You are considering a new product launch. The project will cost $1,950,000, have
ID: 2651582 • Letter: Y
Question
You are considering a new product launch. The project will cost $1,950,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 180 units per year; price per unit will be $24,000, variable cost per unit will be $15,000, and fixed costs will be $540,000 per year. The required return on the project is 10 percent, and the relevant tax rate is 34 percent.
Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within ±10 percent. What are the upper and lower bounds for these projections? What is the base-case NPV? What are the best-case and worst-case scenarios? (Negative amount should be indicated by a minus sign. Round your NPV answers to 2 decimal places. (e.g., 32.16))
Evaluate the sensitivity of your base-case NPV to changes in fixed costs. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places. (e.g., 32.161))
What is the cash break-even level of output for this project (ignoring taxes)? (Round your answer to 2 decimal places. (e.g., 32.16))
What is the accounting break-even level of output for this project? (Round your answer to 2 decimal places. (e.g., 32.16))
What is the degree of operating leverage at the accounting break-even point? (Round your answer to 3 decimal places. (e.g., 32.161))
You are considering a new product launch. The project will cost $1,950,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 180 units per year; price per unit will be $24,000, variable cost per unit will be $15,000, and fixed costs will be $540,000 per year. The required return on the project is 10 percent, and the relevant tax rate is 34 percent.
Explanation / Answer
Scenario
Unit Sales
Variable Cost
Fixed Cost
NPV
Base
180
15000
540000
834885.29
Best
198
13500
486000
1908138.33
Worst
162
16500
594000
-125393.75
a.)
The base-case, best-case, and worst-case values are shown below. Remember that in the best-case, sales and price increase, while costs decrease. In the worst-case, sales and price decrease, and costs increase.
BASE CASE SCENARIO :
NPV = PV OF INFLOW – PV OF OUTFLOW
NPV ={ [(SP – VC)UNITS - FC ](1-TAX RATE) + DEP (TAX RATE)} X DISCOUNTING FACTOR – PV OF PROJECT COST
={ [ (24000-15000)180 – 540000] (1-.34) + (195000X1/4)(.34) } X [(1/1+.10)^1+.....(1/1+.10)^4} – 1950000
= 2784885.29 – 1950000
= 834885.29
BEST CASE SCENARIO :
NPV = PV OF INFLOW – PV OF OUTFLOW
= { [ (24000-13500)198 – 486000] (1-.34) + (195000X1/4)(.34) } X [(1/1+.10)^1+.....(1/1+.10)^4} – 1950000
= 3858138 – 1950000
= 1908138
WORST CASE SCENARIO :
NPV = PV OF INFLOW – PV OF OUTFLOW
= { [ (24000-16500)162 – 594000] (1-.34) + (195000X1/4)(.34) } X [(1/1+.10)^1+.....(1/1+.10)^4} – 1950000
= 1824606.25 – 1950000
= - 125393.75
b) To compute the sensitivity of the NPV to changes in fixed costs we choose another level of fixed costs. We will use fixed costs of $600,000. The NPV using this level of fixed costs and the other base case values with the tax shield approach, we GET:
={ [ (24000-15000)180 – 600000] (1-.34) + (195000X1/4)(.34) } X [(1/1+.10)^1+.....(1/1+.10)^4} – 1950000
= 2659358.62 – 1950000
NPV = 709358.62
The sensitivity of NPV to changes in fixed costs is:
NPV/FC = (834885.29 – 709358.62)/(540,000 – 600,000)
NPV/FC = –2.092
Hence For every dollar FC increases, NPV falls by $2.092.
c) Cash Break even Output = FC/(SP – VC)
= 540000/(24000-15000)
= 60 UNITS
d-1) Accounting break even output = FC + DEP / (SP – VC)
=[ 540000+(1950000/4)] / (24000-15000)
= 1027500 / 9000
=114.17 UNITS
d-2) degree of operating leverage at the accounting break-even point = 1+ FC / DEP
= 1 + (540000/(1950000/4)
=1+1.108
=2.108
Short form used in answer :
SP = SALE PRICE, VC = VARIABLE COST , FC = FIXED COST, PV = PRESENT VALUE, R = DISCOUNT RATE, N = YEAR, DEP= DEPRECIATION
Scenario
Unit Sales
Variable Cost
Fixed Cost
NPV
Base
180
15000
540000
834885.29
Best
198
13500
486000
1908138.33
Worst
162
16500
594000
-125393.75
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