Question

A firm's cash flows one year from now will be either $2 million if there is a boom or $.96 million if there is a recession. A boom and a recession are equally likely. A new project is available to the firm: It requires an investment today of $.4 million and will generate a cash flow one year from now of $.68 million for sure. The interest rate is 10% Suppose the firm has no debt. Will the project be taken by the all equity firm? Suppose now that the company has debt in the form of zero coupon bonds that expire in one year. The debt has face value F $1.6 million. a. b. Calculate the value of the firm, the value of debt and the value of equity under a boom and under a recession with and without the project. Calculate the expected value of equity with and without the project. What is the increase in equity value from taking the project? Is this greater or smaller than the cost of the project? Will the project be taken by the levered firm? i. ii.

Answer 1

Current Value of the firm=

PV of future expected cash flows given the probabilities of boom & recession

((50%*2)+(50%*0.96)/1.1=

1.345454545

Millions

a. NPV of the project at 10% discount rate=

-0.4+(0.68/1.10)

0.218182

Millions

AS the project returns POSITIVE NPV at the reqd. rate of return of 10% , the project will be undertaken by the firm.

b. i.

Under Boom

without the project

Value of Firm=PV of Cash flows + PV of Debt

Value of Firm=(2/1.1) + (1.6/1.1)=

3.272727

Millions

Value of Firm with the project=(2/1.1) + (1.6/1.1)+0.218182

3.490909

Millions

Under Recession

without the project

Value of Firm=PV of Cash flows + PV of Debt

Value of Firm=(0.96/1.1) + (1.6/1.1)=

2.327273

Millions

Value of Firm with the project=(0.96/1.1) + (1.6/1.1)+0.218182

2.545455

Millions

b.ii

Value of Equity & Debt

Under Boom

without the project

Value of Firm=PV of Cash flows + PV of Debt

Value of Firm=(2/1.1) + (1.6/1.1)=

3.272727

Millions

Value of Debt=1.6/1.1=

1.45

So, Value of equity=3.27-1.45=1.82 mlns.

Value of Firm with the project=(2/1.1) + (1.6/1.1)+0.218182

3.490909

Millions

Value of Debt=1.6/1.1=

1.45

So, Value of equity=3.49-1.45=2.04   mlns.

Under Recession

without the project

Value of Firm=PV of Cash flows + PV of Debt

Value of Firm=(0.96/1.1) + (1.6/1.1)=

2.327273

Millions

Value of Debt=1.6/1.1=

1.45

So, Value of equity=2.33-1.45=0.88 mlns.

Value of Firm with the project=(0.96/1.1) + (1.6/1.1)+0.218182

2.545455

Millions

Value of Debt=1.6/1.1=

1.45

So, Value of equity=2.55-1.45=1.1 mlns.

Value of firm with the project= 1.35+0.22+1.45= 3.02 mlns Less: Value of debt=   1.6/1.1= 1.45 mlns So, Value of equity=(3.02-1.45)=1.57 Value of firm without the project= 1.35 +1.45 mlns= 2.8 mlns Less: Value of debt=   1.6/1.1= 1.45 mlns So, Value of equity=(2.8-1.45)= 1.35 mlns. Increase in value of equity (Taking the project) (1.57-1.35)=0.22 mlns. This is smaller than the cost of the project =0.4 mlns. As there is an overall increase in value to the firm ,as the project brings positive NPV , the project will be taken up by the firm.