Question

Estimating Share Value Using the ROPI Model

Following are the income statement and balance sheet for Texas Roadhouse for the year ended December 29, 2015.

Assume the following forecasts for TXRH’s sales, NOPAT, and NOA for 2016 through 2019. Forecast the terminal period values assuming a 1% terminal period growth rate for all three model inputs: Sales, NOPAT, and NOA.

Round your answers to the nearest dollar.

	Reported	Forecast Horizon				Terminal
$ thousands	2015	2016	2017	2018	2019	Period
Sales	$1,807,368	$2,078,473	$2,390,244	$2,581,464	$2,787,981	Answer
NOPAT	102,495	170,435	196,000	221,680	228,614	Answer
NOA	662,502	761,904	876,189	946,284	1,021,987	Answer

a. Estimate the value of a share of TXRH common stock using the residual operating income (ROPI) model as of December 29, 2015; assume a discount rate (WACC) of 7%, common shares outstanding of 70,091 thousand, net nonoperating obligations (NNO) of $(14,680) thousand, and noncontrolling interest (NCI) from the balance sheet of $7,520 thousand. Note that NNO is negative because the company’s cash exceeds its nonoperating liabilities.

Rounding instructions:

• Use rounded answers for subsequent computations.

• Round answers to the nearest whole number unless otherwise noted.
• Round discount factor to 5 decimal places and stock price per share to two decimal places.

Do not use negative signs with any of your answers below.

TXRH	Reported			Forecast Horizon		Terminal
$ thousands	2015	2016	2017	2018	2019	Period
ROPI (NOPAT - [NOABeg × rw])		Answer	Answer	Answer	Answer	Answer
Discount factor [1 / (1 + rw)t ]		Answer	Answer	Answer	Answer
		Answer	Answer	Answer	Answer
Present value of horizon ROPI	Answer
Present value of terminal ROPI	Answer
NOA	Answer
Total firm value	Answer
NNO	Answer
NCI	Answer
Firm equity value	Answer
Shares outstanding (thousands)	Answer
Stock value per share	Answer

b. TXRH closed at $42.13 on February 26, 2016, the date the Form 10-K was filed with the SEC. How does your valuation estimate compare with this closing price?

Stock prices are a function of many factors. It is impossible to speculate on the reasons for the difference.

Our stock price estimate is higher than the TXRH market price, indicating that we believe that the stock is slightly undervalued. Stock prices are a function of expected NOPAT and NOA, as well as the WACC discount rate. Our higher stock price estimate might be due to more optimistic forecasts or a lower discount rate compared to other investors' and analysts' model assumptions.

Our stock price estimate is higher than the TXRH market price, indicating that we believe that the stock is slightly undervalued. Stock prices are a function of expected NOPAT and NOA, as well as the WACC discount rate. Our higher stock price estimate might be due to more pessimistic forecasts or a higher discount rate compared to other investors' and analysts' model assumptions.

Our stock price estimate is slightly higher than the WMT market price, indicating that we believe that WMT stock is slightly overvalued. Stock prices are a function of expected NOPAT and NOA, as well as the WACC discount rate. Our higher stock price estimate might be due to more pessimistic forecasts or a higher discount rate compared to other investors' and analysts' model assumptions.

Answer 1

Forecast the terminal period values assuming a 1% terminal period growth rate for all three model inputs as follows:

$ thousands	Reported	Forecast Horizon				Terminal
	2015	2016	2017	2018	2019	Period
Sales	$1,807,368	$2,078,473	$2,390,244	$2,581,464	$2,787,981	$2,815,861
NOPAT	$102,495	$170,435	$196,000	$221,680	$228,614	$230,900
NOA	$662,502	$761,904	$876,189	$946,284	$1,021,987	$1,032,207

_____________________________________________________________________________

Working as follows:

$ thousands	Reported	Forecast Horizon				Terminal
	2015	2016	2017	2018	2019	Period
Sales	$1,807,368	$2,078,473	$2,390,244	$2,581,464	$2,787,981	=ROUND(2787981*1.01,0)
NOPAT	$102,495	$170,435	$196,000	$221,680	$228,614	=ROUND(228614*1.01,0)
NOA	$662,502	$761,904	$876,189	$946,284	$1,021,987	=ROUND(1021987*1.01,0)

___________________________________________________________________________

a)

	B	C	D	E	F	G	H
222	$ thousands	Reported	Forecast Horizon				Terminal
223		2015	2016	2017	2018	2019	Period
224	Sales	$1,807,368	$2,078,473	$2,390,244	$2,581,464	$2,787,981	2815861
225	NOPAT	$102,495	$170,435	$196,000	$221,680	$228,614	230900
226	NOA	$662,502	$761,904	$876,189	$946,284	$1,021,987	1032207
227
228
229
230	TXRH	Reported	Forecast Horizon				Terminal
231	$ thousands	2015	2016	2017	2018	2019	Period
232	ROPI		124060	142667	160347	162374	159361
233	Discount factor		0.93458	0.87344	0.81630	0.76290
234			115944	124611	130891	123875

________________________________________________________________________

Working as follows:

	B	C	D	E	F	G	H
222	$ thousands	Reported	Forecast Horizon				Terminal
223		2015	2016	2017	2018	2019	Period
224	Sales	$1,807,368	$2,078,473	$2,390,244	$2,581,464	$2,787,981	2815861
225	NOPAT	$102,495	$170,435	$196,000	$221,680	$228,614	230900
226	NOA	$662,502	$761,904	$876,189	$946,284	$1,021,987	1032207
227
228
229
230	TXRH	Reported	Forecast Horizon				Terminal
231	$ thousands	2015	2016	2017	2018	2019	Period
232	ROPI		=ROUND(D225-(C226*7%),0)	=ROUND(E225-(D226*7%),0)	=ROUND(F225-(E226*7%),0)	=ROUND(G225-(F226*7%),0)	=ROUND(H225-(G226*7%),0)
233	Discount factor		=ROUND(1/((1+7%)^1),5)	=ROUND(1/((1+7%)^2),5)	=ROUND(1/((1+7%)^3),5)	=ROUND(1/((1+7%)^4),5)
234			=ROUND(D232*D233,0)	=ROUND(E232*E233,0)	=ROUND(F232*F233,0)	=ROUND(G232*G233,0)

_________________________________________________________________________________

Compute stock value per share as follows:

Present Value of Horizon ROPI ($115944+$124611+$130891+$123875)	$495,321
Present value of terminal ROPI	2029708
NOA	$662,502
Total firms value	$3,187,531
NNO	$14,680
NCI	$7,520
Firms Equity	$3,194,691
Sharres outstanding (thousands)	70091
Stock value per share	45.58

__________________________________________________________________

Working as follows:

Present Value of Horizon ROPI ($115944+$124611+$130891+$123875)	$495,321
Present value of terminal ROPI	=ROUND(159631/(7%-1%)*0.7629,0)
NOA	662502
Total firms value	=495321+2029708+662502
NNO	14680
NCI	7520
Firms Equity	=3187531+14680-7520
Sharres outstanding (thousands)	70091
Stock value per share	=ROUND(3194691/70091,2)