eUll 0Se e tax shield approach to calculate the OCF. The OCF is: 0CFbase = [($75
ID: 2805385 • Letter: E
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eUll 0Se e tax shield approach to calculate the OCF. The OCF is: 0CFbase = [($75-50)(71,000) _ $790,000](65) + .35($138,000) 0CFbase = $688,550 Now we can calculate the NPV using our base-case projections. There is no salvage value or M NPV is: NPVbase--$690,000 + $688,550(PVIFAI 5%,5) NPVbase $1,618,126.39 To calculate the sensitivity of the NPV to changes in the quantity sold, we will calculate the different quantity. We will use sales of 76,000 units. The OCF at this sales level is: OCFnew [($75-50(76,000)- $790,000)( 65)+35($138,000) ocFnew = $769,800 And the NPV is: NPYnew--$690,000 + $769,800(PVIFA15%,5) NPVnew = $1,890,488.99 So, the change in NPV for every unit change in sales is: ANPV/AS = ($ 1,618,126.39-1,890,488.99) / (71,000-76,000) NPV/AS = +$54.473Explanation / Answer
The new sales figure of 76000 is taken at random to show the sensitivity of NPV to each unit change in sales. In other words it demonstrates the amount by which the NPV changes for every unit change in sales. One will arrive at the same sensitivity figure for any other sales value say 77000 or even 69000. Demonstrating the NPV sensitivity for sales value 77000 below
OCF(base) = [(P-v)Q - FC](1-tax rate) + tax rate x debt = [(75-50) x 77000 - 790000] x 0.65 + 0.35 x 138000 = $ 786050
NPV (base) = - 690000 + 786050(P/A , 15%, 5) = $ 1949961.515
NPV(base) = $ 1618126.39 (when sales is 71000)
Change in NPV = 1949961.515 - 1618126.39 = 326835.1248 and Change in Sales Figure = 77000 - 71000 =6000
Therefore, Sensitivity of NPV to change in Sales Figure = Change in NPV / Change in Sales Figure = $ 54.4725 which is very close to the earlier calculated figure. Hence, the 76000 as stated earlier was used as a random sales figure to demonstrate NPV sensitivity.
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