# Consider a four-year project with the following information: initial fixed asset...

## Question:

Consider a four-year project with the following information:

initial fixed asset investment=$470,671 straight-line depreciation to zero over the four-year life zero salvage value price=$35

variable costs=$25 fixed costs=$184,307

quantity sold=79907 units

tax rate=32%.

Calculate the sensitivity of the OCF to changes in the quantity sold.

## Operating Cash Flow:

Operating cash flow include cash inflow occur from the core business activities such as production and selling of goods and services. It does not include cash inflow from investment or financing activities.

For 79,907 units

{eq}OCF \ = \ \left [ \left ( Price \ - \ Variable \ cost \right ) \ \times \ Quantity \ - \ Fixed \ cost \right ]\left ( 1 \ - \ tax \right ) \ + \ depreciation\left ( tax \ rate \right ) \\ OCF \ = \ \left [ \left ( 35 \ - \ 25 \right ) \ \times \ 79,907 \ - \ 184,307 \right ]\left ( 1 \ - \ 0.32 \right ) \ + \ \frac{470,671}{4\left ( 0.32 \right )} \\ OCF \ = \ 418,038.84 \ + \ 37,653.68 \\ OCF \ = \ 455,692.52 {/eq}

For 80,000 units

{eq}OCF \ = \ \left [ \left ( Price \ - \ Variable \ cost \right ) \ \times \ Quantity \ - \ Fixed \ cost \right ]\left ( 1 \ - \ tax \right ) \ + \ depreciation\left ( tax \ rate \right ) \\ OCF \ = \ \left [ \left ( 35 \ - \ 25 \right ) \ \times \ 80,000 \ - \ 184,307 \right ]\left ( 1 \ - \ 0.32 \right ) \ + \ \frac{470,671}{4\left ( 0.32 \right )} \\ OCF \ = \ 418,671.24 \ + \ 37,653.68 \\ OCF \ = \ 456,324.92 \\ Sensitivity \ = \ \frac{Change \ in \ OCF}{Change \ in \ quantity} \\ Sensitivity \ = \ \frac{\left ( 456,324.92 \ - \ 455,692.52 \right )}{80,000 \ - \ 79,907} \\ Sensitivity \ = \ \frac{632.4}{93} \\ Sensitivity \ = \ 6.80 {/eq}