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Answer :
Final answer:
The accounting break-even point is 38,125 units. The base-case cash flow is $559,500 and the NPV is $68,502.92. The sensitivity of NPV to a 500-unit decrease in projected sales is -$33,166.45, indicating a less profitable project.
Explanation:
a. Calculate the accounting break-even point:
The accounting break-even point is the point at which total sales revenue equals total expenses, resulting in zero profit or loss.
To calculate the accounting break-even point, we need to find the quantity at which the total revenue equals the total expenses.
Break-even point (in units) = Fixed costs / (Price per unit - Variable cost per unit)
Substitute the given values: Break-even point (in units) = $725,000 / ($37 - $21) = 38,125 units
b. Calculate the base-case cash flow and NPV:
Cash flow is the difference between cash inflows and cash outflows throughout the project's life.
Net Present Value (NPV) is a measure of the project's profitability, calculated by discounting the cash flows at the required rate of return and subtracting the initial investment.
In this case, the base-case cash flow can be calculated as: Cash flow = (Price per unit - Variable cost per unit) * Number of units - Fixed costs - Depreciation
Substituting the given values, we get: Cash flow = ($37 - $21) * 70,000 - $725,000 - ($644,000 / 8) = $1,365,000 - $725,000 - $80,500 = $559,500
To calculate the NPV, we need to discount the cash flows at the required rate of return:
NPV = Cash flow / (1 + Rate of return)^n - Initial investment
Substituting the values, we get: NPV = $559,500 / (1 + 0.15)^8 - $644,000 = $68,502.92
The sensitivity of NPV to changes in the sales figure can be calculated by recalculating the NPV with the new sales figure and comparing it with the base-case NPV.
For a 500-unit decrease in projected sales, the new cash flow can be calculated as: New cash flow = ($37 - $21) * (70,000 - 500) - $725,000 - ($644,000 / 8) = $1,341,000 - $725,000 - $80,500 = $535,500
The new NPV can be calculated as: New NPV = $535,500 / (1 + 0.15)^8 - $644,000 = $35,336.47
The sensitivity of NPV to changes in sales figure can be calculated as the difference between the new NPV and the base-case NPV: Sensitivity of NPV = New NPV - Base-case NPV = $35,336.47 - $68,502.92 = -$33,166.45
A negative sensitivity indicates that a decrease in projected sales will result in a decrease in NPV, indicating a less profitable project.
c. What is the sensitivity of OCF to changes in the variable cost figure:
The Operating Cash Flow (OCF) is the cash flow generated by the project's operations, excluding financing and taxes.
The sensitivity of OCF to changes in the variable cost figure can be calculated by recalculating the OCF with the new variable cost figure and comparing it with the base-case OCF.
In this case, a $1 decrease in the estimated variable costs will result in a decrease in the base-case OCF.
Based on the given values, the base-case OCF can be calculated as: Base-case OCF = (Price per unit - Variable cost per unit) * Number of units - Fixed costs - Depreciation = ($37 - $21) * 70,000 - $725,000 - ($644,000 / 8) = $1,365,000 - $725,000 - $80,500 = $559,500
For a $1 decrease in the estimated variable costs, the new OCF can be calculated as: New OCF = ($37 - ($21 - $1)) * 70,000 - $725,000 - ($644,000 / 8) = ($37 - $20) * 70,000 - $725,000 - $80,500 = $1,470,000 - $725,000 - $80,500 = $664,500
The sensitivity of OCF to changes in the variable cost figure can be calculated as the difference between the new OCF and the base-case OCF: Sensitivity of OCF = New OCF - Base-case OCF = $664,500 - $559,500 = $105,000
A positive sensitivity indicates that a decrease in the variable cost figure will result in an increase in OCF, making the project more profitable.
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Solution :
a).
Particulars Details
Selling price per unit 37
Less : variable cost per unit -21
Margin per unit 16
No. of units sold per unit 70,000
Gross margin 11,20,000
Less : fixed cost - 7,25,000
Profit before depreciation and tax 3,95,000
Less : depreciation -80,500
Profit before tax 3,14,500
Less : Tax -1,10,075
Net profit per year 2,04,425
Project Cost 6,44,000
Accounting breakeven point in years 3.15
b).
Calculating the base Cash - Cash flow and NPV
Particulars Amount
Net profit per year 2,04,425
Add : depreciation 80,500
Base Cash cashflow 2,84,925
Required rate of return 15%
Present value of base cash cash flow 12,78,550
received in 8 years.
Project cost -6,44,000
NPV 6,34,550
The present value of base cash cash flow received in 8 years is calculated as Present value of annuity received at the end of each year $ 2,84,925 at the rate of interest 15% for a period of 8 years.
The sensitivity of the NPV to 500 units decrease in projected sales :
Particulars Details
Selling price per unit 37
Less : variable cost per unit -21
Margin per unit 16
Number of units sold per year 69,500
Gross margin 11,12,000
Less : fixed cost -7,25,000
Profit before depreciation and tax 3,87,000
Less : depreciation -80,500
Profit before tax 3,06,500
Less : tax -1,07,275
Net profit per year 1,99,225
Add : depreciation 80,500
Base Cash cashflow 2,79,725
Required rate of return 15%
Present value of base cash cash flow 12,55,216
received in 8 years.
Project cost -6,44,000
NPV 6,11,216
Original NPV 6,34,550
Sensitive NPV -23,334
c).
Particulars Details
Selling price per unit 37
Less : variable cost per unit -20
Margin per unit 17
No. of units sold per year 70,000
Gross Margin 11,90,000
Less : fixed cost -7,25,000
Profit before depreciation and tax 4,65,000
Less : Depreciation -80,500
Profit before tax 3,84,500
Less : tax -1,34,575
Net profit per year 2,49925
Add : depreciation 80,500
Operating cash flow 3,30,425
Original operating cashflow 2,84,925
Sensitivity of OCF 45,500
