Dr. Neil deGrasse Tyson has recommended to the Hayden Planetarium that they sell
ID: 2660779 • Letter: D
Question
Dr. Neil deGrasse Tyson has recommended to the Hayden Planetarium that they sell stuffed animals, such as Disney's loveable Pluto character, to help fund their research efforts on finding planetoids in our outer solar system.
The proposal involves a 4-year project with the following information: initial fixed asset investment = $432,218; straight-line depreciation to zero over the 4-year life; zero salvage value; price = $37, variable costs = $18; fixed costs = $192,403; quantity sold = 86,850 units; tax rate = 35 percent. What is the sensitivity of OCF to changes in quantity sold? That is, how much does OCF change for a one-unit increase in quantity sold? Enter the dollar amount to two decimal places (ex. -$5,000.45 as -5000.45 or +$3,450.70 as 3450.70).
Hint: To avoid rounding error problems, consider the impact of a change of 1,000 units upon the per unit change in OCF. Compare your result to a one-unit increase in quantity sold.
Explanation / Answer
initial fixed asset investment = $432218
depreciation per year till 4 year = 432218/4 = $108054.5
Price = $37
VC = $18
FC = $192403
quantity sold = 86850
Profit = 37*86850-18*86850-192404 = $1457746
profit after depreciation = 1457746-108054.5 = 1349691.5
profit after tax = 1349691.5*(1-.35) = $877299.475
add back depreciation, net cash flow = 877299.475+108054.5 = $985353.975
to calculate sensitivity of OCF
suppose increament in qty sold = 1000
New QTY sold = 86850+1000 = 87850
Profit after depreciaiton = 37*87850-18*87850-192404-108054.5 = $1368691.5
Profit after tax = 1368691.5*(1-.35) = $889649.475
add back depreciation, net cash flow = 889649.475+108054.5 = $997703.975
change in cash flow per 1000 increase in qty = 997703.975-985353.975 = $12350
changein cash flow per unit increash = 12350/1000 = $12.35
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