CTC,
First, I'll repeat your hypothetical: For illustration, let's assume we have a black box that can generate cash at the rate of $1 per year at the end of each year in perpetuity. If we agree that the appropriate discount rate is 10%, then we would agree that the value of the box is $10. But suppose we could forgo this year's $1 dividend, and achieve a perpetuity of $1.50 beginning at the end of next year. Well, we would agree that a year from now the box would be worth $15, and thus $13.63 now (15/1.10).
I'd say your black box is worth $3.87 max.
Let me make another simplification to your model and approach valuation even more conservatively. Ultimately, any company is valued as a money machine. After all is said and done, how much cash does it pile up and what is the value of that cash. Let's say the first dollar of free cash flow is worth a dollar, next year's is worth $.90, the third year's dollar worth $.81, etc., until you reach a year when the dollar a year free cash flow is worth very close to zero in currently dollars. The value of the company producing all this cash is the total of all the cash, the sum of the present values of the cash dribbling in year by year. Of course, depending on the interest rate used for the discount, the sum of the PV of the free cash flow peaks as some point and then starts declining. That peak is the maximum value of the pile of cash thrown off by the company. (A 10% discount peaks in about 10 years, a 5%, the current T-bill rate, in about 20 years, indicating why stocks are worth more in a low interest- rate environment).
You're black box, using your assumptions, is worth $3.87, in a 5% world, it's worth $7.61 max.
Best,
--Steve |
