Question

Estimating Share Value Using the DCF Model

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

a. 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	$2,069,436	$2,369,504	$2,547,217	$2,738,258	$Answer
NOPAT	102,495	169,694	194,299	208,872	224,537	$Answer
NOA	662,502	758,591	868,587	933,731	1,003,760	$Answer

b. Estimate the value of a share of TXRH common stock using the discounted cash flow (DCF) 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
Increase in NOA		$Answer	$Answer	$Answer	$Answer	$Answer
FCFF (NOPAT - Increase in NOA)		Answer	Answer	Answer	Answer	Answer
Discount factor [1 / (1 + rw)t ]		Answer	Answer	Answer	Answer
Present value of horizon FCFF		Answer	Answer	Answer	Answer
Cumulative PV of horizon FCFF	$Answer
Present value of terminal FCFF	Answer
Total firm value	Answer
NNO	Answer
NCI	Answer
Firm equity value	$Answer
Shares outstanding (thousands)	Answer
Stock price per share	$Answer

c. 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.

d. If WACC had been 7.5%, what would the valuation estimate have been? What about if WACC has been 6.5%?

The valuation estimate at 7.5% would be lower than the estimate calculated in part a because the discount rate increased. In contrast, the valuation estimate at 6.5% would be higher than our estimate.

The valuation estimate at 7.5% would be higher than the estimate calculated in part a because the discount rate increased. In contrast, the valuation estimate at 6.5% would be lower than our estimate.

The valuation estimate would be the same regardless of the rate used to compute the estimate.

Answer 1

a..	Reported	Forecast Horizon
$ ' 000s	2015	2016	2017	2018	2019	Terminal Period
Sales	1807368	2069436	2369504	2547217	2738258	2738258*1.01/(0.07-0.01)=	46094010
NOPAT	102495	169694	194299	208872	224537	224537*1.01/(0.07-0.01)=	3779706
NOA	662502	758591	868587	933731	1003760	1003760*1.01/(0.07-0.01)=	16896627

TXRH---- WACC--7%	Reported	Forecast Horizon
$ thousands	2015	2016	2017	2018	2019
Increase in NOA		96089	109996	65144	70029
FCFF (NOPAT - Increase in NOA)		73605	84303	143728	154508
Discount factor [1 / (1 +0.07)^t ]		0.93458	0.87344	0.81630	0.76290
Present value of horizon FCFF		68790	73634	117325	117873
Cumulative PV of horizon FCFF	377621
Present value of terminal FCFF--2019 FCFF*(1+g)/(WACC-g)=(154508*1.01/(0.07-0.01))*0.76290	1984215
Total firm value	2361836
NNO	14680
NCI	-7520
Firm equity value	2368996
Shares outstanding (thousands)	70091
Stock price per share	33.80

c. 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.

d.. TXRH---- 7.5%	Reported	Forecast Horizon
$ thousands	2015	2016	2017	2018	2019
Increase in NOA		96089	109996	65144	70029
FCFF (NOPAT - Increase in NOA)		73605	84303	143728	154508
Discount factor [1 / (1 +0.075)^t ]		0.93023	0.86533	0.80496	0.74880
Present value of horizon FCFF		68470	72950	115695	115696
Cumulative PV of horizon FCFF	372811
Present value of terminal FCFF--2019 FCFF*(1+g)/(WACC-g)=(154508*1.01/(0.075-0.01))*0.74880	1797731
Total firm value	2170542
NNO	14680
NCI	-7520
Firm equity value	2177702
Shares outstanding (thousands)	70091
Stock price per share	31.07
d.. TXRH---- 6.5%	Reported	Forecast Horizon
$ thousands	2015	2016	2017	2018	2019
Increase in NOA		96089	109996	65144	70029
FCFF (NOPAT - Increase in NOA)		73605	84303	143728	154508
Discount factor [1 / (1 +0.065)^t ]		0.93897	0.88166	0.82785	0.77732
Present value of horizon FCFF		69113	74327	118985	120103
Cumulative PV of horizon FCFF	382527
Present value of terminal FCFF--2019 FCFF*(1+g)/(WACC-g)=(154508*1.01/(0.065-0.01))*0.77732	2205512
Total firm value	2588039
NNO	14680
NCI	-7520
Firm equity value	2595199
Shares outstanding (thousands)	70091
Stock price per share	37.03
Valuation of Stock price
At 7% WACC	33.80
At 7.5% WACC	31.07
At 6.5% WACC	37.03
Thus,
The valuation estimate at 7.5% would be lower than the estimate calculated in part a because the discount rate increased. In contrast, the valuation estimate at 6.5% would be higher than our estimate.