Case 100DCF and intrinsic valueWarm up
A toll road has 10 years left on its concession and earns Rs 200 crore of cash a year. At a 10% discount rate, what is it worth, and what goes wrong if you value it as a perpetuity?
1The situation
Meridel Toll Roads owns the concession on a single highway stretch. The concession has 10 years left, after which the road passes back to the government for nothing. The road generates Rs 200 crore of free cash flow a year, flat, with no further capex. Use a 10% discount rate.
A junior analyst's model values Meridel at Rs 2,000 crore: Rs 200 crore divided by 10%.
2Your task
What is Meridel worth, how big is the junior analyst's error, and why?
Quick check
Roughly what is Meridel worth?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
About Rs 1,229 crore; the perpetuity's Rs 2,000 crore overstates it by Rs 771 crore, 63%. Ten flat payments of Rs 200 crore at 10% are worth 200 x 6.145. A perpetuity also counts year 11 onward, worth Rs 771 crore today, which the concession does not have. A finite concession cannot be valued like a business that runs forever.
Step 1How do you value ten years of cash?
Discount each year and add them up, or use the annuity shortcut. Ten payments of Rs 200 crore at 10% are worth Rs 200 crore times an annuity factorThe present value of one rupee a year for a fixed number of years: (1 - (1 + r) to the power -n) / r. of 6.1446, Rs 1,228.9 crore. Year 1's Rs 200 crore is worth Rs 181.8 crore today; year 10's is worth only Rs 77.1 crore. A lease on a shop with ten years to run is worth ten years of rent, discounted, however good the location is.
| 200 | yearly free cash flow, Rs crore |
| 0.10 | discount rate |
| 10 | years left on the concession |
Step 2Where exactly does the perpetuity go wrong?
It keeps counting after the concession ends. Rs 2,000 crore is the value of Rs 200 crore a year forever; the part after year 10 is worth Rs 2,000 crore divided by 1.10 to the tenth, Rs 771 crore today, and Meridel will never receive it. That is a 63% overstatement. The error is bigger the shorter the concession: with five years left, a perpetuity would overstate value by about 164%.
| Method | Value, Rs crore | Against the annuity |
|---|---|---|
| Ten-year annuity at 10% | 1,228.9 | |
| Perpetuity, 200 / 10% | 2,000.0 | +62.7% |
| Undiscounted, 200 x 10 | 2,000.0 | +62.7% |
Step 3What does this mean for an investor in the road?
Part of every year's cash is the investor's own money coming back. In year 1, a 10% return on Rs 1,229 crore is Rs 123 crore; the other Rs 77 crore of the Rs 200 crore is capital being returned, because the asset shrinks to zero by year 10. So a toll road paying out all its cash looks like a 16% yield but earns 10%. Say the limit too: real toll roads usually have tolls that rise with inflation and traffic that grows, which a flat annuity ignores, and concessions sometimes get extended; each is a separate assumption to state, not a reason to use a perpetuity.
Where candidates lose it
The fast wrong answer is Rs 2,000 crore, 200 over 10%, because the perpetuity formula is the one candidates remember. It values a road the investor gives back in ten years as if it were owned forever.
The second miss is getting Rs 1,229 crore and then describing the Rs 200 crore payout as a 16% yield. Most of that cash is the return of capital on a shrinking asset.
What the interviewer asks next
- Tolls rise 5% a year with inflation. What is the concession worth now?
- The government offers a five-year extension. How much is it worth to Meridel today?
- How would you value Meridel's equity if the road carried Rs 600 crore of debt that amortises over the concession?
Company names and figures are illustrative.