Under favorable weather conditions, the management of Flesher Farms expects its
raspberry crop to have a $120,000 market value. An unprotected crop subject to frost has
an expected market value of $80,000. If Flesher protects the raspberries against frost, the
market value of the crop is still expected to be $120,000 under frost-free conditions and
$180,000 if a frost occurs. What must be the probability of a frost for Flesher to be
indifferent to spending $20,000 for tents to provide frost protection?

Answer (B) is correct.
Without protection, the company will have sales of either $80,000 or
$120,000. With protection, the company will have sales of either
$120,000 or $180,000. The $20,000 cost of tents must be subtracted from
these amounts to compute the net contribution. Thus, the contribution if
the berries are protected will be either $100,000 or $160,000. The
problem can be solved algebraically with the following formula (X = the
probability of frost):
X($80,000) + (1 – X)($120,000) = X($160,000) + (1 – X) ($100,000)
$80,000X + $120,000 –
$120,000X
= $160,000X + $100,000 –
$100,000X
$120,000 – $40,000X = $100,000 + $60,000X
$120,000 = $100,000 + $100,000X
$20,000 = $100,000X
X = .200
In other words, if the probability of frost is 20%, management will be
indifferent between providing and not providing protection. At a frost
expectancy of greater than 20%, management should provide protection.