1.15 + 350/1.152 + 300/1.153 = 96,687.76
NPV of B = 190,630.39 > 96,687.76.
Hence, project B should be chosen. The NPV rule is consistent with the incremental IRR rule.
Problem #4
U-Eat-M Pizza is evaluating a new line of no-fat pizzas. The company has paid $40,000 for a
marketing study which indicates the new product would have sales of $650,000 per year for the next
six years. Making no-fat pizza requires a specialized high temperature baking oven made in Chicago
selling for $450,000 with shipping and handling expenses of $10,000. Installing the new oven will
cost $40,000. This new oven will be depreciated according to ACRS as a five-year asset with no
market value at the end of six years. Annual fixed costs are projected at $80,000 and variable costs
are projected at 60% of sales. Net working capital requirements are $75,000 for the six-year life of
the project; the outlay for working capital will be recovered at the end of six years. The tax rate is
34% and the firm requires a 16% return.
1. What is the amount of initial investment that can be depreciated?
2. Calculate the annual depreciation and the ending book value each year for the fixed assets.
What is the book value at the end of two years?
3. Prepare pro forma income statements for the project for years 1 through 6 in order to
determine EBIT, taxes and unlevered net income.
4. Compute the Free Cash Flow for years 1 through 6.
5. What is the initial outlay at time zero (remember all cash flows at time zero, not just the total
cost of equipment)?
6. What is the net present value of this project?
7. What is the IRR of this project?
8. What is the payback for this project?
9. Should the $40,000 marketing study be included in the project analysis? Consider that the
project could not have been evaluated without this study; however, you must pay for this
study whether or not you proceed with the project.
Problem #4 Answers
1.
Equipment Cost + Shipping + Installation = $450,000+$10,000+$40,000=$500,000
2.
Year
ACRS
percentage
1
2
3
4
5
6
20.00%
32.00%
19.20%
11.52%
11.52%
5.76%
Depreciation
.2000
.3200
.1920
.1152
.1152
.0576
x $500,000
x 500,000
x 500,000
x 500,000
x 500,000
x 500,000
= $100,000
= 160,000
=
96,000
=
57,600
=
57,600
=
28,800
Ending
book value
$400,000
240,000
144,000
86,400
28,800
0
*
3.
Year 1
Sales Revenue
-Variable Costs
-Fixed Costs
-Depreciation
Year 2
Year 3
Year 4
Year 5
Year 6
$650,000 $650,000 $650,000 $650,000 $650,000 $650,000
-390,000 -390,000 -390,000 -390,000 -390,000 -390,000
-80,000 -80,000 -80,000 -80,000 -80,000 -80,000
-100,000 -160,000 -96,000 -57,600 -57,600 -28,800
EBIT
-Taxes
80,000
-27,200
20,000
-6,800
84,000
-28,560
122,400
-41,616
122,400
-41,616
151,200
-51,408
Net Income
$52,800
$13,200
$55,400
$80,784
$80,784
$99,792
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Net Income
52,800
+Depreciation
100,000
- Increases in NWC
0
- CapEx
0
13,200
160,000
0
0
55,400
96,000
0
0
80,784
57,600
0
0
80,784
57,600
0
0
99,792
28,800
75000
0
4.
Free Cash Flow
Comment:
$152,000 $173,000 $151,440 $138,384 $138,384 $203,592
For year 6, recovery of net working capital results in a cash inflow of $75,000. Fixed
assets are fully depreciated at the end of year 6 and have zero market value, so there
are no consequences for cash flows from disposal of fixed assets at the end of the
project’s life. Total inflow for year 6 is $203,592 = ($99,792 + $28,800 + $75,000).
5.
Initial cash outflow is $575,000 = $500,000 + $75,000 (Installed cost + net WC).
6.
PV = $152,800/1.16 + $173,200/1.162 + $151,440/1.163 + $138,384/1.164
+ $138,384/1.165 + $203,592/1.166 = $583,338.58
NPV = $583,338.58 - $575,000 = $8,338.58 so the new product line is an acceptable
investment.
7. The IRR is 16.539%.
8.
Yr
Cash Flows
Cumulative
0
1
2
3
4
5
6
-575,000
152,800
173,200
151,440
138,384
138,384
203,592
-575,000
-422,200
-249,000
-97,560
40,824
179,208
382,800
Payback = 3 + 97,560/(138,384) =
3.7 Years
9. The cost of the $40,000 marketing study is a sunk cost and is irrelevant.