Margin of Safety - ESCO NPV Calculation Help
I don't really care if you like DCF / NPV calculations or not as I am just trying to sort this stuff out in my head and want to make sure I'm doing it right. The example that Seth Klarman has in his book "Margin of Safety" is simple, and yet I am diverging from the answers that he gives.
He starts off saying:
Cash flow would equal forty-five cents per share for five years and ninety cents thereafter when the guaranty payments to Emerson had ceased.
Cash flow for the first five years: $0.45
Cash flow for year six and beyond: $0.90
Discount rate 1: 12%
Discount rate 2: 15%
For dr1 = 12%:
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year cf d1 NPV1
1 $0.45 1.12^1 $0.40
2 $0.45 1.12^2 $0.36
3 $0.45 1.12^3 $0.32
4 $0.45 1.12^4 $0.29
5 $0.45 1.12^5 $0.26
6 $0.90 1.12^6 $0.46
$2.08
Tf = $0.9/0.12 = $7.5
NPV of Tf = $7.5 / 1.12^6 = $3.80
Total = $2.08 + $3.8
= $5.88
Klarman = $5.87
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Obviously this is close and I'm happy with this. Onto the next case.
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year cf d1 NPV1
1 $0.45 1.15^1 $0.39
2 $0.45 1.15^2 $0.34
3 $0.45 1.15^3 $0.30
4 $0.45 1.15^4 $0.26
5 $0.45 1.15^5 $0.22
6 $0.90 1.15^6 $0.39
$1.90
Tf = $0.9/0.15 = $6.0
NPV of Tf = $6 / 1.15^6 = $2.59
Total = $1.90 + $2.59
= $4.49
Klarman = $4.70
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I'm not too happy about this discrepancy, but it gets worse. The example continue with him saying:
What if Esco managed to increase its free cash flow by just $2.2 million a year, or twenty cents per share, for the next 10 years, after which it level off? The present value of these flows at 12 percent and 15 percent discount rates is $14.76 and $10.83, respectively.
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year cf inc cf_total d1 d2 NPV1 NPV2
1 $0.45 0.2 $0.65 1.12 1.15 $0.58 $0.57
2 $0.45 0.4 $0.85 1.25 1.32 $0.68 $0.64
3 $0.45 0.6 $1.05 1.40 1.52 $0.75 $0.69
4 $0.45 0.8 $1.25 1.57 1.75 $0.79 $0.71
5 $0.45 1 $1.45 1.76 2.01 $0.82 $0.72
6 $0.90 1.2 $2.10 1.97 2.31 $1.06 $0.91
7 $0.90 1.4 $2.30 2.21 2.66 $1.04 $0.86
8 $0.90 1.6 $2.50 2.48 3.06 $1.01 $0.82
9 $0.90 1.8 $2.70 2.77 3.52 $0.97 $0.77
10 $0.90 2 $2.90 3.11 4.05 $0.93 $0.72
$8.64 $7.41
TF1 = $2.9/0.12 = $24.17
NPV_TF1 = $24.17 / 3.11 = 7.78
Total_1 = 8.64 + 7.78 = $16.42
Klarman = $14.76
TF2 = $2.9/0.15 = $19.33
NPV_TF2 = $19.33 / 4.05 = 4.78
Total_2 = 7.42 + 4.78 = $12.19
Klarman = $10.83
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Messed this up pretty bad and I'm pretty disappointed that I'm not getting this because it feels like really simple math. Help?
2 Replies
hi， i searched this thread. i calculate it.
“ The present value of these flows at 12 percent and 15 percent discount rates is $14.76 and $10.83 ”
i use ai today but the result is also 7.544517376, do you solve this problem ?
ahnuld,
Thanks for the feedback. I'll have to focus on learning how to properly estimate (guess) the future cash flows for companies I am analyzing so that the NPV method actually provides some useful guidelines on how I can value a company.
Mark
You can either assign an exit multiple to the terminal year EBITDA, or normalize free cash flow by taking the terminal year EBIAT (NOPAT), adding the terminal year change in NWC, assume CapEx = Depreciation in perpetuity, and apply a long-term growth-rate.
The second approach will be highly influenced by your growth rate and is not appropriate for high-growth companies as your perpetuity value will comprise too big a piece of the pie of the overall NPV.
To the guy doing this with ChatGPT - lol don’t do that. Learn how to build a DCF in Excel so you intuitively understand what is going on.
