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Page 1: FM S 2012 HW5 Solution

FIRST FINANCIAL MODELSales growth 10%Current assets/Sales 15%Current liabilities/Sales 8%Net fixed assets/Sales 77%Costs of goods sold/Sales 50%Depreciation rate 10%Interest rate on debt 10.00%Interest paid on cash and marketable securities 8.00%Tax rate 40%Dividend payout ratio 40%

Year 0 1 2 3Income statementSales 1,000 1,100 1,210 1,331 Costs of goods sold (500) (550) (605) (666)Interest payments on debt (32) (32) (32) (32)Interest earned on cash and marketable securities 6 9 14 20 Depreciation (100) (117) (137) (161)Profit before tax 374 410 450 492 Taxes (150) (164) (180) (197)Profit after tax 225 246 270 295 Dividends (90) (98) (108) (118)Retained earnings 135 148 162 177

Balance sheetCash and marketable securities 80 144 213 289 Current assets 150 165 182 200 Fixed assets At cost 1,070 1,264 1,486 1,740 Depreciation (300) (417) (554) (715) Net fixed assets 770 847 932 1,025 Total assets 1,000 1,156 1,326 1,513

Current liabilities 80 88 97 106 Debt 320 320 320 320 Stock 450 450 450 450 Accumulated retained earnings 150 298 460 637 Total liabilities and equity 1,000 1,156 1,326 1,513

Year 0 1 2 3 Free cash flow calculationProfit after tax 246 270 295 Add back depreciation 117 137 161 Subtract increase in current assets (15) (17) (18)Add back increase in current liabilities 8 9 10 Subtract increase in fixed assets at cost (194) (222) (254)Add back after-tax interest on debt 19 19 19 Subtract after-tax interest on cash and+A14 mkt. securities (5) (9) (12)Free cash flow 176 188 201

CONSOLIDATED STATEMENT OF CASH FLOWS: RECONCILING THE CASH BALANCES Cash flow from operating activities

Page 2: FM S 2012 HW5 Solution

Profit after tax 246 270 295 Add back depreciation 117 137 161 Adjust for changes in net working capital: Subtract increase in current assets (15) (17) (18) Add back increase in current liabilities 8 9 10 Net cash from operating activities 356 400 448

Cash flow from investing activitiesAquisitions of fixed assets--capital expenditures (194) (222) (254)Purchases of investment securities 0 0 0Proceeds from sales of investment securities 0 0 0Net cash used in investing activities (194) (222) (254)

Cash flow from financing activitiesNet proceeds from borrowing activities 0 0 0Net proceeds from stock issues, repurchases 0 0 0Dividends paid (98) (108) (118)Net cash from financing activities (98) (108) (118)

Net increase in cash and cash equivalents 64 70 76 Check: changes in cash and mkt. securities 64 70 76

Page 3: FM S 2012 HW5 Solution

FIRST FINANCIAL MODEL

4 5

1,464 1,611 #VALUE! (732) (805) #VALUE! (32) (32) #VALUE! 26 33 #VALUE! (189) (220) #VALUE! 538 587 #VALUE! (215) (235) #VALUE! 323 352 #VALUE! (129) (141) #VALUE! 194 211 #VALUE!

371 459 #VALUE! 220 242 #VALUE!

2,031 2,364 #VALUE! (904) (1,124) #VALUE! 1,127 1,240 #VALUE! 1,718 1,941 #VALUE!

117 129 #VALUE! 320 320 #VALUE! 450 450 #VALUE! 830 1,042 #VALUE! 1,718 1,941 #VALUE!

4 5

323 352 #VALUE!189 220 #VALUE!(20) (22) #VALUE!11 12 #VALUE!

(291) (333) #VALUE!19 19 #VALUE!

(16) (20) #VALUE!214 228 #VALUE!

CONSOLIDATED STATEMENT OF CASH FLOWS: RECONCILING THE CASH BALANCES

Page 4: FM S 2012 HW5 Solution

323 352 #VALUE! 189 220 #VALUE!

(20) (22) #VALUE! 11 12 #VALUE! 502 562 #VALUE!

(291) (333) #VALUE!0 0 <-- Not in our model 0 0 <-- Not in our model

(291) (333) #VALUE!

0 0 #VALUE!0 0 #VALUE!

(129) (141) #VALUE!(129) (141) #VALUE!

82 88 #VALUE! 82 88 #VALUE!

Page 5: FM S 2012 HW5 Solution

FIRST FINANCIAL MODEL

Sales growth 10%Current assets/Sales 15%Current liabilities/Sales 8%Net fixed assets/Sales 77%Costs of goods sold/Sales 50%Depreciation rate 10%Interest rate on debt 10.00%Interest paid on cash and marketable secu 8.00%Tax rate 40%Dividend payout ratio 40%

Year 0 1 2 3 4Income statementSales 1,000 1,000 1,000 1,000 1,000 Costs of goods sold (770) (770) (770) (770) (770)Interest payments on debt 49 49 49 49 49 Interest earned on cash and marketable se 8 9 6 (10) (48)Depreciation (100) (253) (422) (704) (1,173)Profit before tax 187 35 (137) (434) (941)Taxes (15) (3) 11 35 75 Profit after tax 172 32 (126) (400) (866)Dividends (69) (13) 50 160 346 Retained earnings 103 19 (76) (240) (520)

Balance sheetCash and marketable securities 80 99 23 (216) (736)Current assets 100 100 100 100 100 Fixed assets At cost 380 633 1,056 1,759 2,932 Depreciation (300) (553) (976) (1,679) (2,852) Net fixed assets 80 80 80 80 80 Total assets 260 279 203 (36) (556)

Current liabilities 150 150 150 150 150 Debt (490) (490) (490) (490) (490)Stock 450 450 450 450 450 Accumulated retained earnings 150 169 93 (146) (666)Total liabilities and equity 260 279 203 (36) (556)

Year 0 1 2 3 4 Free cash flow calculationProfit after tax 32 (126) (400) (866)Add back depreciation 253 422 704 1173 Subtract increase in current assets 0 0 0 0

Here's a basic exercise that will help you understand what's going on in the modeling of financial statements. Replicate the models in sections 3.2, 3.7, and 3.8 (First Financial Model). That is, enter the correct formulas for the cells and see that you get the same results as the book. (This turns out to be more of an exercise in accounting than in finance. If you're like many financial modelers, you'll see that there are some aspects of accounting that you've forgotten!)

Page 6: FM S 2012 HW5 Solution

Add back increase in current liabilities 0 0 0 0 Subtract increase in fixed assets at cost (253) (422) (704) (1173)Add back after-tax interest on debt (45) (45) (45) (45)Subtract after-tax interest on cash and+A14 mkt. secu (8) (6) 9 44 Free cash flow (21) (177) (436) (867)

CONSOLIDATED STATEMENT OF CASH FLOWS: RECONCILING THE CASH BALANCES Cash flow from operating activitiesProfit after tax 32 (126) (400) (866)Add back depreciation 253 422 704 1,173 Adjust for changes in net working capital: Subtract increase in current assets - - - - Add back increase in current liabilities - - - - Net cash from operating activities 285 296 304 307

Cash flow from investing activitiesAquisitions of fixed assets--capital expenditures (253) (422) (704) (1,173)Purchases of investment securities 0 0 0 0Proceeds from sales of investment securities 0 0 0 0Net cash used in investing activities (253) (422) (704) (1,173)

Cash flow from financing activitiesNet proceeds from borrowing activities 0 0 0 0Net proceeds from stock issues, repurchases 0 0 0 0Dividends paid (13) 50 160 346 Net cash from financing activities (13) 50 160 346

Net increase in cash and cash equivalents 19 (76) (240) (520)Check: changes in cash and mkt. securities 19 (76) (240) (520)

Page 7: FM S 2012 HW5 Solution

5

1,000 #VALUE! (770) #VALUE! 49 #VALUE! (123) #VALUE! (1,955) #VALUE! (1,799) #VALUE! 144 #VALUE! (1,655) #VALUE! 662 #VALUE! (993) #VALUE!

(1,729) #VALUE! 100 #VALUE!

4,887 #VALUE! (4,807) #VALUE! 80 #VALUE! (1,549) #VALUE!

150 #VALUE! (490) #VALUE! 450 #VALUE! (1,659) #VALUE! (1,549) #VALUE!

5

(1655) #VALUE!1955 #VALUE!

0 #VALUE!

Here's a basic exercise that will help you understand what's going on in the modeling of financial statements. Replicate the models in sections 3.2, 3.7, and 3.8 (First Financial Model). That is, enter the correct formulas for the cells and see that you get the same results as the book. (This turns out to be more of an exercise in accounting than in finance. If you're like many financial modelers, you'll see that there are some aspects of

Page 8: FM S 2012 HW5 Solution

0 #VALUE!(1955) #VALUE!

(45) #VALUE!113 #VALUE!

(1587) #VALUE!

CONSOLIDATED STATEMENT OF CASH FLOWS: RECONCILING THE CASH BALANCES

(1,655) #VALUE! 1,955 #VALUE!

- #VALUE! - #VALUE! 300 #VALUE!

(1,955) #VALUE!0 <-- Not in our model 0 <-- Not in our model

(1,955) #VALUE!

0 #VALUE!0 #VALUE!

662 #VALUE!662 #VALUE!

(993) #VALUE! (993) #VALUE!

Page 9: FM S 2012 HW5 Solution

EXERCISE 2

Sales growth 10%Current assets/Sales 15%Current liabilities/Sales 8%Net fixed assets/Sales 77%Costs of goods sold/Sales 50%Sales, general and administrative expenses 200 <-- AddedDepreciation rate 10%Interest rate on debt 10.00%Interest paid on cash & marketable securities 8.00%Tax rate 40%Dividend payout ratio 40%

Year 0 1 2 3Income statementSales 1,000 1,150 1,210 1,331 Costs of goods sold (500) (575) (605) (666)SG&A (600) (200) (200)Interest payments on debt (32) (32) (32) (32)Interest earned on cash & marketable securities 6 11 16 16 Depreciation (100) (117) (137) (161)Profit before tax 374 412 251 289 Taxes (150) (163) (96) (111)Profit after tax 225 249 155 178 Dividends (90) (50) (58) (67)Retained earnings 135 200 97 111

Balance sheetCash and marketable securities 80 196 200 210 Current assets 150 173 182 200 Fixed assets At cost 1,070 1,264 1,486 1,740 Depreciation (300) (417) (554) (715) Net fixed assets 770 847 932 1,025 Total assets 1,000 1,215 1,314 1,434

Current liabilities 80 92 97 106 Debt 320 320 320 320 Stock 450 450 450 450 Accumulated retained earnings 150 350 447 558 Total liabilities and equity 1,000 1,208 1,314 1,434

Year 0 1 2 3

The model of section 3.2 includes cost of goods sold but not selling, general, and administrative (SG&A) expenses. Suppose that the firm has $200 of these expenses each year, irrespective of the level of sales. a. Change the model to accommodate this new assumption. Show the resulting profit and loss statements, balance sheets, free cash flows, and valuation. b. Create a data table in which you show the sensitivity of the equity value to the level of SG&A. Let SG&A vary from 0 to $500 per year.

Page 10: FM S 2012 HW5 Solution

Free cash flow calculationProfit after tax 249 155 178 Add back depreciation 117 137 161 Subtract increase in current assets (15) (17) (18)Add back increase in current liabilities 8 9 10 Subtract increase in fixed assets at cost (194) (222) (254)Add back after-tax interest on debt 19 19 19 Subtract after-tax interest on cash & mkt. securities (4) (3) (3)Free cash flow 181 79 92

Valuing the firmWeighted average cost of capital 20%

Year 0 1 2 3 FCF 181 79 92 Terminal valueTotal 181 79 92

NPV of row 61 894 <-- =NPV(B56,C61:G61)Add in initial (year 0) cash and mkt. securities 80Enterprise value 974Subtract out value of firm's debt today -320Equity value 654

Cash and marketable securities as negative debtNPV of row 61 = enterprise value 894Net year 0 debt -240 <-- =-B37+B28Equity value 654

Valuing the firm--using mid-year discountingWeighted average cost of capital 20%

Year 0 1 2 3 FCF 181 79 92 Terminal valueTotal 181 79 92

NPV of row 81 1,005 <-- =NPV(B76,C81:G81)*(1+B76)Add in initial (year 0) cash and mkt. securities 80Enterprise value 1,085Subtract out value of firm's debt today -320Equity value 765

765 #VALUE!Data table: Value as function 0 765

of SG&A 50 765100 765

0 100 200 300 400 500 6000

200

400

600

800

1,000

Effect of SG&A on Equity Value

SG&A

Valu

e

Page 11: FM S 2012 HW5 Solution

150 765200 765250 765300 765350 765400 765450 765500 765550 765600 765

Data table: Value as function 765 0% 3% 6%of SG&A and sales growth 0 765 765 765

50 765 765 765100 765 765 765150 765 765 765200 765 765 765250 765 765 765300 765 765 765350 765 765 765400 765 765 765450 765 765 765500 765 765 765550 765 765 765600 765 765 765

0 100 200 300 400 500 6000

200

400

600

800

1,000

Effect of SG&A on Equity Value

SG&A

Valu

e

Page 12: FM S 2012 HW5 Solution

4 5

1,464 1,611 (732) (805) (200) (200) (32) (32) 17 18 (189) (220) 329 372 (127) (144) 202 228 (76) (86) 126 129

224 231 220 242

2,031 2,364 (904) (1,124) 1,127 1,240 1,571 1,712

117 129 320 320 450 450 684 813 1,571 1,712

4 5

The model of section 3.2 includes cost of goods sold but not selling, general, and administrative (SG&A) expenses. Suppose that the firm has $200 of these expenses each year, irrespective of the level of sales. a. Change the model to accommodate this new assumption. Show the resulting profit and loss statements, balance sheets, free cash flows, and valuation. b. Create a data table in which you show the sensitivity of the equity value to the level of SG&A. Let SG&A vary from 0 to $500 per year.

Page 13: FM S 2012 HW5 Solution

202 228 189 220 (20) (22)11 12

(291) (333)19 19 (3) (3)

106 121

4 5 106 121

1,331 <-- =G59*(1+B3)/(B56-B3)106 1,452

4 5 106 121

1,191 <-- =G72*(1+B3)/(B69-B3)106 1,312

0 100 200 300 400 500 6000

200

400

600

800

1,000

Effect of SG&A on Equity Value

SG&A

Valu

e

Page 14: FM S 2012 HW5 Solution

9% 12% 15%765 765 765765 765 765765 765 765765 765 765765 765 765765 765 765765 765 765765 765 765765 765 765765 765 765765 765 765765 765 765765 765 765

0 100 200 300 400 500 6000

200

400

600

800

1,000

Effect of SG&A on Equity Value

SG&A

Valu

e

Page 15: FM S 2012 HW5 Solution

EXERCISE 3

Sales growth 10%Current assets/Sales 15%Current liabilities/Sales 8%Fixed assets at cost/Sales 100%Costs of goods sold/Sales 50%Depreciation rate 10%Interest rate on debt 10.00%Interest paid on cash & marketable securities 8.00%Tax rate 40%Dividend payout ratio 40%

Year 0 1 2Income statementSales 1,000 1,160 1,100 Costs of goods sold (500) (580) (550)Interest payments on debt (32) (32) (32)Interest earned on cash & marketable securities 6 (14) (39)Depreciation (100) (104) (105)Profit before tax 374 350 374 Taxes (150) (140) (151)Profit after tax 225 210 223 Dividends (90) (94) (99)Retained earnings 135 116 125

Balance sheetCash and marketable securities 80 (438) (525)Current assets 150 174 165 Fixed assets At cost 1,070 1,000 1,100 Depreciation (300) (404) (509) Net fixed assets 770 1,404 1,609 Total assets 1,000 1,140 1,248

Current liabilities 80 93 88 Debt 320 320 320 Stock 450 450 450 Accumulated retained earnings 150 266 390 Total liabilities and equity 1,000 1,116 1,248

Year 0 1 2 Free cash flow calculationProfit after tax 210 223 Add back depreciation 104 105 Subtract increase in current assets 0 (15)Add back increase in current liabilities 0 8 Subtract increase in fixed assets at cost 70 (100)

The model of section 3.2 includes cost of goods sold but not selling, general, and administrative (SG&A) expenses. Suppose that the firm has $200 of these expenses each year, irrespective of the level of sales. a. Change the model to accommodate this new assumption. Show the resulting profit and loss statements, balance sheets, free cash flows, and valuation. b. Create a data table in which you show the sensitivity of the equity value to the level of SG&A. Let SG&A vary from 0 to $500 per year.

Page 16: FM S 2012 HW5 Solution

Add back after-tax interest on debt 19 19 Subtract after-tax interest on cash & mkt. securities 8 21 Free cash flow 410 262

Valuing the firmWeighted average cost of capital 20%

Year 0 1 2 FCF 410 262 Terminal valueTotal 410 262

NPV of row 61 2,493 #VALUE!Add in initial (year 0) cash and mkt. securities 80Enterprise value 2,573Subtract out value of firm's debt today -320Equity value 2,253

Cash and marketable securities as negative debtNPV of row 61 = enterprise value 2,493Net year 0 debt -240 #VALUE!Equity value 2,253

Valuing the firm--using half-year discountingWeighted average cost of capital 26%

Year 0 1 2 FCF 410 262 Terminal valueTotal 410 262

NPV of row 81 3,045 #VALUE!Add in initial (year 0) cash and mkt. securities 80Enterprise value 3,125Subtract out value of firm's debt today -320Equity value 2,805

Growth 2,805 #VALUE!0% 2,8052% 2,8054% 2,8056% 2,8058% 2,805

10% 2,80512% 2,80514% 2,80516% 2,805

0% 2% 4% 6% 8% 10% 12% 14% 16% 18%0

5001,0001,5002,0002,5003,000

Sales Growth and Equity Value

Page 17: FM S 2012 HW5 Solution

#VALUE!

WACC 2,805.27 10% 12%

0% nmf 2,805.27 growth rate of sales 2% nmf 2,805.27

4% nmf 2,805.27 6% nmf 2,805.27 8% nmf 2,805.27

10% 2,805.27 2,805.27 12% 2,805.27 2,805.27 14% 2,805.27 2,805.27 16% 2,805.27 2,805.27

Page 18: FM S 2012 HW5 Solution

3 4 5

1,210 1,331 1,464 (605) (666) (732) (32) (32) (32) (46) (54) (63) (116) (127) (140) 412 452 497 (167) (184) (203) 245 268 294 (109) (120) (132) 136 148 162

(622) (731) (851) 182 200 220

1,210 1,331 1,464 (624) (751) (891) 1,834 2,082 2,355 1,393 1,551 1,724

97 106 117 320 320 320 450 450 450 526 675 837 1,393 1,551 1,724

3 4 5

245 268 294 116 127 140 (17) (18) (20)

9 10 11 (110) (121) (133)

The model of section 3.2 includes cost of goods sold but not selling, general, and administrative (SG&A) expenses. Suppose that the firm has $200 of these expenses each year, irrespective of the level of sales. a. Change the model to accommodate this new assumption. Show the resulting profit and loss statements, balance sheets, free cash flows, and valuation. b. Create a data table in which you show the sensitivity of the equity value to the level of SG&A. Let SG&A vary from 0 to $500 per

Page 19: FM S 2012 HW5 Solution

19 19 19 25 28 32

286 313 343

3 4 5 286 313 343

3,769 #VALUE!286 313 4,111

3 4 5 286 313 343

3,880 #VALUE!286 313 4,222

0% 2% 4% 6% 8% 10% 12% 14% 16% 18%0

5001,0001,5002,0002,5003,000

Sales Growth and Equity Value

Page 20: FM S 2012 HW5 Solution

14% 16% 18% 20% 22% 24% 26% 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27 2,805.27

Page 21: FM S 2012 HW5 Solution

Sales growth 10%Current assets/Sales 15%Current liabilities/Sales 8%Costs of goods sold/Sales 50%Depreciation rate 10%Interest rate on debt 10.00%Interest paid on cash & marketable securities 8.00%Tax rate 40%Dividend payout ratio 40%

Year 0 1 2 3Income statementSales 1,000 1,100 1,210 1,331 Costs of goods sold (500) (550) (605) (666)Interest payments on debt (32) (32) (32) (32)Interest earned on cash & marketable securities 6 15 31 47 Depreciation (100) (109) (115) (126)Profit before tax 374 425 489 554 Taxes (150) (170) (196) (222)Profit after tax 224 255 293 332 Dividends (90) (102) (117) (133)Retained earnings 135 153 176 199

Balance sheetCash and marketable securities 80 304 479 688 Current assets 150 165 182 200 Fixed assets At cost 1,070 1,100 1,209 1,318 Depreciation (300) (409) (524) (650) Net fixed assets 770 692 685 668 Total assets 1,000 1,161 1,346 1,555

Current liabilities 80 88 97 106 Debt 320 320 320 320 Stock 450 450 450 450 Accumulated retained earnings 150 303 479 678 Total liabilities and equity 1,000 1,161 1,346 1,555

Year 0 1 2 3 Free cash flow calculationProfit after tax 255 293 332 Add back depreciation 109 115 126 Subtract increase in current assets (15) (17) (18)Add back increase in current liabilities 8 9 10 Subtract increase in fixed assets at cost (30) (109) (109)Add back after-tax interest on debt 19 19 19

EXERCISE 4--ASSETS AT COST GIVEN BY A STEP FUNCTION

Referring again to the model of section 3.2, suppose that the fixed assets at cost follow the following step

function:Incorporate this function into the model.

Page 22: FM S 2012 HW5 Solution

Subtract after-tax interest on cash & mkt. securities (9) (19) (28)Free cash flow 336 292 332

Valuing the firmWeighted average cost of capital 20%

Year 0 1 2 3 FCF 336 292 332 Terminal valueTotal 336 292 332

NPV of row 61 2,858 <-- =NPV(B56,C61:G61)Add in initial (year 0) cash and mkt. securities 80Enterprise value 2,938Subtract out value of firm's debt today -320Equity value 2,618

Cash and marketable securities as negative debtNPV of row 61 = enterprise value 2,858Net year 0 debt -240 <-- =-B37+B28Equity value 2,618

Valuing the firm--using half-year discountingWeighted average cost of capital 20%

Year 0 1 2 3 FCF 336 292 332 Terminal valueTotal 336 292 332

NPV of row 81 3,430 <-- =NPV(B76,C81:G81)*(1+B76)Add in initial (year 0) cash and mkt. securities 80Enterprise value 3,510Subtract out value of firm's debt today -320Equity value 3,190

Page 23: FM S 2012 HW5 Solution

4 5

1,464 1,611 (732) (805) (32) (32) 65 85 (137) (149) 627 710 (251) (284) 376 426 (151) (170) 226 255

928 1,205 220 242

1,431 1,548 #VALUE! (788) (937) 644 612 1,791 2,058

117 129 320 320 450 450 904 1,160 1,791 2,058

4 5

376 426 137 149 (20) (22)11 12

(113) (117)19 19

Referring again to the model of section 3.2, suppose that the fixed assets at cost follow the following step

function:Incorporate this function into the model.

Page 24: FM S 2012 HW5 Solution

(39) (51)372 415

4 5 372 415

4,569 <-- =G59*(1+B3)/(B56-B3)372 4,984

4 5 372 415

4,569 <-- =G72*(1+B3)/(B69-B3)372 4,984

Page 25: FM S 2012 HW5 Solution

EXERCISE 5--MODELING DIVIDENDS ON A PER-SHARE BASISSales growth 20%Current assets/Sales 20%Current liabilities/Sales 8%Net fixed assets/Sales 80%Costs of goods sold/Sales 50%Depreciation rate 10%Interest rate on debt 10.00%Interest paid on cash and marketable securities 8.00%Tax rate 40%Year 1 dividend per share 0.25Number of shares 1,200Dividend annual growth rate 16%

Year 0 1 2 3Income statementSales 1,000 1,200 1,440 1,728 Costs of goods sold (600) (720) (864)Interest payments on debt (47) (68) (98)Interest earned on cash and marketable securities 3 - - Depreciation (124) (156) (194)Profit before tax 432 496 572 Taxes (173) (198) (229)Profit after tax 259 298 343 Dividends (300) (348) (404)Retained earnings (41) (50) (61)

Balance sheetCash and marketable securities 80 - - - Current assets 200 240 288 346 Fixed assets At cost 1,100 1,384 1,732 2,157 Depreciation (300) (424) (580) (774) Net fixed assets 800 960 1,152 1,382 Total assets 1,080 1,200 1,440 1,728

Current liabilities 80 96 115 138 Debt 400 545 816 1,142 Stock 450 450 450 450 Accumulated retained earnings 150 109 59 (2)Total liabilities and equity 1,080 1,200 1,440 1,728

Year 0 1 2 3 Free cash flow calculationProfit after tax 259 298 343 Add back depreciation 124 156 194 Subtract increase in current assets (40) (48) (58)Add back increase in current liabilities 16 19 23 Subtract increase in fixed assets at cost (284) (348) (425)Add back after-tax interest on debt 28 41 59 Subtract after-tax interest on cash and mkt. securities (2) 0 0 Free cash flow 101 118 137

Page 26: FM S 2012 HW5 Solution

Part b: Table: Debt/Equity (book values) ratio as a function of dividend growth rate Year 1 Year 2 Year 3

0.975 1.604 2.5480% 0.975 1.604 2.548

Dividend growth rate 2% 0.975 1.604 2.5484% 0.975 1.604 2.5486% 0.975 1.604 2.5488% 0.975 1.604 2.548

10% 0.975 1.604 2.54812% 0.975 1.604 2.54814% 0.975 1.604 2.54816% 0.975 1.604 2.54818% 0.975 1.604 2.548

Page 27: FM S 2012 HW5 Solution

EXERCISE 5--MODELING DIVIDENDS ON A PER-SHARE BASIS

4 5

2,074 2,488 (1,037) (1,244) (134) (176) - - (242) (299) 662 769 (265) (308) 397 461 (468) (543) #VALUE! (71) (82)

- - 415 498

2,675 3,306 (1,016) (1,315) 1,659 1,991 2,074 2,488

166 199 1,531 1,994 450 450 (73) (155) 2,074 2,488

4 5

397 461 242 299 (69) (83)28 33

(518) (631)80 106

0 0 159 186

5. Consider the model in section 3.7 (where debt is the plug). a. Suppose that the firm has 1200 shares and that it decides to pay, in year 1, a dividend per share of 25 cents. In addition, suppose that it wants this dividend per share to grow in subsequent years by 16 percent per year. Incorporate these changes into the pro forma model. b. Do a sensitivity analysis in which you show the effect on the debt/equity ratio of the nnual growth rate of dividends. Vary this rate from 0 percent to 18 percent, in steps of 2 percent. For this exercise, define debt as net debt (i.e., debt minus cash and marketable securities).

Page 28: FM S 2012 HW5 Solution

Table: Debt/Equity (book values) ratio as a function of dividend growth rate Year 4 Year 5

4.064 6.764 #VALUE!4.064 6.7644.064 6.7644.064 6.7644.064 6.7644.064 6.7644.064 6.7644.064 6.7644.064 6.7644.064 6.7644.064 6.764

Page 29: FM S 2012 HW5 Solution

EXERCISE 7--TERMINAL VALUE = DEBT + EQUITY AT BOOK VALUESales growth 10%Current assets/Sales 15%Current liabilities/Sales 8%Net fixed assets/Sales 77%Costs of goods sold/Sales 50%Depreciation rate 10%Interest rate on debt 10.00%Interest paid on cash & marketable securities 8.00%Tax rate 40%Dividend payout ratio 40%

Year 0 1 2 3Income statementSales 1,000 1,100 1,210 1,331 Costs of goods sold (500) (550) (605) (666)Interest payments on debt (32) (32) (32) (32)Interest earned on cash & marketable securities 6 9 14 20 Depreciation (100) (117) (137) (161)Profit before tax 374 410 450 492 Taxes (150) (164) (180) (197)Profit after tax 225 246 270 295 Dividends (90) (98) (108) (118)Retained earnings 135 148 162 177

Balance sheetCash and marketable securities 80 144 213 289 Current assets 150 165 182 200 Fixed assets At cost 1,070 1,264 1,486 1,740 Depreciation (300) (417) (554) (715) Net fixed assets 770 847 932 1,025 Total assets 1,000 1,156 1,326 1,513

Current liabilities 80 88 97 106 Debt 320 320 320 320 Stock 450 450 450 450 Accumulated retained earnings 150 298 460 637 Total liabilities and equity 1,000 1,156 1,326 1,513

Year 0 1 2 3 Free cash flow calculationProfit after tax 246 270 295 Add back depreciation 117 137 161 Subtract increase in current assets (15) (17) (18)Add back increase in current liabilities 8 9 10 Subtract increase in fixed assets at cost (194) (222) (254)Add back after-tax interest on debt 19 19 19 Subtract after-tax interest on cash & mkt. securities (5) (9) (12)Free cash flow 176 188 201

Valuing the firm

Page 30: FM S 2012 HW5 Solution

Weighted average cost of capital 20%

Year 0 1 2 3 FCF 176 188 201 Terminal valueTotal 176 188 201

NPV of row 61 1,317 #VALUE!Add in initial (year 0) cash and mkt. securities 80Enterprise value 1,397Subtract out value of firm's debt today -320Equity value 1,077

Cash and marketable securities as negative debtNPV of row 61 = enterprise value 1,317Net year 0 debt -240 #VALUE!Equity value 1,077

Valuing the firm--using mid-year discountingWeighted average cost of capital 20%

Year 0 1 2 3 FCF 176 188 201 Terminal valueTotal 176 188 201

NPV of row 81 1,580 <-- =NPV(B76,C81:G81)*(1+B76)Add in initial (year 0) cash and mkt. securities 80Enterprise value 1,660Subtract out value of firm's debt today -320Equity value 1,340

Growth 1,340 #VALUE!0% 1,0282% 1,1004% 1,1916% 1,3068% 1,461

10% 1,67712% 2,00214% 2,54316% 3,625

#VALUE! WACC 1,340.03 10% 12% 14%

0% 2,030.04 1,696.78 1,458.43 growth rate of sales 2% 2,458.87 1,970.59 1,644.72

0% 2% 4% 6% 8% 10% 12% 14% 16%0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000 Sales Growth and Equity Value

Page 31: FM S 2012 HW5 Solution

4% 3,173.58 2,381.29 1,905.52 6% 4,603.01 3,065.80 2,296.72 8% 8,891.30 4,434.82 2,948.73

10% nmf 8,541.87 4,252.74 12% nmf nmf 8,164.77 14% nmf nmf nmf 16% nmf nmf nmf

Page 32: FM S 2012 HW5 Solution

EXERCISE 7--TERMINAL VALUE = DEBT + EQUITY AT BOOK VALUE

4 5

1,464 1,611 (732) (805) (32) (32) 26 33 (189) (220) 538 587 (215) (235) 323 352 (129) (141) 194 211

371 459 220 242

2,031 2,364 (904) (1,124) 1,127 1,240 1,718 1,941

117 129 320 320 450 450 830 1,042 1,718 1,941

4 5

323 352 189 220 (20) (22)11 12

(291) (333)19 19

(16) (20)214 228

In the valuation exercise of section 3.4, the terminal value is calculated

using a Gordon dividend model on the cash flows. Replace this terminal

value by the year-5 book value of debt plus equity. In making this change,

you are essentially assuming that the book value correctly predicts the market value.7. In the valuation

exercise of section 3.4, the terminal value is calculated using a Gordon dividend model on the cash flows. Replace this terminal value by the

year-5 book value of debt plus equity.

Page 33: FM S 2012 HW5 Solution

4 5 214 228

1,812 #VALUE!214 2,040

4 5 214 228

1,812 #VALUE!214 2,040

16% 18% 20% 22% 24% 26% 1,279.41 1,139.96 1,028.23 936.67 860.24 795.47 1,411.68 1,236.67 1,100.37 991.18 901.71 827.04

0% 2% 4% 6% 8% 10% 12% 14% 16%0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000 Sales Growth and Equity Value

Page 34: FM S 2012 HW5 Solution

1,588.03 1,361.01 1,190.54 1,057.80 951.47 864.35 1,834.92 1,526.79 1,306.48 1,141.07 1,012.28 909.13 2,205.27 1,758.89 1,461.06 1,248.14 1,088.30 963.85 2,822.51 2,107.03 1,677.48 1,390.90 1,186.04 1,032.26 4,056.99 2,687.27 2,002.10 1,590.76 1,316.36 1,120.21 7,760.42 3,847.75 2,543.14 1,890.55 1,498.80 1,237.48 nmf 7,329.19 3,625.21 2,390.21 1,772.47 1,401.65

Page 35: FM S 2012 HW5 Solution

EXERCISE 8--THE EBITDA CALCULATIONS START IN ROW 53Sales growth 10%Current assets/Sales 15%Current liabilities/Sales 8%Net fixed assets/Sales 77%Costs of goods sold/Sales 50%Depreciation rate 10%Interest rate on debt 10.00%Interest paid on cash & marketable securities 8.00%Tax rate 40%Dividend payout ratio 40%

Year 0 1 2 3Income statementSales 1,000 1,100 1,210 1,331 Costs of goods sold (500) (550) (605) (666)Interest payments on debt (32) (32) (32) (32)Interest earned on cash & marketable securities 6 9 14 20 Depreciation (100) (117) (137) (161)Profit before tax 374 410 450 492 Taxes (150) (164) (180) (197)Profit after tax 225 246 270 295 Dividends (90) (98) (108) (118)Retained earnings 135 148 162 177

Balance sheetCash and marketable securities 80 144 213 289 Current assets 150 165 182 200 Fixed assets At cost 1,070 1,264 1,486 1,740 Depreciation (300) (417) (554) (715) Net fixed assets 770 847 932 1,025 Total assets 1,000 1,156 1,326 1,513

Current liabilities 80 88 97 106 Debt 320 320 320 320 Stock 450 450 450 450 Accumulated retained earnings 150 298 460 637 Total liabilities and equity 1,000 1,156 1,326 1,513

Year 0 1 2 3 Free cash flow calculationProfit after tax 246 270 295 Add back depreciation 117 137 161 Subtract increase in current assets (15) (17) (18)Add back increase in current liabilities 8 9 10 Subtract increase in fixed assets at cost (194) (222) (254)Add back after-tax interest on debt 19 19 19 Subtract after-tax interest on cash & mkt. securities (5) (9) (12)Free cash flow 176 188 201

EBITDA CalculationProfit before taxes 410 450 492

Page 36: FM S 2012 HW5 Solution

Add back depreciation 117 137 161 Add back net interest 23 18 12 EBITDA 550 605 666

Valuing the firmWeighted average cost of capital 20%EBITDA multiple for terminal value 6

Year 0 1 2 3 FCF 176 188 201 Terminal valueTotal 176 188 201

NPV of row 68 2,530 #VALUE!Add in initial (year 0) cash and mkt. securities 80Enterprise value 2,610Subtract out value of firm's debt today -320Equity value 2,290

Cash and marketable securities as negative debtNPV of row 61 = enterprise value 2,530Net year 0 debt -240 #VALUE!Equity value 2,290

Valuing the firm--using half-year discountingWeighted average cost of capital (WACC) 20%EBITDA multiple for terminal value 6

Year 0 1 2 3 FCF 176 188 201 Terminal valueTotal 176 188 201

NPV of row 89 3,036 #VALUE!Add in initial (year 0) cash and mkt. securities 80Enterprise value 3,116Subtract out value of firm's debt today -320Equity value 2,796

growth 2,796 #VALUE!6 2,7967 3,1858 3,5739 3,961

10 4,35011 4,73812 5,12613 5,51514 5,903

6 7 8 9 10 11 12 13 140

2,000

4,000

6,000

8,000

EBITDA Multiple and Equity Value

Page 37: FM S 2012 HW5 Solution

#VALUE!

WACC2,796 10% 12% 14%

Data table of equity value as function of 6 3,890 3,632 3,396 EBITDA Multiple 7 4,440 4,144 3,873

8 4,990 4,656 4,350 9 5,540 5,167 4,826

10 6,090 5,679 5,303 11 6,640 6,191 5,780 12 7,190 6,703 6,257 13 7,740 7,214 6,733 14 8,290 7,726 7,210

6 7 8 9 10 11 12 13 140

2,000

4,000

6,000

8,000

EBITDA Multiple and Equity Value

Page 38: FM S 2012 HW5 Solution

EXERCISE 8--THE EBITDA CALCULATIONS START IN ROW 53

4 5

1,464 1,611 (732) (805) (32) (32) 26 33 (189) (220) 538 587 (215) (235) 323 352 (129) (141) 194 211

371 459 220 242

2,031 2,364 (904) (1,124) 1,127 1,240 1,718 1,941

117 129 320 320 450 450 830 1,042 1,718 1,941

4 5

323 352 189 220 (20) (22)11 12

(291) (333)19 19

(16) (20)214 228

538 587

8. Repeat exercise 7, but this time replace the terminal value by an EBITDA ratio times year-5 anticipatedEBITDA. Show a graph of the equity value of the firm as a function of the assumed year-5 EBITDA ratio,varying this ratio from 6 to 14.

Page 39: FM S 2012 HW5 Solution

189 220 6 (1) 732 805

4 5 214 228

4,832 #VALUE!214 5,060

4 5 214 228

4,832 #VALUE!214 5,060

6 7 8 9 10 11 12 13 140

2,000

4,000

6,000

8,000

EBITDA Multiple and Equity Value

Page 40: FM S 2012 HW5 Solution

16% 18% 20% 22% 24% 26%3,179 2,980 2,796 2,627 2,471 2,326 3,624 3,395 3,185 2,991 2,811 2,646 4,069 3,811 3,573 3,354 3,152 2,965 4,513 4,226 3,961 3,718 3,493 3,285 4,958 4,641 4,350 4,081 3,833 3,604 5,403 5,057 4,738 4,445 4,174 3,924 5,848 5,472 5,126 4,808 4,515 4,243 6,292 5,887 5,515 5,172 4,855 4,563 6,737 6,303 5,903 5,535 5,196 4,882

6 7 8 9 10 11 12 13 140

2,000

4,000

6,000

8,000

EBITDA Multiple and Equity Value

Page 41: FM S 2012 HW5 Solution

EXERCISE 9 PROJECT FINANCESales growth 15%Current assets/Sales 15%Current liabilities/Sales 8%Costs of goods sold/Sales 55%Depreciation rate 10%Interest rate on debt 10.00%Interest paid on cash & marketable securities 8.00%Tax rate 40%Dividend payout ratio 0% <-- No dividends until all the debt is paid off

entered into the balance sheet and the interest is put into the profit and loss statement.Principal Debt Of which:at begin. payment

Year of year at end yr. Interest1 Err:523 52.76 Err:5232 167.24 52.76 16.72 3 131.21 52.76 13.12 4 91.57 52.76 9.16 5 47.96 Err:523 4.80

Year 0 1 2 3Income statementSales 1,150 1,323 1,521 Costs of goods sold (633) (727) (836)Interest payments on debt Err:523 Err:523 Err:523Interest earned on cash & marketable securities Err:522 Err:522 Err:523Depreciation (211) (233) (257)Profit before tax Err:523 Err:523 Err:523Taxes Err:523 Err:523 Err:523Profit after tax Err:523 Err:523 Err:523Dividends Err:523 Err:523 Err:523Retained earnings Err:523 Err:523 Err:523

Balance sheetCash and marketable securities - Err:522 Err:523 Err:523Current assets 200 173 198 228 Fixed assets At cost 2,000 2,211 2,443 2,700 Depreciation - (211) (443) (700) Net fixed assets 2,000 2,000 2,000 2,000 Total assets 2,200 Err:522 Err:523 Err:523

Current liabilities 100 92 106 122 Debt Err:523 Err:523 Err:523 Err:523Stock 1,100 1,100 1,100 1,100 Accumulated retained earnings - Err:523 Err:523 Err:523Total liabilities and equity Err:523 Err:522 Err:523 Err:523

FREE CASH FLOW CALCULATIONYear 0 1 2 3

Debt repayment table (essentially a loan table from Chapter 1): The principal amounts are

the plug: =C39-C28-C32

=B31-$B$7*(C30+B30)/2

Page 42: FM S 2012 HW5 Solution

Profit after tax Err:523 Err:523 Err:523Add back depreciation 211 233 257 Subtract increase in current assets 28 (26) (30)Add back increase in current liabilities (8) 14 16 Subtract increase in fixed assets at cost (211) (233) (257)Add back after-tax interest on debt Err:523 Err:523 Err:523Subtract after-tax interest on cash & mkt. securities Err:522 Err:522 Err:523Free cash flow Err:523 Err:523 Err:523

RETURN ON EQUITY (ROE)Year 0 1 2 3 Equity cash flow -1,100 Err:523 Err:523 Err:523RETURN ON EQUITY (ROE) Err:523 #VALUE!

Data table: ROE as a function of initial Err:523 #VALUE!equity investment 2,000 Err:523

1,800 Err:5231,600 Err:5231,400 Err:5231,200 Err:5231,000 Err:523

800 Err:523

600 Err:523400 Err:523200 Err:523

Note that the cash flow generated by depreciation equals the increase in fixed assets at cost.

020

040

060

080

01,0

001,2

001,4

001,6

001,8

002,0

000%

200%

400%

600%

800%

1000%

1200% ROE as a Function of Initial Equity Investment

Equity investment

RO

E

Page 43: FM S 2012 HW5 Solution

<-- No dividends until all the debt is paid off

Repaidprincipal 32.76 36.04 39.64 43.60

Err:523

4 5

1,749 2,011 (962) (1,106)

Err:523 Err:523 #VALUE!Err:523 Err:523

(284) (314)Err:523 Err:523Err:523 Err:523Err:523 Err:523Err:523 Err:523Err:523 Err:523

Err:523 Err:523 262 302

2,985 3,299 (985) (1,299) 2,000 2,000

Err:523 Err:523

140 161 Err:523 Err:523 #VALUE!

1,100 1,100 Err:523 Err:523Err:523 Err:523

4 5

In the project finance pro forma of section 3.9 it is assumed that the firm pays off its initial debt of 1,000 in equal installments of principal over five years. Change this assumption and assume instead that the firm pays off its debt in equal payments of interest and principal over five years.

Page 44: FM S 2012 HW5 Solution

Err:523 Err:523284 314 (34) (39)18 21

(284) (314)Err:523 Err:523Err:523 Err:523Err:523 Err:523

4 5 Err:523 Err:523 #VALUE!

020

040

060

080

01,0

001,2

001,4

001,6

001,8

002,0

000%

200%

400%

600%

800%

1000%

1200% ROE as a Function of Initial Equity Investment

Equity investment

RO

E

Page 45: FM S 2012 HW5 Solution

Sales growth 15%Current assets/Sales 15%Current liabilities/Sales 8%Costs of goods sold/Sales 55%Depreciation rate 10%Interest rate on debt 10.00%Interest paid on cash & marketable securities 8.00%Tax rate 40%Dividend payout ratio 0% <-- No dividends until all the debt is paid off

Year 0 1 2 3Income statementSales 1,150 1,323 1,521 Costs of goods sold (633) (727) (836)Interest payments on debt (100) (84) (66)Interest earned on cash & marketable securities 36 73 76 Depreciation (211) (233) (257)Profit before tax 243 352 438 Taxes (97) (139) (172)Profit after tax 146 213 266 Dividends - - - Retained earnings 146 213 266

Balance sheetCash and marketable securities - 902 922 976 Current assets 200 173 198 228 Fixed assets At cost 2,000 2,211 2,443 2,700 Depreciation - (211) (443) (700) Net fixed assets 2,000 2,000 2,000 2,000 Total assets 2,200 3,074 3,121 3,204

Current liabilities 100 92 106 122 Debt 1,000 836 656 458 Stock 1,100 200 2,000 2,000 Accumulated retained earnings - 146 359 624 Total liabilities and equity 2,200 3,074 3,121 3,204

FREE CASH FLOW CALCULATIONYear 0 1 2 3 Profit after tax 146 213 266 Add back depreciation 211 233 257 Subtract increase in current assets 28 (26) (30)Add back increase in current liabilities (8) 14 16 Subtract increase in fixed assets at cost (211) (233) (257)Add back after-tax interest on debt 100 84 66 Subtract after-tax interest on cash & mkt. securities (36) (73) (76)Free cash flow 230 211 241

EXERCISE 10 PROJECT FINANCEUses functions IPMT and PPMT

the plug: =C39-C28-C32

=B31-$B$7*(C30+B30)/2

Note that the cash flow generated by depreciation equals the increase in fixed assets at cost.

Page 46: FM S 2012 HW5 Solution

RETURN ON EQUITY (ROE)Year 0 1 2 3 Equity cash flow -200 - - - RETURN ON EQUITY (ROE) 10.89% #VALUE!

Data table: ROE as a function of initial 10.89% #VALUE!equity investment 2,000 10.89%

1,800 10.89%1,600 10.89%1,400 10.89%1,200 10.89%1,000 10.89%

800 10.89%

600 10.89%400 10.89%200 10.89%

Note that the cash flow generated by depreciation equals the increase in fixed assets at cost.

020

040

060

080

01,0

001,2

001,4

001,6

001,8

002,0

000%2%4%6%8%

10%12% ROE as a Function of Initial

Equity Investment

Equity investment

ROE

Page 47: FM S 2012 HW5 Solution

<-- No dividends until all the debt is paid off

4 5

1,749 2,011 (962) (1,106) (46) (24) #VALUE! 82 91 (284) (314) 539 658 (211) (257) 328 402 - - 328 402

1,070 1,213 262 302

2,985 3,299 (985) (1,299) 2,000 2,000 3,332 3,515

140 161 240 - #VALUE! 2,000 2,000 952 1,354 3,332 3,515

4 5 328 402 284 314 (34) (39)18 21

(284) (314)46 24

(82) (91)276 316

In the project finance pro forma of section 3.9 it is assumed that the firm pays off its initial debt of 1,000 in equal installments of principal over five years. Change this assumption and assume instead that the firm pays off its debt in equal payments of interest and principal over five years. Hint: You have to use the PMT function to find the annual payments; then set up a loan table (as in Chapter 1) to split the annual payments into an interest and repayment of principal.

Page 48: FM S 2012 HW5 Solution

4 5 - 3,354 #VALUE!

020

040

060

080

01,0

001,2

001,4

001,6

001,8

002,0

000%2%4%6%8%

10%12% ROE as a Function of Initial

Equity Investment

Equity investment

ROE