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Реши задачу

Создано: 9 февраля 2026 г.

Отвечено с использованием GPT-5.2 Thinking от Chat01

Вопрос

IMG_20260209_193942.jpgIMG_20260209_193942.jpg

Реши задачу

Мысль

Calculating NPV and Profitability Index (PI) for two scenarios

To calculate NPV and PI, I’ll take the cash flows for each scenario, discounting them at 10% for each year. For both scenarios, I'll sum the present value of cash flows (CF1 to CF4) and subtract the initial investment of 100,000 rub at t0. I'll also calculate the profitability index by dividing the present value of inflows by the initial investment. I wonder if the negative CF1 scenario means additional financing is needed—I'll keep that in mind.

Clarifying Profitability Index (PI) calculation

The standard formula for PI is the present value of future cash inflows divided by the absolute initial investment. But if there are later negative flows, the formula can be adjusted. Since PI is usually greater than 0, negative CFs can reduce it. I'll compute PI as PV of CFs 1-4 divided by the initial investment of 100k, with or without adjustments based on outflows.

Deciding how to present charts and results

I should compute values carefully, rounding to the hundredths. For the user’s request to "draw graphs" of cash flows, I can either use a simple ASCII table or embed a chart as an image. I can generate line/bar charts with Python, but I need to keep things simple and practical for homework.

Deciding how to generate and display plots

To generate plots, I'll compute the figures and use a single plot with two lines for both scenarios, as requested. I won't use specific colors unless directed to, so I’ll stick with default colors. I'll save the chart as a PNG and provide a download link. Two separate plots might work too.

Thought for 40s

Мысль

Providing calculations and results clearly

I'll present the results with simple calculations, clearly showing the discounted values, N

Thought for 58s

Ответ

Ставка дисконтирования r=10%r=10\%. Начальные инвестиции I0=100 000I_0=100\,000 (в момент t=0t=0).

Дисконт-множители:

(1.1)1=1.1, (1.1)2=1.21, (1.1)3=1.331, (1.1)4=1.4641(1{.}1)^1=1{.}1,\ (1{.}1)^2=1{.}21,\ (1{.}1)^3=1{.}331,\ (1{.}1)^4=1{.}4641

1) Исход «Пластмассовый мир победил»

CF: 33 000; 30 250; 37 268; 29 28233\,000;\ 30\,250;\ 37\,268;\ 29\,282

PV по годам:

  • 33 000/1.1=30 00033\,000/1.1=30\,000
  • 30 250/1.21=25 00030\,250/1.21=25\,000
  • 37 268/1.331=28 00037\,268/1.331=28\,000
  • 29 282/1.4641=20 00029\,282/1.4641=20\,000
PV=  30 000+25 000+28 000+20 000=103 000PV=\;30\,000+25\,000+28\,000+20\,000=103\,000 NPV=PV−I0=103 000−100 000=3 000.00NPV=PV-I_0=103\,000-100\,000=3\,000.00 PI=PVI0=103 000100 000=1.03PI=\frac{PV}{I_0}=\frac{103\,000}{100\,000}=1.03

2) Исход «Поставщик сорвал сроки»

CF: −22 000; 48 400; 46 585; 29 282-22\,000;\ 48\,400;\ 46\,585;\ 29\,282

PV по годам:

  • −22 000/1.1=−20 000-22\,000/1.1=-20\,000
  • 48 400/1.21=40 00048\,400/1.21=40\,000
  • 46 585/1.331=35 00046\,585/1.331=35\,000
  • 29 282/1.4641=20 00029\,282/1.4641=20\,000
PV=  −20 000+40 000+35 000+20 000=75 000PV=\;-20\,000+40\,000+35\,000+20\,000=75\,000 NPV=75 000−100 000=−25 000.00NPV=75\,000-100\,000=-25\,000.00 PI=75 000100 000=0.75PI=\frac{75\,000}{100\,000}=0.75

Графики денежных потоков (включая t=0t=0 с −100 000-100\,000)

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