Determining Fair Value, Steps 3-5: Discount Projected Free Cash Flows to Present, Calculate Discounted Perpetuity Value, and Add It All Up
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Determining Fair Value, Steps 3-5: Discount Projected Free Cash Flows to Present, Calculate Discounted Perpetuity Value, and Add It All Up
Step 3: Discount projected free cash flows to present
After projecting free cash flow and determining a discount rate, the next step is to discount each of the individual year's cash flows to express them in terms of today's dollars. Remember we are using the following formula, and the "discount factor" just represents the denominator in the equation. We can then multiply each year's cash flow by the discount factor to get the present value of each cash flow.
Present value of cash flow in year N = CF at year N / (1 + R)^N
where
CF = Cash flow
R = Required return (discount rate), in this case 9%
N = Number of years in the future
Last year: $500.00
Year 1: 575.00 x (1 / 1.09^1) = 528
Year 2: 661.25 x (1 / 1.09^2) = 557
Year 3: 760.44 x (1 / 1.09^3) = 587
Year 4: 874.50 x (1 / 1.09^4) = 620
Year 5: 1005.68 x (1 / 1.09^5) = 654
Year 6: 1055.96 x (1 / 1.09^6) = 630
Year 7: 1108.76 x (1 / 1.09^7) = 607
Year 8: 1164.20 x (1 / 1.09^8) = 584
Year 9: 1222.41 x (1 / 1.09^9) = 563
Year 10: 1283.53 x (1 / 1.09^10) = 542
We then add up all the discounted cash flows from years 1 through 10, and come up with a value of $5,870 million ($5.87 billion).
Step 4: Calculate discounted perpetuity value
In this step, we use another formula from above:
Perpetuity value = (CFn x (1+ g) ) / (R - g)
where
CFn = Cash flow in the last individual year estimated, in this case year 10 cash flow
g = Long-term growth rate
R = Discount rate, or cost of capital, in this case cost of equity
For example, we'll use use 3% as the perpetuity growth rate, which is close to the historical average growth rate of the U.S. economy. So, we'll assume that after 10 years, Charlie's Bicycles will also grow at this 3% rate. Plugging the numbers into the formula:
($1,284 x (1 + .03) ) / (.09 - .03) = $22,042 million
Notice that for the cash flow figure we used the undiscounted year 10 cash flow, not the discounted $542 million. But because we used the undiscounted amount, we still need to express the perpetuity value in present-value terms using this trusty formula:
Present Value of Cash Flow in Year N = CF at Year N / (1 + R)^N
Therefore,
Present Value of Perpetuity Value = $22,042 million / (1 + .09)^10 = $9,311 million
Step 5: Add it all up
Now that we have the value of all the cash flows of Charlie's Bicycles from year 1 through 10 as well as those from year 11 on, we add up these two values:
Discounted free cash flow:
Years 1–10: $5,870 million + discounted free cash flow
Years 11 on: $9,311 million
This equals $15,181 million.
So there we have it! We have estimated Charlie's Bicycles to be worth $15.2 billion. The final, simple step is to divide this $15.2 billion value by the number of shares Charlie's Bicycles has outstanding. If Charlie's has 100 million shares outstanding, then our estimate of Charlie's intrinsic value is $152 per share.
So … should you buy it?
If Charlie's stock is trading at $100 per share, you should start to get interested in buying the shares. We can forget about what Charlie's P/E ratio is relative to its peers as well as what Wall Street analysts have recently said about the stock. The bottom line is the stock is trading below its estimated intrinsic value. If you have confidence in your free cash flow projections, you can have an equal amount of confidence in buying the stock.