Sweetypiez --
1. Rates of return are figured with:
F = P * (1 + i) ^ N
F: final payouts (including salvage)
P: initial investment
i: rate of return
N: number of years
Murdoch University
"Rate of Return Analysis" (undated)
http://eng.murdoch.edu.au/~g320/LectureNotes/2
Note that the ROR should exceed MARR (the minimum attractive rate of return).
A. $4,000 = $2,000 * (1 + i) ^ 5; i = 14.9%
B. $4,500 = $5,000 * (1 + i) ^ 6; no need to calculate it -- the
rate of return is NEGATIVE
C. $4,200 = $4,000 * (1 + i) ^ 7; i = 0.7% -- doesn't meet MARR
D. $8,200 = $3,000 * (1 + i) ^ 4; i = 28.6% -- by far the best yield
2. Payback period nets up cash outflows against cash in until the
project turns positive. Here you have cash out of $2,200; cash in of
$400 after year 2. Net = $1,800 let to pay -- it will take 6
ADDITIONAL years to achieve payback.
Payback period = 2 years + 6 years = 8 years.
3. MACRS is the Modified Accelerated Cost Recovery System in use in
the U.S. tax code since 1987. It allows usage of the MAXIMUM of
straight-line or double-declining balance depreciation in any year.
As such, it produces the maximum value for any firm paying taxes
(that's why the question asks about a "profitable company.")
Assets are depreciated on the basis of 8 different classes -- most are
depreciated on 3-, 5- or 7-year lives. Obviously this is a 5-year
class asset.
Here are the straight-line percentages:
1: 20% (of $80,000 or price - salvage)
2: 20%
3: 20%
4: 20%
5: 20%
The double-declining balance numbers take straight-line depreciation
for the 1st year and double it. However, at the point that
double-declining percentages are exceeded by a normal straight-line
depreciation (for the full life), a switch is made to straight-line
for the remaining balance. So, watch for when double-declining drops
below 20%:
1. Twice straight-line: 40%
2. Use the remaining balance as if it were straight line: 2 * (60%/5) = 24%
3. 2 * (36%/5) = 14.4% -- so instead we'll now divide 36 by the remaining 3 years;
12%
4. 12%
5. 12%
About.com
"Double Declining Balance Method" (Kennon, undated)
http://beginnersinvest.about.com/library/lessons/bl-doubledecliningbalance.htm
4. Computing the actual rate of return should be done against the
total capital invested: South Guru's equity and the debt. It doesn't
matter if the debt was financed by Southern Guru Copper's investment
bankers -- or another bank. Ultimately, it's Southern Guru's
responsibility to repay the debt.
Secondly, the real rate of return should be calculated on an annual
basis -- not after years of inflation. It still produces handsome
returns -- but 80% per year (on an equity basis alone.)
In the case of U.S. government financings of Chrysler or U.S. airlines
(post Sept. 11), legislators were smart enough in advance to get
warrants for shares of the companies. When recovery came, the
government profited by selling shares in the market.
If World Bank financing were $9.5 million -- total capitalization of
this project would be $10 million and the return still attractive. It
would be a 17.2% annual return over the 7 years (not 304%). Risks of
foreign currency changes could swamp returns of this size.
In fact the major financial issue in a case like this is risk --
exploration risk, as well as currency risk. But that's another
finance class!
5. This uses the same calculations as in problem 1:
F = P * (1 + i) ^ N
A: $1550 = $1000 * (1 + i) ^ 4; i = 11.6% -- doesn't meet MARR
B. $1700 = $1,000 * (1 + i) ^ 4; i = 14.2%
C. $3600 = $2,000 * (1 + i) ^ 4; i = 15.8%
D. returns are negative
E. $1,600 = $1,200 * (1 + i) ^4; I = 7.5%
In the choice among A/B/C, select C.
Between C and E, chose C.
5. This is a standard sensitivity analysis -- look at different
scenarios and the impact on periodic payments. You'll want to use a
spreadsheet for this -- in Excel it uses the PMT function, set up like
this:
PMT(rate, Nper, PV)
Where rate = interest rate; Nper = number of periods for payment (it
can be months or years); PV = present value or loan amount
Note that there are other capabilities of the Excel calculation
function to simplify calculation in financial cases but that's all you
should need here:
Base loan: PMT(10%, 15, 3000000) = $394,421
Change principal:
PMT (10%, 15, 3300000) = $433,863
PMT (10%, 15, 2700000) = $354,979
Change interest:
PMT (12%, 15, 3000000) = $440,473
PMT (8%, 15, 3000000) = $350,489
Change length of loan:
PMT (10%, 10, 3000000) = $488,236
PMT (10%, 30, 3000000) = $318,238
7. PART 1
A. Straight-line = $99,000/5 = $19,800 per year
B. Double-declining balance
1: $39,600
2: $23,760
3: switches now to straight-line on the balance ($35,640) = $11, 880
4: $11,880
5: $11,880
C. Sum-of the years' digits: add up the years' digits (5+4+3+2+1 =
15). Now depreciation is calculated by percentage backwards (5/15 the
first year; 4/15 the 2nd):
1: 33% = $32,670
2: 26.7% = $26,400
3: 20% = $19,800
4. 13.3% = $13,200
5. 6.67% = $6,600
About.com
"Sum of the Year's Digits" (Kennon, undated)
http://beginnersinvest.about.com/library/lessons/bl-sumoftheyearsdigits.htm
PART 2 -- PV of Depreciation, Donation
In reality this calculation would take into account the tax rate.
However, we'll simply discount year 1 and year 2 deductions by the 5%
discount rate (all year one numbers get divided by 1.05; all year two
numbers by 1.05 * 1.05 or 1.10).
A. Straight line:
1: $18,857
2: $18,000
2 donation: ($59,400)/1.10 = $54,000
B. Double-declining balance:
1: $39,600/1.05 = $37,714
2: $23,760/1.10 = $21,600
2 donation ($35,640)/1.10 = $32,400
C. Sum-of-years' digits:
1. $32,670/1.05 = $31,114
2: $26,400/1.10 = $24,000
2 donation ($39,930)/1.10 = $36,300
8. Initial cost of capital is $150,000; annual operating expenses
$49,000; salvage value after 12 years is $3,000. What annual revenues
bring the NPV to 0 with 6% interest?
Let's break this into 2 halves: how many rides are necessary to cover
the constant operating expenses? $49,000/$0.10 = 490,000 rides
How many are required to cover the capital costs? Let's go back to
the PMT function in Excel:
PMT(rate,nper,pv,fv) -- we can use this to figure the capital costs,
with FV being the $3,000 salvage value. Capital costs = $18,069; so
the number of rides required to fund capital costs are 180,690.
The total is 670,690 per trolley, with most of the expense being in
operating items -- not capital costs. That's about 1,838 rides per
day; 918 cars per day.
9. Here we'll be discounting PV amounts by 13%; it means dividing
numbers by the following number each year. Any project that has a
negative PV is unacceptable:
0: 1
1: 1.13
2: 1.13 * 1.13 = 1.28
3. 1.13 ^ 3 = 1.44
So, here goes:
A: -2,500 + 4,779 + 11,250 + 5,000 = $18,529
B: -1,000 - 2,655 + 7,813 + 2,083 = $6,241
C: 2,500 - 6,195 + 1,563 + 2,778 = $646
D: -3,000 + 1,327 + 4,297 + 4,514 = $7,138
10. My but this Best Friends corporation is diversified!
Again, we'll split the annual O&M (operations and maintenance) from
the capital costs. And since we have such a long horizon for this
investment, we'll use 365.25 days per year -- to account for Leap
Years.
OPERATING COSTS
The O&M cost of each round of golf is $7M/(365.25 * 50) = $383.30
CAPITAL COSTS
Now let's run up the capital costs:
Initial investment = -$17,000,000
Salvage value = $11M/(1.04 ^ 90) = $11M/34.1 = $322,580
The total capital in PV terms is $16,677,000 -- but the cost of the
capital is 4% of that basis: so golfers have an annual NET capital
cost of $667,097 -- based in the initial investment, or $36.53 per
round.
PERIODIC COSTS
Now the renovation costs. These are periodic costs, so we only need
consider the initial period to which they're assigned.
Clubhouse renovation costs only need be considered for the initial
period -- and divided by the renovation period to get a daily cost.
From an accounting standpoint, the amount paid in year 1 should go
into a special account for the anticipated maintenance -- accruing
interest until the money is spent.
Renovation:
Year 15: ($3M/(1.04 ^ 15)) / 15 = ($3M/1.8)/15 = $111,111 per year
Reseeding:
Year 3: ($800,000/(1.04 ^ 3))/3 = ($800K/1.12)/3 = $238,085 per year
Miscellaneous:
Year 6: ($2.7M/(1.04 ^ 6)/6 = ($2.7M/1.27)/6 = $354,331 per year
TOTAL RENOVATION COSTS = $703,527/year or $38.52 per golfer
TOTAL COSTS = ANNUAL O&M + CAPITAL + PERIODIC RENOVATION
$7M + $667,097 + $703,527 = $8,370,624; that's $458.35 per round
Let's add up the per golfer totals from each section:
O&M: $383.30
CAP: $36.53
RENOVATION: $38.52
The numbers check!
11. There are lots of repetitive calculations here, so it's time to
consider the IRR function in a spreadsheet. It works by considering
amounts invested over a period, with cash into the project being
negative and returns being positive.
You'd set these up in columns, something like this:
B1: -400000
B2: 90000
B3: 90000
B4: 90000
B5: 90000
B6: 90000
B7: 90000
Then in B8, use this formula (for Excel):
=IRR(B1:B7)
Proposal A = 9.3%
Proposal B = 11.8%
Proposal C = 10.8%
Proposal D = 7.1%
Proposal E = 10.5%
Proposal F = 5.6%
Proposal G = 15.9%
Proposal H = 15.9%
You can see the calculations in the spreadsheet here. You may wish to
download it, in case this website is not available -- and note that
text is case-sensitive:
http://www.mooneyevents.com/IRR.xls
COST/BENEFIT WITH NPV
The same Excel chart includes a discounting of cash flows at 10% per
year -- and now Proposal A doesn't even meet the cost of money -- it
has negative returns:
NPV A: -$7,297
NPV B: $16,398
NPV C: $33,335
NPV D: -$163,508
NPV E: $7,213
NPV F: -$84,711
NPV G: $35,614
NPV H: $117,742
For the benefit/cost:
A: -$7,297/$400,000 = -1.8%
B: $16,398/$200,000 = 8.2%
C: $33,335/$800,000 = 4.2%
D: -16.4%
E: 0.6%
F: -14.1%
G: 11.9%
H: 16.8%
IRR RANK
Using the internal rate of return, you'd choose (in order): H, G, B, C
and A ($2.4 million spent).
BENEFIT/COST
Ranking by benefit/cost, we'd end up with the same ranking for the
first 4, but would drop A due to a negative NPV. Thus $2 million
would be budgeted.
12. The calculations for these two alternatives are also on the spreadsheet:
A. PV analysis: choose the higher NPV -- Proposal A has a higher
cost-benefit at 17.9%
B. Based purely on superior cash flows: choose Proposal B -- it has
almost 35% higher cash flow (despite the higher investment).
C. ROR analysis says choose Proposal A -- higher total and annual returns.
Google search strategy:
"rate of return analysis"
MACRS + depreciation
There are lots of numbers in here and I've done my best to show how
calculations are set up -- and to doublecheck numbers. However if
anything appears to be incorrect or unclear, please request a
clarification before rating this answer.
Best regards,
Omnivorous-GA |
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