Corporate
Finance
Problem Set 6
Suggestion: It may be easiest to transfer this entire
problem set to an Excel spreadsheet and solve the problems there
Use the following information for
questions 1 through 6.
A project has an initial cost of
$52,125, expected net cash inflows of $12,000 per year for 8 years and a cost
of capital of 12%.
10-1 What is the project’s NPV?
N
I
PV
PMT
FV
10-2 What is the project’s IRR?
N
I
PV
PMT
FV
10-3 What is the project’s MIRR,
assuming that interim cash flows can be reinvested at a rate of 3%?
To Calculate Terminal Value
N
I
PV
PMT
FV
Taking the TV and calculating MIRR
N
I
PV
PMT
FV
10-4 What is the project’s profitability
index?
10-5
What is the project’s payback period?
10-6
What is the project’s discounted payback period?
10-7
Your division is considering two investment projects, each of which
requires an up front expenditures of $15 million. You estimate the investments will produce the
following cash flows
Year
Project
A
Project
B
1
5,000,000
20,000,000
2
10,000,000
10,000,000
3
20,000,000
6,000,000
What
are the two projects’ net present values, assuming that the cost of
capital is 5%, 10% or 15%?
What
are the two projects’ IRRs for these same cost of capital?
10-8
Edelman Engineering is considering including two pieces of equipment, a
truck and over and an overhead pulley system, in this year’s capital
budget. The projects are
independent. The cash outlay for the truck is $17,100 and that for the pulley
system is $22,430. The firm’s cost of
capital is 14%. Interim cash flows can
be reinvested at a rate of 3%. After-tax
cash flows including depreciation are as follows:
Year
Truck
Pulley
0
(17100)
(22430)
1
5,100
7,500
2
5,100
7,500
3
5,100
7,500
4
5,100
7,500
5
5,100
7,500
Calculate the IRR, NPV and MIRR for each
project, and indicate the correct accept-reject decision for each
IRR
(Truck)
N
I
PV
PMT
FV
NPV (Truck)
N
I
PV
PMT
FV
Terminal Value
(Truck)
N
I
PV
PMT
FV
MIRR (Truck)
N
I
PV
PMT
FV
Pulley:
IRR
(Pulley)
N
I
PV
PMT
FV
NPV (Pulley)
N
I
PV
PMT
FV
Terminal Value
(Pulley)
N
I
PV
PMT
FV
MIRR (Pulley)
N
I
PV
PMT
FV
10-9
Davis Industries must choose between a gas-powered and electric-powered fork
lift for moving materials in its factory. Since both forklifts perform the same
function the firm will choose only one. (The projects are mutually exclusive). The electric-powered truck will cost more,
but it will be less expensive to operate; it will cost $22,000, whereas the gas-powered
truck will cost $17,500. The cost of
capital that applies to both investments is 12%. The life for both types of truck is estimated
to be 6 years, during which time the net cash flows for the electric-powered
truck will be $6290 per year and those with a gas-powered truck will be $5000
per year. Annual net cash flows include
depreciation expenses. Calculate the NPV,
Profitability Index and IRR for each type of truck, and decide which to recommend.
NPV (Electric)
N
I
PV
PMT
FV
Profitability Index
(Electric)
IRR (Electric)
N
I
PV
PMT
FV
NPV
(Gas)
N
I
PV
PMT
FV
Profitability Index
(Gas)
IRR (Gas)
N
I
PV
PMT
FV
10-11 Your company is considering two
mutually exclusive projects, X and Y, whose costs and net cash flows are shown
below:
Year
X
Y
0
(1000)
(1000)
1
100
1000
2
300
100
3
400
50
4
700
50
The Projects are equally risky, their
cost of capital is 12% and interim cash flow can be invested at 3%.
a) If the decision is based on which project has
the higher MIRR, what project would be selected?
b) If
the decision were based on Payback Period, which project would be chosen?
MIRR calculation for A
N
I
PV
PMT
FV
MIRR calculation for B
N
I
PV
PMT
FV
Payback A
Payback B
10-13
Cummings Products is considering two mutually exclusive investments whose
expected net cash flows are as follows:
Year
Project A
Project B
0
(300)
(405)
1
(387)
134
2
(193)
134
3
(100)
134
4
600
134
5
600
134
6
850
134
7
(180)
0
a. Construct
NPV profiles for Project A and Project B
b. What
are the two projects’ IRR?
c. If
you were told that each project’s cost capital was 10%, which project, if
either, should be selected? If the cost
of capital were 17%, what would be proper choice?
d. What
is the crossover rate, and what is its significance?
10-21 Your division is considering two
investment projects, each of which requires an up-front expenditure of $25
million. You estimate the cost of
capital is 10% and that the investments will produce following after-tax cash
flows(in millions of dollars):
Year
Project A
Project B
0
(25)
(25)
1
5
20
2
10
10
3
15
8
4
20
6
a. What
is the payback period for each of the projects?
b. What
is the discounted payback period for each of the projects?
c. If
the two projects are independent and the cost of capital is 10%, which project
or projects should the firm undertake?
d. If
the two projects are mutually exclusive and the cost of capital is 5%, which
project should firm undertake?
e. If
the two projects are mutually exclusive and cost capital is 15%, which project
should the firm undertake?
f. What
is the crossover rate?
12-7 Upton Corporation makes all
purchases of small computers, stocks them at conveniently located warehouses,
ships them to its chain of retail stores, and has a staff to advise customers
and help them set up their new computers. Upton’s balance sheet as of December
31, 2010 the shown here (millions of dollars):
Cash
3.5
Accounts
Payable
9.0
Receivables
26.0
Notes
Payable
18.0
Inventories
58.0
Accruals
8.5
Total Current Assets
87.5
Total Current Liabilities
35.5
Net
Fixed Assets
35.0
Long
Term Debt
6.0
Common
Stock
15.0
Retained
Earnings
66.0
Total
Assets
122.5
Total Liabilities & Equity
122.5
Sales for 2010 were $350,000,000 and net
income for the year was $10.5 million, so the firm’s profit margin was 3.0%.
Upton paid dividends of $4.2 million to the common shareholders so its payout
ratio was 40%. Its tax rate is 40%., and
it operated at full capacity. Assume
that all assets/sales ratios, spontaneous liabilities/sales ratios, the profit
margin, and the payout ratio remain constant in 2011. Sales are projected to
increase to $70,000,000, or by 20%, during 2011. Assuming all existing
relationships remain constant:
a. Calculate
the required assets that will be required to support the projected increase in
sales.
b. Calculate
the spontaneous liabilities that will arise with the increase in sales
c. Calculate
the AFN to determine Upton’s projected external capital requirements.
d. Use
the forecasted financial statement method to forecast Upton’s balance sheet for
December XXXXXXXXXXAssume that all
additional external capital is raised as a bank loan at the end of the year and
is reflected in notes payable (because the debt is added at the end of the
year, there will be no additional interest expense due to the new debt), assume
Upton’s profit margin and dividend payout ratio will be the same in 2011 as
they were in 2010. What is the amount of
the notes payable reported on 2011 forecasted balance sheet? (Hint: you don’t
need to forecast the income statements because you are given the projected
sales, profit margin, and dividend payout ratio; these figures allow you to
calculate 2011 addition to retained earnings for the balance sheet.)