Notes to Spreadsheet Calculating Fair Values
and Changes in Fair Values
These notes contain (1) a description of the values in the rows associated with the note,
and in some cases, (2) the formula used to calculate the value shown in the cell to which
the first occurrence of the note is related.
a) The periodic interest rate is used to discount expected cash flows to determine fair
values of the futures. It is assumed to be 6% per year, or .5% per month.
b) Futures prices are quoted in different units. Soybeans are quoted in cents per
bushel, soybean oil is quoted in cents per pound, and soybean meal is quoted in
dollars per ton. This cell, and the following two cells, are used to determine how
many units in total of soybeans, soybean oil, and soybean meal are involved under
the futures contracts each month. For soybeans, there are 5,000 bushels in a
contract; for soybean oil, 60,000 pounds; and for soybean meal, 100 tons.
c)
Contracts entered into per hedging month are determined by taking the number of
tons of input or output per day of each commodity listed in the text, converting to
monthly requirements by multiplying by 22 days per month, converting that to the
appropriate contract units (bushels, pounds, or tons), dividing that by the number
of units per contract, and multiplying by .7, since Smith and Sons is hedging only
70% of purchase and sales requirements.
B5: = ROUNDUP(((1000
pounds
days
pounds
bushels
tons
*2000
*22
)/(60
*5000
)) x .7,0)
ton
month
bushel
contract
day
B46: =ROUNDUP(((183
pounds
days
pounds
tons
*2000
*22
)/60000
x .7,0)
ton
month
contract
day
B98: =ROUNDUP(((800
days
tons
tons
*22
)/100
x .7,0)
month
contract
day
d) The total quantity of units (bushels, pounds, or tons) hedged per month. Changes
in futures or spot prices are multiplied by these quantities to determine the
undiscounted value of futures contracts due to price changes.
e) Months to maturity of the contract at June 30, the first date for which
calculations/journal entries are required. In conjunction with the number
described in note f, this is used to determine how many periods cash flows should
be discounted. The assumption used in this case is that July futures effectively
mature at the end of June, since holding them past that point could result in Smith
having to take physical delivery of the beans, or could result in liquidity
problems, in the case of the soybean oil and meal.
f) Specifies how many months the calculation date is from June 30, the first date for
which calculations/journal entries are required. In conjunction with the number
described in note e, it is used to determine how many periods cash flows should
be discounted. See note e for additional assumptions.
g) Calculation of the fair value of the futures contracts due to a change between the
price specified in the futures contracts, and the current futures price. The change
in futures prices is multiplied by the total units under contract, then discounted for
the appropriate time period. Smith and Sons is long soybeans, so if futures prices
go down, the futures are a liability. They are short soybean oil and soybean meal,
so if futures prices decline, the futures are assets. This explains the leading minus
sign in the formula for soybeans.
Total
units
C16: = ROUND(-(( (C8 – C13) *
Number of periods to discount
B6) / ((1 + C1) ˆ (C10 – C15) )), 0)
Difference between
original & current
futures prices
Discount
factor
h) Calculation of the portion of the fair value of the futures contracts due to a change
between the spot price at the time the future was entered into, and the current spot
price. The change in spot prices is multiplied by the total units under contract,
then discounted for the appropriate time period. Changes in this amount are
designated by Smith and Sons as hedging variability in cash flows of the
anticipated transactions, measured by discounted changes in the spot prices.
Total
units
Number of periods to discount
C17: = ROUND(-(( (C9 –C14) * B6)/((1 + C1) ˆ (C10 – C15) )),0)
Difference between
original & current
spot prices
Discount
factor
i) The portion of the fair value of the futures due to a change in the difference
between the futures and spot prices at inception of the futures, and the current
futures and spot prices. This portion is effectively the difference between the fair
value due to a change in futures prices (see note g) and the portion of the fair
value due to a change in spot prices (see note h). Any change in the relation
between futures and spot price will not be effective in hedging changes in cash
flows of the anticipated transaction, measured by discounted changes in spot
prices. Changes in these values are reflected immediately in net income.
j) Since the futures had zero fair value at inception, at this first measurement date,
the changes in fair values are equal to the entire fair values described in notes g, h,
and i.
k) In periods subsequent to the first measurement date of the fair values of the
futures and their components, the changes in values are simply the current fair
values less the preceding month’s fair values.
l) Smith and Sons is short soybean oil and soybean meal. This explains the leading
minus sign in cell C16 that is missing in cells C57 and C109. See note g for
additional details relating to this amount.
m) See notes h and l.
n) See notes i and l.