Question

You are the financial analyst for a tennis racket manufacturer. The company is considering using a graphite like material in its tennis rackets. The company has estimated the information in the following table about the market for a racket with the new material. The company expects to sell the racket for four years. The equipment required for the project has no salvage value. The required return for projects of this type is 12 percent, and the company has a 34 percent tax rate.

		Pessimistic				Expected				Optimistic
	Market size		112,000				127,000				152,000
	Market share		21	%			24	%			26	%
	Selling price	$	157			$	162			$	168
	Variable costs per unit	$	111			$	106			$	105
	Fixed costs per year	$	972,000			$	927,000			$	897,000
	Initial investment	$	1,296,000			$	1,228,000			$	1,160,000

Calculate the NPV for each case for this project. (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))

Pessimistic		$
Expected		$
Optimistic		$

no excel, please!

Answer 1

Solution :

Here, we have,

	Unit Sales*	Price	Variable costs	Fixed costs
Pessimistic	23,250	157	111	972,000
Expected	30,480	162	106	927,000
Optimistic	39,520	168	105	897,000

* Unit sales = Market size * Market share

Now,

Operating cash flow ( OCF ) = ( Sales - Costs ) * ( 1 - tax ) + Tax * Depreciation

Where,

Depreciation = Initial investment / Number of years

Then, we have,

Pessimistic :

OCF = [ (157 - 111) * 23,250 - 972,000 ] * ( 1 - 0.34 ) + 0.34 * 1,296,000 / 4

OCF = 174,510

NPV = - 1,296,000 + 174,510 / ( 1 + 0.12 )^1 + 174,510 / ( 1 + 0.12 )^2 + 174,510 / ( 1 + 0.12 )^3 + 174,510 / ( 1 + 0.12 )^4

NPV = - $765,952.17

Expected :

OCF = [ (162 - 106 ) * 30,480 - 927,000 ] * ( 1 - 0.34 ) + 0.34 * 1,228,000 / 4

OCF = 619,100.80

NPV = - 1,228,000 + 619,100.80 / ( 1 + 0.12 )^1 + 619,100.80 / ( 1 + 0.12 )^2 + 619,100.80 / ( 1 + 0.12 )^3 + 619,100.80 / ( 1 + 0.12 )^4

NPV = $652,425.41

Optimistic :

OCF = [ ( 168 - 105 ) * 39,520 - 897,000 ] * ( 1 - 0.34 ) + 0.34 + 1,160,000 / 4

OCF = 1,149,821.60

NPV = - 1,160,000 + 1,149,821.60 / ( 1 + 0.12 )^1 + 1,149,821.60 / ( 1 + 0.12 )^2 + 1,149,821.60 / ( 1 + 0.12 )^3 + 1,149,821.60 / ( 1 + 0.12 )^4

NPV = $2,332,409.89