Question

You are looking into a factory to make strained peas. You estimate that the equipment will cost $50,000, which you would depreciate over the 10-year life of the project to a book value of zero. The salvage value of the equipment is zero. You think you can sell 15,000 cans at $2/can. The cost of producing the cans is $0.80 each. Your tax rate will be 40%. You plan to maintain an inventory equal to 25% of revenues and you can salvage 80% of this working capital at the end of the project’s life. You plan to use your garage, which means you will have to pay $2,000/year to park your car elsewhere (the good news is that the $2,000/year is tax deductible). To estimate the cost of capital for the project you look at the following comparable firms:
Company D/E Tax rate Beta on stock
Gerber 1.00 0.50 1.5

Brio 0.50 0.40 1.3
You plan to finance this project entirely with equity. The current T-Bond rate is 11.5% and the MRP is 5.5%. You also assume all debt betas are equal to zero in your analysis.

a) What is the appropriate discount rate for the project?

b) What are the after-tax cash flows?

c) What is the NPV?

Answer 1

a)

The Unlevered cost of equity of comparable firms must be used

Unlevered Beta = Levered Beta/(1+(1-t)*D/E)

For Gerber,     Unlevered Beta = 1.5/(1+(1-0.5)*1) = 1

For Brio,     Unlevered Beta = 1.3/(1+(1-0.4)*0.5) = 1

So, the average unlevered beta of Tea firms is 1, so the Beta of this project proposed to be financed entirely with equity is also 1

So, From CAPM

cost of equity = 11.5% + 1*5.5% = 17% which is the appropriate discount rate of the project

b) Cashflows in year 0 = -$50000

and Net working capital = 25% of Revenues= $30000*0.25= $7500

So, total cashflows in year 0 = -$57500

Cashflows per year (1-10)

Revenues = 15000* $2 =$30000

Less: Production cost = 15000 *$0.8 = $12000

Less :Depreciation =$50000/10 =$5000

Less: Rental cost = $2000

Profit before Tax = $11000

Less: Tax(40%) = $4400

Profit after tax = $6600

Add : Depreciation =$5000

Cashflows = $11600

Additional Cashflow in year 10 due to sale of Working capital = $7500*0.8= $6000

c)

NPV = -57500+ 11600/1.17+ ...+11600/1.17^10+ 6000/1.17^10

=-57500+11600/0.17*(1-1/1.17^10)+6000/1.17^10  

= - $2211.974