Example Exam Question
German business mogul, N. Tropenuhr, can choose one of two
options to enter into the California power generation business.
One option would be to put up a huge wind turbine in a pasture
at the end of a mountain pass. The model he would use for this
is the PowerWheel, which has a cost basis of $ 185 875, a life of
4 years, and with a total salvage value of $ 7 000 on Dec 31 of
the 4th year. Mr. Tropenuhr hires the world’s most renowned
meteorologists, who guess that he will be able to generate
power for a full day according to the schedule below:
Year
Days of Use
Year
Days of Use
Year
Days of Use
Year
Days of Use
1
240
2
320
3
350
4
215
Assume that Mr. Tropenuhr will use the units of production
depreciation schedule for the PowerWheel. Set up the equation
for computing the book value at the end of each year, then find
each year-end book value.
Example Exam Question
Year
Days of Use
Year
Days of Use
Year
Days of Use
Year
Days of Use
1
240
2
320
3
350
4
215
Total Service Units = 240 days + 320 days + 350 days + 215 days
= 1125 days of generation capability
Dn = Total Units Consumed (I – S) = TUC ($ 185 875 – $ 7 000) = $159(TUC)
Total Service Units
1125
Bn = Bn –1 – Dn
Yr
Dn
Bn
1
($159) 240 = $ 38 160
$ 185 875 – $ 38 160 = $ 147 715
2
($159) 320 = $ 50 880
$ 147 715 – $ 50 880 = $ 96 835
3
($159) 350 = $ 55 650
$ 96 835 – $ 55 650 = $ 41 185
4
($159) 215 = $ 34 185
$ 41 185 – $ 34 185 = $
7 000
Example Exam Question
The second option would be to construct an electric generation
facility fueled by natural gas, and designed by an old, but
famous Olympic decathlete. Mr. Tropenuhr can install the
eighth revision of the plant design for a total cost basis of
$ 12 800 000. The Jenner-8R model plant will run at full
capacity until his underground natural gas field runs out in 5
years. He will then scrap the plant for a $ 4 000 000 salvage
value at the end of the 5th year.
Assume that for his U.S. investors, Mr. Tropenuhr will use
straight line depreciation for the Jenner 8R. Set up the
equation for computing the book value at the end of each year,
then compute the book value at the end of each year.
However for his E.U. investors, Mr. Tropenuhr will use the
sum of year’s digits depreciation method for the system.
Again, set up the equation for computing the book value at the
end of each year, then compute the end-of-year book value.
Example Exam Question
Straight Line Depreciation:
Dn = (I – S) = ($ 12 800 000 – $ 4 000 000) = $1 760 000 / yr
N
5 yrs
Bn = I – Dn(n) = $ 12 800 000 – $ 1 760 000 (n)
Yr
Dn
Bn
1
$ 1 760 000
$ 12 800 000 – $ 1 760 000 (1) = $ 11 040 000
2
$ 1 760 000
$ 12 800 000 – $ 1 760 000 (2) = $ 9 280 000
3
$ 1 760 000
$ 12 800 000 – $ 1 760 000 (3) = $ 7 520 000
4
$ 1 760 000
$ 12 800 000 – $ 1 760 000 (4) = $ 5 760 000
5
$ 1 760 000
$ 12 800 000 – $ 1 760 000 (5) = $ 4 000 000
Example Exam Question
Sum Of Year’s Digits Depreciation:
SOYD = N(N+1) = 5(5+1) = 15
2
2
Dn = (N – N + 1)(I – S) = (5 – n + 1)($ 12 800 000 – $ 4 000 000)
SOYD
15
= (5 – n + 1)($ 8 800 000) = (5 – n + 1)($ 586 667)
15
Bn = Bn –1 – Dn
Yr
Dn
Bn
1
(5 – 1 + 1)($ 586 667) = $ 2 933 333
$ 12 800 000 – $ 2 933 333 = $ 9 866 667
2
(5 – 2 + 1)($ 586 667) = $ 2 346 667
$ 9 986 667 – $ 2 346 667 = $ 7 520 000
3
(5 – 3 + 1)($ 586 667) = $ 1 760 000
$ 7 520 000 – $ 1 760 000 = $ 5 760 000
4
(5 – 4 + 1)($ 586 667) = $ 1 173 333
$ 5 760 000 – $ 1 173 333 = $ 4 586 667
5
(5 – 5 + 1)($ 586 667) = $
$ 4 586 667 – $
586 667
586 667 = $ 4 000 000
Example Exam Question
Madoff Monet was an investment banker in subprime mortgage
derivatives before his recent setback. Now he has taken his
final bonus and put it into a similar bundled risk investment.
He will invest in hog operations that have contracted swine flu
(but to distribute the risk, he and his buddies will invest in a lot
of diseased livestock operations, instead of only one farmer).
Assume that, despite his brilliant plan, $25 000 000 of the
Monet money becomes worth only $2 500 at the end of the 3
year quarantine period. Construct an algebraic equation that
calculates the average yearly rate at which his investment
deflates. Then compute that deflation rate.
Take the viewpoint of the former farmer’s that Mr. Monet buys
out, and compute what their total original investment was
worth 26 years ago (using a 4% rate of inflation, and only using
table factors) to be worth the $25 million in today’s dollars.
Example Exam Question
Deriving Equation for Deflation:
1
n
1
n
F
F
F
n
F  P(1  f )   (1  f )     1  f  f     1
P
 P
 P
n
F
 f  1  
 P
1
n
Computing:
 $2500 
f  1 

$
25000000


- or - 95.36% / yr
1
3
 .9536
Example Exam Question
Computing Initial Price Using 4% Inflation Rate:
$C
= $A (1 + f ) – n
= $A (P/F, f, n)
= $25 000 000 (P/F, 4%, 26)
= $25 000 000 (P/F, 4%, 25) (P/F, 4%, 1)
= $25 000 000 (.3751) (.9615)
= $ 9 016 466