You are considering setting up a firm to produce widgets. The cost of the projec

Question

You are considering setting up a firm to produce widgets. The cost of the project is $30 today. The demand for widgets is uncertain. It can be either high or low with equal probability. When the demand is high cash flows in t = 1 are $66 and when the demand is low cash flows in t = 1 are $34. The discount rate is 10%.

a)

What is the NPV of the project?

b)

Suppose you can commission a study that tells you whether the demand for widgets will be high or low. The study takes one year to complete. That is, if you commission the study you must decide in t = 1 whether to invest. If you invest the cash flows will arrive in t = 2. Whatis the maximum amount you are willing to pay for the study today?

Explanation / Answer

The NPV of debt financing is no longer equal to the NPV of equity financing. (If debt financing is used to financing a project instead of equity financing, the government will provide a subsidy to the firm that increases firm value!)

Using a 10% discount rate is $66 / 0.10 = $660. The decrease in value from $1000 to $660 is caused by the corporate income tax liability. Therefore, any reduction of the corporate income tax liability should increase firm value. Logically, if the corporate tax liability could be reduced to zero (in all economic states), then the firm value should be restored to $1000.

Firm L has the same exact assets as Firm U, managed in the same way that Firm U manages its assets. These assets produce the same expected cash flows as Firm U (with the same risk), plus an extra $10.20 = (D)(rD)(Tc). Therefore,

VL = VU + PV of a perpetuity of cash flows expected to be equal to (D)(rD)(Tc)

Assuming the corporate income tax rate for the firm will remain at 34% forever, this additional cash flow is just as risky as the firm's debt.

VL = VU + [(D)(rD)(Tc)] / rD

VL = VU + (D)(Tc)

VL = $660 + $600 (34%) =$864

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