Your run a toy company that is considering updating your electric tricycle line.

Question

Your run a toy company that is considering updating your electric tricycle line. The upgrades will cost $30 million and will add a fixed cost of $1 million per year, but will decrease your variable costs by $40 per unit. This project will be good for 5 years. Assume 5-year straight-line depreciation, a 40% tax rate, and a 10% cost of capital.

What is the NPV of this project if you sell 300,000 units per year?

What is the break-even number of units you must sell in order to make this project profitable?

Explanation / Answer

Aswer :-

Total Cost = $30 million

Additional Fised Cost charge per year = $1 million

Decrease Variable Cost = $40 per unit

Sell Quantity = 300000 units

Tax rate = 40%

cost of capital = 10%

Year = 5 years

Depreciation = 30000000 / 5 year

= 6000000

=40 * 300000

=12000000

=40 * 300000

=12000000

=40 * 300000

=12000000

=40 * 300000

=12000000

=40 * 300000

=12000000

=(1000000 * 1 year)

=(1000000)

=(1000000 * 2 year)

=(2000000)

=(1000000 * 3 year)

=(3000000)

=(1000000 * 4 year)

=(4000000)

=(1000000 * 5 year)

=(5000000)

NPV = Present Value of Cash Inflow - Initial Investment

Present Value of Cash Inflow = 8181000+6938400+5857800+4917600+4098600

= 29993400

NPV = 29993400 - 30000000

NPV = -6600

(NPV is negative, project rejected).

Year 1 2 3 4 5 Saving in variable cost per unit 40 40 40 40 40 Quantity 300000 300000 300000 300000 300000 Saving in variable cost

=40 * 300000

=12000000

=40 * 300000

=12000000

=40 * 300000

=12000000

=40 * 300000

=12000000

=40 * 300000

=12000000

Less :- Additional Fixed cost

=(1000000 * 1 year)

=(1000000)

=(1000000 * 2 year)

=(2000000)

=(1000000 * 3 year)

=(3000000)

=(1000000 * 4 year)

=(4000000)

=(1000000 * 5 year)

=(5000000)

Total saving in cost =11000000 =10000000 =9000000 =8000000 =7000000 Less :- Depreciation =(6000000) =(6000000) =(6000000) =(6000000) =(6000000) Saving After depreciation =5000000 =4000000 =3000000 =2000000 =1000000 Less :- tax @ 40% (2000000) (1600000) (1200000) (800000) (400000) Saving After depreciation & tax =3000000 =2400000 =1800000 =1200000 =600000 Add :- Depreciation 6000000 6000000 6000000 6000000 6000000 Cash Inflow 9000000 8400000 7800000 7200000 6600000 PVIF @ 10% .909 .826 .751 .683 .621 Present Value (cash flow * PVIF) 8181000 6938400 5857800 4917600 4098600

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