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ɞɨɥɝɨɜɵɟ ɨɛɹɡɚɬɟɥɶɫɬɜɚ, ɤɨɬɨɪɵɟ ɢɯ ɜɥɚɞɟɥɶɰɵ ɯɨɬɹɬ ɢɫɩɨɥɶɡɨɜɚɬɶ ɧɚ
ɩɨɤɪɵɬɢɟ ɧɟɩɪɟɞɜɢɞɟɧɧɵɯ ɪɚɫɯɨɞɨɜ ɜ ɛɭɞɭɳɟɦ. ɉɟɧɫɢɨɧɧɵɟ ɮɨɧɞɵ
ɨɛɟɫɩɟɱɢɜɚɸɬ ɫɜɨɢɯ ɤɥɢɟɧɬɨɜ ɞɟɧɟɠɧɵɦɢ ɫɪɟɞɫɬɜɚɦɢ ɧɚ ɩɟɪɢɨɞ ɩɨɫɥɟ ɜɵɯɨɞɚ ɧɚ ɩɟɧɫɢɸ.
Ⱥɧɧɭɢɬɟɬ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɫ ɩɨɦɨɳɶɸ ɤɨɷɮɮɢɰɢɟɧɬɚ ɚɧɧɭɢɬɟɬɚ
(k
), ɤɨɬɨɪɵɣ ɪɚɫɩɪɟɞɟɥɹɟɬ ɤɪɟɞɢɬ Ʉ ɧɚ ɪɚɜɧɵɟ ɫɭɦɦɵ ɩɥɚɬɟɠɟɣ ɫ
ɚɧ
ɭɱɟɬɨɦ ɩɪɨɰɟɧɬɚ ɧɚ t ɥɟɬ, ɬ.ɟ. ɩɪɟɜɪɚɳɚɟɬ «ɪɚɡɨɜɵɣ ɩɥɚɬɟɠ ɫɟɣɱɚɫ» ɜ
ɩɥɚɬɟɠɧɵɣ ɪɹɞ:
t
(1 )
rr
t
r
(1 ) 1
ɝɞɟ Ʉ
— ɫɭɦɦɚ ɪɚɡɨɜɵɯ ɜɵɩɥɚɬ ɞɟɧɟɠɧɵɯ ɫɪɟɞɫɬɜ, ɬɵɫ. ɪɭɛ.;
ɪɩ
Ʉ
— ɫɭɦɦɚ ɤɪɟɞɢɬɚ, ɬɵɫ. ɪɭɛ.:
r — ɝɨɞɨɜɚɹ ɩɪɨɰɟɧɬɧɚɹ ɫɬɚɜɤɚ.
ɄɄ ,
ɪɩ
ȼɵɪɚɠɟɧɢɟ
t
(1 )
rr
kɚɧ =
t
r
(1 ) 1
ɧɚɡɵɜɚɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɚɧɧɭɢɬɟɬɚ.
ɉɪɢɦɟɪ. Ʉɨɦɦɟɪɱɟɫɤɢɣ ɛɚɧɤ ɩɪɟɞɨɫɬɚɜɢɥ ɤɥɢɟɧɬɭ ɤɪɟɞɢɬ ɧɚ 3 ɝɨɞɚ ɜ ɪɚɡɦɟɪɟ 600 ɬɵɫ. ɪɭɛ. ɩɨɞ 16% ɝɨɞɨɜɵɯ, ɧɚɱɢɫɥɹɟɦɵɯ ɩɨ ɫɯɟɦɟ
ɫɥɨɠɧɵɯ ɩɪɨɰɟɧɬɨɜ ɧɚ ɧɟɩɨɝɚɲɟɧɧɵɣ ɨɫɬɚɬɨɤ. ɉɨ ɞɨɝɨɜɨɪɭ ɤɪɟɞɢɬ
ɜɨɡɜɪɚɳɚɟɬɫɹ ɪɚɜɧɵɦɢ ɫɭɦɦɚɦɢ ɜ ɤɨɧɰɟ ɤɚɠɞɨɝɨ ɝɨɞɚ (ɩɨɫɬɧɭɦɟɪɚɧɞɨ). Ɍɪɟɛɭɟɬɫɹ ɪɚɫɫɱɢɬɚɬɶ ɪɚɡɦɟɪ ɝɨɞɨɜɨɝɨ ɩɥɚɬɟɠɚ.
Ɋɟɲɟɧɢɟ.
3
Ʉ 600 ɬɵɫ.600ɬɵɫ. 0, 44 267, 4
ɪɩ
0,16(1 0,16)
3
(1 0 ,1 6) 1
ɬɵɫ. ɪɭɛ.
Ɉɩɥɚɬɚ ɩɨ ɡɚɤɥɸɱɟɧɧɵɦ ɫɞɟɥɤɚɦ ɦɨɠɟɬ ɩɪɟɞɭɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɪɚɡɨɜɵɣ ɩɥɚɬɟɠ, ɬɚɤ ɢ ɪɹɞ ɜɵɩɥɚɬ, ɪɚɫɩɪɟɞɟɥɟɧɧɵɯ ɜɨ ɜɪɟɦɟɧɢ: ɜɵɩɥɚɬɭ
ɚɪɟɧɞɧɨɣ ɩɥɚɬɵ, ɜɵɩɥɚɬɵ ɡɚ ɩɪɢɨɛɪɟɬɟɧɧɨɟ ɢɦɭɳɟɫɬɜɨ ɜ ɪɚɫɫɪɨɱɤɭ,
ɢɧɜɟɫɬɢɪɨɜɚɧɢɟ ɫɪɟɞɫɬɜ ɜ ɪɚɡɥɢɱɧɵɟ ɩɪɨɝɪɚɦɦɵ ɢ ɬ.ɩ. ȼ ɛɨɥɶɲɢɧɫɬɜɟ
ɫɥɭɱɚɟɜ ɩɥɚɬɟɠɢ ɩɪɨɢɡɜɨɞɹɬɫɹ ɱɟɪɟɡ ɨɩɪɟɞɟɥɟɧɧɵɟ ɩɪɨɦɟɠɭɬɤɢ ɜɪɟɦɟɧɢ, ɬ.ɟ. ɨɛɪɚɡɭɟɬɫɹ ɩɨɬɨɤ ɩɥɚɬɟɠɟɣ.
Ɉɛɨɛɳɚɸɳɢɦɢ ɩɨɤɚɡɚɬɟɥɹɦɢ
ɪɟɧɬɵ ɹɜɥɹɸɬɫɹ ɧɚɪɚɳɟɧɧɚɹ ɢ ɫɨ-
ɜɪɟɦɟɧɧɚɹ (ɬɟɤɭɳɚɹ) ɫɭɦɦɚ ɩɨɬɨɤɚ ɩɥɚɬɟɠɟɣ.
ɇɚɪɚɳɟɧɧɚɹ ɫɭɦɦɚ — ɷɬɨ ɫɭɦɦɚ ɜɫɟɯ ɱɥɟɧɨɜ ɩɨɬɨɤɚ ɩɥɚɬɟɠɟɣ ɫ
ɧɚɱɢɫɥɟɧɧɵɦɢ ɧɚ ɧɢɯ ɩɪɨɰɟɧɬɚɦɢ ɧɚ ɤɨɧɟɰ ɫɪɨɤɚ, ɬ.ɟ. ɧɚ ɞɚɬɭ ɩɨ-
131
ɫɥɟɞɧɟɣ ɜɵɩɥɚɬɵ. ɇɚɪɚɳɟɧɧɚɹ ɫɭɦɦɚ ɞɟɧɟɠɧɵɯ ɫɪɟɞɫɬɜ, ɜɧɨɫɢɦɵɯ
ɱɟɪɟɡ ɪɚɜɧɵɟ ɩɪɨɦɟɠɭɬɤɢ ɜɪɟɦɟɧɢ ɜ ɬɟɱɟɧɢɟ ɜɫɟɝɨ ɫɪɨɤɚ ɪɟɧɬɵ
ɜɦɟɫɬɟ ɫ ɧɚɱɢɫɥɟɧɧɵɦɢ ɩɪɨɰɟɧɬɚɦɢ, ɩɨɤɚɡɵɜɚɟɬ ɛɭɞɭɳɭɸ ɫɬɨɢɦɨɫɬɶ ɤɚɩɢɬɚɥɚ.
ɋɨɜɪɟɦɟɧɧɚɹ (ɬɟɤɭɳɚɹ) ɫɭɦɦɚ ɩɨɬɨɤɚ ɩɥɚɬɟɠɟɣ — ɷɬɨ ɫɭɦɦɚ
ɜɫɟɯ ɟɝɨ ɱɥɟɧɨɜ, ɭɦɟɧɶɲɟɧɧɚɹ (ɞɢɫɤɨɧɬɢɪɨɜɚɧɧɚɹ) ɧɚ ɩɪɨɰɟɧɬɧɭɸ
ɫɬɚɜɤɭ ɡɚ ɨɩɪɟɞɟɥɟɧɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ, ɫɨɜɩɚɞɚɸɳɢɣ ɫ ɧɚɱɚɥɨɦ ɩɨ-
ɩɥɚɬɟɠɟɣ ɢɥɢ ɩɪɟɞɲɟɫɬɜɭɸɳɢɣ ɟɦɭ.
ɬɨɤɚ
ɇɚɪɚɳɟɧɧɚɹ ɫɭɦɦɚ ɪɟɧɬɵ
ɇɚ ɜɧɨɫɢɦɵɟ ɩɥɚɬɟɠɢ ɜ ɬɟɱɟɧɢɟ ɜɫɟɝɨ ɫɪɨɤɚ ɧɚɱɢɫɥɹɸɬɫɹ ɩɪɨɰɟɧɬɵ ɩɨ ɮɨɪɦɭɥɟ
1
t
Ʉ(1 ) ,
FV r
ɝɞɟ FV — ɛɭɞɭɳɚɹ ɫɬɨɢɦɨɫɬɶ ɤɚɩɢɬɚɥɚ, ɪɭɛ.;
Ʉ
— ɟɠɟɝɨɞɧɵɣ ɜɡɧɨɫ, ɪɭɛ.;
r — ɩɪɨɰɟɧɬɧɚɹ ɫɬɚɜɤɚ, %;
t — ɩɟɪɢɨɞ ɩɨɬɨɤɚ ɩɥɚɬɟɠɟɣ.
ɇɚɪɚɳɟɧɧɚɹ ɫɭɦɦɚ (Ʉɧ) ɤ ɤɨɧɰɭ ɫɪɨɤɚ ɜɵɩɥɚɬɵ ɪɟɧɬɧɵɯ ɩɥɚɬɟɠɟɣ
ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
t
(1 ) 1
r
r
ȼɟɥɢɱɢɧɚ
t
(1 ) 1
r
r
ɄɄ .
ɧ
ɹɜɥɹɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɧɚɪɚɳɟɧɢɹ ɪɟɧɬɵ,
ɤɨɬɨɪɵɣ ɧɚɡɵɜɚɸɬ ɬɚɤɠɟ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɧɚɤɨɩɥɟɧɢɹ ɞɟɧɟɠɧɨɣ ɟɞɢɧɢɰɵ ɡɚ ɩɟɪɢɨɞ.
ɉɪɢɦɟɪ. ɉɨɦɟɳɟɧɢɟ ɫɞɚɟɬɫɹ ɜ ɚɪɟɧɞɭ ɫɪɨɤɨɦ ɧɚ 5 ɥɟɬ. Ⱥɪɟɧɞɧɵɟ
ɩɥɚɬɟɠɢ ɜ ɪɚɡɦɟɪɟ 100 ɬɵɫ. ɪɭɛ. ɜɧɨɫɹɬɫɹ ɤɪɟɞɢɬɨɪɨɦ ɟɠɟɝɨɞɧɨ ɜ ɤɨɧɰɟ ɝɨɞɚ ɜ ɛɚɧɤ ɡɚ ɫɱɟɬ ɜɥɚɞɟɥɶɰɚ ɩɨɦɟɳɟɧɢɹ. Ȼɚɧɤ ɧɚ ɜɧɟɫɟɧɧɵɟ ɫɭɦɦɵ ɧɚɱɢɫɥɹɟɬ ɩɪɨɰɟɧɬɵ ɜ ɪɚɫɱɟɬɟ 10% ɝɨɞɨɜɵɯ. Ɉɩɪɟɞɟɥɢɬɟ ɫɭɦɦɭ,
ɩɨɥɭɱɟɧɧɭɸ ɜɥɚɞɟɥɶɰɟɦ ɩɨɦɟɳɟɧɢɹ ɜ ɤɨɧɰɟ ɫɪɨɤɚ ɚɪɟɧɞɵ, ɩɪɢ ɭɫɥɨɜɢɢ, ɱɬɨ ɫɨ ɫɱɟɬɚ ɞɟɧɶɝɢ ɧɟ ɢɡɵɦɚɥɢɫɶ. ɉɪɢɦɟɦ ɨɛɨɡɧɚɱɟɧɢɹ:
x ɟɠɟɝɨɞɧɵɣ ɜɡɧɨɫ — Ʉ;
x ɩɪɨɰɟɧɬɧɚɹ ɫɬɚɜɤɚ — r;
x ɫɪɨɤ ɚɪɟɧɞɵ — n.
ɉɪɟɞɫɬɚɜɢɦ ɷɬɭ ɮɢɧɚɧɫɨɜɭɸ ɨɩɟɪɚɰɢɸ ɫɥɟɞɭɸɳɟɣ ɫɯɟɦɨɣ,
(ɬɚɛɥ. 4.9).
132
Ɍɚɛɥɢɰɚ 4.9. Ɍɵɫ. ɪɭɛ.
ɉɟɪɢɨɞ
ɜɡɧɨɫɚ,
ɝɨɞ
1-ɣ 100,0 — — — —
1-ɣ ɜɡɧɨɫ 2-ɣ ɜɡɧɨɫ 3-ɣ ɜɡɧɨɫ 4-ɣ ɜɡɧɨɫ 5-ɣ ɜɡɧɨɫ
2-ɣ
3-ɣ
4-ɣ
5-ɣ
100,0•1,1
100,0•1,1
100,0•1,1
100,0•1,1
100,0 — — —
2
100,0•1,1
3
100,0•1,12 100,0•1,1
4
100,0•1,13 100,0•1,12 100,0•1,1
100,0 — —
100,0 —
100,0
ɉɨ ɞɚɧɧɵɦ ɩɪɢɦɟɪɚ ɪɚɫɫɱɢɬɚɟɦ ɧɚɪɚɳɟɧɧɭɸ ɫɭɦɦɭ ɪɟɧɬɧɵɯ
ɩɥɚɬɟɠɟɣ.
5
(1 0 ,1) 1
Ʉ 100 ɬɵɫ.610,0
ɧ
0,1
ɬɵɫ. ɪɭɛ.
ɉɪɢɦɟɪ. ɇɚ ɫɛɟɪɟɝɚɬɟɥɶɧɵɣ ɫɱɟɬ ɤɚɠɞɵɣ ɝɨɞ ɤɥɚɞɭɬ K0 =10 000 ɪɭɛ.
ɇɚ ɷɬɭ ɫɭɦɦɭ ɧɚɱɢɫɥɹɸɬ 10% ɝɨɞɨɜɵɯ ɜ ɬɟɱɟɧɢɟ 5 ɥɟɬ. Ʉɚɤɨɜ ɪɚɡɦɟɪ
ɜɤɥɚɞɚ ɜ ɤɨɧɰɟ ɩɨɫɥɟɞɧɟɝɨ ɩɹɬɨɝɨ ɝɨɞɚ?
Ɋɟɲɟɧɢɟ.
K 10 000 62 000
t
(1 0 ,1) 1
5
0,1
ɪɭɛ.
ȿɫɥɢ ɩɟɪɜɵɣ ɩɥɚɬɟɠ ɩɪɨɢɡɜɨɞɢɬɫɹ ɧɟɦɟɞɥɟɧɧɨ, ɚ ɩɨɫɥɟɞɭɸɳɢɟ —
ɱɟɪɟɡ ɪɚɜɧɵɟ ɢɧɬɟɪɜɚɥɵ (ɩɪɟɧɭɦɟɪɚɧɞɨ), ɬɚɤɢɟ ɪɟɧɬɵ ɬɚɤɠɟ ɧɚɡɵɜɚɸɬɫɹ ɚɜɚɧɫɨɜɵɦɢ. Ɍɨɝɞɚ ɫɭɦɦɚ ɱɥɟɧɨɜ ɬɚɤɨɣ ɪɟɧɬɵ ɜɵɱɢɫɥɹɟɬɫɹ ɩɨ
ɮɨɪɦɭɥɟ
t
(1 ) 1
r
r
r
ɝɞɟ Ʉ
— ɚɜɚɧɫɨɜɵɣ ɩɥɚɬɟɠ, ɪɭɛ.
ɚɜ
ɄɄ(1 ) ,
ɧɚɜ
ɉɪɢɦɟɪ. ɂɧɜɟɫɬɨɪ ɟɠɟɝɨɞɧɨ ɜ ɧɚɱɚɥɟ ɝɨɞɚ (ɩɪɟɧɭɦɟɪɚɧɞɨ) ɞɟɥɚɟɬ
ɜɡɧɨɫ ɜ ɪɚɡɦɟɪɟ 500 ɬɵɫ. ɪɭɛ. ɩɨɞ 12% ɝɨɞɨɜɵɯ. Ɉɩɪɟɞɟɥɢɬɶ, ɤɚɤɚɹ
ɫɭɦɦɚ ɛɭɞɟɬ ɧɚ ɫɱɟɬɟ ɩɨ ɢɫɬɟɱɟɧɢɢ 5 ɥɟɬ?
Ɋɟɲɟɧɢɟ.
0,12
5
ɬɵɫ. ɪɭɛ.
t
(1 ) 1 (1 0, 12 ) 1
r
ɄɄ(1 ) 50 0 ɬɵɫ. (1 0,12) 3544,8
ɛ
r
r
133
ɋɨɜɪɟɦɟɧɧɚɹ ɜɟɥɢɱɢɧɚ ɪɟɧɬɵ
ɋɨɜɪɟɦɟɧɧɚɹ ɜɟɥɢɱɢɧɚ ɪɟɧɬɵ ɹɜɥɹɟɬɫɹ ɫɭɦɦɨɣ ɜɫɟɯ ɩɨɫɬɭɩɥɟɧɢɣ
ɪɟɧɬɵ, ɞɢɫɤɨɧɬɢɪɨɜɚɧɧɵɯ ɧɚ ɦɨɦɟɧɬ ɩɪɢɜɟɞɟɧɢɹ ɩɨ ɜɵɛɪɚɧɧɨɣ ɫɬɚɜɤɟ. Ⱦɥɹ ɪɟɧɬɵ ɫ ɟɠɟɝɨɞɧɵɦɢ ɜɡɧɨɫɚɦɢ Ʉ ɫɨɜɪɟɦɟɧɧɚɹ ɜɟɥɢɱɢɧɚ (Ʉ
ɬɟɤ
ɜɵɱɢɫɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
t
r
r
1(1 )
ɝɞɟ
r
1(1 )
ɄɄ ,
ɬɟɤ
t
r
— ɞɢɫɤɨɧɬɢɪɨɜɚɧɧɵɣ ɦɧɨɠɢɬɟɥɶ ɞɥɹ ɚɧɧɭɢɬɟɬɚ. Ɉɧ ɩɨɤɚɡɵ-
ɜɚɟɬ, ɱɟɦɭ ɪɚɜɟɧ ɫ ɩɨɡɢɰɢɢ ɬɟɤɭɳɟɝɨ ɦɨɦɟɧɬɚ ɪɚɡɦɟɪ ɚɧɧɭɢɬɟɬɚ ɫ ɪɟɝɭɥɹɪɧɵɦɢ ɞɟɧɟɠɧɵɦɢ ɩɨɫɬɭɩɥɟɧɢɹɦɢ, ɩɪɨɞɨɥɠɚɸɳɟɝɨɫɹ t ɪɚɜɧɵɯ ɩɟɪɢɨɞɨɜ ɫ ɡɚɞɚɧɧɨɣ ɩɪɨɰɟɧɬɧɨɣ
ɫɬɚɜɤɨɣ r.
ɉɪɢɦɟɪ. Ɏɢɪɦɨɣ ɩɪɟɞɭɫɦɚɬɪɢɜɚɟɬɫɹ ɫɨɡɞɚɧɢɟ ɜ ɬɟɱɟɧɢɟ 3 ɥɟɬ
ɮɨɧɞɚ ɢɧɜɟɫɬɢɪɨɜɚɧɢɹ ɜ ɪɚɡɦɟɪɟ 1350 ɬɵɫ. ɪɭɛ. Ɏɢɪɦɚ ɢɦɟɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɚɫɫɢɝɧɨɜɚɬɶ ɧɚ ɷɬɢ ɰɟɥɢ ɟɠɟɝɨɞɧɨ 412 ɬɵɫ. ɪɭɛ., ɩɨɦɟɳɚɹ ɢɯ ɜ
ɛɚɧɤ ɩɨɞ 10% ɝɨɞɨɜɵɯ. Ʉɚɤɚɹ ɫɭɦɦɚ ɩɨɬɪɟɛɨɜɚɥɚɫɶ ɛɵ ɮɢɪɦɟ ɞɥɹ ɫɨɡɞɚɧɢɹ ɮɨɧɞɚ ɜ 1500 ɬɵɫ. ɪɭɛ., ɟɫɥɢ ɛɵ ɨɧɚ ɦɨɝɥɚ ɩɨɦɟɫɬɢɬɶ ɟɟ ɜ ɛɚɧɤ
ɨɞɧɨɜɪɟɦɟɧɧɨ ɧɚ 3 ɝɨɞɚ ɩɨɞ 10% ɝɨɞɨɜɵɯ?
Ɋɟɲɟɧɢɟ.
1. Ɉɩɪɟɞɟɥɹɟɦ ɬɟɤɭɳɭɸ ɫɬɨɢɦɨɫɬɶ ɫɭɦɦɵ ɟɠɟɝɨɞɧɵɯ ɜɡɧɨɫɨɜ
(Ʉ
) ɜ ɬɟɱɟɧɢɟ 3 ɥɟɬ ɩɨɞ 10% ɝɨɞɨɜɵɯ:
ɬɟɤ
3
0,1
ɬɵɫ. ɪɭɛ.
1(10,1)
Ʉ 412 ɬɵɫ.1030,0
ɬɟɤ
2. ɇɚɪɚɳɟɧɧɚɹ ɫɭɦɦɚ ɩɪɢ ɟɠɟɝɨɞɧɵɯ ɩɥɚɬɟɠɚɯ ɜ ɪɚɡɦɟɪɟ
412 ɬɵɫ. ɪɭɛ. ɩɨɞ 10% ɝɨɞɨɜɵɯ ɫɨɫɬɚɜɢɬ
Ʉ 412 ɬɵɫ. 13596, 68
ɧ
(1 0, 1) 1
3
0,1
ɬɵɫ. ɪɭɛ.
)
ɋɭɦɦɚ ɞɢɫɤɨɧɬɢɪɨɜɚɧɢɹ
ɇɚ ɩɪɚɤɬɢɤɟ ɱɚɫɬɨ ɞɢɫɤɨɧɬɢɪɭɸɬ ɪɹɞ ɩɥɚɬɟɠɟɣ ɡɚ ɨɩɪɟɞɟɥɟɧɧɵɣ
ɩɟɪɢɨɞ ɜɪɟɦɟɧɢ. ɉɪɟɞɩɨɥɨɠɢɦ, ɱɬɨ ɢɦɟɟɦ ɞɟɥɨ ɫ ɚɪɟɧɞɨɣ, ɩɪɢɱɟɦ
ɩɥɚɬɟɠɢ ɩɨ ɝɨɞɚɦ ɨɞɢɧɚɤɨɜɵɟ.
Ɋɚɫɱɟɬɵ ɬɚɤɨɣ ɨɩɟɪɚɰɢɢ ɫɥɟɞɭɸɳɢɟ: ɧɚɞɨ ɩɪɢɜɟɫɬɢ ɤɚɠɞɵɣ ɪɚɡɨɜɵɣ ɩɥɚɬɟɠ ɤ ɦɨɦɟɧɬɭ t = 0 ɢ ɩɪɨɫɭɦɦɢɪɨɜɚɬɶ ɩɨɥɭɱɟɧɧɵɟ ɜɟɥɢɱɢɧɵ.
ȼɟɥɢɱɢɧɭ Ʉ
ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɧɚɡɵɜɚɸɬ ɫɭɦɦɨɣ ɞɢɫɤɨɧɬɢɪɨɜɚɧɢɹ.
ɞ
134
t
ɪ
(1 ) 1
r
t
(1 )
ir
t
— ɪɚɫɱɟɬɧɵɣ ɩɟɪɢɨɞ, ɥɟɬ;
ɝɞɟ t
— ɩɨɫɬɨɹɧɧɵɣ ɩɥɚɬɟɠ, ɪɭɛ.
K
t
KK ,
ɞ
ɉɪɢɦɟɪ. Ⱦɨɦ ɫɞɚɟɬɫɹ ɜ ɧɚɟɦ ɧɚ 5 ɥɟɬ, ɟɠɟɝɨɞɧɵɟ ɩɥɚɬɟɠɢ (K
) ɫɨ-
t
ɫɬɚɜɥɹɸɬ 80 000 ɪɭɛ., ɩɪɨɰɟɧɬɧɚɹ ɫɬɚɜɤɚ ɪɚɜɧɚ 0,1. Ɉɩɪɟɞɟɥɢɬɶ ɬɟɤɭɳɭɸ ɫɬɨɢɦɨɫɬɶ ɩɥɚɬɟɠɟɣ ɡɚ 5 ɥɟɬ.
Ɋɟɲɟɧɢɟ.
K 80 000 80 000 3,779 302 320
ɞ
(1 0 ,1) 1
0,1(1 0,1)
5
5
ɭɛ.
Ɋɟɧɬɚ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶɸ ɛɨɥɟɟ 50 ɥɟɬ ɧɚɡɵɜɚɟɬɫɹ ɜɟɱɧɨɣ.
4.3. Ⱦɢɧɚɦɢɱɟɫɤɢɟ ɩɨɤɚɡɚɬɟɥɢ ɨɰɟɧɤɢ
ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɢɧɜɟɫɬɢɰɢɨɧɧɵɯ ɩɪɨɟɤɬɨɜ
ȼ Ɇɟɬɨɞɢɱɟɫɤɢɯ ɪɟɤɨɦɟɧɞɚɰɢɹɯ ɩɨ ɨɰɟɧɤɟ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɢɧɜɟɫɬɢɰɢɨɧɧɵɯ ɩɪɨɟɤɬɨɜ ɩɪɟɞɥɨɠɟɧɨ ɨɮɢɰɢɚɥɶɧɨɟ ɧɚɡɜɚɧɢɟ ɞɚɧɧɨɝɨ
ɤɪɢɬɟɪɢɹ — ɱɢɫɬɵɣ ɞɢɫɤɨɧɬɢɪɨɜɚɧɧɵɣ ɞɨɯɨɞ (ɑȾȾ).
ɑɢɫɬɵɣ ɞɢɫɤɨɧɬɢɪɨɜɚɧɧɵɣ ɞɨɯɨɞ (NPV) ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɤɚɤ ɪɚɡ-
ɧɨɫɬɶ ɞɢɫɤɨɧɬɢɪɨɜɚɧɧɵɯ ɞɟɧɟɠɧɵɯ ɩɨɬɨɤɨɜ (ɪɚɫɯɨɞɨɜ ɢ ɞɨɯɨɞɨɜ),
ɩɪɨɢɡɜɨɞɢɦɵɯ ɜ ɩɪɨɰɟɫɫɟ ɨɫɭɳɟɫɬɜɥɟɧɢɹ ɢɧɜɟɫɬɢɰɢɢ ɡɚ ɩɪɨɝɧɨɡɧɵɣ
ɩɟɪɢɨɞ.
ɋɭɬɶ ɤɪɢɬɟɪɢɹ ɫɨɫɬɨɢɬ ɜ ɫɪɚɜɧɟɧɢɢ ɬɟɤɭɳɟɣ ɫɬɨɢɦɨɫɬɢ ɛɭɞɭɳɢɯ
ɞɟɧɟɠɧɵɯ ɩɨɫɬɭɩɥɟɧɢɣ ɨɬ
ɪɚɫɯɨɞɚɦɢ.
ɉɪɢɦɟɧɟɧɢɟ ɞɚɧɧɨɝɨ ɦɟɬɨɞɚ ɩɪɟɞɭɫɦɚɬɪɢɜɚɟɬ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɟ
ɩɪɨɯɨɠɞɟɧɢɟ ɫɥɟɞɭɸɳɢɯ ɫɬɚɞɢɣ:
x ɪɚɫɱɟɬɚ ɞɟɧɟɠɧɨɝɨ ɩɨɬɨɤɚ ɢɧɜɟɫɬɢɰɢɨɧɧɨɝɨ ɩɪɨɟɤɬɚ;
x ɜɵɛɨɪɚ ɫɬɚɜɤɢ ɞɢɫɤɨɧɬɢɪɨɜɚɧɢɹ, ɭɱɢɬɵɜɚɸɳɟɣ ɞɨɯɨɞɧɨɫɬɶ ɚɥɶ-
ɬɟɪɧɚɬɢɜɧɵɯ ɜɥɨɠɟɧɢɣ ɢ ɪɢɫɤ ɩɪɨɟɤɬɚ;
x ɨɩɪɟɞɟɥɟɧɢɹ ɱɢɫɬɨɝɨ ɞɢɫɤɨɧɬɢɪɨɜɚɧɧɨɝɨ ɞɨɯɨɞɚ.
ɪɟɚɥɢɡɚɰɢɢ ɩɪɨɟɤɬɚ ɫ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ
Ⱦɢɫɤɨɧɬɢɪɨɜɚɧɧɵɣ ɞɨɯɨɞ
ɉɨɞ ɞɢɫɤɨɧɬɢɪɨɜɚɧɧɵɦ ɞɨɯɨɞɨɦ ɩɨɧɢɦɚɸɬɫɹ ɩɪɢɜɟɞɟɧɧɵɟ ɤ ɧɚɫɬɨɹɳɟɣ ɫɬɨɢɦɨɫɬɢ ɫɭɦɦɨɣ ɱɢɫɬɨɝɨ ɞɟɧɟɠɧɨɝɨ ɩɨɬɨɤɚ ɡɚ ɩɟɪɢɨɞ ɷɤɫɩɥɭɚɬɚɰɢɢ ɢɧɜɟɫɬɢɰɢɨɧɧɨɝɨ ɩɪɨɟɤɬɚ.
135
Ⱦɢɫɤɨɧɬɢɪɨɜɚɧɧɵɟ ɡɧɚɱɟɧɢɹ ɱɢɫɬɨɝɨ ɞɟɧɟɠɧɨɝɨ ɩɨɬɨɤɚ (ȾȾ) ɨɬɪɚɠɚɸɬ ɬɟɤɭɳɭɸ, ɩɪɢɜɟɞɟɧɧɭɸ ɫɬɨɢɦɨɫɬɶ ɨɠɢɞɚɟɦɵɯ ɜ ɛɭɞɭɳɟɦ ɮɢɧɚɧɫɨɜɵɯ ɪɟɡɭɥɶɬɚɬɨɜ:
T
ȾȾ (1 ) ,
— ɱɢɫɬɵɣ ɞɟɧɟɠɧɵɣ ɩɨɬɨɤ ɧɚ t-ɦ ɲɚɝɟ ɪɚɫɱɟɬɚ, ɪɭɛ.;
ɝɞɟ C
t
ɋ r
t
¦
0
t
t — ɲɚɝ ɪɚɫɱɟɬɚ (ɝɨɞ, ɤɜɚɪɬɚɥ, ɦɟɫɹɰ ɢ ɬ.ɞ.);
— ɫɬɚɜɤɚ ɞɢɫɤɨɧɬɢɪɨɜɚɧɢɹ;
r
— ɪɚɫɱɟɬɧɵɣ ɩɟɪɢɨɞ.
Ɍ
t
ȼ ɨɫɧɨɜɟ ɪɚɫɱɟɬɨɜ ɞɚɧɧɵɦ ɦɟɬɨɞɨɦ ɥɟɠɢɬ ɤɨɧɰɟɩɰɢɹ ɨ ɪɚɡɧɨɣ
ɫɬɨɢɦɨɫɬɢ ɞɟɧɟɝ ɜɨ ɜɪɟɦɟɧɢ. ɉɪɨɰɟɫɫ ɩɟɪɟɫɱɟɬɚ ɛɭɞɭɳɟɣ ɫɬɨɢɦɨɫɬɢ
ɞɟɧɟɠɧɨɝɨ ɩɨɬɨɤɚ ɜ ɬɟɤɭɳɭɸ ɧɚɡɵɜɚɸɬɫɹ ɞɢɫɤɨɧɬɢɪɨɜɚɧɢɟɦ.
ɇɚ ɪɚɧɧɢɯ ɫɬɚɞɢɹɯ ɪɚɫɱɟɬɚ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɢɯ ɰɟɥɹɦɢ ɢ ɫɩɟɰɢɮɢɤɨɣ ɮɢɧɚɧɫɨɜɵɟ ɩɨɤɚɡɚɬɟɥɢ ɢ ɭɫɥɨɜɢɹ ɮɢɧɚɧɫɨɜɨɣ ɪɟɚɥɢɡɭɟɦɨɫɬɢ
ɨɰɟɧɢɜɚɸɬɫɹ ɜ ɬɟɤɭɳɢɯ ɢɥɢ ɩɪɨɝɧɨɡɧɵɯ ɰɟɧɚɯ. Ɉɫɬɚɥɶɧɵɟ ɩɨɤɚɡɚɬɟɥɢ
ɨɩɪɟɞɟɥɹɸɬɫɹ
ɜ ɬɟɤɭɳɢɯ ɢɥɢ ɞɟɮɥɢɪɨɜɚɧɧɵɯ ɰɟɧɚɯ.
ɑɢɫɬɵɣ ɞɢɫɤɨɧɬɢɪɨɜɚɧɧɵɣ ɞɨɯɨɞ (ɑȾȾ), ɢɥɢ ɱɢɫɬɚɹ ɬɟɤɭɳɚɹ
ɫɬɨɢɦɨɫɬɶ (NPV), — ɪɚɡɧɢɰɚ ɦɟɠɞɭ ɨɛɳɟɣ ɫɭɦɦɨɣ ɞɢɫɤɨɧɬɢɪɨɜɚɧ-
ɧɵɯ ɞɟɧɟɠɧɵɯ ɩɨɬɨɤɨɜ ɡɚ ɜɟɫɶ ɫɪɨɤ ɪɟɚɥɢɡɚɰɢɢ ɩɪɨɟɤɬɚ ɢ ɩɟɪɜɨɧɚɱɚɥɶɧɵɦɢ ɢɧɜɟɫɬɢɰɢɨɧɧɵɦɢ ɡɚɬɪɚɬɚɦɢ:
NPV I C r
ɝɞɟ I
— ɪɚɡɦɟɪ ɩɟɪɜɨɧɚɱɚɥɶɧɨɣ ɢɧɜɟɫɬɢɰɢɢ.
0
T
0
t
¦
t
0
(1 ) ,
t
ȿɫɥɢ ɜ ɢɧɜɟɫɬɢɰɢɨɧɧɨɦ ɩɪɨɟɤɬɟ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɟ
ɢɧɜɟɫɬɢɪɨɜɚɧɢɟ ɮɢɧɚɧɫɨɜɵɯ ɪɟɫɭɪɫɨɜ ɜ ɬɟɱɟɧɢɟ ɪɹɞɚ ɥɟɬ, ɬɨ ɮɨɪɦɭɥɚ
ɞɥɹ ɪɚɫɱɟɬɚ NPV ɢɦɟɟɬ ɫɥɟɞɭɸɳɢɣ ɜɢɞ:
NPV I r C r
NT
nt
¦¦
nt
00
ɝɞɟ N — ɪɚɫɱɟɬɧɵɣ ɩɟɪɢɨɞ ɫɬɪɨɢɬɟɥɶɫɬɜɚ;
n — ɩɨɪɹɞɤɨɜɵɣ ɧɨɦɟɪ ɝɨɞɚ ɫɬɪɨɢɬɟɥɶɫɬɜɚ;
T — ɪɚɫɱɟɬɧɵɣ ɩɟɪɢɨɞɚ ɷɤɫɩɥɭɚɬɚɰɢɢ ɨɛɴɟɤɬɚ;
r — ɝɨɞɨɜɚɹ ɩɪɨɰɟɧɬɧɚɹ ɫɬɚɜɤɚ, %;
t — ɩɨɪɹɞɤɨɜɵɣ ɧɨɦɟɪ ɝɨɞɚ ɷɤɫɩɥɭɚɬɚɰɢɢ.
nt
(1 ) (1 ) ,
Ⱦɥɹ ɩɪɢɡɧɚɧɢɹ ɩɪɨɟɤɬɚ ɷɮɮɟɤɬɢɜɧɵɦ ɧɟɨɛɯɨɞɢɦɨ, ɱɬɨɛɵ NPV
ɩɪɨɟɤɬɚ ɛɵɥ ɩɨɥɨɠɢɬɟɥɶɧɵɦ; ɩɪɢ ɫɪɚɜɧɟɧɢɢ ɚɥɶɬɟɪɧɚɬɢɜɧɵɯ ɩɪɨɟɤɬɨɜ ɩɪɟɞɩɨɱɬɟɧɢɟ ɞɨɥɠɧɨ ɨɬɞɚɜɚɬɶɫɹ ɩɪɨɟɤɬɭ ɫ ɛɨɥɶɲɢɦ ɡɧɚɱɟɧɢɟɦ NPV.
136
ɉɨɫɤɨɥɶɤɭ ɩɪɢɬɨɤ ɞɟɧɟɠɧɵɯ ɫɪɟɞɫɬɜ ɪɚɫɩɪɟɞɟɥɟɧ ɜɨ ɜɪɟɦɟɧɢ, ɟɝɨ
ɞɢɫɤɨɧɬɢɪɨɜɚɧɢɟ ɩɪɨɢɡɜɨɞɢɬɫɹ ɩɨ ɩɪɨɰɟɧɬɧɨɣ ɫɬɚɜɤɟ r. ȼɚɠɧɵɦ ɦɨɦɟɧɬɨɦ ɹɜɥɹɟɬɫɹ ɜɵɛɨɪ ɭɪɨɜɧɹ ɩɪɨɰɟɧɬɧɨɣ ɫɬɚɜɤɢ, ɩɨ ɤɨɬɨɪɨɣ ɩɪɨɜɨɞɢɬɫɹ ɞɢɫɤɨɧɬɢɪɨɜɚɧɢɟ.
ɉɪɢɦɟɪ. Ɉɛɳɢɣ ɫɪɨɤ ɫɬɪɨɢɬɟɥɶɫɬɜɚ ɨɛɴɟɤɬɚ — 3 ɝɨɞɚ. Ɉɛɳɚɹ
ɫɭɦɦɚ ɤɚɩɢɬɚɥɶɧɵɯ ɜɥɨɠɟɧɢɣ — 200 000 ɬɵɫ. ɪɭɛ. ɋɭɳɟɫɬɜɭɸɬ ɞɜɚ
ɜɚɪɢɚɧɬɚ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɤɚɩɢɬɚɥɶɧɵɯ ɜɥɨɠɟɧɢɣ ɩɨ ɝɨɞɚɦ (ɬɚɛɥ. 4. 10).
Ɉɩɪɟɞɟɥɢɬɶ ɥɭɱɲɢɣ
ɜɚɪɢɚɧɬ.
Ɍɚɛɥɢɰɚ 4.10
ȼɚɪɢɚɧɬ
1-ɣ 100 000,0 60 000,0 40 000,0 200 000,0
2-ɣ 30 000,0 70 000,0 100 000,0 200 000,0
Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɤɚɩɢɬɚɥɶɧɵɯ ɜɥɨɠɟɧɢɣ ɩɨ ɝɨɞɚɦ,
ɬɵɫ. ɪɭɛ.
1-ɣ 2-ɣ 3-ɣ
ȼɫɟɝɨ,
ɬɵɫ. ɪɭɛ.
Ⱦɥɹ ɪɟɲɟɧɢɹ ɩɨɫɬɚɜɥɟɧɧɨɣ ɡɚɞɚɱɢ ɧɟɨɛɯɨɞɢɦɨ ɪɚɫɩɨɥɚɝɚɬɶ ɢɧɮɨɪɦɚɰɢɟɣ ɨ ɩɪɨɰɟɧɬɧɨɣ ɫɬɚɜɤɟ. Ⱦɨɩɭɫɬɢɦ, ɱɬɨ ɛɚɧɤɨɜɫɤɢɣ ɩɪɨɰɟɧɬ
ɧɚ ɞɟɧɟɠɧɵɟ ɫɪɟɞɫɬɜɚ, ɩɨɥɨɠɟɧɧɵɟ ɧɚ ɞɟɩɨɡɢɬɧɵɣ ɫɱɟɬ, ɫɨɫɬɚɜɥɹɟɬ
12%. Ɂɚɞɚɱɭ ɪɟɲɚɟɦ ɞɜɭɦɹ ɫɩɨɫɨɛɚɦɢ: ɦɟɬɨɞɨɦ ɞɢɫɤɨɧɬɢɪɨɜɚɧɢɹ ɢ
ɦɟɬɨɞɨɦ ɧɚɪɚɳɢɜɚɧɢɹ.
Ɉɛɳɚɹ ɫɭɦɦɚ ɩɪɢɜɟɞɟɧɧɵɯ ɡɚɬɪɚɬ (Ʉ
) ɤ ɪɚɫɱɟɬɧɨɦɭ ɝɨɞɭ ɨɩɪɟɞɟ-
ɩɪ
ɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
Iɩɪ = I1• k1ɞ + I2• k2ɞ + I3• k3ɞ,
ɝɞɟ I
, I2, I3 — ɢɧɜɟɫɬɢɪɨɜɚɧɧɵɣ ɤɚɩɢɬɚɥ ɩɨ ɝɨɞɚɦ ɫɬɪɨɢɬɟɥɶɫɬɜɚ ɨɛɴɟɤɬɚ,
1
, k2ɞ, k3ɞ — ɤɨɷɮɮɢɰɢɟɧɬɵ ɞɢɫɤɨɧɬɢɪɨɜɚɧɢɹ.
k
1ɞ
ɬɵɫ. ɪɭɛ.;
Ʉɨɷɮɮɢɰɢɟɧɬɵ ɞɢɫɤɨɧɬɢɪɨɜɚɧɢɹ ɢ ɧɚɪɚɳɟɧɢɹ ɨɩɪɟɞɟɥɹɸɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
k = (1 + r)
ɝɞɟ Ɍ — ɩɪɢ ɞɢɫɤɨɧɬɢɪɨɜɚɧɢɢ ɪɚɜɟɧ 1, ɩɪɢ ɧɚɪɚɳɟɧɢɢ — ɧɨɦɟɪ ɩɨɫɥɟɞɧɟɝɨ
ɝɨɞɚ;
t — ɩɨɪɹɞɤɨɜɵɣ ɧɨɦɟɪ ɝɨɞɚ.
T–t
,
Ʉɨɷɮɮɢɰɢɟɧɬɵ ɞɢɫɤɨɧɬɢɪɨɜɚɧɢɹ ɩɨ ɩɪɨɰɟɧɬɧɨɣ ɫɬɚɜɤɟ 12% ɫɨɫɬɚɜɥɹɸɬ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ:
x ɞɥɹ 1-ɝɨ ɝɨɞɚ — (1+0,12)
1—1
= (1+0,12)0 = 1,0;
137
x ɞɥɹ 2-ɝɨ ɝɨɞɚ — (1+0,12)
x ɞɥɹ 3-ɝɨ ɝɨɞɚ — (1+0,12)
1) I
= 100 000 ɬɵɫ. • 1,0 + 60 000 ɬɵɫ.• 0,893 + 40 000 ɬɵɫ. • 0,797 =
ɩɪ
1—2
= (1+0,12)-1 = 0,893;
1—3
= (1+0,12)-2 = 0,797.
= 185 500 ɬɵɫ. ɪɭɛ.;
2) I
= 30 000 ɬɵɫ.• 1,0 + 70 000 ɬɵɫ.• 0,893 + 100 000 ɬɵɫ.• 0,797 =
ɩɪ
= 172 200 ɬɵɫ. ɪɭɛ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɷɮɮɟɤɬɢɜɧɟɟ ɜɬɨɪɨɣ ɜɚɪɢɚɧɬ, ɝɞɟ ɦɟɧɶɲɟ ɩɪɢɜɟɞɟɧɧɵɟ ɡɚɬɪɚɬɵ.
Ⱥɧɚɥɨɝɢɱɧɵɟ ɪɟɡɭɥɶɬɚɬɵ ɩɨɥɭɱɚɸɬɫɹ, ɟɫɥɢ ɪɟɲɢɬɶ ɡɚɞɚɱɭ ɦɟɬɨɞɨɦ ɧɚɪɚɳɢɜɚɧɢɹ ɡɚɬɪɚɬ.
Ⱦɥɹ ɪɚɫɱɟɬɚ ɧɚɪɚɳɟɧɧɵɯ ɡɚɬɪɚɬ ɢɫɩɨɥɶɡɭɟɬɫɹ ɫɥɟɞɭɸɳɚɹ ɮɨɪɦɭɥɚ:
Iɧ = I
, k2ɧ, k3ɧ — ɤɨɷɮɮɢɰɢɟɧɬɵ ɧɚɪɚɳɟɧɢɹ.
ɝɞɟ k
1ɧ
1 •k1ɧ
+ I
2•k2ɧ
+ I
3•k3ɧ
,
Ʉɨɷɮɮɢɰɢɟɧɬɵ ɧɚɪɚɳɢɜɚɧɢɹ, ɩɨ ɩɪɨɰɟɧɬɧɨɣ ɫɬɚɜɤɟ 12% ɫɨɫɬɚɜɥɹɸɬ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ:
x ɞɥɹ 1-ɝɨ ɝɨɞɚ — (1+0,12)
x ɞɥɹ 2-ɝɨ ɝɨɞɚ — (1+0,12)
x ɞɥɹ 3-ɝɨ ɝɨɞɚ — (1+0,12)
1) I
= 100 000 ɬɵɫ.• 1,254 + 60 000 ɬɵɫ.• 1,12 + 40 000 ɬɵɫ. • 1,0 =
ɧ
3—1
= (1+0,12)2 = 1,254;
3—2
= (1+0,12)1 = 1,12;
3—3
= (1+0,12)0 = 1,0.
= 232 600 ɬɵɫ. ɪɭɛ.;
2) I
= 30 000 ɬɵɫ.• 1,254 + 70 000 ɬɵɫ.• 1,12 + 100 000 ɬɵɫ.• 1,0 =
ɧ
= 216 000 ɬɵɫ. ɪɭɛ.
ȿɫɬɟɫɬɜɟɧɧɨ, ɬɚɤɠɟ ɷɮɮɟɤɬɢɜɧɟɟ ɜɬɨɪɨɣ ɜɚɪɢɚɧɬ, ɝɞɟ ɦɟɧɶɲɟ ɩɪɢɜɟɞɟɧɧɵɟ ɡɚɬɪɚɬɵ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɞɥɹ ɩɪɢɜɟɞɟɧɢɹ ɪɚɡɧɨɜɪɟɦɟɧɧɵɯ ɡɚɬɪɚɬ ɜ ɫɨɩɨɫɬɚɜɢɦɵɣ ɜɢɞ ɢɫɩɨɥɶɡɭɸɬɫɹ ɞɜɚ ɦɟɬɨɞɚ:
1) ɞɢɫɤɨɧɬɢɪɨɜɚɧɢɹ ɡɚɬɪɚɬ ɤ ɪɚɫɱɟɬɧɨɦɭ ɝɨɞɭ;
2) ɧɚɪɚɳɢɜɚɧɢɹ ɡɚɬɪɚɬ ɤ ɪɚɫɱɟɬɧɨɦɭ ɝɨɞɭ.
ɇɚ ɜɨɩɪɨɫ, ɨɛɨɫɧɨɜɚɧɧɨ ɥɢ ɦɟɬɨɞɨɥɨɝɢɱɟɫɤɢ ɢ ɦɟɬɨɞɢɱɟɫɤɢ ɩɪɢɜɨɞɢɬɶ ɤ ɪɚɫɱɟɬɧɨɦɭ ɝɨɞɭ ɤɚɤ
ɟɞɢɧɨɜɪɟɦɟɧɧɵɟ, ɬɚɤ ɢ ɬɟɤɭɳɢɟ ɡɚɬɪɚɬɵ
ɢ ɪɟɡɭɥɶɬɚɬɵ, ɛɨɥɶɲɢɧɫɬɜɨ ɡɚɩɚɞɧɵɯ ɢ ɨɬɟɱɟɫɬɜɟɧɧɵɯ ɷɤɨɧɨɦɢɫɬɨɜ
ɨɬɜɟɱɚɸɬ ɭɬɜɟɪɞɢɬɟɥɶɧɨ. Ɍɚɤɠɟ ɨɧɢ ɭɬɜɟɪɠɞɚɸɬ, ɱɬɨ ɧɟɬ ɩɪɢɧɰɢɩɢɚɥɶɧɨɣ ɪɚɡɧɢɰɵ ɦɟɠɞɭ ɬɟɤɭɳɢɦɢ ɢ ɟɞɢɧɨɜɪɟɦɟɧɧɵɦɢ ɡɚɬɪɚɬɚɦɢ, ɬɚɤ
ɤɚɤ ɢ ɬɟ ɢ ɞɪɭɝɢɟ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɪɚɫɫɪɟɞɨɬɨɱɟɧɧɵɟ ɜɨ ɜɪɟɦɟɧɢ
ɡɚɬɪɚɬɵ ɬɪɭɞɨɜɵɯ, ɦɚɬɟɪɢɚɥɶɧɵɯ, ɮɢɧɚɧɫɨɜɵɯ, ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɢ ɩɪɨɱɢɯ ɪɟɫɭɪɫɨɜ.
Ɉɞɧɚɤɨ ɬɟɤɭɳɢɟ ɡɚɬɪɚɬɵ
ɡɚɜɢɫɹɬ ɨɬ ɨɛɴɟɦɚ ɤɚɩɢɬɚɥɶɧɵɯ ɜɥɨɠɟɧɢɣ, ɩɨɫɤɨɥɶɤɭ ɟɞɢɧɨɜɪɟɦɟɧɧɵɟ ɡɚɬɪɚɬɵ ɧɚɩɪɚɜɥɟɧɵ ɧɚ ɫɨɡɞɚɧɢɟ ɛɨɥɟɟ ɷɮɮɟɤɬɢɜɧɵɯ ɫɪɟɞɫɬɜ ɢ ɩɪɟɞɦɟɬɨɜ ɬɪɭɞɚ ɞɥɹ ɷɤɨɧɨɦɢɢ ɩɨɬɪɟɛɥɹɟɦɵɯ ɪɟɫɭɪɫɨɜ.
138
Ʉɚɩɢɬɚɥɶɧɵɟ ɜɥɨɠɟɧɢɹ ɩɟɪɜɨɧɚɱɚɥɶɧɨ ɩɪɟɞɧɚɡɧɚɱɟɧɵ ɞɥɹ ɫɧɢɠɟɧɢɹ ɫɟɛɟɫɬɨɢɦɨɫɬɢ, ɩɨɜɵɲɟɧɢɹ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ ɬɪɭɞɚ, ɭɜɟɥɢɱɟɧɢɹ ɩɪɢɛɵɥɢ.
ɉɪɢɦɟɪ. ɉɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶ ɩɟɪɢɨɞɚ ɪɟɚɥɢɡɚɰɢɢ ɢɧɜɟɫɬɢɰɢɨɧ-
ɧɨɝɨ ɩɪɨɟɤɬɚ — 2 ɝɨɞɚ. ɋɦɟɬɧɚɹ ɫɬɨɢɦɨɫɬɶ ɩɪɨɟɤɬɚ — 140 ɦɥɧ ɪɭɛ.
ɉɨɥɟɡɧɵɣ ɫɪɨɤ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɩɪɨɟɤɬɚ — 4 ɝɨɞɚ. Ⱦɟɧɟɠɧɵɟ ɩɪɢɬɨɤɢ ɢ
ɨɬɬɨɤɢ ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥ. 4.11. Ⱦɢɫɤɨɧɬɧɚɹ ɫɬɚɜɤɚ — 10%. Ɍɪɟɛɭɟɬɫɹ
ɨɩɪɟɞɟɥɢɬɶ ɱɢɫɬɵɣ ɞɢɫɤɨɧɬɢɪɨɜɚɧɧɵɣ ɞɨɯɨɞ ɢ ɞɢɫɤɨɧɬɢɪɨɜɚɧɧɵɣ
ɫɪɨɤ ɨɤɭɩɚɟɦɨɫɬɢ.
Ɍɚɛɥɢɰɚ 4.11
Ƚɨɞ ɉɨɤɚɡɚɬɟɥɶ
2011 ɝ. 2012 ɝ. 2013 ɝ. 2014 ɝ. 2015 ɝ. 2016 ɝ.
ɂɧɜɟɫɬɢɰɢɹ,
ɦɥɧ ɪɭɛ. –60 –80 — — — —
ɑɢɫɬɚɹ ɩɪɢɛɵɥɶ,
ɦɥɧ ɪɭɛ. — — 38,0 49,0 51,0 54,0
Ⱥɦɨɪɬɢɡɚɰɢɹ,
ɦɥɧ ɪɭɛ. — — 2,0 2,0 2,0 2,0
ɉɪɢɬɨɤ ɞɟɧɟɠɧɵɯ
ɫɪɟɞɫɬɜ, ɦɥɧ ɪɭɛ. — — 40,0 51,0 53,0 56,0
Ʉɨɷɮɮɢɰɢɟɧɬ ɞɢɫɤɨɧɬɢɪɨɜɚɧɢɹ
Ⱦɢɫɤɨɧɬɢɪɨɜɚɧɧɵɣ
ɩɪɢɬɨɤ ɢ ɨɬɬɨɤ,
ɦɥɧ ɪɭɛ.
ɋɚɥɶɞɨ ɧɚɤɨɩɥɟɧɧɨɝɨ ɩɨɬɨɤɚ, ɦɥɧ ɪɭɛ.
ɑɢɫɬɵɣ ɞɢɫɤɨɧɬɢɪɨɜɚɧɧɵɣ ɞɨɯɨɞ,
ɦɥɧ ɪɭɛ.
1,0 0,91 1,0 0,91 0,82 0,75
–60 –72,8 40,0 46,4 43,5 42,0
–132,8 –92,8 –46,4 –2,9 39,1
39,1
Ⱦɢɫɤɨɧɬɢɪɨɜɚɧɧɵɣ ɫɪɨɤ ɨɤɭɩɚɟɦɨɫɬɢ 3 ɝɨɞɚ ɢ 1 ɦɟɫɹɰ.
Ɋɚɫɱɟɬ NPV ɩɨ ɮɨɪɦɭɥɟ
NPV = – (60 ɦɥɧ • 1,0 + 80 ɦɥɧ • 0,91) + (40 ɦɥɧ • 1,0 + 51 ɦɥɧ • 0,91 +
+ 53 ɦɥɧ
• 0,82 + 56 ɦɥɧ • 0,75) = – 132,8 ɦɥɧ + (40,0 ɦɥɧ + 46,4 ɦɥɧ +
+ 43,5 ɦɥɧ + 42,0 ɦɥɧ) = — 132,8 ɦɥɧ + 171,9 ɦɥɧ = 39,1 ɦɥɧ ɪɭɛ.
ɑɢɫɬɵɣ ɧɚɪɚɳɟɧɧɵɣ ɞɨɯɨɞ (ɑɇȾ) ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɥɟɞɭɸɳɢɦ
ɨɛɪɚɡɨɦ:
139
ɑ
T
ɇȾ (1 ) ,
— ɪɚɡɦɟɪ ɩɟɪɜɨɧɚɱɚɥɶɧɨɣ ɢɧɜɟɫɬɢɰɢɢ;
ɝɞɟ I
0
— ɩɪɢɬɨɤ ɞɟɧɟɠɧɵɯ ɫɪɟɞɫɬɜ (ɱɢɫɬɚɹ ɩɪɢɛɵɥɶ + ɚɦɨɪɬɢɡɚɰɢɹ) ɜ t-ɦ, ɝɨ-
C
t
ɋ rI
¦
1
t
t
t
0
ɞɭ, ɬɵɫ. ɪɭɛ.;
r — ɝɨɞɨɜɚɹ ɩɪɨɰɟɧɬɧɚɹ ɫɬɚɜɤɚ, %.
ɉɪɢɦɟɪ. ɉɨ ɢɫɯɨɞɧɵɦ ɞɚɧɧɵɦ (ɬɚɛɥ. 4.11) ɪɚɫɫɱɢɬɚɬɶ ɱɢɫɬɵɣ ɧɚɪɚɳɟɧɧɵɣ ɞɨɯɨɞ ɨɬ ɪɟɚɥɢɡɚɰɢɢ ɢɧɜɟɫɬɢɰɢɨɧɧɨɝɨ ɩɪɨɟɤɬɚ. Ƚɨɞɨɜɚɹ
ɩɪɨɰɟɧɬɧɚɹ ɫɬɚɜɤɚ — 10%. Ɋɟɡɭɥɶɬɚɬɵ ɪɚɫɱɟɬɨɜ ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥ. 4.12.
Ɍɚɛɥɢɰɚ 4.12
Ƚɨɞ ɉɨɤɚɡɚɬɟɥɶ
2011 ɝ. 2012 ɝ. 2013 ɝ. 2014 ɝ. 2015 ɝ. 2016 ɝ.
ɂɧɜɟɫɬɢɰɢɹ, ɦɥɧ ɪɭɛ. –60 –80 — — — —
ɑɢɫɬɚɹ ɩɪɢɛɵɥɶ,
ɦɥɧ ɪɭɛ.
— — 38,0 49,0 51,0 54,0
Ⱥɦɨɪɬɢɡɚɰɢɹ,
ɦɥɧ ɪɭɛ.
— — 2,0 2,0 2,0 2,0
ɉɪɢɬɨɤ ɞɟɧɟɠɧɵɯ
ɫɪɟɞɫɬɜ, ɦɥɧ ɪɭɛ.
— — 40,0 51,0 53,0 56,0
Ʉɨɷɮɮɢɰɢɟɧɬ ɧɚɪɚɳɟɧɢɹ
1,1 1,0 1,33 1,21 1,1 1,0
ɇɚɪɚɳɟɧɧɵɣ ɩɪɢɬɨɤ
ɢ ɨɬɬɨɤ, ɦɥɧ ɪɭɛ. –66,0 –80,0 53,2 61,7 58,3 56,0
ɋɚɥɶɞɨ ɧɚɤɨɩɥɟɧɧɨɝɨ
ɩɨɬɨɤɚ, ɦɥɧ ɪɭɛ.
ɑɢɫɬɵɣ ɧɚɪɚɳɟɧɧɵɣ
–146,0 –92,8 –31,1 27,2 83,2
83,2
ɞɨɯɨɞ, ɦɥɧ ɪɭɛ.
ɉɪɢ ɪɟɚɥɢɡɚɰɢɹ ɞɚɧɧɨɝɨ ɦɟɬɨɞɚ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ ɪɹɞ ɞɨɩɭɳɟɧɢɣ:
1) ɫɭɳɟɫɬɜɨɜɚɧɢɟ ɬɨɥɶɤɨ ɨɞɧɨɣ ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ — ɫɬɨɢɦɨɫɬɢ
ɤɚɩɢɬɚɥɚ;
2) ɡɚɞɚɧɧɵɣ ɫɪɨɤ ɪɟɚɥɢɡɚɰɢɢ ɩɪɨɟɤɬɚ;
3) ɧɚɞɟɠɧɨɫɬɶ ɞɚɧɧɵɯ;
4) ɩɪɢɧɚɞɥɟɠɧɨɫɬɶ ɩɥɚɬɟɠɟɣ ɤ ɨɩɪɟɞɟɥɟɧɧɵɦ ɦɨɦɟɧɬɚɦ ɜɪɟɦɟɧɢ;
5) ɫɭɳɟɫɬɜɨɜɚɧɢɟ ɫɨɜɟɪɲɟɧɧɨɝɨ ɪɵɧɤɚ ɤɚɩɢɬɚɥɚ.
Ⱦɚɧɧɵɣ ɦɟɬɨɞ ɢɦɟɟɬ ɨɩɪɟɞɟɥɟɧɧɵɟ ɧɟɞɨɫɬɚɬɤɢ. ȼ ɫɜɹɡɢ ɫ ɬɪɭɞɧɨɫɬɶɸ ɢ ɧɟɨɞɧɨɡɧɚɱɧɨɫɬɶɸ ɩɪɨɝɧɨɡɢɪɨɜɚɧɢɹ ɢ ɮɨɪɦɢɪɨɜɚɧɢɹ ɞɟɧɟɠɧɨɝɨ ɩɨɬɨɤɚ
ɨɬ ɢɧɜɟɫɬɢɰɢɣ, ɚ ɬɚɤɠɟ ɫ ɩɪɨɛɥɟɦɨɣ ɜɵɛɨɪɚ ɫɬɚɜɤɢ ɞɢɫ-
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