Money borrowed for one year carries interest of 5.o, money borrowed
two years is 6.o, and money borrowed for two years carries an interest
rate of 7.0 per year. First year costs are $2,000,000 and expect no
additional revenue. In the second year, costs will be $5,000,000 but
have 30 percent chance of generating $10,000,000 in additional
revenue, a 20 percent chance of generating $6,000,000 in additional
revenue, and a fifty percent chance of not being to sell anything
because your contractor is behind schedule. In the final year, you
have a fifty percent chance of $2,000,000 in additional costs (The
contractor is a friend of your boss and you can't sue for breach of
contract). and a fifty percent chance that you finished paying the
bills in the second year. You have fifty percent chance that revenue
in the third year will be $2,000,000, a thirty percent chance it will
be $5,000,000 and a 20 percent chance it will be $12,000,000. At that
point salvage won't be worth the trouble.

How do you decide if this is a viable project?

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Request for Question Clarification by elmarto-ga on 03 Aug 2003 20:15 PDT

Hi douger!
I think there is a typo in the first sentence. It says:

"Money borrowed for one year carries interest of 5.o, money borrowed
two years is 6.o, and money borrowed for two years carries an interest
rate of 7.0 per year"

So, money borrowed for two years carries an interest rate of 6.0% or
7.0% ?

Also, I assume that in the cases where you mention 5.0 and 6.0 you're
also referring to the interest rate in a "per year" basis. Is this
correct?

If you can clarify this, I think I can help you with this question.


Best wishes!
elmarto

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Clarification of Question by douger-ga on 04 Aug 2003 08:47 PDT

Elmarto:

     Money borrowed for first year is 5.0%, two years carries an
interest of 6.0% and three years at 7.0%

There are two concepts that are used in evaluating this project.  The
first is Expected Value.  This is calculated by taking the
probabilities that a set of cash flows will occur and multiplying each
cash flow by its probability to arrive at an expected cash flow.  The
second is Net Present Value.  This is obtained by adding the expected
net cash flows together after discounting them based on when they
occur.

First, we need to calculate the Expected Value for the expenses and
revenues for each year.

Year 1: -$2 million in costs with no revenue.

Year 2: -$5 million in costs with a 30% chance of $10,000,000 in
revenue, a 20% chance of $6,000,000 in revenue, and a 50% chance of no
revenue.  The expected revenue = 0.3 ($10 million) + 0.2 ($6 million)
+ 0.5 (zero dollars) = $4.2 million.

Year 3: a 50% chance of -$2 million in costs and a 50% chance of zero
dollars in costs.  The expected costs = 0.5 (-$2 million) + 0.5 (zero
dollars) = -$1 million.  A 50% chance of $2,000,000 in revenue, a 30%
chance of $5,000,000 in revenue, and a 20% chance of $12,000,000 in
revenue yields an expected revenue of 0.5 ($2 million) + 0.3 ($5
million) + 0.2 ($12 million) = $4.9 million

So, we now have expected costs and revenues for each year.  These are:

Year 1: costs of -$2 million; revenue of zero dollars
Year 2: costs of -$5 million; revenue of $4.2 million
Year 3: costs of -$1 million; revenue of $4.9 million

Now we calculate the net cash flows for each year by adding the costs
and revenues together.  This yields:

Year 1: cash flow of -$2 million
Year 2: cash flow of -$800,000
Year 3: cash flow of $3.9 million

There is no salvage value, so there are no additional cash flows.

Now we use the Net Present Value formula and the interest rates that
were given to discount the cash flows back to the present so that we
can evaluate the attractiveness of the project.  If the Net Present
Value is positive, then the project is generally viewed as being worth
doing.

The Net Present Value formula is calculated by taking the future
values and dividing them by (1 + i)^n where i is the interest rate for
the period and n is the number of periods from the present time.

So, the Net Present Value = -$2 million/1.05^1 + -$800,000/1.06^2 +
$3.9 million/1.07^3 = $566,802.66.

Because the Net Present Value is positive, this is a viable project,
assuming one can withstand the risks of the most negative possible
outcomes.

Sincerely,

Wonko

Source: "Principles of Engineering Economy," Eighth Edition, by Grant,
Ireson, and Leavenworth, John Wiley & Sons, 1990

Excellent answer, very detailed and thorough.