Question

We are evaluating a project that costs $848,000, has an eight-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 62,000 units per year. Price per unit is $40, variable cost per unit is $20, and fixed costs are $636,000 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.)

ΔNPV/ΔQ          $  

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)  increase  decrease  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.)

ΔOCF/ΔVC          $

Answer 1

a. Break even point is defined as the point where total costs (i.e. expenses) and total sales (i.e revenue) are equal. It is a point where there is no profit or loss.

Hence, break even point is where Revenue - Total Costs = 0 ... (1)

Total Costs (TC) = Fixed Cost (FC) + Variable cost per unit (VC) * Number of units (N) ...(2)

Revenue = Price per unit (P) * N ...(3)

From equations 1,2 & 3-

(P*N) - [FC + (VC*N)] = 0

Hence, the break even quantity (units) N = Fixed Cost / (Price per unit - Variable cost per unit) = 848,000/(40 - 20) = 42,400 units

b1. NPV Calculation

Let's first calculate the net cash flow for each year of the project.

Base Cash Flow Table

Year	Cash Inflow	Cash Outflow	Net Cash Flow
0	0	-848,000	-848,000
1	Revenue: 62,000 units *price per unit of 40=24,80,000	FC = 636,000 VC=62,000 units *20= -12,40,000 Taxes = [Revenue-FC - Total VC-Depreciation as per SLM]*Tax rate = [24,80,000 - 6,36,000 - 12,40,000-(848,000/8)]*0.35= -1,74,300	=24,80,000-6,36,000-12,40,000-1,74,300=4,29,700
2	Same as year 1	Same as year 1	4,29,700
3	Same as year 1	Same as year 1	4,29,700
4	Same as year 1	Same as year 1	4,29,700
5	Same as year 1	Same as year 1	4,29,700
6	Same as year 1	Same as year 1	4,29,700
7	Same as year 1	Same as year 1	4,29,700
8	Same as year 1	Same as year 1	4,29,700

Net Present Value (NPV) = Present Value of all Net Cash Flows = CF at t=0 + CF at t=1 discounted by 20% (i.e 1+0.2) + CF at t=2 discounted by (1+0.2)^2 and so forth until CF at t=8 discounted by (1+0.2)^8

Hence NPV = 8,00,827.57

b2. Sensitivity Analysis

Let us first determine the NPV when sales increase by 1 unit and when it decreases by 1 unit.

When Sales increases by 1 unit

Year	Cash Inflow	Cash Outflow	Net Cash Flow
0	0	-848,000	-848,000
1	Revenue: 62,001 units *price per unit of 40=24,80,040	FC = 636,000 VC=62,001 units *20= -12,40,020 Taxes = [Revenue-FC - Total VC-Depreciation as per SLM]*Tax rate = [24,80,040 - 6,36,000 - 12,40,020-(848,000/8)]*0.35= -1,74,307	=24,80,040-6,36,000-12,40,020-1,74,307=4,29,713
2	Same as year 1	Same as year 1	4,29,713
3	Same as year 1	Same as year 1	4,29,713
4	Same as year 1	Same as year 1	4,29,713
5	Same as year 1	Same as year 1	4,29,713
6	Same as year 1	Same as year 1	4,29,713
7	Same as year 1	Same as year 1	4,29,713
8	Same as year 1	Same as year 1	4,29,713

NPV = 800,877.45

When Sales decreases by 1 unit

Year	Cash Inflow	Cash Outflow	Net Cash Flow
0	0	-848,000	-848,000
1	Revenue: 61,999 units *price per unit of 40=24,79,960	FC = 636,000 VC=61,999 units *20= -12,39,980 Taxes = [Revenue-FC - Total VC-Depreciation as per SLM]*Tax rate = [24,79,960- 6,36,000 - 12,39,980-(848,000/8)]*0.35= -1,74,293	=24,79,960-6,36,000-12,39,980-1,74,293=4,29,687
2	Same as year 1	Same as year 1	4,29,687
3	Same as year 1	Same as year 1	4,29,687
4	Same as year 1	Same as year 1	4,29,687
5	Same as year 1	Same as year 1	4,29,687
6	Same as year 1	Same as year 1	4,29,687
7	Same as year 1	Same as year 1	4,29,687
8	Same as year 1	Same as year 1	4,29,687

NPV = 800,777.68

Sensitivity of NPV to change in one unit of sales = 800,877.85 - 800,777.68/62,001-61,999 = $ 50.085

Hence, for every 1 unit change in sales, the NPV will change by $50.085.

b3. From above answer, we know the sensitivity of NPV to change in sales by 1 unit.

Hence, if sales drop by 500 units, NPV will drop by $50.085 * 500 = $ 24,042.5