Question

Problem 9-1 Sensitivity Analysis and Break-Even Point

We are evaluating a project that costs $520,000, has a five-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 64,000 units per year. Price per unit is $46, variable cost per unit is $26, and fixed costs are $832,000 per year. The tax rate is 35 percent, and we require a return of 20 percent on this project.

a. Calculate the accounting break-even point. (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.)

Break-even point           units

b-1 Calculate the base-case cash flow and NPV. (Do not round intermediate calculations and round your NPV answer to 2 decimal places, e.g., 32.16.)

Cash flow	$
NPV	$

b-2 What is the sensitivity of NPV to changes in the sales figure? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.)

?NPV/?Q          $

b-3 Calculate the change in NPV if sales were to drop by 500 units. (Enter your answer as a positive number. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

NPV would (Click to select)increasedecrease by $

c. What is the sensitivity of OCF to changes in the variable cost figure? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.)

?OCF/?VC          $

Answer 1

We need to calculate the Depreciation before we can go on to solving any of the other parts

Part A: Breakeven sales units can be calculated using the following formula:

At breakeven number of units there is 0 profit

So if the company sells 46800 units, it will not earn any profit nor make any loss.

Part B-1: Cash flow in base case NPV would be calculated as follows

(Sales Units*SP -Variable cos per unit*Sales units-Fixed cost- depreciation)*(1-tax rate)+Depreciation

(64000*46-26*64000-832000- 104000)*(1-0.35)+104000

Cash flow = 327600

Part B-2: Cash flow if sales price per unit falls by $1 would be calculated as follows

(Sales Units*SP -Variable cos per unit*Sales units-Fixed cost- depreciation)*(1-tax rate)+Depreciation

(64000*45-26*64000-832000- 104000)*(1-0.35)+104000

Cash flow = 286000

Change in Sales was 64000*(46-45) = $64000

Following is the calculation of sensitivity of NPV to Sales:

This means that for every $1 reduction in sales value, the NPV ruduces by $1.94 and vice versa

Part B-3: Cash flow if number of units fall by 500 would be calculated as follows

(Sales Units*SP -Variable cos per unit*Sales units-Fixed cost- depreciation)*(1-tax rate)+Depreciation

(63500*46-26*63500-832000- 104000)*(1-0.35)+104000

Cash flow = 321100

This means that due to a fall in number of units by 500, the NPV decreases by 19438.98

Part C: Cash flow if variable per unit falls by $1 would be calculated as follows

(Sales Units*SP -Variable cos per unit*Sales units-Fixed cost- depreciation)*(1-tax rate)+Depreciation

(64000*46-25*64000-832000- 104000)*(1-0.35)+104000

Cash flow = 362375

Change in Variable cost was 64000*(26-25) = $64000

Following is the calculation of sensitivity of NPV to VC:

This means that for every $1 reduction in VC, the NPV increases by $1.62 and vice versa