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Файл:Анализ и оценка эффективности инвестиций. Учебник для студентов вузов, обучающихся по экономическим специальностям
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x ɩɪɟɞɫɬɨɹɳɢɟ ɪɟɡɭɥɶɬɚɬɵ ɢ ɡɚɬɪɚɬɵ ɜ ɬɟɯ ɠɟ ɜɚɥɸɬɚɯ, ɜ ɤɨɬɨɪɵɯ
ɩɪɨɟɤɬɨɦ ɩɪɟɞɭɫɦɨɬɪɟɧɵ ɩɪɢɨɛɪɟɬɟɧɢɟ ɪɟɫɭɪɫɨɜ ɢ ɩɪɨɞɚɠɚ
ɩɪɨɞɭɤɰɢɢ;
x ɧɚɥɨɝɢ, ɫɛɨɪɵ, ɨɬɱɢɫɥɟɧɢɹ ɢ ɬ.ɩ., ɩɪɟɞɭɫɦɨɬɪɟɧɧɵɟ ɡɚɤɨɧɨɞɚ-
ɬɟɥɶɫɬɜɨɦ.
Ɏɢɧɚɧɫɨɜɚɹ ɨɰɟɧɤɚ ɢɧɜɟɫɬɢɰɢɨɧɧɨɝɨ ɩɪɨɟɤɬɚ ɩɨɡɜɨɥɹɟɬ ɩɪɨɝɧɨɡɢɪɨɜɚɬɶ ɮɢɧɚɧɫɨɜɨɟ ɫɨɫɬɨɹɧɢɟ ɩɪɨɟɤɬɚ ɩɨ ɛɚɡɨɜɵɦ ɮɨɪɦɚɦ ɮɢɧɚɧɫɨɜɨɣ ɨɬɱɟɬɧɨɫɬɢ:
x ɨɬɱɟɬɭ ɨ ɩɪɢɛɵɥɹɯ ɢ ɭɛɵɬɤɚɯ;
x
ɨɬɱɟɬɭ ɨ ɞɜɢɠɟɧɢɢ ɞɟɧɟɠɧɵɯ ɫɪɟɞɫɬɜ;
x ɛɚɥɚɧɫɨɜɨɦɭ ɨɬɱɟɬɭ.
ɗɤɨɧɨɦɢɱɟɫɤɚɹ ɨɰɟɧɤɚ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɢɧɜɟɫɬɢɰɢɨɧɧɨɝɨ ɩɪɨɟɤɬɚ —
ɷɬɨ ɨɰɟɧɤɚ ɟɝɨ ɫɩɨɫɨɛɧɨɫɬɢ ɩɪɢɧɨɫɢɬɶ ɞɨɯɨɞ ɫ ɩɨɦɨɳɶɸ ɪɹɞɚ ɩɨɤɚɡɚɬɟɥɟɣ (ɤɪɢɬɟɪɢɟɜ). ɍɫɥɨɜɧɨ ɢɯ ɦɨɠɧɨ ɩɨɞɪɚɡɞɟɥɢɬɶ ɧɚ ɩɪɨɫɬɵɟ ɢ
ɫɥɨɠɧɵɟ ɢɥɢ ɧɚ ɫɬɚɬɢɱɟɫɤɢɟ ɢ ɞɢɧɚɦɢɱɟɫɤɢɟ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɬɨɝɨ,
ɭɱɢɬɵɜɚɸɬ ɨɧɢ ɩɪɢɧɰɢɩ ɜɪɟɦɟɧɧɨɣ ɫɬɨɢɦɨɫɬɢ ɞɟɧɟɝ ɢɥɢ ɧɟɬ.
Ɏɢɧɚɧɫɨɜɵɟ ɲɤɨɥɵ ɢ ɯɨɡɹɣɫɬɜɟɧɧɚɹ ɩɪɚɤɬɢɤɚ ɜ ɪɚɡɜɢɬɵɯ ɫɬɪɚɧɚɯ
ɩɨ-ɪɚɡɧɨɦɭ ɨɪɢɟɧɬɢɪɨɜɚɧɵ ɧɚ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɬɨɣ ɢɥɢ ɢɧɨɣ ɝɪɭɩɩɵ
ɦɟɬɨɞɨɜ.
ȼ ɩɪɚɤɬɢɤɟ ɚɧɝɥɢɣɫɤɢɯ ɢ ɚɦɟɪɢɤɚɧɫɤɢɯ ɤɨɪɩɨɪɚɰɢɣ ɢɫɩɨɥɶɡɭɸɬɫɹ
ɦɟɬɨɞɵ ɨɰɟɧɤɢ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɢɧɜɟɫɬɢɰɢɣ ɫ ɭɱɟɬɨɦ ɮɚɤɬɨɪɚ ɜɪɟɦɟɧɢ.
Ɍɟɯɧɢɤɚ ɢɯ ɪɚɫɱɟɬɚ ɢ ɢɧɬɟɪɩɪɟɬɚɰɢɢ ɬɪɟɛɭɟɬ ɜɵɫɨɤɨɝɨ ɩɪɨɮɟɫɫɢɨɧɚɥɢɡɦɚ. ȼɦɟɫɬɟ ɫ ɬɟɦ ɭɱɟɬɭ ɢɡɞɟɪɠɟɤ, ɢɯ ɩɥɚɧɢɪɨɜɚɧɢɸ ɢ ɨɛɨɫɧɨɜɚɧɢɸ
ɭɞɟɥɹɟɬɫɹ ɦɟɧɶɲɟ ɜɧɢɦɚɧɢɹ.
ȼ Ƚɟɪɦɚɧɢɢ ɫɤɪɭɩɭɥɟɡɧɨɟ, ɩɨɫɬɚɬɟɣɧɨɟ ɩɥɚɧɢɪɨɜɚɧɢɟ ɢɡɞɟɪɠɟɤ
ɫɨɱɟɬɚɟɬɫɹ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɪɨɫɬɵɯ ɦɟɬɨɞɨɜ ɨɰɟɧɤɢ ɢɧɜɟɫɬɢɰɢɣ.
ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɬɟɯ ɢɥɢ ɢɧɵɯ ɦɟɬɨɞɨɜ ɨɰɟɧɤɢ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɢɧɜɟɫɬɢɰɢɨɧɧɵɯ ɩɪɨɟɤɬɨɜ ɡɚɜɢɫɢɬ ɨɬ ɩɨɫɬɚɜɥɟɧɧɵɯ ɥɨɤɚɥɶɧɵɯ ɰɟɥɟɣ,
ɤɨɬɨɪɵɟ ɞɥɹ ɭɱɚɫɬɜɭɸɳɢɯ ɜ ɢɧɜɟɫɬɢɰɢɨɧɧɨɦ ɩɪɨɰɟɫɫɟ ɦɨɝɭɬ ɛɵɬɶ
ɪɚɡɧɵɦɢ. Ɋɭɤɨɜɨɞɢɬɟɥɹɦ ɨɪɝɚɧɢɡɚɰɢɢ ɞɥɹ ɩɪɢɧɹɬɢɹ ɢɧɜɟɫɬɢɰɢɨɧɧɨɝɨ
ɪɟɲɟɧɢɹ ɜɚɠɧɵ ɩɨɤɚɡɚɬɟɥɢ (ɤɪɢɬɟɪɢɢ), ɤɨɬɨɪɵɟ
ɯɚɪɚɤɬɟɪɢɡɭɸɬ ɜɥɢɹɧɢɟ ɪɟɚɥɢɡɚɰɢɢ ɢɧɜɟɫɬɢɰɢɣ ɧɚ ɤɨɧɟɱɧɵɟ ɮɢɧɚɧɫɨɜɵɟ ɪɟɡɭɥɶɬɚɬɵ ɞɟɹɬɟɥɶɧɨɫɬɢ ɨɪɝɚɧɢɡɚɰɢɢ:
x ɪɟɧɬɚɛɟɥɶɧɨɫɬɶ ɩɪɨɢɡɜɨɞɫɬɜɚ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɚɹ ɨɬɞɚɱɭ ɜɥɨ-
ɠɟɧɧɵɯ ɫɪɟɞɫɬɜ ɜ ɚɤɬɢɜɵ ɩɪɟɞɩɪɢɹɬɢɹ;
x ɪɟɧɬɚɛɟɥɶɧɨɫɬɶ ɩɪɨɞɚɠ, ɪɚɫɫɱɢɬɚɧɧɚɹ ɧɚ ɨɫɧɨɜɟ ɩɨɤɚɡɚɬɟɥɹ
ɱɢɫɬɨɣ ɩɪɢɛɵɥɢ;
x ɪɟɡɭɥɶɬɚɬɵ ɚɧɚɥɢɡɚ ɨɩɟɪɚɰɢɨɧɧɵɯ ɡɚɬɪɚɬ;
x ɪɟɡɭɥɶɬɚɬɵ ɚɧɚɥɢɡɚ ɜɚɥɨɜɨɝɨ ɞɨɯɨɞɚ ɩɪɟɞɩɪɢɹɬɢɹ;
x ɷɮɮɟɤɬɢɜɧɨɫɬɶ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɦɚɬɟɪɢɚɥɶɧɵɯ, ɬɪɭɞɨɜɵɯ ɢ ɮɢ-
ɧɚɧɫɨɜɵɯ
ɪɟɫɭɪɫɨɜ.
91
Ⱦɥɹ ɤɪɟɞɢɬɨɪɨɜ ɝɥɚɜɧɵɦɢ ɩɨɤɚɡɚɬɟɥɹɦɢ ɨɰɟɧɤɢ ɷɮɮɟɤɬɢɜɧɨɫɬɢ
ɢɧɜɟɫɬɢɰɢɣ ɩɪɢɧɹɬɨ ɫɱɢɬɚɬɶ:
x ɭɪɨɜɟɧɶ ɥɢɤɜɢɞɧɨɫɬɢ ɚɤɬɢɜɨɜ (ɤɨɷɮɮɢɰɢɟɧɬ ɛɵɫɬɪɨɣ ɥɢɤɜɢɞ-
ɧɨɫɬɢ);
x ɫɨɨɬɧɨɲɟɧɢɟ ɨɛɨɪɨɬɧɵɯ ɚɤɬɢɜɨɜ ɢ ɤɪɚɬɤɨɫɪɨɱɧɵɯ ɨɛɹɡɚ-
ɬɟɥɶɫɬɜ;
x ɫɨɨɬɧɨɲɟɧɢɟ ɦɟɠɞɭ ɫɨɛɫɬɜɟɧɧɵɦ ɢ ɡɚɟɦɧɵɦ ɤɚɩɢɬɚɥɨɦ ɩɪɟɞ-
ɩɪɢɹɬɢɹ;
x ɫɨɨɬɧɨɲɟɧɢɟ ɦɟɠɞɭ ɞɨɯɨɞɧɨɫɬɶɸ ɚɤɬɢɜɨɜ ɢ ɭɪɨɜɧɟɦ ɪɢɫɤɚ;
x ɤɨɷɮɮɢɰɢɟɧɬ ɱɢɫɬɨɣ ɜɵɪɭɱɤɢ.
Ⱦɥɹ ɢɧɜɟɫɬɨɪɚ ɩɪɚɤɬɢɱɟɫɤɢɣ ɢɧɬɟɪɟɫ ɜɵɡɵɜɚɸɬ
ɤɚɡɚɬɟɥɢ:
x ɪɟɧɬɚɛɟɥɶɧɨɫɬɶ ɫɨɛɫɬɜɟɧɧɨɝɨ ɤɚɩɢɬɚɥɚ;
x ɱɢɫɬɚɹ ɩɪɢɛɵɥɶ, ɩɪɢɯɨɞɹɳɚɹ ɧɚ ɨɞɧɭ ɨɛɵɤɧɨɜɟɧɧɭɸ ɚɤɰɢɸ;
x ɫɨɨɬɧɨɲɟɧɢɟ ɞɢɜɢɞɟɧɞɨɜ ɢ ɚɤɬɢɜɨɜ;
x ɫɨɨɬɧɨɲɟɧɢɟ ɱɢɫɬɨɣ ɩɪɢɛɵɥɢ ɢ ɰɟɧɵ ɨɞɧɨɣ ɨɛɵɤɧɨɜɟɧɧɨɣ ɚɤ-
ɰɢɢ;
x ɫɨɨɬɧɨɲɟɧɢɟ ɪɵɧɨɱɧɨɣ ɢ ɧɨɦɢɧɚɥɶɧɨɣ ɰɟɧɵ ɚɤɰɢɣ;
x ɨɬɧɨɫɢɬɟɥɶɧɨɟ ɢɡɦɟɧɟɧɢɟ ɰɟɧ ɧɚ ɚɤɰɢɸ;
x ɤɨɷɮɮɢɰɢɟɧɬ ɜɵɩɥɚɬɵ ɞɢɜɢɞɟɧɞɨɜ;
x ɤɨɷɮɮɢɰɢɟɧɬ ɩɨɤɪɵɬɢɹ
Ɋɟɲɚɸɳɢɦ ɨɛɳɢɦ ɤɪɢɬɟɪɢɟɦ ɨɰɟɧɤɢ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɢɧɜɟɫɬɢɰɢɨɧɧɵɯ ɩɪɨɟɤɬɨɜ ɹɜɥɹɟɬɫɹ ɱɢɫɬɵɣ ɞɟɧɟɠɧɵɣ ɩɨɬɨɤ ɫ ɭɱɟɬɨɦ ɢɧɜɟɫɬɢɰɢɨɧɧɨɝɨ ɪɢɫɤɚ.
ɞɢɜɢɞɟɧɞɨɜ.
ɫɥɟɞɭɸɳɢɟ ɩɨ-
3.3. Ʉɨɧɰɟɩɰɢɹ ɨɰɟɧɤɢ ɫɬɨɢɦɨɫɬɢ
ɤɚɩɢɬɚɥɚ ɜɨ ɜɪɟɦɟɧɢ
Ʉɨɧɰɟɩɰɢɹ ɨɰɟɧɤɢ ɫɬɨɢɦɨɫɬɢ ɞɟɧɟɝ ɜɨ ɜɪɟɦɟɧɢ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ,
ɱɬɨ ɫɬɨɢɦɨɫɬɶ ɞɟɧɟɝ ɜɨ ɜɪɟɦɟɧɢ ɢɡɦɟɧɹɟɬɫɹ ɫ ɭɱɟɬɨɦ ɧɨɪɦɵ ɩɪɢɛɵɥɢ
ɧɚ ɮɢɧɚɧɫɨɜɨɦ ɪɵɧɤɟ, ɜ ɤɚɱɟɫɬɜɟ ɤɨɬɨɪɨɣ ɢɫɩɨɥɶɡɭɟɬɫɹ ɧɨɪɦɚ ɫɫɭɞɧɨɝɨ ɩɪɨɰɟɧɬɚ. Ʉɨɧɰɟɩɰɢɹ ɫɬɨɢɦɨɫɬɢ ɞɟɧɟɝ ɜɨ ɜɪɟɦɟɧɢ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ
ɜ ɞɜɭɯ ɚɫɩɟɤɬɚɯ.
ɉ ɟ ɪ ɜ ɵ ɣ ɚ ɫ ɩ ɟ ɤ ɬ
Ⱦɟɧɟɠɧɵɟ ɫɪɟɞɫɬɜɚ ɜ ɞɚɧɧɵɣ ɦɨɦɟɧɬ ɢ ɱɟɪɟɡ ɨɩɪɟɞɟɥɟɧɧɵɣ ɩɪɨɦɟɠɭɬɨɤ ɜɪɟɦɟɧɢ ɩɪɢ ɪɚɜɧɨɣ ɧɨɦɢɧɚɥɶɧɨɣ ɫɬɨɢɦɨɫɬɢ ɢɦɟɸɬ ɪɚɡɧɭɸ ɩɨɤɭɩɚɬɟɥɶɧɭɸ ɫɬɨɢɦɨɫɬɶ. Ɍɚɤ, 1000 ɪɭɛ. ɱɟɪɟɡ ɤɚɤɨɟ-ɬɨ ɜɪɟɦɹ ɩɪɢ ɭɪɨɜɧɟ
ɢɧɮɥɹɰɢɢ 10% ɛɭɞɭɬ ɢɦɟɬɶ ɩɨɤɭɩɚɬɟɥɶɧɭɸ ɫɩɨɫɨɛɧɨɫɬɶ ɥɢɲɶ 900 ɪɭɛ.
ȼ ɬ ɨ ɪ ɨ ɣ ɚ ɫ ɩ ɟ
ɤɚɩɢɬɚɥɚ ɢ ɩɨɥɭɱɟɧɢɟɦ ɞɨɯɨɞɨɜ ɨɬ ɷɬɨɝɨ ɨɛɨɪɨɬɚ.
ɫɜɹɡɚɧ ɫ ɩɨɤɭɩɚɬɟɥɶɧɨɣ ɫɩɨɫɨɛɧɨɫɬɶɸ ɞɟɧɟɝ.
ɤ ɬ ɫɜɹɡɚɧ ɫ ɨɛɪɚɳɟɧɢɟɦ ɞɟɧɟɠɧɵɯ ɫɪɟɞɫɬɜ ɤɚɤ
92
ȼ ɰɟɥɨɦ ɧɟɪɚɜɧɨɰɟɧɧɨɫɬɶ ɪɚɡɧɨɜɪɟɦɟɧɧɵɯ ɡɚɬɪɚɬ ɢ ɪɟɡɭɥɶɬɚɬɨɜ
ɥɸɛɨɣ ɮɢɧɚɧɫɨɜɨɣ ɨɩɟɪɚɰɢɢ ɨɛɵɱɧɨ ɩɪɨɹɜɥɹɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ ɩɨɥɭɱɟɧɢɟ ɞɨɯɨɞɚ ɫɟɝɨɞɧɹ ɫɱɢɬɚɟɬɫɹ ɛɨɥɟɟ ɩɪɟɞɩɨɱɬɢɬɟɥɶɧɵɦ, ɱɟɦ ɩɨɥɭɱɟɧɢɟ ɞɨɯɨɞɚ ɡɚɜɬɪɚ, ɚ ɪɚɫɯɨɞɵ ɫɟɝɨɞɧɹ ɦɟɧɟɟ ɩɪɟɞɩɨɱɬɢɬɟɥɶɧɵ, ɱɟɦ
ɪɚɫɯɨɞɵ ɡɚɜɬɪɚ.
ɉɨɧɹɬɢɟ «ɜɪɟɦɟɧɧɚɹ ɫɬɨɢɦɨɫɬɶ ɞɟɧɟɝ» ɩɪɢɨɛɪɟɥɨ ɨɫɨɛɭɸ ɚɤɬɭɚɥɶɧɨɫɬɶ ɜ ɧɚɲɟɣ ɫɬɪɚɧɟ ɫ ɩɟɪɟɯɨɞɨɦ ɤ ɪɵɧɨɱɧɨɣ ɷɤɨɧɨɦɢɤɟ
. ɉɪɢɱɢɧ
ɛɵɥɨ ɧɟɫɤɨɥɶɤɨ: ɢɧɮɥɹɰɢɹ, ɪɚɫɲɢɪɢɜɲɢɟɫɹ ɜɨɡɦɨɠɧɨɫɬɢ ɜɥɨɠɟɧɢɹ
ɜɪɟɦɟɧɧɨ ɫɜɨɛɨɞɧɵɯ ɫɪɟɞɫɬɜ, ɫɧɹɬɢɟ ɜɫɟɜɨɡɦɨɠɧɵɯ ɨɝɪɚɧɢɱɟɧɢɣ ɜ
ɨɬɧɨɲɟɧɢɢ ɮɨɪɦɢɪɨɜɚɧɢɹ ɮɢɧɚɧɫɨɜɵɯ ɪɟɫɭɪɫɨɜ ɯɨɡɹɣɫɬɜɭɸɳɢɦɢ
ɫɭɛɴɟɤɬɚɦɢ. ȼɫɟ ɷɬɨ ɫɜɹɡɚɧɨ ɫ ɬɟɦ, ɱɬɨ ɞɟɧɶɝɢ, ɩɨɦɢɦɨ ɩɪɨɱɟɝɨ, ɢɦɟɸɬ ɟɳɟ ɨɞɧɭ ɨɛɴɟɤɬɢɜɧɨ ɫɭɳɟɫɬɜɭɸɳɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ: ɜɪɟɦɟɧɧɭɸ
ɰɟɧɧɨɫɬɶ.
ȼ ɧɚɢɛɨɥɟɟ ɨɛɳɟɦ ɫɦɵɫɥɟ ɩɨɧɹɬɢɟ «ɜɪɟɦɟɧɧɚɹ ɰɟɧɧɨɫɬɶ ɞɟɧɟɝ»
ɨɡɧɚɱɚɟɬ, ɱɬɨ ɪɭɛɥɶ, ɢɦɟɸɳɢɣɫɹ
ɜ ɪɚɫɩɨɪɹɠɟɧɢɢ ɫɟɝɨɞɧɹ, ɢ ɪɭɛɥɶ,
ɨɠɢɞɚɟɦɵɣ ɤ ɩɨɥɭɱɟɧɢɸ ɜ ɛɭɞɭɳɟɦ, ɧɟ ɪɚɜɧɨɰɟɧɧɵ.
ɂɫɯɨɞɹ ɢɡ ɷɬɨɝɨ ɢɡ ɬɟɨɪɢɢ ɜɪɟɦɟɧɧɨɣ ɰɟɧɧɨɫɬɢ ɞɟɧɟɝ ɜɵɬɟɤɚɸɬ
ɞɜɚ ɜɚɠɧɵɯ ɫɥɟɞɫɬɜɢɹ:
x ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɭɱɟɬɚ ɮɚɤɬɨɪɚ ɜɪɟɦɟɧɢ ɩɪɢ ɪɚɫɱɟɬɚɯ ɷɮɮɟɤɬɢɜ-
ɧɨɫɬɢ ɢɧɜɟɫɬɢɰɢɣ;
x ɧɟɤɨɪɪɟɤɬɧɨɫɬɶ ɩɪɨɫɬɨɝɨ ɫɭɦɦɢɪɨɜɚɧɢɹ ɞɟɧɟɠɧɵɯ ɩɨɬɨɤɨɜ, ɨɬ-
ɧɨɫɹɳɢɯɫɹ ɤ ɪɚɡɧɵɦ ɩɟɪɢɨɞɚɦ.
Ɋɟɚɥɢɡɚɰɢɹ ɢɧɜɟɫɬɢɰɢɨɧɧɨɝɨ ɩɪɨɟɤɬɚ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɜ ɬɟɱɟɧɢɟ
ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɩɟɪɢɨɞɚ ɜɪɟɦɟɧɢ, ɢ ɦɟɠɞɭ ɜɥɨɠɟɧɢɟɦ ɫɪɟɞɫɬɜ ɢ ɨɬɞɚɱɟɣ ɜ ɜɢɞɟ ɱɢɫɬɨɝɨ ɞɟɧɟɠɧɨɝɨ ɩɨɬɨɤɚ ɧɟɢɡɛɟɠɟɧ ɪɚɡɪɵɜ, ɬɚɤ ɧɚɡɵɜɚɟɦɵɣ ɜɪɟɦɟɧɧɨɣ ɥɚɝ, ɤɨɬɨɪɵɣ ɧɟɨɛɯɨɞɢɦɨ ɭɱɢɬɵɜɚɬɶ.
ɉɨɷɬɨɦɭ ɞɥɹ ɨɰɟɧɤɢ ɨɠɢɞɚɟɦɵɯ ɮɢɧɚɧɫɨɜɵɯ ɪɟɡɭɥɶɬɚɬɨɜ ɪɚɡɧɵɯ
ɩɟɪɢɨɞɨɜ ɜɪɟɦɟɧɢ ɩɪɢɦɟɧɹɸɬ ɦɟɬɨɞ ɞɢɫɤɨɧɬɢɪɨɜɚɧɢɹ ɢ ɧɚɪɚɳɟɧɢɹ —
ɩɪɢɜɟɞɟɧɢɟ ɞɟɧɟɠɧɵɯ ɫɭɦɦ ɜ ɫɨɩɨɫɬɚɜɢɦɵɣ ɜɢɞ ɩɨ ɮɚɤɬɨɪɭ ɜɪɟɦɟɧɢ.
ɉɨ ɷɤɨɧɨɦɢɱɟɫɤɨɣ
ɫɭɬɢ ɨɩɟɪɚɰɢɹ ɞɢɫɤɨɧɬɢɪɨɜɚɧɢɹ ɨɛɪɚɬɧɚ ɩɪɨɰɟɫɫɭ
ɧɚɪɚɳɟɧɢɹ (ɪɢɫ. 3.3).
ɇɚɪɚɳɟɧɢɟ Ⱦ (1+ȿ)
ɉɟɪɢɨɞɵ ɩɥɚɧɢɪɨɜɚɧɢɹ 1 2 3 … t
t
Ɉɠɢɞɚɟɦɵɟ ɪɟɡɭɥɶɬɚɬɵ Ⱦ1 Ⱦ2 Ⱦ3 .... Ⱦt
Ⱦ / ( 1+E )t Ⱦɢɫɤɨɧɬɢɪɨɜɚɧɢɟ
Ɋɢɫ. 3.3. ɍɱɟɬ ɮɚɤɬɨɪɚ ɜɪɟɦɟɧɢ ɜ ɮɢɧɚɧɫɨɜɵɯ ɪɚɫɱɟɬɚɯ
93
Ⱦɢɫɤɨɧɬɢɪɨɜɚɧɧɵɟ ɩɨɤɚɡɚɬɟɥɢ ɪɚɫɫɱɢɬɵɜɚɸɬ ɫ ɭɱɟɬɨɦ ɧɟɪɚɜɧɨɰɟɧɧɨɫɬɢ ɪɟɡɭɥɶɬɚɬɨɜ ɢ ɡɚɬɪɚɬ ɢɧɜɟɫɬɢɰɢɨɧɧɨɝɨ ɩɪɨɟɤɬɚ ɜɨ ɜɪɟɦɟɧɢ.
Ɋɚɡɧɨɜɪɟɦɟɧɧɵɟ ɞɟɧɟɠɧɵɟ ɩɨɬɨɤɢ ɩɪɢɜɨɞɹɬ ɜ ɫɨɩɨɫɬɚɜɢɦɨɟ ɡɧɚɱɟɧɢɟ
ɩɭɬɟɦ ɞɢɫɤɨɧɬɢɪɨɜɚɧɢɹ.
ȼ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɭɫɥɨɜɢɣ ɩɪɨɜɟɞɟɧɢɹ ɪɚɫɱɟɬɨɜ ɨɰɟɧɤɢ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɢɧɜɟɫɬɢɰɢɨɧɧɵɯ ɩɪɨɟɤɬɨɜ ɜ ɦɟɬɨɞɚɯ ɞɢɫɤɨɧɬɢɪɨɜɚɧɢɹ ɢ ɧɚɪɚɳɟɧɢɹ ɩɪɢɦɟɧɹɸɬɫɹ ɩɪɨɫɬɵɟ ɢ ɫɥɨɠɧɵɟ ɩɪɨɰɟɧɬɵ.
ɉɪɨɫɬɵɟ ɩɪɨɰɟɧɬɵ ɩɪɢɦɟɧɹɸɬɫɹ ɜ ɤɪɚɬɤɨɫɪɨɱɧɵɯ ɮɢɧɚɧɫɨɜɵɯ
ɨɩɟɪɚɰɢɹɯ ɫɪɨɤɨɦ ɦɟɧɟɟ ɨɞɧɨɝɨ ɝɨɞɚ, ɤɨɝɞɚ ɢɫɩɨɥɶɡɭɟɬɫɹ ɧɚɢɛɨɥɟɟ
ɭɩɪɨɳɟɧɧɚɹ ɫɢɫɬɟɦɚ ɪɚɫɱɟɬɧɵɯ ɚɥɝɨɪɢɬɦɨɜ.
Ȼɚɡɨɣ ɞɥɹ ɢɫɱɢɫɥɟɧɢɹ ɩɪɨɰɟɧɬɨɜ ɡɚ ɤɚɠɞɵɣ ɩɥɚɧɨɜɵɣ ɩɟɪɢɨɞ ɜ
ɫɥɭɱɚɟ ɩɪɨɫɬɵɯ ɩɪɨɰɟɧɬɨɜ ɹɜɥɹɟɬɫɹ ɩɟɪɜɨɧɚɱɚɥɶɧɚɹ (ɢɫɯɨɞɧɚɹ) ɫɭɦɦɚ
ɫɞɟɥɤɢ. ȼ ɫɯɟɦɟ ɩɪɨɫɬɵɯ ɩɪɨɰɟɧɬɨɜ ɩɪɟɞɩɨɥɚɝɚɟɬɫɹ ɧɟɢɡɦɟɧɧɨɫɬɶ ɛɚɡɵ, ɫ ɤɨɬɨɪɨɣ ɩɪɨɢɫɯɨɞɢɬ ɧɚɱɢɫɥɟɧɢɟ.
1. Ȼɭɞɭɳɚɹ ɫɬɨɢɦɨɫɬɶ ɜɤɥɚɞɚ ɫ ɭɱɟɬɨɦ ɧɚɱɢɫɥɟɧɧɨɣ ɫɭɦɦɵ ɩɪɨ-
ɰɟɧɬɚ ɱɟɪɟɡ t ɥɟɬ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
FV = PV(1+r • t),
ɝɞɟ FV — ɛɭɞɭɳɚɹ ɫɬɨɢɦɨɫɬɶ ɞɟɧɟɠɧɵɯ ɩɨɬɨɤɨɜ, ɬɵɫ. ɪɭɛ.;
PV — ɩɟɪɜɨɧɚɱɚɥɶɧɚɹ ɫɭɦɦɚ ɢɧɜɟɫɬɢɪɨɜɚɧɧɵɯ ɞɟɧɟɠɧɵɯ ɫɪɟɞɫɬɜ, ɬɵɫ. ɪɭɛ.;
t — ɤɨɥɢɱɟɫɬɜɨ ɢɧɬɟɪɜɚɥɨɜ, ɩɨ ɤɨɬɨɪɵɦ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɪɚɫɱɟɬ ɩɪɨ-
ɰɟɧɬɧɵɯ ɩɥɚɬɟɠɟɣ;
r — ɩɪɨɰɟɧɬɧɚɹ ɫɬɚɜɤɚ.
Ɇɧɨɠɢɬɟɥɶ (1+ t • r) ɧɚɡɵɜɚɟɬɫɹ ɦɧɨɠɢɬɟɥɟɦ ɧɚɪɚɳɟɧɢɹ ɫɭɦɦɵ
ɩɪɨɫɬɵɯ ɩɪɨɰɟɧɬɨɜ. ȿɝɨ ɡɧɚɱɟɧɢɟ ɜɫɟɝɞɚ ɞɨɥɠɧɨ ɛɨɥɶɲɟ ɟɞɢɧɢɰɵ.
ɋɭɦɦɚ ɩɪɨɫɬɨɝɨ ɩɪɨɰɟɧɬɚ (Ɋ) ɜ ɩɪɨɰɟɫɫɟ ɧɚɪɚɳɟɧɢɹ ɫɬɨɢɦɨɫɬɢ
ɤɚɩɢɬɚɥɚ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ:
Ɋ = PV • t • r.
ɉɪɢɦɟɪ. Ɉɩɪɟɞɟɥɢɬɶ ɛɭɞɭɳɭɸ ɫɬɨɢɦɨɫɬɶ ɜɤɥɚɞɚ ɢ ɫɭɦɦɭ ɩɪɨɫɬɨ-
ɝɨ ɩɪɨɰɟɧɬɚ ɡɚ ɝɨɞ ɩɪɢ ɫɥɟɞɭɸɳɢɯ ɭɫɥɨɜɢɹɯ:
x ɩɟɪɜɨɧɚɱɚɥɶɧɚɹ ɫɭɦɦɚ ɜɤɥɚɞɚ — 50 000 ɪɭɛ.;
x ɩɪɨɰɟɧɬɵ ɧɚɱɢɫɥɹɸɬɫɹ ɟɠɟɤɜɚɪɬɚɥɶɧɨ;
x ɝɨɞɨɜɚɹ ɩɪɨɰɟɧɬɧɚɹ ɫɬɚɜɤɚ — 12%.
x ɩɪɨɰɟɧɬɧɚɹ ɫɬɚɜɤɚ, ɜɵɩɥɚɱɢɜɚɟɦɚɹ ɟɠɟɤɜɚɪɬɚɥɶɧɨ — 3%.
Ɋɟɲɟɧɢɟ.
ɫɭɦɦɚ ɩɪɨɰɟɧɬɚ ɫɨɫɬɚɜɢɬ
Ɋ = 50 000 •4 •0,03 = 6000 ɪɭɛ.;
Ȼɭɞɭɳɚɹ ɫɬɨɢɦɨɫɬɶ ɜɤɥɚɞɚ ɫɨɫɬɚɜɢɬ
FV = 50 000 • (1+4 •0,03) = 56 000 ɪɭɛ.
94
ɉɪɢɦɟɪ. Ɉɩɪɟɞɟɥɢɬɶ ɩɟɪɢɨɞ ɧɚɱɢɫɥɟɧɢɹ ɩɪɢ ɝɨɞɨɜɨɣ ɩɪɨɰɟɧɬɧɨɣ
ɫɬɚɜɤɟ r = 0,1, ɡɚ ɤɨɬɨɪɵɣ ɩɟɪɜɨɧɚɱɚɥɶɧɵɣ ɤɚɩɢɬɚɥ 100 ɬɵɫ. ɪɭɛ. ɜɵɪɚɫɬɟɬ ɞɨ 140 ɬɵɫ. ɪɭɛ. ɩɨ ɩɪɨɫɬɵɦ ɩɪɨɰɟɧɬɚɦ.
Ɋɟɲɟɧɢɟ.
FV = PV(1+ r • t),
ɨɬɫɸɞɚ
FV PVPV
t =
140 ɬɵɫ. 100 ɬɵɫ.
r 100 ɬɵɫ.0,1
ɝɨɞɚ.
4
ɉɪɢɦɟɪ. Ɋɚɫɫɱɢɬɚɬɶ ɩɪɨɫɬɭɸ ɫɬɚɜɤɭ ɩɪɨɰɟɧɬɨɜ r, ɩɪɢ ɤɨɬɨɪɨɣ
ɩɟɪɜɨɧɚɱɚɥɶɧɵɣ ɤɚɩɢɬɚɥ ɜ ɪɚɡɦɟɪɟ 200 ɬɵɫ. ɪɭɛ. ɞɨɫɬɢɝɧɟɬ
230 ɬɵɫ. ɪɭɛ. ɱɟɪɟɡ 2 ɝɨɞɚ.
Ɋɟɲɟɧɢɟ.
FV PV
r
tPV
230 ɬɵɫ. 200 ɬɵɫ.
2200ɬɵɫ.
0, 075, ɢɥɢ 7, 5 %.
2. ɇɚɫɬɨɹɳɚɹ ɫɬɨɢɦɨɫɬɶ ɞɟɧɟɠɧɵɯ ɫɪɟɞɫɬɜ Ʉɧ ɫ ɭɱɟɬɨɦ ɧɚɱɢɫ-
ɥɟɧɧɨɣ ɫɭɦɦɵ ɩɪɨɫɬɨɝɨ ɩɪɨɰɟɧɬɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ:
1
PV FV
(1 )
tr
.
Ɇɧɨɠɢɬɟɥɶ
1
(1 )tr
ɧɚɡɵɜɚɟɬɫɹ ɞɢɫɤɨɧɬɧɵɦ ɦɧɨɠɢɬɟɥɟɦ ɫɭɦ-
ɦɵ ɩɪɨɫɬɵɯ ɩɪɨɰɟɧɬɨɜ, ɟɝɨ ɡɧɚɱɟɧɢɟ ɜɫɟɝɞɚ ɞɨɥɠɧɨ ɛɵɬɶ ɦɟɧɶɲɟ
ɟɞɢɧɢɰɵ.
ɋɭɦɦɚ ɩɪɨɫɬɨɝɨ ɩɪɨɰɟɧɬɚ ɜ ɩɪɨɰɟɫɫɟ ɞɢɫɤɨɧɬɢɪɨɜɚɧɢɹ ɫɬɨɢɦɨɫɬɢ
ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
P = FV – PV.
ɉɪɢɦɟɪ. Ɉɩɪɟɞɟɥɢɬɶ ɧɚɫɬɨɹɳɭɸ (ɬɟɤɭɳɭɸ) ɫɬɨɢɦɨɫɬɶ ɜɤɥɚɞɚ ɢ
ɫɭɦɦɭ ɞɢɫɤɨɧɬɚ ɩɨ ɩɪɨɫɬɨɦɭ ɩɪɨɰɟɧɬɭ ɡɚ ɝɨɞ ɩɪɢ ɫɥɟɞɭɸɳɢɯ ɭɫɥɨɜɢɹɯ:
x ɤɨɧɟɱɧɚɹ ɫɭɦɦɚ ɜɤɥɚɞɚ — 50 000 ɪɭɛ.;
x ɩɪɨɰɟɧɬɵ ɧɚɱɢɫɥɹɸɬɫɹ ɟɠɟɤɜɚɪɬɚɥɶɧɨ;
x ɝɨɞɨɜɚɹ ɩɪɨɰɟɧɬɧɚɹ ɫɬɚɜɤɚ — 12%.
x ɞɢɫɤɨɧɬɧɚɹ ɫɬɚɜɤɚ, ɜɵɩɥɚɱɢɜɚɟɦɚɹ ɟɠɟɤɜɚɪɬɚɥɶɧɨ — 3%.
Ɋɟɲɟɧɢɟ.
ɇɚɫɬɨɹɳɚɹ ɫɬɨɢɦɨɫɬɶ ɜɤɥɚɞɚ ɫɨɫɬɚɜɢɬ
50 000 44 642,8
PV
1
(1 4 0, 03)
95
ɪɭɛ.;
ɇɚɱɢɫɥɟɧɧɚɹ ɫɭɦɦɚ ɞɢɫɤɨɧɬɚ ɫɨɫɬɚɜɢɬ
Ɋ = 50 000 – 44 642,8 = 5357,2 ɪɭɛ.
ɋɥɨɠɧɵɟ ɩɪɨɰɟɧɬɵ ɲɢɪɨɤɨ ɩɪɢɦɟɧɹɸɬɫɹ ɜ ɞɨɥɝɨɫɪɨɱɧɵɯ ɮɢɧɚɧ-
ɫɨɜɵɯ ɨɩɟɪɚɰɢɹɯ ɫɨ ɫɪɨɤɨɦ ɛɨɥɟɟ ɨɞɧɨɝɨ ɝɨɞɚ. Ⱦɥɹ ɪɚɫɱɟɬɚ ɩɨ ɫɥɨɠɧɵɦ ɩɪɨɰɟɧɬɚɦ ɢɫɩɨɥɶɡɭɟɬɫɹ ɛɨɥɟɟ ɨɛɲɢɪɧɚɹ ɫɢɫɬɟɦɚ ɪɚɫɱɟɬɧɵɯ ɚɥɝɨɪɢɬɦɨɜ.
Ȼɚɡɨɣ ɞɥɹ ɢɫɱɢɫɥɟɧɢɹ ɩɪɨɰɟɧɬɨɜ ɡɚ ɤɚɠɞɵɣ ɩɥɚɧɨɜɵɣ ɩɟɪɢɨɞ ɩɪɢ
ɫɥɨɠɧɵɯ ɩɪɨɰɟɧɬɚɯ ɹɜɥɹɸɬɫɹ ɩɟɪɜɨɧɚɱɚɥɶɧɚɹ (ɢɫɯɨɞɧɚɹ) ɫɭɦɦɚ ɫɞɟɥɤɢ ɢ ɤ ɷɬɨɦɭ ɜɪɟɦɟɧɢ ɧɚɤɨɩɥɟɧɧɵɟ ɩɪɨɰɟɧɬɵ.
1. ɉɪɢ ɪɚɫɱɟɬɟ ɛɭɞɭɳɟɣ ɫɭɦɦɵ ɜɤɥɚɞɚ ɜ ɩɪɨɰɟɫɫɟ ɟɝɨ ɧɚɪɚɳɟɧɢɹ
ɩɨ ɫɥɨɠɧɵɦ ɩɪɨɰɟɧɬɚɦ ɢɫɩɨɥɶɡɭɟɬɫɹ ɫɥɟɞɭɸɳɚɹ ɮɨɪɦɭɥɚ:
PV = FV(1 + r)t.
ɇɚɱɢɫɥɟɧɧɚɹ ɫɭɦɦɚ ɩɪɨɰɟɧɬɚ Ɋ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
Ɋ = FV – PV.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɟɫɥɢ ɢɧɜɟɫɬɢɰɢɹ ɨɫɭɳɟɫɬɜɥɟɧɚ ɧɚ ɭɫɥɨɜɢɹɯ ɫɥɨɠɧɨɝɨ ɩɪɨɰɟɧɬɚ, ɬɨ ɝɨɞɨɜɨɣ ɞɨɯɨɞ ɩɨ ɨɩɪɟɞɟɥɟɧɧɨɣ ɝɨɞɨɜɨɣ ɫɬɚɜɤɟ ɢɫɱɢɫɥɹɟɬɫɹ ɧɟ ɫ ɢɫɯɨɞɧɨɣ ɫɬɨɢɦɨɫɬɢ ɢɧɜɟɫɬɢɪɨɜɚɧɧɨɝɨ ɤɚɩɢɬɚɥɚ, ɚ ɫ ɨɛɳɟɣ ɫɭɦɦɵ, ɜɤɥɸɱɚɸɳɟɣ ɪɚɧɟɟ ɧɚɱɢɫɥɟɧɧɵɟ ɢ ɧɟɜɨɫɬɪɟɛɨɜɚɧɧɵɟ ɢɧɜɟɫɬɨɪɨɦ ɩɪɨɰɟɧɬɵ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɩɪɨɢɫɯɨɞɢɬ ɤɚɩɢɬɚɥɢɡɚɰɢɹ ɩɪɨɰɟɧ-
ɬɨɜ ɩɨ ɦɟɪɟ ɢɯ ɧɚɱɢɫɥɟɧɢɹ, ɬ.ɟ
. ɢɫɯɨɞɧɚɹ ɛɚɡɚ ɜɫɟ ɜɪɟɦɹ ɜɨɡɪɚɫɬɚɟɬ.
ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɜ ɪɚɫɱɟɬɚɯ ɫɥɨɠɧɨɝɨ ɩɪɨɰɟɧɬɚ ɜ ɫɥɭɱɚɟ ɦɧɨɝɨɤɪɚɬɧɨɝɨ ɟɝɨ ɧɚɱɢɫɥɟɧɢɹ ɡɧɚɱɢɬɟɥɶɧɨ ɜɵɝɨɞɧɟɟ, ɩɨɫɤɨɥɶɤɭ ɜɥɨɠɟɧɧɵɣ ɤɚɩɢɬɚɥ ɩɨɫɬɨɹɧɧɨ ɜɨɡɪɚɫɬɚɟɬ (ɪɢɫ. 3.4).
Ɋɢɫ. 3.4. Ⱦɨɯɨɞɵ ɩɨ ɩɪɨɫɬɵɦ ɢ ɫɥɨɠɧɵɦ ɩɪɨɰɟɧɬɚɦ
Ɋɢɫɭɧɨɤ 3.4 ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɡɚ ɩɟɪɢɨɞ ɦɟɧɟɟ 1 ɝɨɞɚ ɜɵɝɨɞɧɨ ɜɤɥɚɞɵɜɚɬɶ ɤɚɩɢɬɚɥ ɩɨ ɩɪɨɫɬɵɦ ɩɪɨɰɟɧɬɚɦ. Ɂɚ ɩɟɪɢɨɞ ɛɨɥɟɟ 1 ɝɨɞɚ — ɩɨ
ɫɥɨɠɧɵɦ ɩɪɨɰɟɧɬɚɦ. ɇɚ ɩɟɪɢɨɞ 1 ɝɨɞ — ɪɟɡɭɥɶɬɚɬ ɨɞɢɧɚɤɨɜ.
96
Ɏɨɪɦɭɥɚ ɫɥɨɠɧɵɯ ɩɪɨɰɟɧɬɨɜ ɢɫɩɨɥɶɡɭɟɬɫɹ ɩɪɢ ɨɰɟɧɤɟ ɷɮɮɟɤɬɢɜ-
F
ɧɨɫɬɢ ɢɧɜɟɫɬɢɰɢɣ. ȼɵɪɚɠɟɧɢɟ (1 + r)
t
ɧɚɡɵɜɚɸɬ ɦɭɥɶɬɢɩɥɢɰɢɪɭɸɳɢɦ
ɦɧɨɠɢɬɟɥɟɦ, ɢɥɢ ɦɧɨɠɢɬɟɥɟɦ ɧɚɪɚɳɟɧɢɹ ɫɥɨɠɧɵɯ ɩɪɨɰɟɧɬɨɜ.
ɗɤɨɧɨɦɢɱɟɫɤɢɣ ɫɦɵɫɥ ɦɧɨɠɢɬɟɥɹ ɫɨɫɬɨɢɬ ɜ ɫɥɟɞɭɸɳɟɦ: ɨɧ ɩɨɤɚɡɵɜɚɟɬ ɛɭɞɭɳɭɸ ɫɬɨɢɦɨɫɬɶ ɜɥɨɠɟɧɧɨɝɨ ɤɚɩɢɬɚɥɚ ɱɟɪɟɡ t ɥɟɬ ɩɪɢ ɡɚɞɚɧɧɨɣ ɩɪɨɰɟɧɬɧɨɣ ɫɬɚɜɤɟ r.
ɉɪɢɦɟɪ. Ɉɩɪɟɞɟɥɢɬɶ ɛɭɞɭɳɭɸ ɫɬɨɢɦɨɫɬɶ ɜɤɥɚɞɚ ɢ ɫɭɦɦɭ
ɫɥɨɠɧɨɝɨ ɩɪɨɰɟɧɬɚ ɡɚ ɜɟɫɶ ɩɟɪɢɨɞ ɢɧɜɟɫɬɢɪɨɜɚɧɢɹ ɩɪɢ ɫɥɟɞɭɸɳɢɯ
ɭɫɥɨɜɢɹɯ:
x ɩɟɪɜɨɧɚɱɚɥɶɧɚɹ ɫɬɨɢɦɨɫɬɶ
ɜɤɥɚɞɚ — 50 000 ɪɭɛ.;
x ɝɨɞɨɜɚɹ ɩɪɨɰɟɧɬɧɚɹ ɫɬɚɜɤɚ — 12%.
x ɩɪɨɰɟɧɬɧɚɹ ɫɬɚɜɤɚ, ɜɵɩɥɚɱɢɜɚɟɦɚɹ ɟɠɟɤɜɚɪɬɚɥɶɧɨ, — 3%;
x ɨɛɳɢɣ ɩɟɪɢɨɞ ɢɧɜɟɫɬɢɪɨɜɚɧɢɹ — 1 ɝɨɞ.
Ɋɟɲɟɧɢɟ.
Ȼɭɞɭɳɚɹ ɫɬɨɢɦɨɫɬɶ ɫɨɫɬɚɜɢɬ
50 000 (1 0, 03) 56 275FV ɪɭɛ.
4
ɇɚɱɢɫɥɟɧɧɚɹ ɫɭɦɦɚ ɩɪɨɰɟɧɬɚ ɪɚɜɧɚ
Ɋ = 56 275 – 50 000 = 6275 ɪɭɛ.
ɉɪɢ ɜɥɨɠɟɧɢɢ ɤɚɩɢɬɚɥɚ ɧɚ ɞɟɩɨɡɢɬɧɵɣ ɫɱɟɬ ɦɨɠɟɬ ɛɵɬɶ ɫɢɬɭɚɰɢɹ,
ɤɨɝɞɚ ɫɪɨɤ ɨɩɟɪɚɰɢɢ ɫɨɫɬɚɜɥɹɟɬ ɧɟɰɟɥɨɟ ɱɢɫɥɨ ɥɟɬ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɤɪɟɞɢɬɨɪɵ ɢɫɩɨɥɶɡɭɸɬ ɫɦɟɲɚɧɧɵɣ ɩɨɪɹɞɨɤ ɧɚɱɢɫɥɟɧɢɹ ɩɪɨɰɟɧɬɨɜ:
ɫɥɨɠɧɵɟ ɩɪɨɰɟɧɬɵ ɧɚɱɢɫɥɹɸɬɫɹ ɧɚ ɩɟɪɢɨɞ, ɢɡɦɟɪɟɧɧɵɣ ɰɟɥɵɦɢ ɝɨɞɚɦɢ, ɚ ɩɪɨɰɟɧɬɵ ɡɚ ɞɪɨɛɧɭɸ ɱɚɫɬɶ ɫɪɨɤɚ ɧɚɱɢɫɥɹɸɬɫɹ ɩɨ ɩɪɨɫɬɨɣ
ɩɪɨɰɟɧɬɧɨɣ ɫɬɚɜɤɟ. Ɍɨɝɞɚ ɛɭɞɭɳɚɹ (ɧɚɪɚɳɟɧɧɚɹ) ɫɬɨɢɦɨɫɬɶ ɜɥɨɠɟɧ
ɧɨɝɨ ɤɚɩɢɬɚɥɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
VPV r r
ɝɞɟ n — ɱɢɫɥɨ ɩɨɥɧɵɯ ɥɟɬ ɜ ɫɨɫɬɚɜɟ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɢ ɨɩɟɪɚɰɢɢ;
n — ɱɢɫɥɨ ɞɧɟɣ ɜ ɨɬɪɟɡɤɟ ɜɪɟɦɟɧɢ, ɩɪɢɯɨɞɹɳɟɦɫɹ ɧɚ ɧɟɩɨɥɧɵɣ ɝɨɞ;
k — ɜɪɟɦɟɧɧɚɹ ɛɚɡɚ.
(1 ) (1 ) .
k
n
t
ɉɪɢɦɟɪ. ɂɧɜɟɫɬɨɪ ɜɤɥɚɞɵɜɚɟɬ 100 ɬɵɫ. ɪɭɛ. ɧɚ ɞɟɩɨɡɢɬɧɵɣ ɫɱɟɬ
ɛɚɧɤɚ ɩɨɞ 12% ɝɨɞɨɜɵɯ. Ⱦɟɣɫɬɜɢɟ ɞɨɝɨɜɨɪɚ ɪɚɫɩɪɨɫɬɪɚɧɹɟɬɫɹ ɧɚ ɩɟɪɢɨɞ ɫ 1 ɝɨ ɢɸɧɹ 2011 ɝ. ɩɨ 31 ɞɟɤɚɛɪɹ 2014 ɝ. Ɉɩɪɟɞɟɥɢɬɶ ɛɭɞɭɳɭɸ
ɫɬɨɢɦɨɫɬɶ ɩɟɪɜɨɧɚɱɚɥɶɧɨɝɨ ɤɚɩɢɬɚɥɚ ɩɨ ɮɨɪɦɭɥɟ ɫɥɨɠɧɵɯ ɩɪɨɰɟɧɬɨɜ
ɢ ɩɨ ɮɨɪɦɭɥɟ, ɩɪɟɞɭɫɦɚɬɪɢɜɚɸɳɟɣ ɫɦɟɲɚɧɧɵɣ ɩɨɪɹɞɨɤ ɢɫɱɢɫɥɟɧɢɹ
ɩɪɨɰɟɧɬɨɜ.
-
97
Ɋɟɲɟɧɢɟ.
ɜ ɫɥɭɱɚɟ ɧɚɱɢɫɥɟɧɢɹ ɫɥɨɠɧɵɯ ɩɪɨɰɟɧɬɨɜ ɡɚ ɜɟɫɶ ɫɪɨɤ ɞɨɝɨɜɨɪɚ
100 ɬɵɫ. (1 0,12) (1 0, 01) 140, 5 ɬɵɫ.1,07 150,3FV ɬɵɫ. ɪɭɛ.;
37
ɫɦɟɲɚɧɧɵɦ ɫɩɨɫɨɛɨɦ:
100 ɬɵɫ. (1 0,12) (1 214 / 360 0,12)
FV
140,5 ɬɵɫ. 1,071 150, 5 ɬɵɫ. ɪɭɛ.
3
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɦɟɲɚɧɧɵɦ ɦɟɬɨɞɨɦ ɧɚɱɢɫɥɟɧɢɹ ɩɪɨɰɟɧɬɨɜ ɢɧɜɟɫɬɨɪ ɩɨɥɭɱɢɬ ɧɚ 200 ɪɭɛ. ɛɨɥɶɲɟ.
2. ɉɪɢ ɪɚɫɱɟɬɟ ɧɚɫɬɨɹɳɟɣ ɫɬɨɢɦɨɫɬɢ ɞɟɧɟɠɧɵɯ ɫɪɟɞɫɬɜ ɜ ɩɪɨɰɟɫɫɟ
ɞɢɫɤɨɧɬɢɪɨɜɚɧɢɹ (Ʉ
) ɩɨ ɫɥɨɠɧɵɦ ɩɪɨɰɟɧɬɚɦ ɢɫɩɨɥɶɡɭɟɬɫɹ ɫɥɟɞɭɸ-
ɧ
ɳɚɹ ɮɨɪɦɭɥɚ:
PV FV
ɝɞɟ FV — ɛɭɞɭɳɚɹ ɫɬɨɢɦɨɫɬɶ ɜɤɥɚɞɚ;
t — ɱɢɫɥɨ ɢɧɬɟɪɜɚɥɨɜ, ɩɨ ɤɨɬɨɪɵɦ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɪɚɫɱɟɬ ɩɪɨɰɟɧɬɧɵɯ
ɩɥɚɬɟɠɟɣ;
r — ɩɪɨɰɟɧɬɧɚɹ ɫɬɚɜɤɚ.
1
r
(1 )
,
t
ɇɚɱɢɫɥɟɧɧɚɹ ɫɭɦɦɚ ɞɢɫɤɨɧɬɚ D ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ
P = FV – PV.
ɉɪɢɦɟɪ. Ɉɩɪɟɞɟɥɢɬɶ ɧɚɫɬɨɹɳɭɸ ɫɬɨɢɦɨɫɬɶ ɞɟɧɟɠɧɵɯ ɫɪɟɞɫɬɜ
ɢ ɫɭɦɦɭ ɞɢɫɤɨɧɬɚ ɩɨ ɫɥɨɠɧɵɦ ɩɪɨɰɟɧɬɚɦ ɡɚ 5 ɥɟɬ ɩɪɢ ɫɥɟɞɭɸɳɢɯ
ɭɫɥɨɜɢɹɯ:
x ɛɭɞɭɳɚɹ ɫɬɨɢɦɨɫɬɶ ɜɤɥɚɞɚ — 50 000 ɪɭɛ.;
x ɩɪɨɰɟɧɬɧɚɹ ɫɬɚɜɤɚ, ɜɵɩɥɚɱɢɜɚɟɦɚɹ ɟɠɟɝɨɞɧɨ — 10%.
Ɋɟɲɟɧɢɟ.
ɇɚɫɬɨɹɳɚɹ ɫɬɨɢɦɨɫɬɶ ɫɨɫɬɚɜɢɬ
50 000
PV
(1 0 ,1)
5
31 056,0
ɪɭɛ.;
ɧɚɱɢɫɥɟɧɧɚɹ ɫɭɦɦɚ ɞɢɫɤɨɧɬɚ
P = 50 000 – 31 056,0 = 18 944,0 ɪɭɛ.
3. ɉɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɩɪɨɰɟɧɬɧɨɣ ɫɬɚɜɤɢ, ɢɫɩɨɥɶɡɭɟɦɨɣ ɜ ɪɚɫɱɟɬɚɯ
ɫɬɨɢɦɨɫɬɢ ɞɟɧɟɠɧɵɯ ɫɪɟɞɫɬɜ ɩɨ ɫɥɨɠɧɵɦ ɩɪɨɰɟɧɬɚɦ, ɩɪɢɦɟɧɹɟɬɫɹ
ɫɥɟɞɭɸɳɚɹ ɮɨɪɦɭɥɚ:
98
1/
t
FV
§·
i
¨¸
PV
©¹
1.
ɉɪɢɦɟɪ. Ɉɩɪɟɞɟɥɢɬɶ ɝɨɞɨɜɭɸ ɫɬɚɜɤɭ ɞɨɯɨɞɧɨɫɬɢ ɨɛɥɢɝɚɰɢɢ ɩɪɢ
ɫɥɟɞɭɸɳɢɯ ɭɫɥɨɜɢɹɯ:
x ɧɨɦɢɧɚɥ ɨɛɥɢɝɚɰɢɢ, ɩɨɞɥɟɠɚɳɟɣ ɩɨɝɚɲɟɧɢɸ ɱɟɪɟɡ 3 ɝɨɞɚ, ɫɨ-
ɫɬɚɜɥɹɟɬ 5000 ɪɭɛ.;
x ɰɟɧɚ, ɩɨ ɤɨɬɨɪɨɣ ɨɛɥɢɝɚɰɢɹ ɪɟɚɥɢɡɭɟɬɫɹ ɜ ɦɨɦɟɧɬ ɟɟ ɷɦɢɫɫɢɢ,
ɫɨɫɬɚɜɥɹɟɬ 3000 ɪɭɛ.
Ɋɟɲɟɧɢɟ.
Ƚɨɞɨɜɚɹ ɫɬɚɜɤɚ ɞɨɯɨɞɧɨɫɬɢ ɫɨɫɬɚɜɢɬ
§·
r
¨¸
3000
©¹
11,1910,19,ɢɥɢ 19%.
1/3
5000
ɉɪɢɦɟɪ. ɂɧɜɟɫɬɨɪ ɢɦɟɟɬ 300 000 ɪɭɛ. ɢ ɠɟɥɚɟɬ ɩɨɥɭɱɢɬɶ ɱɟɪɟɡ
2 ɝɨɞɚ 400 000 ɪɭɛ. Ʉɚɤɨɜɨ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɞɨɥɠɧɨ ɛɵɬɶ ɦɢɧɢɦɚɥɶɧɨɟ
ɡɧɚɱɟɧɢɟ ɝɨɞɨɜɨɣ ɩɪɨɰɟɧɬɧɨɣ ɫɬɚɜɤɢ?
Ɋɟɲɟɧɢɟ.
ɉɨɥɶɡɭɟɦɫɹ ɮɨɪɦɭɥɨɣ
§·
350 000
r
¨¸
300 000
©¹
1/ 2
10,08,ɢɥɢ 8%.
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɞɥɹ ɬɨɝɨ ɱɬɨɛɵ ɩɨɥɭɱɢɬɶ ɧɟɨɛɯɨɞɢɦɭɸ ɫɭɦɦɭ,
ɧɭɠɧɨ ɜɥɨɠɢɬɶ ɞɟɧɟɠɧɵɟ ɫɪɟɞɫɬɜɚ ɩɨ ɝɨɞɨɜɨɣ ɫɬɚɜɤɟ ɧɟ ɧɢɠɟ 8%.
4. ɗɮɮɟɤɬɢɜɧɚɹ ɩɪɨɰɟɧɬɧɚɹ ɫɬɚɜɤɚ ɜ ɩɪɨɰɟɫɫɟ ɧɚɪɚɳɟɧɢɹ ɫɬɨɢɦɨɫɬɢ ɞɟɧɟɠɧɵɯ ɫɪɟɞɫɬɜ ɩɨ ɫɥɨɠɧɵɦ ɩɪɨɰɟɧɬɚɦ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɩɨ
ɮɨɪɦɭɥɟ
t
r
§·
r
11,
ɷ
¨¸
t
©¹
ɝɞɟ r
— ɷɮɮɟɤɬɢɜɧɚɹ ɫɪɟɞɧɟɝɨɞɨɜɚɹ ɩɪɨɰɟɧɬɧɚɹ ɫɬɚɜɤɚ ɩɪɢ ɧɚɪɚɳɟɧɢɢ
ɷ
ɫɬɨɢɦɨɫɬɢ ɞɟɧɟɠɧɵɯ ɫɪɟɞɫɬɜ ɩɨ ɫɥɨɠɧɵɦ ɩɪɨɰɟɧɬɚɦ;
r — ɝɨɞɨɜɚɹ ɩɪɨɰɟɧɬɧɚɹ ɫɬɚɜɤɚ, ɢɫɩɨɥɶɡɭɟɦɚɹ ɩɪɢ ɧɚɪɚɳɟɧɢɢ ɫɬɨɢɦɨ-
ɫɬɢ ɞɟɧɟɠɧɵɯ ɫɪɟɞɫɬɜ ɩɨ ɫɥɨɠɧɵɦ ɩɪɨɰɟɧɬɚɦ, %;
t — ɱɢɫɥɨ ɧɚɱɢɫɥɟɧɢɣ ɜ ɝɨɞɭ.
ɉɪɢɦɟɪ. Ɉɩɪɟɞɟɥɢɬɶ ɷɮɮɟɤɬɢɜɧɭɸ ɫɪɟɞɧɟɝɨɞɨɜɭɸ ɩɪɨɰɟɧɬɧɭɸ
ɫɬɚɜɤɭ ɩɪɢ ɫɥɟɞɭɸɳɢɯ ɭɫɥɨɜɢɹɯ:
x ɞɟɧɟɠɧɚɹ ɫɭɦɦɚ 5000 ɪɭɛ. ɩɨɦɟɳɟɧɚ ɜ ɤɨɦɦɟɪɱɟɫɤɢɣ ɛɚɧɤ ɧɚ
ɞɟɩɨɡɢɬ ɫɪɨɤɨɦ ɧɚ 1 ɝɨɞ;
99
x ɝɨɞɨɜɚɹ ɩɪɨɰɟɧɬɧɚɹ ɫɬɚɜɤɚ, ɩɨ ɤɨɬɨɪɨɣ ɟɠɟɤɜɚɪɬɚɥɶɧɨ ɨɫɭɳɟɫɬ-
ɜɥɹɟɬɫɹ ɧɚɱɢɫɥɟɧɢɟ ɩɪɨɰɟɧɬɚ, ɫɨɫɬɚɜɥɹɟɬ 12%.
Ɋɟɲɟɧɢɟ.
ɗɮɮɟɤɬɢɜɧɚɹ ɫɪɟɞɧɟɝɨɞɨɜɚɹ ɩɪɨɰɟɧɬɧɚɹ ɫɬɚɜɤɚ ɫɨɫɬɚɜɢɬ
4
0,12
§·
110,125,ɢɥɢ 12,5%.
r
ɷ
¨¸
4
©¹
Ɋɟɡɭɥɶɬɚɬɵ ɪɚɫɱɟɬɨɜ ɩɨɤɚɡɵɜɚɸɬ, ɱɬɨ ɭɫɥɨɜɢɹ ɪɚɡɦɟɳɟɧɢɹ ɜɤɥɚɞɚ
ɧɚ 1 ɝɨɞ ɩɨɞ 12% ɝɨɞɨɜɵɯ ɩɪɢ ɟɠɟɤɜɚɪɬɚɥɶɧɨɦ ɧɚɱɢɫɥɟɧɢɢ ɩɪɨɰɟɧɬɨɜ
ɪɚɜɧɨɡɧɚɱɧɵ ɭɫɥɨɜɢɹɦ ɧɚɱɢɫɥɟɧɢɹ ɷɬɢɯ ɩɪɨɰɟɧɬɨɜ 1 ɪɚɡ ɜ ɝɨɞ ɩɨɞ
12,5% ɝɨɞɨɜɵɯ.
ɉɪɢ ɨɰɟɧɤɟ ɫɬɨɢɦɨɫɬɢ ɞɟɧɟɝ ɜɨ ɜɪɟɦɟɧɢ ɩɨ ɫɥɨɠɧɵɦ ɩɪɨɰɟɧɬɚɦ
ɧɚɞɨ ɢɦɟɬɶ ɜ ɜɢɞɭ, ɱɬɨ ɧɚ ɪɟɡɭɥɶɬɚɬ ɨɰɟɧɤɢ ɨɤɚɡɵɜɚɟɬ ɜɥɢɹɧɢɟ ɧɟ
ɬɨɥɶɤɨ ɫɬɚɜɤɚ ɩɪɨɰɟɧɬɚ, ɧɨ ɢ
ɱɢɫɥɨ ɢɧɬɟɪɜɚɥɨɜ ɜɵɩɥɚɬ ɜ ɬɟɱɟɧɢɟ ɨɞ-
ɧɨɝɨ ɢ ɬɨɝɨ ɠɟ ɨɛɳɟɝɨ ɩɥɚɬɟɠɧɨɝɨ ɩɟɪɢɨɞɚ.
ɉɪɢɦɟɪ. ȿɫɥɢ ɜɤɥɚɞ ɜ ɫɭɦɦɟ 100 000 ɪɭɛ. ɯɪɚɧɢɬɶ ɜ ɛɚɧɤɟ 2 ɝɨɞɚ,
ɬɨ ɩɪɢ ɝɨɞɨɜɨɣ ɫɬɚɜɤɟ 12% ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɱɚɫɬɨɬɵ ɧɚɱɢɫɥɟɧɢɹ ɩɪɨɰɟɧɬɨɜ ɧɚɤɨɩɥɟɧɧɚɹ ɫɭɦɦɚ ɫɨɫɬɚɜɢɬ:
ɚ) ɩɪɢ ɧɚɱɢɫɥɟɧɢɢ ɩɪɨɰɟɧɬɚ 1 ɪɚɡ ɜ ɝɨɞ
100 000• (1+0,12)2 = 125 440,0 ɪɭɛ.;
ɛ) ɩɪɢ ɩɨɥɭɝɨɞɨɜɨɦ ɧɚɱɢɫɥɟɧɢɢ ɩɪɨɰɟɧɬɨɜ
100 000 • (1+0,12/2)
2•2
= 100 000• (1+0,06)4 = 126 247,69 ɪɭɛ.;
ɜ) ɩɪɢ ɟɠɟɤɜɚɪɬɚɥɶɧɨɦ ɧɚɱɢɫɥɟɧɢɢ ɩɪɨɰɟɧɬɨɜ
100 000 • (1+0,12/4)
2•4
= 100 000• (1+0,03)8 = 126 677,0 ɪɭɛ.;
ɝ) ɩɪɢ ɟɠɟɦɟɫɹɱɧɨɦ ɧɚɱɢɫɥɟɧɢɢ ɩɪɨɰɟɧɬɨɜ
100 000 • (1+0,12/12)
2•12
= 100 000 • (1+0,01)24 = 126 973,46 ɪɭɛ.
ɉɪɢɦɟɪ. ɉɟɪɟɞ ɢɧɜɟɫɬɨɪɨɦ ɫɬɨɢɬ ɡɚɞɚɱɚ ɪɚɡɦɟɫɬɢɬɶ 100 ɬɵɫ. ɪɭɛ.
ɧɚ ɞɟɩɨɡɢɬɧɵɣ ɜɤɥɚɞ ɫɪɨɤɨɦ ɧɚ 1 ɝɨɞ. ɉɟɪɜɵɣ ɛɚɧɤ ɩɪɟɞɥɚɝɚɟɬ ɢɧɜɟɫɬɨɪɭ ɜɵɩɥɚɱɢɜɚɬɶ ɞɨɯɨɞ ɩɨ ɫɥɨɠɧɵɦ ɩɪɨɰɟɧɬɚɦ ɜ ɪɚɡɦɟɪɟ 3% ɜ
ɤɜɚɪɬɚɥ; ɜɬɨɪɨɣ — ɜ ɪɚɡɦɟɪɟ 7% 2 ɪɚɡɚ ɜ ɝɨɞ, ɬɪɟɬɢɣ — 13% 1 ɪɚɡ ɜ
ɝɨɞ. Ɉɩɪɟɞɟɥɢɬɶ, ɤɚɤɨɣ ɜɚɪɢɚɧɬ ɥɭɱɲɟ. Ɋɟɡɭɥɶɬɚɬɵ ɪɚɫɱɟɬɨɜ ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥ. 3.5.
100
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