Posted: September 13th, 2017
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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