Chapter 8;Prospective Analysis: Valuation Implementation.

Chapter 8;Prospective Analysis: Valuation Implementation.

Discussion Questions
1.  How would the forecasts in Table 8-2 change if TJX were to maintain a sales growth rate of 10 percent per year from 2011 to 2020 (and all the other assumptions are kept unchanged)?
2011    2012    2013    2014    2015    2016    2017    2018    2019    2020
Sales growth rate    10.0%    10.0%    10.0%    10.0%    10.0%    10.0%    10.0%    10.0%    10.0%    10.0%
NOPAT margin    7.9%    7.5%    7.1%    6.7%    6.3%    5.9%    5.5%    5.0%    4.5%    4.0%
WC to sales    0.6%    1.0%    1.0%    1.0%    1.0%    1.0%    1.0%    1.0%    1.0%    1.0%
LT assets to sales    33.4%    34.0%    34.3%    34.5%    34.8%    35.0%    35.3%    35.5%    35.8%    36.0%
Debt ratio    57.5%    57.5%    57.5%    57.5%    57.5%    57.5%    57.5%    57.5%    57.5%    57.5%
After tax cost of debt    2.73%    2.73%    2.73%    2.73%    2.73%    2.73%    2.73%    2.73%    2.73%    2.73%

Income Statement
Sales           24,136            26,550            29,205            32,126            35,338            38,872            42,759            47,035            51,739            56,912
Net operating profit after tax             1,907              1,991              2,074              2,152              2,226              2,293              2,352              2,352              2,328              2,277
–    Net interest expense after tax               124                146                161                179                198                219                243                269                298                330
=     Net Income             1,783              1,846              1,912              1,974              2,028              2,074              2,109              2,082              2,030              1,946
–     Preferred dividends                   –                      –                      –                      –                      –                      –                      –                      –                      –
=     Net income to common           1,783            1,846            1,912            1,974            2,028            2,074            2,109            2,082            2,030
1,946

2011    2012    2013    2014    2015    2016    2017    2018    2019    2020
Beginning Balance Sheet
Beg. Net working capital             144                   266                      292                      321                      353                      389                      428                      470                      517                      569
+     Beg. Net long-term assets             7,754              9,027            10,003            11,083            12,280            13,605            15,073            16,697            18,497            20,488
=     Net operating assets           7,899            9,293          10,295          11,405          12,633          13,994          15,500          17,168          19,014          21,058

Net debt             4,541              5,343              5,919              6,557              7,264              8,046              8,912              9,871              10,932              12,107
+     Preferred stock                   –                      –                      –                      –                      –                      –                      –                      –                      –                      –
+     Common stock             3,357              3,950              4,376              4,847              5,370              5,948              6,588            7,297            8,082            8,950
=     Net capital           7,899            9,293          10,295          11,405          12,633          13,994          15,500          17,168          19,014          21,058

Ratios
Operating return on assets    24.1%    21.4%    20.1%    18.9%    17.6%    16.4%    15.2%    13.7%    12.2%    10.9%
Return on equity    53.1%    46.7%    43.7%    40.7%    37.8%    34.9%    32.0%    28.5%    25.1%    21.7%
Book value of assets growth    23.7%    17.7%    10.8%    10.8%    10.8%    10.8%    10.8%    10.8%    10.8%    10.8%
Book value of equity growth    16.2%    17.7%    10.8%    10.8%    10.8%    10.8%    10.8%    10.8%    10.8%    10.8%
Net operating asset turnover    3.1    2.9    2.8    2.8    2.8    2.8    2.8    2.7    2.7    2.7

2011    2012    2013    2014    2015    2016    2017    2018    2019    2020
Cash flows
Net Income             1,783             1,846              1,912              1,974              2,028              2,074              2,109              2,082              2,030
1,946
–     Change in net working capital             (121)                   (27)                     (29)                      (32)                      (35)                      (39)                      (43)                     (47)                      (52)
(57)
–     Change in net long-term assets             (1,273)           (976)           (1,081)           (1,197)           (1,325)           (1,467)           (1,625)           (1,799)           (1,992)
(2,049)
+     Change in net debt               802                576                638                707                782                866                959                1,061                1,175
1,211
=     Free cash flow to equity               1,190                1,420                1,440                1,451                1,450                1,434                1,400                1,298                1,161
1,051

Net operating profit after tax             1,907              1,991              2,074              2,152              2,226              2,293              2,352              2,352              2,328
2,277
–     Change in net working capital             (121)                   (27)                     (29)                      (32)                      (35)                      (39)                      (43)                     (47)                      (52)
(57)
–     Change in net long-term assets             (1,273)           (976)           (1,081)           (1,197)           (1,325)           (1,467)           (1,625)           (1,799)           (1,992)
(2,049)
=     Free cash flow to capital               513                989                964                924                866                787                684                506                285
171
Note:  2021 input values same as 2020.

2. Recalculate the forecasts in Table 8-2 assuming that the NOPAT profit margin is held steady for the first five years of the forecast and then declines by 0.1 percentage points per year thereafter (keeping all the other assumptions unchanged).
2011    2012    2013    2014    2015    2016    2017    2018    2019    2020
Sales growth rate    5.7%    6.6%    7.1%    6.9%    6.7%    6.5%    6.3%    6.1%    5.9%    5.7%
NOPAT margin    7.9%    7.9%    7.9%    7.9%    7.9%    7.8%    7.7%    7.6%    7.5%    7.4%
WC to sales    0.6%    1.0%    1.0%    1.0%    1.0%    1.0%    1.0%    1.0%    1.0%    1.0%
LT assets to sales    33.4%    34.0%    34.3%    34.5%    34.8%    35.0%    35.3%    35.5%    35.8%    36.0%
Debt ratio    57.5%    57.5%    57.5%    57.5%    57.5%    57.5%    57.5%    57.5%    57.5%    57.5%
After tax cost of debt    2.73%    2.73%    2.73%    2.73%    2.73%    2.73%    2.73%    2.73%    2.73%    2.73%

Income Statement
Sales           23,193            24,724            26,479            28,306            30,203            32,166            34,192            36,278            38,418            40,608
Net operating profit after tax             1,832             1,953              2,092              2,236              2,386              2,509              2,633              2,757              2,881              3,005
–    Net interest expense after tax               124                136                146                158                169                182                194                208                221                236
=     Net Income             1,708             1,817              1,945              2,079              2,217              2,327              2,438              2,549              2,660              2,769
–     Preferred dividends                   –                      –                      –                      –                      –                      –                      –                      –                      –                      –
=     Net income to common             1,708             1,817              1,945              2,079              2,217              2,327              2,438              2,549              2,660              2,769

2011    2012    2013    2014    2015    2016    2017    2018    2019    2020
Beginning Balance Sheet
Beg. Net working capital             144                   247        265       283       302    322       342       363       384       406
+     Beg. Net long-term assets             7,754              8,406            9,069            9,766            10,495            11,258            12,053            12,879            13,735            14,619
=     Net operating assets           7,899            8,653         9,334          10,049          10,797          11,580          12,395          13,241          14,119          15,025

Net debt             4,541             4,975              5,367              5,778              6,208              6,658              7,126              7,613              8,118              8,639
+     Preferred stock                   –                      –                      –                      –                      –                      –                      –                      –                      –                      –
+     Common stock             3,357              3,678              3,967              4,271              4,589              4,922              5,268            5,628            6,001            6,386
=     Net capital           7,899            8,653          9,334          10,049          10,797          11,580          12,395          13,241          14,119          15,025

Ratios
Operating return on assets    23.2%    22.6%    22.4%    22.3%    22.1%    21.7%    21.2%    20.8%    20.4%    20.0%
Return on equity    50.9%    49.4%    49.0%    48.7%    48.3%    47.3%    46.3%    45.3%    44.3%    43.4%
Book value of assets growth    23.7%    9.6%    7.9%    7.7%    7.5%    7.2%    7.0%    6.8%    6.6%    6.4%
Book value of equity growth    16.2%    9.6%    7.9%    7.7%    7.5%    7.2%    7.0%    6.8%    6.6%    6.4%
Net operating asset turnover    2.9    2.9    2.8    2.8    2.8    2.8    2.8    2.7    2.7    2.7

2011    2012    2013    2014    2015    2016    2017    2018    2019    2020
Cash flows
Net Income             1,708              1,817             1,945              2,079              2,217              2,327              2,438              2,549              2,660              2,769
–     Change in net working capital             (103)                   (18)       (18)                      (19)                      (20)                      (20)                      (21)                      (21)                      (22)                      (23)
–     Change in net long-term assets             (652)             (663)           (697)           (730)           (763)           (795)           (826)           (856)           (884)           (833)
+     Change in net debt               434                391                411                431                450                469                487                504                521                492
=     Free cash flow to equity               1,388                1,528                1,642                1,760              1,884              1,981              2,078              2,177              2,275              2,405

Net operating profit after tax             1,832              1,953              2,092              2,236              2,386              2,509              2,633              2,757              2,881              3,005
–     Change in net working capital             (103)                   (18)       (18)                      (19)                      (20)                      (20)                      (21)                      (21)                      (22)                      (23)
–     Change in net long-term assets             (652)             (663)           (697)           (730)           (763)           (795)           (826)           (856)           (884)           (833)
=     Free cash flow to capital               1,077                1,273                1,377                1,487                1,604                1,694                1,786                1,880                1,975                2,149
Note:  2021 input values same as 2020.

3. Recalculate the forecasts in Tables 8-2  assuming that the ratio of net operating working capital to sales is 3 percent, and the ratio of net long-term assets to sales holds steady at 33.4 percent for all the years from fiscal 2011 to fiscal 2020. Keep all the other assumptions unchanged.
2011    2012    2013    2014    2015    2016    2017    2018    2019    2020
Sales growth rate    5.7%    6.6%    7.1%    6.9%    6.7%    6.5%    6.3%    6.1%    5.9%    5.7%
NOPAT margin    7.9%    7.5%    7.1%    6.7%    6.3%    5.9%    5.5%    5.0%    4.5%    4.0%
WC to sales    0.6%    3.0%    3.0%    3.0%    3.0%    3.0%    3.0%    3.0%    3.0%    3.0%
LT assets to sales    33.4%    33.4%    33.4%    33.4%    33.4%    33.4%    33.4%    33.4%    33.4%    33.4%
Debt ratio    57.5%    57.5%    57.5%    57.5%    57.5%    57.5%    57.5%    57.5%    57.5%    57.5%
After tax cost of debt    2.73%    2.73%    2.73%    2.73%    2.73%    2.73%    2.73%    2.73%    2.73%    2.73%

Income Statement
Sales           23,193            24,724            26,479            28,306            30,203            32,166            34,192            36,278            38,418            40,608
Net operating profit after tax             1,832              1,854              1,880              1,897              1,903              1,899              1,881              1,814              1,729              1,624
–    Net interest expense after tax               124                141                151                162                172                184                195                207                219                232
=     Net Income             1,708              1,713              1,729              1,735              1,730              1,714              1,685              1,607              1,509              1,392
–     Preferred dividends                   –                      –                      –                      –                      –                      –                      –                      –                      –                      –
=     Net income to common             1,708              1,713              1,729              1,735              1,730              1,714              1,685              1,607              1,509              1,392

2011    2012    2013    2014    2015    2016    2017    2018    2019    2020
Beginning Balance Sheet
Beg. Net working capital             144.1             742              794             849              906              965              1,026              1,088              1,153              1,218
+     Beg. Net long-term assets             7,754            8,258            8,844            9,454           10,088            10,743            11,420            12,117            12,832            13,563
=     Net operating assets           7,899          8,999          9,638          10,303          10,994          11,708          12,446          13,205          13,984          14,781

Net debt             4,541              5,174              5,542              5,924              6,321              6,732              7,156              7,593              8,040              8,499
+     Preferred stock                   –                      –                      –                      –                      –                      –                      –                      –                      –                      –
+     Common stock             3,357              3,825              4,097              4,379            4,673            4,976            5,290            5,613            5,944            6,283
=     Net capital           7,899          8,999          9,638          10,303          10,994          11,708          12,446          13,205          13,984          14,781

Ratios
Operating return on assets    23.2%    20.6%    19.5%    18.4%    17.3%    16.2%    15.1%    13.7%    12.4%    11.0%
Return on equity    50.9%    44.8%    42.2%    39.6%    37.0%    34.4%    31.9%    28.6%    25.4%    22.2%
Book value of assets growth    23.7%    13.9%    7.1%    6.9%    6.7%    6.5%    6.3%    6.1%    5.9%    5.7%
Book value of equity growth    16.2%    13.9%    7.1%    6.9%    6.7%    6.5%    6.3%    6.1%    5.9%    5.7%
Net operating asset turnover    2.9    2.8    2.8    2.8    2.8    2.8    2.8    2.8    2.8    2.8

Cash flows    2011    2012    2013    2014    2015    2016    2017    2018    2019    2020

Net Income             1,708              1,713              1,729              1,735              1,730              1,714              1,685              1,607              1,509              1,392
–     Change in net working capital           (598)             (53)             (55)             (57)             (59)             (61)             (63)             (64)             (66)             (69)
–     Change in net long-term assets           (503)           (586)           (610)           (633)           (656)           (677)           (697)           (715)           (731)           (773)
+     Change in net debt             633                367                382                397                411                424                437                448                458                484
=     Free cash flow to equity           1,240               1,442                1,446                1,441                1,427                1,401                1,363                1,276                1,171                1,034

2011    2012    2013    2014    2015    2016    2017    2018    2019    2020

Net operating profit after tax             1,832              1,854              1,880              1,897              1,903              1,899              1,881              1,814              1,729              1,624
–     Change in net working capital           (598)             (53)             (55)             (57)             (59)             (61)             (63)             (64)             (66)             (69)
–     Change in net long-term assets           (503)           (586)           (610)           (633)           (656)           (677)           (697)           (715)           (731)           (773)
=     Free cash flow to capital           731               1,215                1,215                1,206                1,188                1,160                1,121                1,035                932                782
Note:  2021 input values same as 2020. Also, net operating working capital to sales ratio for 2011 is an actual.

4.  Calculate TJX’s cash payouts to its shareholders in the years 2011–2020 that are implicitly assumed in the projections in Table 8-2.
The cash payouts made to shareholders are simply the free cash flows to equity. These are the surplus cash flows available after reinvesting needed funds in working capital and assets. The values are presented in Table 8-2 and are $1,387.6 in 2011, declining to $1,024.7 in 2020.
5.  How would the abnormal earnings calculations in Table 8-3 change if the cost of equity assumption is changed to 12%?
2011    2012    2013    2014    2015    2016    2017    2018    2019    2020
Equity Valuation
Abnormal earnings               1,305                1,277                1,257                1,226                1,183                1,125                1,054                931                787                622
Abnormal ROE    38.9%    34.7%    31.7%    28.7%    25.8%    22.9%    20.0%    16.5%    13.1%    9.7%

6.  What would be the total equity value (as calculated for scenarios in Table 8-6 using abnormal earnings) if the sales growth in years 2021 and beyond is 8.5 percent and the company is able to generate abnormal returns at the same level as in fiscal 2020 forever (keeping all the other assumptions in the table unchanged)?
2011    2012    2013    2014    2015    2016    2017    2018    2019    2020    2021
Sales growth rate    5.7%    6.6%    7.1%    6.9%    6.7%    6.5%    6.3%    6.1%    5.9%    5.7%    8.5%
NOPAT margin    7.9%    7.5%    7.1%    6.7%    6.3%    5.9%    5.5%    5.0%    4.5%    4.0%    4.0%
WC to sales    0.6%    1.0%    1.0%    1.0%    1.0%    1.0%    1.0%    1.0%    1.0%    1.0%    1.0%
LT assets to sales    33.4%    34.0%    34.3%    34.5%    34.8%    35.0%    35.3%    35.5%    35.8%    36.0%    36.0%
Debt ratio    57.5%    57.5%    57.5%    57.5%    57.5%    57.5%    57.5%    57.5%    57.5%    57.5%    57.5%
After tax cost of debt    2.73%    2.73%    2.73%    2.73%    2.73%    2.73%    2.73%    2.73%    2.73%    2.73%    2.73%

Income Statement
Sales           23,193            24,724            26,479            28,306            30,203            32,166            34,192            36,278            38,418            40,608         44,060
Net operating profit after tax             1,832              1,854              1,880              1,897              1,903              1,898              1,881              1,814              1,729              1,624     1,762
–    Net interest expense after tax               124                136                146                158                169                182                194                208                221                236            256
=     Net Income             1,708              1,719              1,734              1,739              1,733              1,716              1,686              1,606              1,507              1,389          1,507
–     Preferred dividends                   –                      –                      –                      –                      –                      –                      –                      –                      –                      –                   –
=     Net income to common             1,708              1,719              1,734              1,739              1,733              1,716              1,686              1,606              1,507              1,389          1,507

2011    2012    2013    2014    2015    2016    2017    2018    2019    2020    2021
Beginning Balance Sheet
Beg. Net working capital             144                   247                      265                      283                      302                      322                      342                      363                      384                      406                   441
+     Beg. Net long-term assets             7,754              8,406            9,069            9,766            10,495            11,258            12,053            12,879            13,735            14,619         15,862
=     Net operating assets           7,989            8,653          9,334          10,049          10,797          11,580          12,395          13,241          14,119          15,025       16,302

Net debt             4,541              4,975              5,367              5,778              6,208              6,658              7,126              7,613              8,118              8,639          9,373
+     Preferred stock                   –                      –                      –                      –                      –                      –                      –                      –                      –                      –                      –
+     Common stock             3,357              3,678              3,967              4,271              4,589              4,922              5,268            5,628            6,001            6,386         6,929
=     Net capital           7,899            8,653          9,334          10,049          10,797          11,580          12,395          13,241          14,119          15,025       16,302

Ratios
Operating return on assets    23.2%    21.4%    20.1%    18.9%    17.6%    16.4%    15.2%    13.7%    12.2%    10.8%    10.8%
Return on equity    50.9%    46.7%    43.7%    40.7%    37.8%    34.9%    32.0%    28.5%    25.1%    21.7%    21.7%
Book value of assets growth    23.7%    9.6%    7.9%    7.7%    7.5%    7.2%    7.0%    6.8%    6.6%    6.4%    8.5%
Book value of equity growth    16.2%    9.6%    7.9%    7.7%    7.5%    7.2%    7.0%    6.8%    6.6%    6.4%    8.5%
Net operating asset turnover    2.9    2.9    2.8    2.8    2.8    2.8    2.8    2.7    2.7    2.7    2.7

Valuation    2011    2012    2013    2014    2015    2016    2017    2018    2019    2020    2021
Abnormal earnings               1,414                1,396                1,386                1,364                1,331                1,285                1,224                1,113                981                829                899
Discount factor             0.92              0.85              0.78              0.71              0.66              0.60             0.56              0.51             0.47              0.43              0.43
Present value of abnormal earnings               1,300                1,180                1,077                975                874                776                680                568                460                357                388
Beginning book value
3,357

PV abnormal earnings 2011 to 2020             8,247

PV abnormal earnings 2021 on           143,653

Total equity value of TJX            155,257

The 8.5% terminal growth rate leads the terminal value to explode, since the cost of equity is 8.77%. The denominator in the terminal value perpetuity is then .0877-.085 or .0027. This is clearly an unreasonable assumption that grossly overvalues TJX.

7.  Calculate the proportion of terminal value to total estimated value of equity under the abnormal earnings method and the discounted cash flow method for the Scenario 2 results shown in Table 8-6. Why are these proportions different?
Under the abnormal earnings method, the terminal value in Table 8-6 comprises 35.5% of the total value (6381.3/17985.1). In contrast, the terminal in the free cash flow to equity method is 51.3% of the total value (9219.2/17985.1). The reason for the difference is that the abnormal earnings method contains the current book value of equity as its base, and then counts only superior earnings each year. By the terminal years, given competition, this superior performance is expected to be modest. In contrast, the free cash flow method values the full cash flows to shareholders, whether they are generated by normal of abnormal performance. The cash flows therefore grow steadily during the terminal value period, even though much of this performance reflects merely a normal return on capital.

8.    What will TJX’s cost of equity be if the equity market risk premium is 5 percent?

Market risk premium    5.0%
??Common equity beta            0.8
4.0%
? Risk free rate    3.4%
= Cost of common equity    7.4%

9.  Assume that TJX changes its capital structure so that its market value weight of debt to capital increases to 30%, and its after-tax interest rate on debt at this new leverage level is 3.5%. Assume that the equity market risk premium is 6.7%. What will be the cost of equity at the new debt level? What will be the new weighted average cost of capital?
The first task is to compute the new equity beta. The beta of TJX’s assets will not change, since its assets are unchanged. But the equity beta will increase somewhat to reflect the increased financial risk faced by shareholders. Under the prior capital structure, where the pre-tax cost of debt was 4.4%, the risk premium was 6.7% and the risk free rate was 3.41%, TJX’s debt beta was (4.4%-3.41%)/6.7% or 0.15. Given its equity beta of 0.8 and its debt weighting of 20%, the asset beta for the company was as follows:
Asset beta = Equity beta * (1 – Debt weight) + Debt beta * (Debt weight)
= 0.8*.8 + 0.15*.2 = 0.67
Under the new capital structure, the debt beta will increase. If the after-tax cost of debt is 3.5%, and the tax rate is 38%, the pre-tax cost of debt is 5.65%, and the debt beta will be (5.65%-3.41%)/6.7% or 0.33. The adjusted equity beta is then as follows
Equity beta = [Asset beta – Debt beta * (Debt weight)]/(1-Debt weight)
= [0.67 – .33*0.3]/0.7 = 0.82
Given the modest change in capital structure, the change in equity beta is very small – probably not worth worrying about.
The revised cost of equity and WACC will then be as follows:
Cost of Equity
Market risk premium    6.7%
? Common equity beta    0.82
5.5%
? Risk free rate    3.41%
= Cost of common equity    8.91%

Weighted Average Cost of Capital
After tax cost of debt    3.5%
? Debt weight    30.0%
?
Cost of common equity    8.91%
? (1-Debt weight)    70.0%
= Weighted Average Cost of Capital    7.3%
The insight for students here is to note that making modest changes in capital structure will not make a material difference in the firm’s cost of equity or WACC.
10.  Nancy Smith says she is uncomfortable making the assumption that TJX’s dividend payout will vary from year to year. If she makes a constant dividend payout assumption, what changes does she have to make in her other valuation assumptions to make them internally consistent with each other?
If Nancy Smith doesn’t want to allow dividend payout to vary across the years, then she can hold the dividend payout constant. However, then she will have to allow for the capital structure to vary from year to year, since a constant dividend payout may not result in a stream of equity values that will result in a constant debt-to-equity ratio. If the capital structure is allowed to vary, then the cost of capital will vary in each period as well.

1. Similar to problem 8-6, caclulate the value of the firm using the assumptions and format below. Answers should be provided in Excel and use formula and cell references.
Cells with numbers rather than formula will not receive credit. Assume 2026 is the terminal year and all assumptions stay the same.
2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026
Sales growth rate 7.00% 6.00% 7.00% 6.50% 6.00% 5.00% 4.50% 4.00% 4.00% 3.00% 3.00%
NOPAT margin 8.00% 8.00% 8.00% 8.00% 8.00% 7.50% 7.50% 7.00% 7.00% 6.00% 6.00%
WC to sales 1.00% 1.50% 2.00% 2.00% 2.00% 1.50% 1.50% 1.00% 1.00% 1.00% 1.00%
LT assets to sales 20.00% 21.00% 22.00% 23.00% 25.00% 25.00% 24.00% 23.00% 22.00% 21.00% 21.00%
Debt ratio 60.00% 60.00% 60.00% 60.00% 60.00% 60.00% 60.00% 60.00% 60.00% 60.00% 60.00%
After tax cost of debt 3.00% 3.00% 3.00% 3.00% 3.00% 3.00% 3.00% 3.00% 3.00% 3.00% 3.00%
2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026
Beginning Balance Sheet
Beg. Net working capital
Beg. Net long-term assets
Net operating assets
Net debt
Preferred stock
Common stock
Net capital
Income Statement
Sales 30,000
Net operating profit after tax
Net interest expense after tax
Net Income
Preferred dividends
Net income to common
2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026
Valuation
Cost of Equity 8% 8% 8% 8% 8% 8% 8% 8% 8% 8% 8%
Abnormal Earnings
Discount Factor
Present Value of Abnormal Earnings
Beginning Book Value
PV Abnormal Earnings 2016-2025
PV Abnormal Earnings 2026 on
Total Value of Equity

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