## \$TSCO.L – my Tesco CAPM valuation

BLUF: Share price 291p, estimated value 360p, implied upside 24%

Todd Wenning did an interesting valuation on TSCO (Tesco)
(http://www.cleareyesinvesting.com/2014/03/why-i-sold-this-dividend-stock-for-loss.html) and found it to be overvalued, even at today’s prices.

Being something of a starry-eyed admirer of Aswath Damodaran, I thought I’d have a go at a valuation using CAPM.

I had done a similar valuation for SBRY (Sainsbury) back in January (https://mcturra2000.wordpress.com/2014/01/08/sbry-a-qnd-valuation-using-capm/). I reckoned a a fair value for it of 480p against a price at the time of 362p. The price is now 306p, reflecting increasing investor pessimism about the sector.

So, what’s my valuation of TSCO? I am going to use a single-stage model, the familiar: P = D1/(r-g) where
P is the estimate of fair value
D1 is the dividend for the comping year
r is the required rate of return
g is the growth rate.

That appears to be the one Todd is using.

D1 is easy enough: I use 14.77p. What about r and g? That’s when things get tricky. To calculate r according to CAPM, I need rf, a risk-free rate, a beta b for the stock, and ERP, the equity risk premium.

I have accumulated some resources about Aswath on one of my webpages: http://www.markcarter.me.uk/money/aswath.htm , which you can check out to obtain information about the risk-free rate, ERPs, and betas. When I collate the information he provides, I obtain
rf = 2.95%
ERP = 4.96%

Betas are a bit tricky. You can use Digital Look to obatain betas. Here’s what they have for the supermarkets: TSCO 0.82, MRW 0.79, SBRY 0.76.

If you don’t like using individually-calculated betas, then you can make them up yourself. Conveniently, Aswath gives betas in the US for the retail/wholesale food sector: unlevered: 0.68, levered 0.78. Assuming you’re OK with those figures, you would obtain a levered beta for TSCO using the formula:
levered beta = unlevered beta * (1+ (1-tax rate) * debt/equity) = 0.68*(1+(1-0.293) * 7040/15686) = 0.90.

I’m not sure I like the idea of using the US figures, so I’m just going to stick with the value from Digital Look of 0.82. If you wanted to get fancy and do what Damodaran does, then what you would do is convert the LEVERED betas 0.82, 0.79 and 0.76 into UNLEVERED betas, take a median and mean, and use that as an unlevered beta for TSCO, which you would that convert back into a levered beta. That’s if you wanted to do some smoothing. I can’t be bothered, I’ll just use the 0.82.

We now have enough information to calculate a required rate of return: r = rf + b * ERP
= 2.95% +0.82 * 4.96%
= 7.02%

We’re almost there. We only need to figure out a value for g. That’s easy: I’m just going to use the risk-free rate, in accordance with Aswath’s suggestion. I forget the complete justification for this, but it basically involves an arbitrage argument between bonds and equities.

So here’s my estimate of TSCO’s worth:
SP = 14.77/(0.0702 – 0.0295) = 360p

TSCO currently sells at 291p, suggesting that it’s undervalued. So how comes Todd thinks it is overvalued?

The answer lies in an ideological difference about how “r”, the required return is calculated. He’s using a required return for him, whereas I’m using a required return by the market, adjusted for risk (which comes through in the beta). His way of looking at is “I require my building society to give me an annual rate of return of 5%, and if I can’t get it, I wont invest”. Well, what if you can’t get that return? The latter approach is to take what the building societies give you (implicitly adjusting for risk), rather than what you want.

That doesn’t mean that valuation work is useless, because you can still generate alpha by buying shares in companies whose price is less than appraised value.

We can get fancier in our valuation of TSCO. Let’s use a two-stage model, where we have an initial growth phase, and a perpetual one. The formula gets hairier, and is dervied at the following website: http://en.wikipedia.org/wiki/Dividend_discount_model

I present the formula below:
p(d0, g, r, N, ginf) := d0*(1+g)/(r-g) *(1- (1+g)^N/(1+r)^N) + d0 *(1+g)^N * (1+ginf)/(1+r)^N / (r-ginf);

If you have Maxima, you can copy and paste that formula right into a worksheet, and it will work. Maxima is a computer algebra system, and free. wxMaxima goes one better by even including a nice graphical front-end all in one nice package: http://andrejv.github.io/wxmaxima/ . There’s binaries for Windows and OS X. Most Linux systems should also package a version up for you. There’s no need to spend money on a system like Mathematica when wxMaxima is full-featured and does everything you need, and more, for free.

Suppose I change my assumptions about the likely dividend record on TSCO. Suppose I assume that TSCO is stuck in a rut in such a way that its dividends will remain flat for 5 years, and only then grow at GDP? In that case, I would plug in values d0=14.77, g = 0, r= 0.0702, N = 5, ginf = 0.0295, and come out with
p = 330p.

So, even with a go-nowhere assumption, that brings my estimate of intrinsic value down by 10%, which is still above the current share price.

Of course, you may make different assumptions – like the dividends will actually decline – maybe for a short time, maybe they’ll even be a secular decline – in which case, your valuation will be radically lower.

After all that: I do not hold shares in TSCO.

Edit 24-Mar-2014: Corrected a factual error. Changed “which is still below the current share price” to “which is still above the current share price” Computer programmer living in Scotland.
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### 4 Responses to \$TSCO.L – my Tesco CAPM valuation

1. ShadowStock says:

Thanks for the work. Just found you, “good stuff”, different, informative blog posts. links are great. John

2. investimouse says:

“So, even with a go-nowhere assumption, that brings my estimate of intrinsic value down by 10%, which is still below the current share price”

Above the current share price surely – 290-ish today.

But anyway, thanks for the evaluation. Awesome maths going on there.

• mcturra2000 says:

Yes, indeed, ABOVE the current share price. Well spotted. I will correct the text. Many thanks.

3. Steven de Salas says:

Hi Mark,

I also read Todd Wenning’s blog and found his reasoning to be sound if you apply a valuation based on fundamentals. Maybe I’m biased in my interpretation though, as value analysis is the only analysis I do these days, my assesment of TSCO can be seen on this url: