1. 2. 3. 4. 5 6. 7. 1. 2. 3. 4. 5 6. 7. 1. 2. 3. 1. 2.

33 1 33 20 = 13.4 33 13.4 = 46.4

9% 9% 7% 2 ( 1+ K2) f2 = 1 ( 34. ) ( 1+ K ) 1 7% 11.04%

n ( 1+ K ) = ( 1+ K )( 1+ f )( 1+ f ) Λ ( 1+ f ) ( 35. ) n 1 2 3 ( 1 + K n ) n fn = n ( + K ) ( 1 1 3.6 1 ) n 1 n

FV = PV + I = PV + 1 0 1 0 r ( PV ) = 0 PV ( 1 + 0 r )

FV 1 = 500 + 500 10% = 500( 1+ 10%) = 550( ) 0 1 500 550 FV = PV ( 1+ r)( 1+ r)( 1+ r) 3 0 = PV ( 1+ r) 3 = 500( 1+ 10%) = 665. 5( ) 0 3 0 1 2 3 500 665.5 FV3 = PV0 ( FV10%,3) = 500 1331. = 665. 50( )

PV 0 = FVn n ( 4. 3) ( 1+ r) r n 7% 8% 9% 10% 11% 12% 13% 1 1.070 1.080 1.090 1.100 1.110 1.120 1.130 2 1.145 1.166 1.188 1.210 1.232 1.254 1.277 3 1.225 1.260 1.295 1.331 1.368 1.405 1.443 4 1.311 1.360 1.412 1.464 1.518 1.574 1.630 5 1.403 1.469 1.539 1.611 1.685 1.762 1.842 6 1.501 1.587 1.677 1.772 1.870 1.974 2.082 7 1.606 1.714 1.828 1.949 2.076 2.211 2.353 8 1.718 1.851 1.993 2.144 2.305 2.476 2.658 9 1.838 1.999 2.172 2.358 2.558 2.773 3.004 10 1.967 2.157 2.367 2.594 2.839 3.106 3.359 PV0 = FVn ( PVr, n) ( 4. 4) 1 ( 1+ r) n 1 3 PV0 = FV3 3 = 6655. ( 11. ) = 500( ) ( 1+ 10%) PV = FV ( PV ) = 665. 5 0. 751 = 500( ) 0 3 10%,3 0 1 2 3 665.5 500

r n 7% 8% 9% 10% 11% 12% 13% 1 0.935 0.926 0.917 0.909 0.901 0.893 0.885 2 0.873 0.857 0.842 0.826 0.812 0.797 0.783 3 0.816 0.794 0.772 0.751 0.731 0.712 0.693 4 0.763 0.735 0.708 0.683 0.659 0.636 0.613 5 0.713 0.681 0.650 0.621 0.593 0.567 0.543 6 0.666 0.630 0.596 0.564 0.535 0.507 0.480 7 0.623 0.583 0.547 0.513 0.482 0.452 0.425 8 0.582 0.540 0.502 0.467 0.434 0.404 0.376 9 0.544 0.500 0.460 0.424 0.391 0.361 0.333 10 0.508 0.463 0.422 0.386 0.352 0.322 0.295 0 1 2 3 4 600 600 600 600.0 660. 0=600 (1+10%) 726.0=600 (1+10%) 798.6=600 (1+10%) FV =2784.6( )

n 1 t FVn = A ( 1 + r) ( 4. 5) t= 0 n ( 1+ r) 1 FVn = A r ( 4. 6) 4 ( FV 4 500 1 + 10%) 1 = 500 4 641 2784 6 10% =. =. ( ) ( 1+ ) n r 1 r FVn = A( FVA r, n) ( 4. 7) r n 7% 8% 9% 10% 11% 12% 13% 1 1.000 1.000 1.000 1.000 1.000 1.000 1.000 2 2.070 2.080 2.090 2.100 2.110 2.120 2.130 3 3.215 3.246 3.278 3.310 3.342 3.374 3.407 4 4.440 4.506 4.573 4.641 4.710 4.779 4.850 5 5.751 5.867 5.985 6.105 6.228 6.353 6.480 6 7.153 7.336 7.523 7.716 7.913 8.115 8.323 7 8.654 8.923 9.200 9.487 9.783 10.089 10.405 8 10.260 10.637 11.028 11.436 11.859 12.300 12.757 9 11.978 12.488 13.021 13.579 14.164 14.776 15.416 10 13.816 14.487 15.193 15.937 16.722 17.549 18.420

0 1 2 3 4 600 (1+10%) =545 600 (1+10%) =496 600 (1+10%) =451 600 (1+10%) =410 600 600 600 600 PV =1902( ) n 1 PV0 = A ( t 1 + r ) t= 1 n 1 [ 1 / ( 1 + r) ] = A ( 4. 8) r PV 0 = A( PVA r, n ) ( 4. 9) PV 0 = 600 317. = 1902( ) n r PV A 1 [ 1 / ( 1 + ) ] 0 = lim ( ) n r 1 = A ( 4. 10) r

r n 7% 8% 9% 10% 11% 12% 13% 1 0.935 0.926 0.917 0.909 0.901 0.893 0.885 2 1.808 1.783 1.759 1.736 1.713 1.690 1.668 3 2.624 2.577 2.531 2.487 2.444 2.402 2.361 4 3.387 3.312 3.240 3.170 3.102 3.037 2.974 5 4.100 3.993 3.890 3.791 3.696 3.605 3.517 6 4.767 4.623 4.486 4.355 4.231 4.111 3.998 7 5.389 5.206 5.033 4.868 4.172 4.564 4.423 8 5.971 5.747 5.535 5.335 5.146 4.968 4.799 9 6.515 6.247 5.995 5.759 5.537 5.328 5.132 9 6.515 6.247 5.535 5.759 5.537 5.328 5.132 10 7.024 6.710 6.418 6.415 5.889 5.650 5.426 2 FV 1 = 100 ( 1+ 012. / 2) = 112. 36( ) 2 FV 1 = 100 ( 1+ 0. 12 / 4) = 112. 55( ) 12 FV 1 = 100 ( 1+ 0. 12 / 12 = 112. 68( ) 112. 36 100 r E = = 12. 36% 100 rn mn FVn = PV ( 1 0 + m ) ( 4. 11)

FV = r 1 PV ( 1 + 0 m ) I = FV PV 1 1 0 r m = PV0 [( 1 + ) 1] m r m I PV0[( 1+ ) 1] 1 r m E = = PV PV 0 0 rn m re = ( 1 + ) 1 ( 4. 12) m m r m r re = lim[( 1 + ) 1] = e 1 ( 4. 13) m m r = 012. E e 1 = 11275. 1 = 12. 75% 5000 = A( PVA ) 10%,5 5000 5000 A = = = 1319( ) ( PVA ) 0. 2638 10%,5

r N m r ( 1 ) 12 N m + rem = ( 1 + ) m rn m/ 12 rem = ( 1 + ) 1 ( 4. 14) m 12n 1 [ 1/ ( 1+ rem) ] PV0 = A M ( 415. ) rem. / r EM = ( 1 + 0 12 2 12 ) 1 2 = 6 ( 1 + 0. 06) 1 = 0. 0097588

12 25 1 [ 1 / 1. 0097588] 10000 = A M 0. 0097588 = 10000 = A 96 9087 M (. ) A M = 10319. ( )

n I M V = B0 = t + n (5. 1) t= 1 ( 1+ Kb) ( 1+ Kb) = I( PVA ) + M( PV ) Kb, n Kb, n

120 120 B0 = 1 + 2 + Λ ( 1 + 0. 12) ( 1 + 012. ) 120 1000 + 25 + 25 ( 1 + 012. ) ( 1 + 0. 12) = 25 120 1000 t 25 t= 1 ( 1 + 0. 12) ( 1 + 012. ) = 1000 + K = K + Risk Pr emium( ) b RF Kb K = K + RF = K + + R 25 120 1000 B0 = t + 25 t= 1 ( 1+ 016. ) ( 1+ 016. ) = 120( PVA ) + 1000( PV ) = 75612. 16%,25 16%,25

25 120 1000 B0 = t + 25 t= 1 ( 1+ 0. 08 ) ( 1+ 0. 08 ) = 120( PVA ) + 1000( PV ) 8%,25 8%,25 = 1427

n Dt Pn P0 = t + n 2 t 1 1+ K 1+ K (5. ) ( ) ( ) = S S P 0 3 Dt P3 = t + ( 1 + K ) ( 1 + K ) t= 1 S D1 D2 D3 D4 = + 2 + 3 + ( 1 + KS) ( 1 + KS) ( 1 + KS) ( 1 + KS) 1 15. 2 20 = + 2 + 3 + 3 ( 1 + 01. ) ( 1+ 0. 1) ( 1 + 0. 1) ( 1 + 0. 1) = 18. 68( ) S 3 P 0 ( 1 + ) P 0 K S Dt = t (5. 3) ( + K ) t= 1 1 S 3

2 n D0( 1 + g) D0 ( 1 + g) D0 ( 1 + g) P0 = + 2 + Λ + n ( 1 + K ) ( 1+ K ) ( 1 + K ) = n t= 1 D 0 S ( 1 + g) ( 1 + K ) S D0 ( 1 + g) D1 P0 = K g K g S t t S S S (5. 4) (5. 5) 2 1 6%) P 0 = ( + = 35.33 12% 6% D = D ( 1 + 10%) = 2 ( 1 + 10%) = 2. 2 ( ) 1 0 D D 2 2 = D ( 1+ 10%) = 2 ( 1+ 10%) = 2. 42( ) 2 0 3 3 = D ( 1+ 10%) = 2 ( 1+ 10%) = 2. 66( ) 3 0 D = D ( 1 + 3%) = 2. 66 ( 1 + 3%) = 2. 74 ( ) 4 0 D 4 2 74 P3 = 22 85 K g =. =. ( ) 0. 15 0. 03 S

P 0 D1 D2 D3 P3 = + 2 + 3 + 1 + K ( 1+ K ) ( 1+ K ) ( 1+ K ) S S S S 2. 2 2. 42 = + 1 + 015. ( 1+ 015. ) 2052. 2. 66 + ( 1+ 015. ) 2 3 3 3 22. 85 + ( 1+ 015. ) 0 1 2 3 4 1.913 1.830 1.750 15. 024 P = 20. 52 0 2.2 2.42 2.66 2.74 2. 74 P 3 = = 22. 85 015. 0. 03

Μ n Dt Pn P0 = t + ( n t 1 1+ K ) ( = 1+ K ) S S

T p CF CF = t 0 t= 1 0 ( 61. ) 20 T p = 2 + = 2. 4 50

' 30. 580 T p = 2 + = 2. 8( ) 37. 565 0 1 2 3 4 5 6 7 8 B C -1000 400 300 300 200 200 200 200 200-1000 200 200 300 300 400 400 400 400 T P B = 3 ; T = 4. P C n CFt NPV = t CF ( 6. 2) t= ( 1 + r ) 0 1

400 400 400 400 0 1 2 3 4 1000 NPV = 1000 + 400 400 400 400 + 2 + 3 + 4 11. 11. 11. 11. = 267. 92( ) n CFt t = CF0 ( 6. 3) t= 1 ( 1+ IRR)

IRR = NPV r + 1 NPV + VPV r r 1 ( 2 1) ( 6. 4) 1 2 35. 48 IRR = 0. 2 + ( 35 48 + 2 52 0. 22 0. 2 ).. = 0. 2187 = 2187%. n CFt t PI = = 1 CF 0 400( PVA 10%,4 ) 1267. 92 PI = = = 1268. 1000 1000 ( 6. 5)

100 + 300 + 400 + 600 = 250 4 = 75( ) 2 1000 = = 500( ) 2 75 ARR = = 15% 500

1224 100 500 1000 G F 600 1200 100 1273 ( ) r(%) F G 0 5 10 15 20 25 376.0 267.9 173.1 89.8 13.9 52.8 627.0 403.2 214.7 57.2 78.5 194.6

E 216 / 0 1 2 3 4 5 6 7 8 1000 403 / H 0 1 2 3 4 5 6 7 8 2000 NPV = 1000 + 216( PVA ) = 241( ) NPV E H 8%,8 = 2000 + 403( PVA ) = 316( ) 8%,8 8 t 100 + 216( 1+ IRR ) = 0 t= 1 IRR 8 = 14% t 2000 + 403( 1+ IRR ) = 0 t= 1 IRR E H = 12% E H

NPV > NPV, IRR > IRR H E E H (H-E) 0 187 / 1000 NPV = 1000 + 187( PVA ) = 75( ). NPV > 0 H E 8%.8 H E NPV H E 8 t = 1000 + 187( 1+ IRR ) = 0 IRR t= 1 H E = 10% H E + + + +

+ + + + + ( ) CF CF CF IRR(%) NPV( ) (r=10%) J 4000 +2500 2500 25 400 1934 n n 1 CF ( 1+ ERR) = CF ( 1+ r) ( 6. 6) 0 t

( ) CF 1 CF CF 1+ 10% PI ( ) r=0% K -100 +200 182 1.82 82 L -1000 +15000 13636 1.36 3636 ( ) CF 1 CF CF 1+ 10% ( ) PI r=0% L-K -9900 +4800 13454 1.36 3554

16 / A-3 0 1 2 3 32 12 / B-6 0 1 2 3 4 5 6 42

NPVA 3 7. 792 NEAA 3 = = = 3133. ( ) PVA 2. 487 NEA B 6 10%,3 NPVB 6 10. 26 = = = 2. 356( ) PVA 4. 355 10%,6 NEAA > NEA 3 B 6 1 2 3 4 500 400 300 100

n I M B0 = t + n 1 t 1 1+ K 1+ K (5. ) ( ) ( ) = b b K = K ( 1 T) ( 7. 1) bt b n I M B0 f = t + n 7 2 ( t 1 1+ K ) ( = 1+ K (. ) ) b b 60 60 1000 1000 10 = + ( 1+ K / 2 ) ( 1+ K / 2 ) 60 t= 1 b K bt = 12. 12%(1 0. 33) = 8. 12% D p Pe = ( 7. 3) K p b

Dp Kp = ( 7. 4) P e D ' p Kp = ( 75. ) P f e K = K + β( K K ) ( 7. 6) S RF m RF KS β KS Dt P0 = ( t + ) t= 1 1 K S D1 P0 = K g D1 KS = + g P 0 S ( 7. 7)

K ' S D1 = g P f + 0 ( 7. 8) β K = K + β( K K ) S RE m RF = 11% + 0. 95( 18% 11%) = 17. 65% D K = 1 S P + g 0 175. = + 9% 25 = 16% K S = 13% + 4% = 17% 17. 65% + 16% + 17% K S = = 16. 88% 17% 3

WACC = W K n i= 1 i i ( 7. 9) K i W i =

K i Wi ( ) IRR(%) A 200 25 B 100 21 C 300 19 D 400 18 E 200 15 F 300 12

β

( ) ( ) ( ) IRR(%) A 75000 15629 8 13 B 100000 15528 10 9 C 50000 15775 4 D 25000 14792 2 12 E 50000 12858 6

160 100 60 60 40 20 20 10 10 80 50 30 33% 26.4 16.5 9.9 53.6 33.5 20.1 73.6 43.5 30.1 + NOCFt = ( R t OCt D t )( 1 T) + D t (8. 1)

- = = 0 1 2 1. 1.1 300 500 800 1.2 1000 1000 2. 650 650 3. 198 198 498 500 1650 2648

3 4 5 6 7 8 1. 2000 2000 2000 2000 2000 2000 2. 3.00 3.24 3.50 3.78 4.08 4.41 3. 6000 6480 6998.4 7558.3 8162.9 8816 4. 4900 5292 5717.4 6172.6 6666.4 7199.7 5. 100 100 100 100 100 100 6. 40 40 40 40 40 40 7. 125 125 125 125 125 125 8. 835 923 1018 1120.7 1231.5 1351.3 (3 4 5 6 7) 9. 275.6 304.6 335.9 369.8 406.4 445.9 10. 559.4 618.4 682.1 750.9 825.1 905.4 11. (5+6+7) 265 265 265 265 265 265 12. 824.4 883.4 947.1 1015.9 1090.1 1170.4 13. 52 56.2 60.7 65.5 70.7 14. (12-13) 772.4 827.2 886.4 950.4 1019.4 1170.4

n n NOCF NOCF NPV = t t = ( t= 1+ K ) ( 1+ i ) ( t= 1+ K ) 0 0 r 1+ K = ( 1+ K )( 1+ i) (8. 3) n r K K + i (8. 4) n r 0 1 2 3 4 5 6 7 8-498 -500-1650 772.4 827.2 886.4 950.4 1019.4 286 8 r=2 n -498-998 -2648-1875.6-1048.4-162 788.4 1807.8 466 6-498 -416.7-1145.7 447.0 398.9 356.3 318.3 284.5 665 0% -498-914.7-2060.4-1613.4-1214.5-858.2-539.9-255.4 410 t 162 5 + = 5. 2 950. 4 255 4 7 +. 665 7 = 7.. 4 2470. 7 = 12. 2060. 4

K = k p n i= 1 K i i ( 9. 1) P k P k W 0.30 60% 18.0% 0.40 20% 8.0% 0.30 20% 6.0% =1.00 K =20.0% N 0.30 25% 7.5% 0.40 15% 6.0% 0.30 5% 1.5% =1.00 K =15.0% n 2 σ = ( k i = k i) pi ( 9. 2) t= 1

K (%) K K (K K ) P (K K ) P W 60 40 1600 0.3 480 20 0 0.4 0 20 40 1600 0.3 480 K =20% N σ2=960 % σ=30.98% 25 10 100 0.3 30 15 0 0 0.4 0 5 10 100 0.3 30 K =15% σ2=60 % σ=7.75%6 K = W k + W k + Λ + W k ( 9. 3) p A A B B Z Z Kp = WA k A + WBk B + WC k C = 05. 18% + 0. 25 16% + 025. 20% = 18%

σ 2 2 2 2 σ = W σ + W σ + W W σ σ Corr( A, B) ( 9. 4) A 4 B B A B A A σ 2 2 σa, σ B σ σ ( Cov( A, B) = Corr( A, B) σ A σ B) K p = WW K W + WN K N = 0. 2 20% + 0. 8 15% = 16% 2 2 σ = 960, σ = 30. 98, σ = 60σ = 7. 75, W W N N 2 2 2 2 σ = W σ + W σ + 2W W σ σ Corr( W, N) p W W N N W N W N 2 2 = 0. 2 960 + 08. 60 + 0. 2 08. 3098. 7. 75 10. = 12. 4 σ σ

σ = W σ + W σ p W W N N σ = W σ + W σ 2 2 2 2 p W W N N σ = W σ W σ p W W N N Corr(W,N) +1.0 +0.5 +0.0 0.5 1.0 σ 12.40 10.47 8.77 6.20 0 N W 1 0.5 0 0.5 1 0 1 15.00% 7.75 7.75 7.75 7.75 7.75 0.1 0.9 15.50% 10.07 8.94 7.63 6.05 3.88 0.2 0.8 16.00% 12.4 10.74 8.77 6.2 0 0.3 0.7 16.50% 14.72 12.89 10.76 8.09 3.87 0.4 0.6 17.00% 17.04 15.36 13.24 10.84 7.74 0.5 0.5 17.50% 19.36 17.75 15.97 13.96 11.61 0.6 0.4 18.00% 21.69 20.32 18.84 17.25 15.49 0.7 0.3 18.50% 24.01 22.94 21.81 20.62 19.36 0.8 0.2 19.00% 26.33 25.59 24.83 24.05 23.23 0.9 0.1 19.50% 28.66 28.28 27.89 27.5 27.11 1 0 20.00% 30.98 30.98 30.98 30.98 30.98 σ

σ σ

R R 1 2 3 10% 20% 30% 20% 0-20% 0.4 0.4 0.2 A B 18% 4% 0. 56% 2.24%

σ α α K = αk + ( 1 α) K ( 10. 1) p i m K p

Ki Km σ 2 p = σ 2 m ( 1 α) 2 + σ 2 i α 2 + 2α( 1 α) Cov( m, i) ( 10. 2) σ 2 p σ m 2 σ 2 i α K p = Ki Km α ( 10. 3) α K K, σ σ, p m p m K p / α dk p Ki K m α σ / α = 0 = = 2 ( 10. 5) dσ ( Cov( m, i)) σ / σ p K m K m K = σ σ m m RF p m m ( 10. 6) Cov( m, i) Ki = K RF + ( K m K RF ) ( 10. 7 ) σ 2 m Cov( m, i) βi = 2 σ m

Cov( m, i) σi β = 2 = Corr( m, i) ( 10. 9) σ σ m m Km = K + K i RF = K + RF ( K K ) β i m RF ( K K ) ( K K ) m RF β i m RF Km

K i β = α + β K + ( 10. 10) m α β ε Ki Km K i dki β = = ( 1011. ) K m dkm 19 1 19 2 19 3 19 4 19 5 K (%) 39 14 28 40-6 K (%) 32-5 22 23 6 19 1 39 16 256 32 16.4 268.96 262.4 19 2 14 9 81 5 20.6 424.36 185.4 19 3 28 5 25 22 6.4 40.96 32 19 4 40 17 289 23 7.4 54.76 125.8 19 5 6 29 841 6 9.6 92.16 278.4 115 1492 78 881.2 884 23 15.6 σ 5 ( K K ) 2 t= 1 σ S = st s t 1 σ 2 σ m 5 2 ( Kmt Km) t i 2 1492 = = 373 5 1 8812. = 5 1 220. 3

Kst Ks Kmt Km Cov( s, m) 5 ( )( ) 884 = = t t 1 221 1 5 1 Cov( s, m) 221 βs = 2 = = 1. 0 σ 220. 3 m Corr s m Cov ( (, ) s, m ) 221 = = = 0. 77 σ σ ( 19. 31( 14. 84)) s α = K β K = 23 10. 15. 6 m s s m = 7. 4 K = 7. 4 + K s m β = n W β p i i t= 1 β ( 1012. ) β = W β + W β + W β + W β p A A B B C C D D = 0. 25 0. 8 + 0. 25 0. 8 + 0. 25 0. 8 + 0. 25 0. 8 = 0. 8 β p = 0. 25 15. + 0. 25 08. + 0. 25 08. + 025. 08. = 0975. β p = 01. 15. + 03. 08. + 03. 080.. 3 08. = 087.

β β β β

K = K + i( K K ) i RF m RF = 6% + 1. 2 0 = 6% K = K + β ( K K ) i RF i m RF = 6% + 12. 4% = 10. 8% K = K + β ( K K ) i RF i m RF = 6% + 12. 8% = 16. 6% KRF R S T U β 2.0 0.6 1.0 0.2

() β A B C D E F 90 110 60 130 70 40 500 0.6 1.2 0.7 1.8 0.9 2.5 β 18% 11% 15% 1.7 0.6 1.2

10% 5% 0 5% 10% 28.49 1300.21 538.54 219.25 855.11 474.27 410.30 410.30 410.30 600.67 35.74 345.74 791.52 480.20 281.47 NPV( )

( ) ( ) NPV( ) 0.25 0.50 0.25 1000 2000 3000 20000 30000 40000 NPV E(NPV)=727.94 NPV σ(npv)=2270.48 4225.18 410.30 2133.44 CV = σ( NPV) NPV E ( NPV) = 312.

Ki = K + β ( K K ) RF i m RF K s = 8% + 1. 2( 12% 8%) = 12. 8% ' K s ' K s = 8% + 138. ( 12% 8%) = 1352%. WACC = WdKd( 1 T) + WsKs = 0. 5( 10%)(1 0. 33) + 0. 5( 12. 8%) = 9. 75%

10.11% - 0.79(9.75%) (WACC) j = = 10. 95% 0. 3 β L = β µ [ 1+ ( 1 T)(D / S)] ( 14. 15) β β µ

ROA EBIT A = =

215000 27000 5 P CF ( ) Pi CF ( ) CF P 0.2 70000 0.2 120000 0.6 0.2 60000 30000 0.6 0.2 80000 20000 CFt CV = σ( ) E( CF ) t 0 1 2 3 4 5 6 10 40 50 100 150 100 150 100 150 150 100 100 50 20

( ) 0.3 0.4 0.3 (EBIT) 30000 240 60 120 60 40000 320 60 160 100 50000 400 60 200 140 σ( EBIT) A = 0. 3( 60 100) + 04. ( 100 100) + 0. 3( 140 100) 2 2 2 = 3098. ( ) FC ( ). TC = 60000 = 27 3% A 220000

0.3 0.4 0. 3 ( ) 30000 40000 50000 240 320 400 100 100 100 90 120 150 (EBIT) 50 100 150 σ FC 100000 ( ). TC = = 455% B 220000 σ σ Q * B * FC 100000 Q B = = = 20000( ) P V 8 3 * 60000 Q A = 15000( ) 8 4

DOL = EBIT / EBIT = ( 14. 1) Q / Q 30000-25% 40000 +25% 50000 60000-40% 100000 +40% 140000 40% DL = = 25% 16. Q( P V) DOL = = ( 14. 2) Q( P V) FC 320000 160000 DOL 320000 = = 1. 6 100000

/ 0% 20% 40% 0 6 12 30 (5 ) 24 (4 ) 18 (3 )

0.3 0.4 0.3,,, EBIT 6 10 14 I i=10% 0 0 0 EBT 6 10 14 T=40% 2.4 4 5.6 EAT 3.6 6 8.4 EPS 5 0.72 1.2 1.68 20%,, EBIT 6 10 14 I i=10%) 0.6 0.6 0.6 EBT 5.4 9.4 13.4 T=40% 2.16 3.76 5.36 EAT 3.24 5.64 8.04 EPS 0.81 1.41 2.01 (40% EBIT 6 10 14 I i=10%) 1.2 1.2 1.2 EBT 4.8 8.8 12.8 T=40% 1.92 3.52 5.12 EAT 2.88 5.28 7.68 EPS 0.96 1.76 2.56 (0 ) (20% ) (40 ) E(EPS) 1.20 1.41 1.76 σ(eps) 0.372 0.465 0.616 σ( EPS) E( EPS) 0.31 0.33 0.35

EPS / EPS DFL = = ( 14. 3) EBIT / EBIT DFL = 45. 45% 10 40% = 114. EBIT Q P V FC DFL = EBIT I = ( ) ( 14. 4) Q( P V) FC I DFL = 10 10 = 114. 10 1. 2 EPS EPS / EPS DCL = = Q / Q ( 14. 5) DCL = ( DOL)( DFL) ( 14. 6) Q ( P V) DCL = ( 14. 7) Q( P V FC I) 40% 45. 45% DCL = ( DOL)( DFL) = = 16. 114. = 182. 25% 40%

EBIT ( BEP = ) ( EBIT I)( 1 T) Dp EPS = ( 14. 8) N ( ) + * * ( EBIT I1 )( 1 T) ( EBIT I2 )( 1 T) = N N 1 * * ( EBIT 20)( 1 0. 4) ( EBIT 140)( 1 0. 4) 150 100 2

EBIC EBIT VL = = = Vu ( 14. 9) WACC K su

KSL = Ksu + ( Ksu Kd) D / S ( 1410. ) V = V + TD ( 14. 11) L u K = K + ( K K )( 1 T)( D / S) ( 14. 12) SL Su Su d

VL = Vu + TD( ) ( ) ( 1413. ) σ σ

KSL = K RF + β u ( K M K RF) + βu ( K M K RF)( 1 T)(D / S) ( 14. 14) β K = SL K RF β ( K K ) u M RF β ( K K )( 1 T)(D / S) u M RF K = K + β ( K K ) 14.14 SL RF L M RF K + β ( K K ) RF L M RF = K + β ( K K ) + β ( K K )( 1 T)(D / S) RF u M RF u M RF βl = βu[ 1 + ( 1 T)( D / S)] ( 14. 15) β β β β

( EBIT Kd D )( 1 T) S = K D1 EPS P0` = = K K s V = EBIT( T) S + L D = 1 WACC D WACC V K T) S = V K d (1 + s s L s β L

β

FCC EBIT T) = + + + (1

67

EBIT 4000000 D 2000000 D s 15% K d 10% N 0 600000 33%

1 2000 6000 2000 2000 2000 0 2 2000 5000 1667 2000 1333 0 3 2000 4000 1333 2000 667 0 4 2000 3000 1000 2000 0 0 5 2000 2000 667 1333 0 667 6 2000 1000 333 667 0 1333 7 2000 0 0 0 2000

50 50 50 50 50 50 50 50 100 100 100 100 50% 50% 50 150 50 50 150 50 50 50 200 200 100 100 75% 50%

PMT P ( 1+ = ni ) + P r ( 16. 1) n i = 8% = = 4% 2 2 10000 ( 1+ 6 4%) PMT = + 10000 55%. 6 = 2616.67 PMT p i i n ( 1+ ) = n ( 16. 2) ( 1+ i) 1

P i PMT = + i + 1 ( 16. 3) 1 ( 1 i) n PMT = [ P P ( P n n 1) ] i + ( 16. 4) N N C + C1X = C2X ( 16. 5) 200000 C = + 10000 10 C = 50 C 1 2 = 300 + 50

200000 + 10000 + 50X = ( 300 + 5) X 10 0 1 2 3 4 5 1. 1000 2. 50 50 50 50 50 3. 50 40% 20 20 20 20 20 4. 80 128 76 48 44 5. 100 6. 16 7. 1030 50 98 46 18 128 8. 747.1 6% 1. 275 275 275 275 275 2. 275 40% 110 110 110 110 110 3. 165 165 165 165 165 4. 736.7 6%

11

20 1000 10% 1000 = t + 20 789( ) t= 1 ( 1 + 013%). ( 1 + 013. )

P = 20 t= 1 0 I P t + ( 1+ 10%) ( 1 + 10%) 20 1000 5% 1000 = t + t= 1 ( 1 + 10%) ( 1 + 10%) = 425. 7 + 148 = 573. 7 20 20

=

1988 % 1989 % 5.7 5.0 15.4 14.8 15.8 15.1 3.2 1.1 40.1 36.0 5.7 8.1 8.0 13.8 12.2 2.4 25.9 24.3

200 600 100 400 800 200 900 1200 2000 1500 3000 2300 5000 5000

2000 1200 800 3000 1500 2300

( ) ( ) ( ) ICP = / 365 ACP = / 365 APP = / 365

A B C 300 400 600 700 600 400 1000 1000 1000 500 350 200 100 250 400 400 400 400 1000 1000 1000

A B C 1800 1800 1800 1260 1280 1300 300 300 300 120 160 240 150 200 300 250 200 100 200 150 100 + = + / 365

S Q J (. ) 191

C Q 2 ( 9. 2) Q 2 TC S Q J Q = + C ( 19. 3) 2 d( TC) S C = J ( ) + (. ) dq Q 2 19 4 2 d( TC) = 0 dq S C J * 2 =, Q * Q 2 * 2JS Q = ( 19. 5) C 2 250 3600 * EOQ = Q = = 90000 = 300( ) 20

Q Q Q/2 ( ) C S/Q (S/Q) J TC 2 ( 1 2 3 4 5 6 = 3 + 5 100 50 1000 36.0 9000 10000 200 100 2000 18.0 4500 6500 300 150 3000 12.0 3000 6000 400 200 4000 9.0 2250 6250 500 250 5000 7.2 1800 6800 600 300 6000 6.0 1500 7500

2% 360 = 36. 7% 98% 30 10

CF0 = ( VC)(S)( ACP / 365) ( 19. 7) CFt = [ S( 1 VC) S( BD) S( R)( D)]( 1 T) ( 19. 8) CF = VC(S / 365) ACP VC(S / 365) ACP ( 19. 9) 0 N N 0 0 CF = {[ S ( 1 VC) S ( BD ) S R D ] t N N N N N N S ( 1 VC) S ( BD ) S R D ]}( 1 T) 0 0 0 0 0 0 t VF NPV = VF0 ( 1911. ) K

1/10,n/30 2/10,n/4U ACP 16 15.5 S 2800 3000 BD 2 3 R 55 60 VF = VC[(S / 365) ACP (S / 365) ACP ] + I 0 N N 0 0 CF 0 = 0. 6[( 3000( 365) 1255. ( 2800 / 365) 16] + 4 = 2. 7945+ 4 = 67945. ( ) CF = { S [( 1 VC) BD R D ] t N N N N S [( 1 VC) BD R D ]}( 1 T) 0 0 0 0 = { 3000[( 1 0. 6) 3% ( 2%)(60%)] 2800[( 1 0. 6) 2% ( 1%)(55%)]} ( 1 0. 33) = ( 1074 1048. 6)( 0. 67) = 17. 018( ) CFt VPV = CF0 K 17. 018 = 10% 6. 7945 = 163. 38855( )

5 6 7 8 9 10 11 12 26000 28000 30000 35000 35000 30000 28000 26000 5200 5600 6000 7000 7000 6000 5600 5200 3120 3360 3600 4200 4200 3600 3360 3120 ( 60%) (90% 2808 3204 3240 3780 3780 3240 3024 (10% 312 336 360 420 420 360 2400 2800 2800 2400 2240 2080 (40%) 1500 1800 5736 6376 8440 6600 5900 7264

6 7 8 9 10 11 12 50% 2800 3000 3500 3500 3000 2800 2600 90% 2520 2700 3150 3150 2700 2520 2340 2520 2700 3150 3150 2700 2520 300 350 350 300 280 260 10% 720 840 840 720 672 624 ( 12% 1000 1100 1200 1000 980 950 240 300 400 240 220 200 1000 1000 1000 1000 1000 1000 5780 6290 6940 6410 5852 5554 7 8 9 10 11 12 5736 6376 8440 6600 5900 7264 5780 6290 6940 6410 5852 5554 44 86 1500 190 48 1710 1450 1406 1492 2992 3182 3230 1406 1492 2992 3182 3230 4940 2000 2000 2000 2000 2000 2000 594508 992 1182 1230 2940

C r ( 19. 12) 2 C 2 T C b ( 19. 13 ) TC = C T r 2 + C b ( 19. 14) d( TC) r T = ( 2 ) b dc 2 C d ( TC ) = 0 dc T b * C = 2 ( 1915. ) r 2 600000 100 C * = = 109544. 5( ) 12% 12

600000 = 5. 48 109544. 4

( )

(CF ) (K) (CF ) 1 2 3 300000 600000 900000 12% 15% 18% 50000 110000 175000

360 ( 201. ) 100% 2% 360 = = 36. 7% 100% 2% 30 10

K n 012. 4 = ( 1 + ) 1 = ( 1 + ) 1 = 12. 55% ( 20. 2) n 4 I = = 1200 = 13. 64% ( 20. 3) M 1 1000 1200 I n ( 1 + ) 1. 0 ( 20. 4) M I

I n = ( 1+ ) 10. M I 300 4 = ( 1+ ) 10. = 12. 96% 10000 300 2( 360 / T) I ( 205. ) M( n + 1) 2( 360 / T) I 2( 360 / 90) 1200 = = 19. 2% M( n + 1) 10000( 4 + 1) I 12500 12% = = 15% ( 20. 6) M( 10. B) 12500( 10. 20%)

19 2 19 1 19 0 5 4659 2623 2464 6 918 631 433 7 3740 1992 2031 8 145 50 25 3885 2042 2056 ( ) 4951 2727 2450 9 330 230 250 10 149 67 91 11 318 112 92 797 409 433 12 1450 647 628 1450 647 628 13 1785 1248 1000 14 516 206 206 15 404 217 184 2704 1389 4950.99 2727 2450

1065 = = = 1. 34 797 = 2. 0

= = 1065 332 797 0 91. 1.1 = 10 = = 5667 332 17

373 = = = 24( ) / 360 5667 / 360 30 5667 = = 15. 3740 2.5 5667 = = = 11. 4950 = 1.4

= = 2246 4950 45% = 45 712. 65 = = 6. 9 102. 9 7 + + 537 = = = 9. 5% 5667 7 537 = = = 1085%. 4950 ` 9.8

537 = = = 19. 86% 2704 = 17.8

19 2 19 1 19 0 100 100 100 75.1-78.5-79.9 24.9 2l 5 22.1 12.3 11.3 12.7 12.6 10.2 9.5 1.8 0.8 0.8 10.8 9.5 8.7 30 3.2 2.8 2.6 7.5 6.6 6.1

( ) 208 260 373 466.3 153 191.2 332 41 5 1066 1332.5 ( ) 3885 4856.3 ( ) 4951 6188.8 ( ) 330 467 583.8 797 1450 ( ) 1785 516 580.4 404 751.5 2704 ( ) 4951

1992 1991 1990 1 27394 164.56 11.810 2 309.61 273.96 74.27 3 99.26 63.97 287.73 4 4.15 5 1992 1991 1990 83.71 69.15 82.97 5803 94.38 141.53 141.74 163.53 227.50 824.55 666.02 711.75 6 205.00 2.39 2.39 7 916.90 567. 54 408.78 277.88 207.00 152.22 8 639.02 360.54 256.56 9 98.71 71.05 83.37 10 737.73 431.59 339.93 11 11. 64 9. 00 1300 954. 37 442.98 355.32 1778.92 1109.00 1067.07 1992 1991 1990 12 3000 13 90.00 14 12.39 102.19 103.32 15 30.19 239.66 307.83 16 117.92 121.98 104.90 250.50 493.3 516.5 17 200.0 9000 90.00 18 44.8 44.8 51.2 244.8 134.8 141.2 19 950 950.00 20 161.50 1992 1991 1990 (21) 172.54 1284.04 480.79 410.00 177.92 1109.00 1067.07

1992 1991 1990 1218.05 1207.66 993.95 : (768.82) (751.25) (457.03) 449.23 456.41 536.92 (1) 12.18 12.08 9.57 (2) 13.65 10.01 9.57 (3) 70.88 54.78 93.50 (4) 85.70 84.97 69.93 (182.41) (161.84) (182.57) 266.82 294.57 354.35 (1) 34.76 (2) 64.53 (3) 27.95 2.67 24.64 127.24 2.67 24.64 (1) 10.00 10.00 (2) 24.53 11.55 11.66 (34.53) (21.55) (11.66) 359.53 275.69 367.33 : (22.42) (2.30) 337.11 273.39 367.3 (1) 45.19 41.48 (2) 337.11 228.20 315.85 (3) (50.57) (124.03) (177.74) 286.54 149.36 189.59 0.30 0.12