Assume that a firm plans to pay $ 10 bln of dividends each year indefinitely long in the future. Let r 0.05 be the annual return to treasury bonds.

Question

Assume that a firm plans to pay $ 10 bln of dividends each year indefinitely long in the future. Let r 0.05 be the annual return to treasury bonds. Finally, let the replacement value of firm's capital be K $ 150 bln.

a) Compute the average q. Does the financial market over- or undervalue firm's assets?

b) Assume that average q equals marginal q, and that the installation cost is given by:

C(I)=I² /200

What is the firm's level of investment I

Answer 1

The Present value of the dividend stream is ∑₁^∞(1/(1+5%)D = D/.05 = 200 Billion

Replacement Value = 150. q=(200/150) = 4/3

So 150 in machines generates 200 in dividend.

Marginal replacement cost = d(I(Q)/dq = I/100 Invest up to the point where I/100 = 4/3 or I= 133billion.

Hope this helps

Please feel free to reach out for help.

Lenny