Question

Elegant Bakehouse specialises in wedding cakes with each cake sold for $800. The flour, sugar and other relevant materials such as ribbons costs Elegant Bakehouse a standard cost of $75. The fixed costs incurred for such things as bakery upkeep and administrative expenses are $54,000. Brian, the owner of Elegant Bakehouse, just bought a new baking oven for $100,000 which is to be depreciated over 10 years to a salvage value of zero.

What is the NPV break-even level of sales (assume a tax rate of 30%, an 10-year project life, and a discount rate of 10%).

Answer 1

Calculation of NVP Break-even level of Sales:

First of all, we have to calculate NPV break even cash flow for calculating Break-even level of sales.

NPV break even cash flow = Annual cash flow at which NPV is equal to Zero.

Therefore, $100000 = Cumulative present value of Annual Cash flow for 10 years

$100000 = Annual Cash flow*(PVIFA_{10%,10 years})

$100000 = Annual Cash flow*6.145

Annual Cash flow = $100000/6.145

Annual Cash flow = $16273.393

Therefore, Break even Annual cash flow = $16273.393

Particulars	Amount ($)
Sales Per cake	800
Less: Variable Cost per cake	75
Contribution per cake	725

Profit after tax = Cash flow - Depreciation

=$16273.393-$10000

= $6273.393

Profit before tax = $6273.393/0.70 = $8961.99

Total Contribution = Profit before tax + Fixed Cost + Depreciation

= $8961.99+$54000+$10000

= $72961.99

Break-even units = Total contribution/Contribution per unit

= $72961.99/$725

= 100.63 i.e. 101 cakes

NPV break-even level of Sales is 101 cakes. Therefore, Elegant Bakehouse has to make sale of 101 cakes to achieve break-even level of sales.