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Project Management
Notes Calculating the Simple Benefit-Cost Ratio
n+1 = the number of years over which benefits and costs are analyzed
B = the benefits of the project in year i, i=0 to n
i
C = the costs of the project in year i
i
d = the discount rate
First, discount the costs and benefits in future years. The discounted benefits of the project in
year i are equal to B /(1+d) The discounted costs of the project in year i are equal to C /(1+d) i
i.
i i
Then, sum both the discounted benefits and the discounted costs over all years (0 though n) and
divide the sum of the discounted benefits by the sum of the discounted costs:
(B /(1+d) )/ (C /(1+d) ), summed over i = 0 to n.
i
i
i i
10.5.1 Calculating the Incremental Benefit-Cost Ratio
This method is applicable if there are two or more alternative projects to compare to the base
case. It is also known as the “Challenger-Defender Method.”
B = the total discounted benefits of an alternative k, calculated as above
k
C = the total discounted costs of an alternative k, calculated as above
k
First, discount all future costs and benefits to obtain C and B for each alternative and for the
k k
base case. Then start by identifying the base case as the defender, represented by the subscript
“f.” Pick the alternative with the least value of total discounted costs as the challenger “c.”
Calculate the incremental benefit-cost ratio to compare the challenger and defender: (B -B )/(C -
f d f
C ). If the incremental B/C ratio is greater than 1, the challenger becomes the defender. Otherwise,
d
the defender remains. In either case, the next alternative in order or increasing value of C is
k
picked as the new challenger. Continue to compare challenger to defender following the above
logic until all alternatives have been considered. The surviving defender is the economically
preferred alternative.
This procedure is mathematically equivalent to Net Present Value, and it always gives the same
result, but use of this procedure may provide greater insights into the relationships between
costs and benefits of the different projects.
10.6 Other Assessment Methods
The other assessment methods for assessing profitability are discussed below:
10.6.1 Net Present Value
In capital budgeting, net present value, or NPV, is a technique used to evaluate the potential
profitability of a new investment or project. This includes a valuation of the cash outflows to
sustain an investment against its future cash inflows. For example, say that an investment’s
future cash returns have a present value of $100,000, after discounting cash outflows on the
investment project. An assessment of whether the investment is profitable will generally depend
on whether its current market value, if sold today, would return more than $100,000.
10.6.2 Discounted Payback Period
The discounted payback period is a capital budgeting technique used to calculate the number of
years it will take an investment or project to break even. A discounted payback period will not
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