chart below is also based upon the Contract Pricing Reference Guide, Vol 2, Chapter 9, and
introduces the “mid-year” Discount Factors for solving NPV problems.
In the chart above:
The initial period (when t = 0) includes 12 monthly payments.
Rather than sum the present
values of each of the 12 payments, where t would equal 0, then 1/12, then 2/12, then 3/12…all the

CON 170, The Fundamentals of Cost and Price Analysis
CON 170, Unit 2, Quantitative Methods for Contract Pricing
53
way to 11/12, we can simply calculate the present value of the entire year’s cash flows using the
“mid-year” t-value of .5.
From the Discount Factor Table below, this would equate to a “mid-year”
DF of .9975.
The next period in the chart above (when t = 1) includes 1 payment every 4 months, which
equates to 3 payments in the year.
Rather than sum the present values of each of the 3 payments,
where t would equal 1, then 4/12, then 8/12, we can simply calculate the present value of the entire
year’s cash flows using the “mid-year” t-value between t = 1 and t = 2, which is t = 1.5.
From the
Discount Factor Table below, this would equate to a “mid-year” DF of .9925.
The final period in the chart above (when t = 2) includes 1 payment at the 6 month point.
In
this case, simply calculate the present value of the year’s cash flow by using the t-value halfway
between t = 2 and t = 3, which is t = 2.5.
From the Discount Factor Table below, this equates to a
“mid-year” DF of .9901.
As the chart indicates, analysts should use “mid-year” Discount Factors when an offeror proposes
consecutive monthly, consecutive quarterly, or even mid-year payments.
The “mid-year” Discount
Factors enable us to calculate the present value of consecutive monthly payments, quarterly
payments, and a single payment in the middle of a year with a single calculation, using a “t” value
that ends in “.5”.
In examining Contractor B’s proposed cash flow of 36 consecutive monthly payments, it is
appropriate to use “mid-year” Discount Factors; but, do we have to use the “mid-year” factors and
make
36
calculations?
Thankfully, no.
The “mid-year” Discount Factors enable us to calculate the
PV of the 12 monthly payments in a year with a single calculation.
Thus, for Contractor B’s
proposed monthly cash flow over 3 years, we can calculate the PV with 3 calculations (not 36), using
the “t” value for each year from the OMB Discount Factor Table:
t = .5, t = 1.5, and t = 2.5.
The next chart highlights the “mid-year” Discount Factors in our OMB Discount Factor Table.
Notice, the “t” values for the “mid-year” Discount Factors end in “.5”.
To calculate the PV of
Contractor B’s payments, we would use the 3 “mid-year” Discount Factors highlighted in the slide
below.

CON 170, The Fundamentals of Cost and Price Analysis
54
CON 170, Unit 2, Quantitative Methods for Contract Pricing
With this understanding of “end of year” and “mid-year” Discount Factors,” we are ready to
calculate the NPV of each offeror, and determine which is most advantageous to the Government.

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