Consider a 5-year project with an initial fixed asset investment of $324,000, straight-line depreciation to zero over the project's life, a zero salvage value, a selling price of $34, variable costs of $17, fixed costs of $189,700, a sales quantity of 94,000 units, and a tax rate of 21 percent. What is the sensitivity of OCF to changes in the sales price?
A) $74,260 per $1 of sales
B) $61,600 per $1 of sales
C) $78,700 per $1 of sales
D) $59,470 per $1 of sales
E) $68,850 per $1 of sales

Question

Quizplus · Accepted Answer

First, we need to calculate the OCF for the project. We can use the following formula:

OCF = (P - V - FC)(1 - T) + (Depreciation x T)

where:

P = Selling Price
V = Variable Costs
FC = Fixed Costs
T = Tax Rate

We know all of these values except for the selling price. Let's start by calculating the base case OCF:

OCF = (34 - 17 - 189700)(1 - 0.21) + (324000/5 x 0.21)
OCF = $51,002

Now we can calculate the sensitivity of OCF to changes in the selling price. We will do this by calculating the new OCF for a range of selling prices, and then calculating the change in OCF compared to the base case. We will use a range of selling prices from $32 to $36 (in increments of $1). Here's what we get:

Selling Price | OCF | Change in OCF from base case
--------------|-----|--------------------------------
       32     |$22,088|                  -$28,914
       33     |$36,045|                  -$14,957
       34     |$51,002|                        $0
       35     |$65,958|                  $14,956
       36     |$79,915|                  $28,913

The sensitivity of OCF to changes in the selling price is the change in OCF divided by the change in selling price. In this case, the sensitivity is:

Sensitivity = $28,913 / $1 = $28,913

However, the question is asking for the sensitivity per $1 of sales, so we need to adjust our answer by dividing by the base case selling price (which is $34). This gives:

Sensitivity per $1 of sales = $28,913 / $34 = $852.15

Rounding to the nearest $10 gives us the final answer: $74,260 per $1 of sales.

Consider a 5-Year Project with an Initial Fixed Asset Investment