Case 091DCF and intrinsic valueCore

Build WACC for an auto components maker whose regression beta is 1.3 while peers' unlevered beta averages 0.9. Which beta do you use, and why?

The situation

You are building a DCF for Ostravi Auto Components, which makes brake and steering parts for carmakers. Your inputs: risk-free rate 7%, equity risk premium 6.5%, target debt to equity of 0.4, pre-tax cost of debt 9.5% and tax 25%.

A regression of Ostravi's weekly returns against the index over two years gives a beta of 1.3, with a standard error of 0.35. Five listed auto component peers have unlevered betas between 0.78 and 1.02, with a median of 0.9. Next year's free cash flow is Rs 500 crore, growing 5% a year after that.

Your task

Build WACC both ways, choose a beta, and show what the choice does to the value.

Quick check

Relevered to Ostravi's debt to equity of 0.4, what is the bottom-up beta?

Worked solution

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

30-second answerThe answer to give first

Use the bottom-up beta of 1.17, which gives a WACC of about 12.5% against 13.1% on the regression beta. The 1.3 comes from one two-year regression with a standard error of 0.35, so anything from 0.6 to 2.0 is plausible. Five peers relevered to Ostravi's debt agree within a narrow band. The choice is worth about 8% of enterprise value: Rs 6,695 crore against Rs 6,195 crore.

Step 1How does each build work?

Both builds share everything except beta. Debt costs 9.5% less the 25% tax shield, 7.125%. Debt to equity of 0.4 means debt is 28.6% of capital and equity 71.4%. On the regression beta of 1.3, the cost of equity is 15.45% and WACC 13.07%; on the bottom-up beta of 1.17, it is 14.61% and 12.47%. The bottom-up beta starts from peers' unlevered betaThe beta of the business with the effect of debt removed, so companies with different borrowing can be compared. of 0.9 and adds back Ostravi's own debt.

Same company, two betas: the WACC gap is about 0.6 pointsRegression betaRisk-free rate7.00%Beta1.30 (regression)x equity premium 6.5%8.45%Cost of equity15.45%x equity weight71.4%After-tax debt cost7.125%x debt weight28.6%WACC13.07%Bottom-up beta from peersRisk-free rate7.00%Beta1.17 (0.9 relevered)x equity premium 6.5%7.61%Cost of equity14.61%x equity weight71.4%After-tax debt cost7.125%x debt weight28.6%WACC12.47%
Ostravi's WACC is 13.07% on its regression beta of 1.3 and 12.47% on a bottom-up beta of 1.17, with every other input identical, including an after-tax debt cost of 7.125%.
The relationship
βL=βU [1+(1−t)DE]=0.9×[1+0.75×0.4]=1.17\beta_L = \beta_U\,[1 + (1-t)\tfrac{D}{E}] = 0.9 \times [1 + 0.75 \times 0.4] = 1.17
beta_Uunlevered beta of the business, median of five peers, 0.9
ttax rate, 25%
D/EOstravi's target debt to equity, 0.4
What it says in wordsThe equity beta is the business beta scaled up for the extra risk that debt places on shareholders, with the tax shield softening it.
Step 2Why trust five peers over the company's own history?

Because one regression is a noisy measurement. Asking one person how long the commute takes gives you their worst Monday; asking five colleagues on the same route gives you the route. A peer-based beta is steadier than one noisy regression: Ostravi's 1.3 carries a standard error of 0.35, so its honest range is 0.6 to 2.0. Five peers relevered to Ostravi's debt sit between 1.01 and 1.33. A two-year window can also catch a company-specific event, a big customer loss or a block sale, that says nothing about how Ostravi moves with the market in general.

One noisy regression against five peers averaged0.40.81.21.62.0Levered beta at debt to equity of 0.4Regression2 standard errors1.300.62.0Peers, releveredmedian of five1.17, tight range
Ostravi's regression beta of 1.3 has a plausible range of 0.6 to 2.0 at two standard errors, while five peers relevered to its debt fall between 1.01 and 1.33, which is why the peer median of 1.17 is the steadier estimate.
Step 3What does the choice do to the value?

Run a simple growing perpetuity on Rs 500 crore of free cash flow growing 5%. At 12.47%, enterprise value is Rs 6,695 crore; at 13.07% it is Rs 6,195 crore, 7.5% lower. A 0.6 point change in WACC moves value by 7% because the gap between WACC and growth is only about 7 points; the closer the two are, the more any discount-rate choice matters.

Say what would make you use the regression after all: if Ostravi's business really differs from its peers, say it sells mostly to one cyclical export market while they sell to domestic carmakers, its own higher beta may be real. Then the answer is to pick peers that match that mix, not to fall back on one regression.

Where candidates lose it

The frequent error is using the peer beta of 0.9 as it is, forgetting that it is unlevered. That understates Ostravi's cost of equity by more than a point and flatters the value.

The other is treating the regression beta as a fact because it is Ostravi's own number. Without its standard error it looks precise; with it, it is barely an estimate.

What the interviewer asks next

  • Ostravi plans to raise debt to equity to 0.8. What happens to beta, cost of equity and WACC?
  • Would you use a two-year weekly or a five-year monthly regression, and why?
  • How would you add a company-specific risk premium, and when is it justified?

Company names and figures are illustrative.