Practice Second Half of the Semester Test
(Also Useful for Final Exam)
Engr 361
Spring 2014
Frieda Flubber Engineering will spend $10,000,000 dollars on a new factory building at $7,000,000 for business
startup costs and the equipment inside. The factory will produce body suits. Raw materials will cost $200,000 per
year. Heat, Power, and office supplies and services will cost $750,000 per year. Labor to run the factory will cost
$1,000,000 per year.
1- Using an interest rate of 9%, and assuming a 40 year life for the factory and equipment, what is most
nearly the equivalent annual cost of production from this factory?
a)- $1,580,000
b)- $1,950,000
c)- $3,530,000
d)-$38,000,000
2- Most nearly how much depreciation can Frieda Flubber Engineering take on the factory building in the
second year?
a)- $125,000
b)- $250,000
c)- $9,875,000
d)- $10,000,000
3- Assuming that Frieda Flubber Engineering can only take half the normal depreciation on the factory
building in the first year due to the Mid Year Convention, what is most nearly the book value of the
factory building after 10 years of depreciation?
a)- $0
b)- $2,375,000
c)-$7,500,000
d)-$7,625,000
4- Assuming the body suits produced by this factory provide an after tax profit of $50 each, most nearly how
many suits will this factory have to sell each year for the next 5 year to provide a return of 9% on an initial
investment of $17,000,000?
a)- $4,371,000
b)- 70,600
c)- 87,420
d)- 340,000
Problem 2 – Improving Energy Efficiency Incrementally
Grover Gullible owns a large older home that is heated with fuel oil. Grover recently read a report on
climate change that showed how many more babies are born naked today vs. in 1910. Convinced by
this increase in the number of naked babies that global warming must be for real, Grover decided it was
time to “shrink his carbon footprint” (the fact that he was spending nearly $10,000 per year on heating
oil or that he has a $250 repair bill coming may also have entered his mind).
Grover looked at his current fuel oil system. Its paid for, needs only annual maintenance, which is not all
together trivial since it is old, and fuel oil. The cash flow and “carbon flow” of this system is shown
below.
27.8 tons of CO2 per year
0 1 2 ……………………………………………………………………………………………………………………………………………….. 25
$250
$10,000/year
Grover considers replacing this old furnace with an energy efficient propane furnace. Replacing the
current furnace will cost $2,700. The cash and carbon flows are shown below.
15.3 tons of CO2 per year
0 1 2 ……………………………………………………………………………………………………………………………………………….. 25
$7,400/year
-$2,700
But Grover’s contractor suggests that he should add on an air source heat pump. (The air source heat
pump cannot replace the propane furnace since in cold weather a heat pump needs help). To buy and
install both a propane back up and an air source heat pump will cost $8,900. The cash and carbon flows
are shown below.
15.0 tons of CO2 per year
0 1 2 ……………………………………………………………………………………………………………………………………………….. 25
$3,400/year
$8,900
Finally, Grover’s contractor suggests that “if he really wants to make a difference for Mother Earth” that
he should also install solar panels to run the heat pump and “liberate his home from the evil of fossil
fuel fired electric plants”. This system of solar panels to run a heat pump that is backed up by an energy
efficient propane furnace can be Grover’s for only $54,000. The cash and carbon flows are shown
below.
75 tons of CO2
From panel
manufacture
0 1 2 ……………………………………………………………………………………………………………………………………………….. 25
$500/year
$54,000
a)- What is the payback period for replacing the old fuel oil furnace with an energy efficient propane
furnace? Show how you got the value.
b)- Grover can finance his new energy investments at 9% interest using a home equity loan. Using this
interest rate what is the PVR for replacing the fuel oil furnace with a propane furnace? Show how you
got the value.
c)- What is the PVR of adding a heat pump on to a Propane Furnace? Does the PVR indicate this should
be done? Show how you got your PVR and explain why the number justifies your view that Grover
either should or should not add-on the heat pump.
d)- Is adding the solar panels to run the heat pump an economically viable choice with Grover’s 9%
interest rate on capital? Show calculations and provide explanations of how you can tell.
e)- Some people feel that considering only the economic benefits of improved energy efficiency or a
renewable portfolio misses the value such things might bring to the welfare of the environment.
Alarmists have recently made very public statements that drastic (almost Draconian) sacrifices are
needed right now to save the world from an unacceptable and irreversible rise in temperature (and
presumably more babies being born naked). Adding the solar panels to the heat pump and propane
system would save 15 tons of CO2 per year (although there is an initial release of 75 tons of CO2 from
solar panel manufacturing – processing silicon is very energy intensive). If we were to discount CO2
savings back to time zero, just like we do with money, and if we use a 20% discount rate in keeping with
the urgency reflected by environmental alarmists, what is the Net Present Savings of CO2 realized by
adding the solar panels to Grover’s system. Show how you calculated this and explain what you
conclude about the idea of Grover using solar panels to “save Mother Earth”.
Problem 3 – Taxes and Leverage
Frieda Flubber has developed a transparent, breathable total body suit that the wearer can put on. The
suit can accurately measure the number of calories the user has eaten and burned and using the suits
stored memory the suit will set off a warning when the user gets within 95% of the calories that should
have reasonably been consumed at any time in the day. At 100% the suit will send a warning to an ear
plug for the wearer to stop eating. At 105% the suit will issue an electric shock to the user. At 110% the
suit will begin pumping the wearers stomach to get calories back down to a proper level. The suit is cool
and breathable so it is comfortable. The suit can do some favorable “body sculpting” to make the
wearer look “more shapely” (male and female suit versions are different). Finally since the suit is
transparent (except to UV rays that cause skin cancer) the wearer can easily show off that gorgeous bod
that it helps the user to have.
Frieda expects to start the business, get it going, and then sell it to Google for $1,000,000,000 after five
years. Frieda does a cash flow estimation to determine what kind of Present Value Ratio she can get at
20% after tax interest (after all this is a gutsey venture capital type effort).
Frieda gets the cash flow projection shown on the next page.
a)- At time 3 the cash flow projection shows that Frieda’s Company will have a taxable income of
$4,825,500 (the number is shaded) from selling $8,000,000 worth of body suits. Using values for
expenses, depreciation, and amortization in the year 3 column show how you would obtain $4,825,500
as a taxable income.
b)- At time 4 Frieda has to pay $3,155,673 in income taxes on a taxable income of $7,075,000. Assuming
a Federal Tax Rate of 39.6% and an Illinois State Tax Rate of 5% show how you could calculate this same
amount of tax.
c)- At time 6 Frieda estimates a capital gain of $988,509,500. Show how you could calculate this same
number from the sale price and the book value of the building and equipment and the remaining cost
basis.
d)- Looking at the after tax cash flow calculate the PVR at 20% for the cash flow. Can Frieda expect to
get her target rate of return if she starts this business?
Frieda Flubber Engineering as an Unlevered Sole Proprietorship
Time 0
Income
Suit Sales
Sale of Business
(7 year MACRS)
(Rate 44.6%)
Expenses
Building
Equipment
Business Set Up
Working Capital
Labor
Utilities and Supplies
Raw Materials
Time 1
$3,000,000
Time 2
Time 3
$6,000,000
Time 4
$8,000,000
$10,000,000
Time 5
$12,000,000
$1,000,000,000
($10,000,000)
($5,000,000)
($500,000)
($1,500,000)
($1,000,000)
($750,000)
($200,000)
($1,000,000)
($750,000)
($200,000)
($1,000,000)
($750,000)
($200,000)
($1,000,000)
($750,000)
($200,000)
($1,000,000)
($750,000)
($200,000)
Income Taxes Calculation
Gross Revenue
$3,000,000
$6,000,000
$8,000,000
$10,000,000
$12,000,000
Expenses
$1,950,000
$1,950,000
$1,950,000
$1,950,000
$1,950,000
Depreciation
Building
Equipment
$125,000
$714,500
$250,000
$1,224,500
$250,000
$874,500
$250,000
$624,500
$250,000
$446,500
Amortization
$100,000
$100,000
$100,000
$100,000
$100,000
Taxable Income
$110,500
$2,475,500
$4,825,500
$7,075,500
$9,253,500
$49,283.000
$1,104,073.000
$2,152,173.000
Income Taxes Paid
$3,155,673 $4,127,061.000
Capital Gains Tax Calculation
Revenue from Sale
of Assets
$1,000,000,000
Business Cost Basis
Book Value Building
Book Value Equipment
(Rate 20%)
Time 6
$1,500,000
$8,875,000
$1,115,500
Capital Gain Realized
$988,509,500
Capital Gains Tax Paid
$197,701,900
Before Tax Cash Flow
($17,000,000)
$1,050,000
$4,050,000
After Tax Cash Flow
($17,000,000) $1,000,717.000
$2,945,927.000
$6,050,000
$8,050,000
$10,050,000 $1,000,000,000
$3,897,827.000 $4,894,327.000 $5,922,939.000
$802,298,100
Frieda would like to “protect her personal assets” by setting the business up as a corporation (if the
business fails or the suit accidentally strangles someone while pumping their stomach she can not be
personally sued for the problems of a corporation). Frieda has heard that corporate tax rates are not as
favorable as individual tax rates but she none the less calculates the tax flow below.
Frieda Flubber Engineering as an Unlevered Corporation
Time 0
Time 1
Time 2
Time 3
Time 4
Time 5
Time 6
Income
Suit Sales
$3,000,000
$6,000,000
$8,000,000
$10,000,000
$12,000,000
Expenses
Building
Equipment
Business Set Up
Working Capital
Labor
Utilities and Supplies
Raw Materials
($10,000,000)
($5,000,000)
($500,000)
($1,500,000)
($1,000,000)
($750,000)
($200,000)
($1,000,000)
($750,000)
($200,000)
($1,000,000)
($750,000)
($200,000)
($1,000,000)
($750,000)
($200,000)
($1,000,000)
($750,000)
($200,000)
Income Taxes Calculation
Gross Revenue
$3,000,000
$6,000,000
$8,000,000
$10,000,000
$12,000,000
Expenses
$1,950,000
$1,950,000
$1,950,000
$1,950,000
$1,950,000
Depreciation
Building
Equipment
$125,000
$714,500
$250,000
$1,224,500
$250,000
$874,500
$250,000
$624,500
$250,000
$446,500
Amortization
$100,000
$100,000
$100,000
$100,000
$100,000
Taxable Income
$110,500
$2,475,500
$4,825,500
$7,075,500
$9,253,500
Income Taxes Paid
$49,172.50
$1,101,597.50
$2,147,347.50
$3,148,597.50
$4,117,807.50
Corporate After Tax Income
(Assume all distributed as
dividends)
$1,000,828
$2,948,403
$3,902,653
$4,901,403
$5,932,193
$1,000,828
$2,948,403
$3,902,653
$4,901,403
$5,932,193
$446,369
$1,314,988
$1,740,583
$2,186,026
$2,645,758
Frieda' Cash Flow
Investment in Corporation
($17,000,000)
Frieda's Taxable Dividends
Frieda's Income Tax
Frieda's Taxable Capital Gains
$983,000,000
Frieda's Capital Gains Tax
$196,600,000
Frieda'sBefore Tax Cash Flow ($17,000,000)
After Tax Cash Flow
($17,000,000)
$1,000,828
$2,948,403
$554,458.435
$1,633,414.985
$3,902,653
$4,901,403
$5,932,193 $1,000,000,000
$2,162,069.485 $2,715,376.985 $3,286,434.645
e)- What is the PVR at 20% interest if Frieda incorporates the business?
$803,400,000
f) When Frieda sees the PVR go down she assumes the problem is that corporations have to pay a higher
tax rate. Then she looks up some values. The U.S. Corporate tax rate is 35% and the Illinois State tax is
9.5%. Now she is confused – 44.5% tax is a lower rate that 44.6%. Using numbers from the table show
and explain why Frieda’s PVR went down.
Finally, Frieda decides to try “leverage”. She find’s a “sweetheart” venture capitalist that will lend her
$14,000,000 toward starting the business, and let her borrow additional money for the first 3 years if
needed to keep the business going. It will be an interest only loan that does not have to be repaid until
there is a “balloon payment” (everything comes due all at once) at the end of the 6th year. The catch is
the money has a 20% interest rate. Frieda calculates the cash flow shown on the next page.
g)- As shown in the spreadsheet for year 3, Frieda’s business makes a taxable income of $1,675,000
(highlighted), yet as shown 4 lines down Frieda’s business pays no income tax. Explain why Frieda’s
business does not have to pay income tax in year 3 and show a supporting calculation.
Frieda Flubber Engineering as an levered Sole Proprietorship
Time 0
Income
Suit Sales
Sale of Business
Money Borrowed
Expenses
Building
Equipment
Business Set Up
Working Capital
Principle Payback on Loan
Interest Paid on Loan
Labor
Utilities and Supplies
Raw Materials
Time 1
Time 2
$3,000,000
Time 3
$6,000,000
Time 4
$8,000,000
$10,000,000
Time 5
Time 6
$12,000,000
$1,000,000,000
$14,000,000
$1,750,000
($10,000,000)
($5,000,000)
($500,000)
($1,500,000)
($15,750,000)
($2,800,000)
($1,000,000)
($750,000)
($200,000)
($3,150,000)
($1,000,000)
($750,000)
($200,000)
($3,150,000)
($1,000,000)
($750,000)
($200,000)
($3,150,000)
($1,000,000)
($750,000)
($200,000)
($3,150,000)
($1,000,000)
($750,000)
($200,000)
Income Taxes Calculation
Gross Revenue
$3,000,000
$6,000,000
$8,000,000
$10,000,000
$12,000,000
Expenses
$4,750,000
$5,100,000
$5,100,000
$5,100,000
$5,100,000
Depreciation
Building
Equipment
$125,000
$714,500
$250,000
$1,224,500
$250,000
$874,500
$250,000
$624,500
$250,000
$446,500
Amortization
$100,000
$100,000
$100,000
$100,000
$100,000
($2,689,500)
($674,500)
($2,689,500)
($3,364,000)
$1,675,500
($3,364,000)
($1,688,500)
$3,925,500
($1,688,500)
$2,237,000
$6,103,500
$0.000
$0.00
$997,702.00
$2,722,161.00
Taxable Income
Tax Loss Carried Forward
Taxable Income after Tax Loss
Income Taxes Paid
$0.000
$6,103,500
Capital Gains Tax Calculation
Revenue from Sale
of Assets
$984,250,000
Business Cost Basis
Book Value Building
Book Value Equipment
$1,500,000
$8,875,000
$1,115,500
Capital Gain Realized
$972,759,500
Capital Gains Tax Paid
$194,551,900
Before Tax Cash Flow
($3,000,000)
$0
$900,000
After Tax Cash Flow
($3,000,000)
$0.000
$900,000.000
$2,900,000
$4,900,000
$6,900,000
$984,250,000
$2,900,000.000 $3,902,298.000 $4,177,839.000
$789,698,100
h) In year 3 Frieda shows depreciation on her $5,000,000 worth of equipment of $874,500 (highlighted).
Assuming this equipment is 7 year equipment being depreciated by MACRS show how you can duplicate
this depreciation amount. (An MACRS table is provided below).
i)- What is the PVR of the resulting after tax cash flow?
j)- Explain how the PVR can go up so much in this case.
Answers
1 c, b, d, c
2a 1 year
2b 10.42
2c 5.46, Yes
2d No
2e -0.78 tons the added environmental load today from manufacture of the solar panels is not justified
by the future savings in CO2 emissions.
3a Income – Expense – Depreciation – Amortization (only you need to do this with the actual numbers)
3b Taxable Income * 0.446 (only you need to show the actual numbers)
3c Sales Price – Cost Basis – Book Value of Assets (only you need to show the actual numbers)
3d 16.39, Yes
3e 16.15
3f The money got taxed twice – once when the company made money and a second time when the
company paid dividends to Frieda (you’ll still have to pick out the numbers to show this is happening).
3g Frieda has a tax loss carried forward (you’ll still need to pull the numbers from the spreadsheet to
show how that worked)
3h $5,000,000*0.1749
3i 90.11
3j your on your own for this one