Question

17. Following are financial statement numbers and select ratios for American Eagle Outfitters for 2016, the year ended January 28, 2017.

	Current	Forecast Horizon				Terminal Year
($ thousands)	2016	2017	2018	2019	2020
Sales	3,609,865	3,754,260	3,866,887	3,982,894	4,102,381	4,143,405
Net operating profit after tax (NOPAT)	207,262	213,993	220,413	227,025	233,836	236,174
Net operating assets (NOA)	825,956	859,098	884,871	911,417	938,760	948,148

Forecast assumptions and other financial information for AE Outfitters are as follows:

Sales growth 2017	4%
Sales growth 2018 to 2020	3%
Terminal growth rate	1%
Net operating profit margin (NOPM)	5.7%
Net operating asset turnover (NOAT)	4.37
Discount rate	5%
Shares outstanding in thousands	181,886
Stockholders' equity	$1,204,569
Net nonoperating obligations (NNO)	$(378,613)

Required:

a.   Use the residual operating income (ROPI) model to estimate the value of AE Outfitters’ equity per share at January 28, 2017.

b.   AE Outfitters’ shares closed at $14.28 per share on March 10, 2017, the date the 10-K was filed with the SEC. How does your valuation compare with this closing price?

Answer 1

a.   Use the residual operating income (ROPI) model to estimate the value of AE Outfitters’ equity per share at January 28, 2017.

Answer:

	Current	Forecast Horizon				Terminal Year
($millions)	2016	2017	2018	2019	2020
Sales	3,609,865	3,754,260	3,866,887	3,982,894	4,102,381	4,143,405
NOPAT	207,262	213,993	220,413	227,025	233,836	236,174
NOA	825,956	859,098	884,871	911,417	938,760	948,148
ROPI (NOPAT- [NOABeg × rw])		172,695	177,458	182,781	188,265	189,236
Discount factor [1 / (1 + rw)t ]		$0.95238	$0.90703	$0.86384	$0.82270
PV of horizon ROPI		164,472	160,960	157,893	154,886
Cumulative PV of horizon ROPI	638,211
PV of terminal ROPI	3,892,123
NOA	825,956
Total firm value	5,356,290
Less NNO	-378613
Firm equity value	$5,734,903
Shares outstanding (millions)	181,886
Stock value per share	$31.53

b.   AE Outfitters’ shares closed at $14.28 per share on March 10, 2017, the date the 10-K was filed with the SEC. How does your valuation compare with this closing price?

Answer:

The estimated market price per share is $31.53 at January 28, 2017. AE Outfitters shares closed at $14.28 per share which means that the firm is undervalued when comparing to the estimated per share price of $31.53 which we calculated using ROPI Model . The reason for this undervalue might be either due the lower discount rate or due to aggressive growth projections.

Calculation:

The ROPI model is prepared to determine the firm equity value which is same as the sum of net operating asset book value and the PV of anticipated residual operating income. Here we need to estimate the value of AE Outfitters’ equity per share.

ROPI = Net operating profit after tax - (Net Operating Assets_Beg * r_w)

The Net operating profit after tax (NOPAT) , Net Operating Assets (NOA) and the r_w is given in the question. There might be difference due to the rounding.

r_w / Discount rate = 5%

2017:

ROPI = 213,993 - (825,956 × 5%) = 172,695

2018:

ROPI = 220,413 - (859,098 × 5%) = 177,458

2019:

ROPI = 227,025 - (884,871 × 5%) = 182,781

2020:

ROPI = 233,836 - (911,417 × 5%) = 188,265

Terminal Year:

ROPI = 236,174 - (938,760 × 5%) = 189,236

Then we need to calculate the Discount factor. Which can calculate using formula [1 / (1 + r_w)^t ]

2017:

Discount factor = [1 / (1 + 5%)¹ ] = 0.95238

2018:

Discount factor = [1 / (1 + 5%)² ] = 0.90703

2019:

Discount factor =[1 / (1 + 5%)³ ] = 0.86384

2020:

Discount factor = [1 / (1 + 5%)⁴ ] = 0.82270

Now, we can calculate the PV of horizon ROPI, by multiplying the ROPI with Discount factor.

2017:

PV of horizon ROPI = 172,695 * 0.95238 = 164,472

2018:

PV of horizon ROPI = 177,458 * 0.90703 = 160,960

2019:

PV of horizon ROPI =182,781 * 0.86384 = 157,893

2020:

PV of horizon ROPI = 188,265 * 0.82270 = 154,886

Cumulative present value of horizon ROPI is the total of the PV of horizon ROPI = 164,472 + 160,960 + 157,893 + 154,886 = 638,211

Then we need to calculate the PV of terminal ROPI. That is:

PV of terminal ROPI = Terminal Year ROPI/(Discount rate - Terminal growth rate)/(1+growth rate)^No. of years = $189,236 / [0.05 - 0.01] / (1.05)⁴ = $3,892,123.14 million

The total firm value is the sum of the Cumulative present value of horizon ROPI, PV of terminal ROPI and NOA of 2016 ,

Total Firm value = 638,211 + 3,892,123.14 + 825,956 = 5,356,290

Now, we can calculate the Firm equity value. It is the Total firm value minus the Net nonoperating obligations.

Net nonoperating obligations is given in the question, which is negative. That is - 378,613.

Firm equity value = 5,356,290 - -378,613 = 5,734,903

We are asked to find the the value of AE Outfitters’ equity per share. To get that we need to divide the firm equity value with Shares outstanding.

Shares outstanding = 181,886 in thousands

Stock value per share = 5,734,903 / 181,886  = 31.53