Case 030DCF and intrinsic valueHard

DCF model test: value a bearings maker with both an exit multiple and a perpetual growth terminal value, using the mid-year convention, and reconcile the two.

Harris WilliamsRichmond · 2018

The situation

Ekavir Bearings makes industrial bearings. Your forecast gives unlevered free cash flow of Rs 100, 110, 120, 130 and 140 crore over the next five years, and year 5 EBITDA of Rs 220 crore. Its WACC is 10%.

The model test asks for two terminal values: an exit at 9.0x year 5 EBITDA, and perpetual growth of 4.0% a year on the year 5 cash flow. Cash is assumed to arrive evenly through each year, so use the mid-year convention.

Your task

What enterprise value does each method give, what does each one imply about the other's input, and what do you conclude from the gap?

Quick check

Which method do you expect to give the higher value here?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

About Rs 1,699 crore on the 9.0x exit and about Rs 2,050 crore on 4% growth, a gap of roughly Rs 351 crore. The five forecast years are worth Rs 470 crore either way. A 9.0x exit implies only 2.4% growth forever, while 4% growth implies about 11.6x EBITDA. Two inputs that far apart cannot both be right, so you say which one you believe.

Step 1What does the mid-year convention change before any terminal value?

A shop takes money every day of the year, not in one lump on 31 March. The mid-year convention treats each year's cash as arriving at the middle of the year, so year 1 is discounted 0.5 years, year 2 is discounted 1.5 years, and so on. That lifts every present value slightly. Ekavir's five years are worth Rs 469.5 crore with mid-year timing against Rs 447.7 crore if every cash flow waited until the year end, about 5% more.

YearFree cash flowDiscount periodFactor at 10%Present value
11000.50.95395.3
21101.50.86795.3
31202.50.78894.6
41303.50.71693.1
51404.50.65191.2
Total600469.5
Rs crore. Discounting each year's cash flow from the middle of the year at 10% values Ekavir's five forecast years at Rs 469.5 crore, the common base for both terminal value methods.
Step 2Why are the two terminal values discounted for different lengths of time?

This is the line the model test is really checking. An exit multiple is a sale price agreed at the end of year 5, so it is discounted a full 5.0 years; a perpetual growth value is a stream of cash flows that also arrive mid-year, so it is discounted 4.5 years. The exit value is 9.0 times Rs 220 crore, Rs 1,980 crore, worth Rs 1,229.4 crore today. The Gordon growthA formula that values a cash flow growing at a constant rate forever: next year cash flow divided by the discount rate minus the growth rate. value is Rs 140 crore times 1.04 over 6%, Rs 2,426.7 crore, worth Rs 1,580.3 crore today. Discount the perpetuity a full five years by habit and you understate it by about Rs 74 crore.

Where each cash flow sits on the clock under the mid-year conventionYear 0Year 1Year 2Year 3Year 4Year 51000.9531100.8671200.7881300.7161400.651factorPerpetuity TV at 4.5 years: factor 0.651Exit sale at 5.0 years:factor 0.621Cash flows arrive through the year, so each is discounted half a year less than a year-end flow
Under the mid-year convention Ekavir's yearly cash flows and its perpetual growth terminal value are discounted from the middle of the year, while the exit multiple terminal value is a year-end sale price and is discounted a full five years.
The relationship
EVexit=469.5+9.0×2201.105=1,699.0EVgrowth=469.5+140×1.04/(0.10−0.04)1.104.5=2,049.9EV_{exit} = 469.5 + \frac{9.0 \times 220}{1.10^{5}} = 1,699.0 \qquad EV_{growth} = 469.5 + \frac{140 \times 1.04 / (0.10 - 0.04)}{1.10^{4.5}} = 2,049.9
469.5present value of the five forecast years, mid-year
9.0 x 220exit value at the end of year 5
140 x 1.04the first cash flow after the forecast
0.10 - 0.04WACC less perpetual growth
What it says in wordsEnterprise value is the forecast years plus the terminal value, each discounted from the point in time its cash actually arrives.
Step 3How do you make each method check the other?

Turn each answer into the other's input. A 9.0x exit is the same as assuming Ekavir's cash flow grows 2.4% a year forever, and 4% growth forever is the same as an exit at about 11.6x EBITDA. To get the implied multiple, restate the perpetuity value at the year 5 point, Rs 2,545 crore, and divide by Rs 220 crore. To get the implied growth, solve the Gordon formula for the growth rate that produces Rs 1,980 crore at year 5. Terminal value is about 72% of value on the exit method and 77% on the growth method, which is why this one assumption deserves more of your time than any forecast year.

Same cash flows, two terminal values, and each implies the other's inputExit multiple: 9.0x EBITDA4701,229PV of years 1 to 5mid-year discountingPV of terminal valueTV 1,980, discounted 5.0 yearsEV 1,699Implied perpetual growth 2.4%Perpetual growth: 4.0%4701,580PV of years 1 to 5mid-year discountingPV of terminal valueTV 2,427, discounted 4.5 yearsEV 2,050Implied exit multiple 11.6x
Both methods share Rs 470 crore of forecast value; the 9.0x exit gives Rs 1,699 crore and implies 2.4% growth forever, while 4.0% growth gives Rs 2,050 crore and implies a 11.6x exit, so the two inputs disagree.

Now reach a view rather than averaging. If peers in bearings trade near 9x, the 4% growth assumption is the one that is too rich, or the 10% WACC is too low; if you can defend 4%, you should be able to defend a multiple near 12x. A sensible close says the value is about Rs 1,700 crore on market evidence, up to about Rs 2,050 crore only if Ekavir really compounds at 4% forever, and the next question is which peers support which. The limit: both methods inherit the same five-year forecast, so a cross-check catches an inconsistent terminal value, not an optimistic forecast.

Where candidates lose it

The common loss is discounting both terminal values by the same number of years. Under the mid-year convention the exit value is a year-end price and the perpetuity is a mid-year stream; treating them alike moves value by Rs 60 crore or more and is exactly what a model test grader looks for.

The second is reporting two numbers and averaging them. The point of running both is that each implies the other's input; a gap this wide means one assumption is wrong, and the interviewer wants to hear which.

What the interviewer asks next

  • What perpetual growth rate makes the two methods agree exactly at 9.0x?
  • How would a 1 point rise in WACC move each method, and which moves more?
  • Why might the exit multiple be the better anchor for a sale process and the growth method better for a long-term holder?

Asked at Harris Williams, Investment Banking, Richmond, 2018 (Wall Street Oasis): final was in person super day with 2-3 different rounds: one DCF model test, 1 behavioral rounds

Company names and figures are illustrative.