Certainly! Let's break down the problem step by step. Here’s the translation and solution outline: --- ## **Problem Statement (Translation & Key Data)** A company wants to invest **2,000,000 TL** in a new production system. The firm's cost of capital is **%26** (.26). Economic life is **15 years**. Other data: - **Production Amount:** Start with 100,000 units/year, decreases by 5% each year. - **Raw Material Cost:** Each product uses 2 units, initial price is 10 TL/unit, annual price increase by inflation rate. - **General Expenses:** First year 500,000 TL, annual inflation **%33**. - **Major Maintenance:** Every 5 years, 700,000 TL. - **Sales Price:** Initial 27.5 TL/unit, annual price increase by inflation **%33**. ### Questions: a) Calculate the unit production for 1st, 5th, 10th, 15th years. b) Calculate the total raw material cost for the 2nd year. c) Calculate IRR (Internal Rate of Return) of the investment. d) Assess the real rate of return according to firm's target profit, and if the investment is suitable. --- ## **Step-by-Step Solution** --- ### **a) Unit Production Calculation** Initial: 100,000 units/year, decreases by 5% each year. General formula for year \( n \): \[ Q_n = Q_ \times (1 - .05)^{n-1} \] Where \( Q_ = 100,000 \) - **1st year:** \[ Q_1 = 100,000 \times (.95)^ = 100,000 \] - **5th year:** \[ Q_5 = 100,000 \times (.95)^4 \approx 100,000 \times .8145 = 81,450 \] - **10th year:** \[ Q_{10} = 100,000 \times (.95)^9 \approx 100,000 \times .6302 = 63,020 \] - **15th year:** \[ Q_{15} = 100,000 \times (.95)^{14} \approx 100,000 \times .487 = 48,700 \] --- ### **b) Raw Material Cost for 2nd Year** - Each product uses **2 units**. - 2nd year production: \[ Q_2 = 100,000 \times .95^1 = 95,000 \] - Total raw material needed: \[ \text{Total units} = 95,000 \times 2 = 190,000 \] - 2nd year unit price (10 TL initial, inflation 33%): \[ \text{Year 2 Price} = 10 \times 1.33 = 13.3 \text{ TL/unit} \] - **Total Raw Material Cost:** \[ 190,000 \times 13.3 = 2,527,000 \text{ TL} \] --- ### **c) IRR (Internal Rate of Return) Calculation** #### **Cash Flow Table Construction** **Years 1-15:** - Revenue: \( Q_n \times \text{Sale Price}_n \) - Raw Material Cost: \( Q_n \times 2 \times \text{Raw Mat. Price}_n \) - General Expenses: \( 500,000 \times 1.33^{n-1} \) - Maintenance: Every 5th year, add 700,000 TL cost. **Initial Investment:** \( -2,000,000 \) (Year ) #### **Example for Year 1:** - Production: 100,000 - Sale Price: 27.5 TL - Revenue: \( 100,000 \times 27.5 = 2,750,000 \) - Raw Mat.: \( 100,000 \times 2 \times 10 = 2,000,000 \) - General Expenses: 500,000 - Maintenance: **Net Cash Flow (Year 1):** \[ 2,750,000 - 2,000,000 - 500,000 = 250,000 \] **Continue for all 15 years, considering inflation for prices and costs, and 700,000 TL maintenance in years 5, 10, 15.** Calculate IRR using the full cash flow table (this is typically done with Excel or a financial calculator). --- ### **d) Real Rate of Return Assessment** - **Nominal Rate of Return:** 26% (cost of capital) - **Inflation:** 33% - **Real Rate (Fisher Equation):** \[ 1 + r_{real} = \frac{1 + r_{nominal}}{1 + i} \] \[ 1 + r_{real} = \frac{1.26}{1.33} \approx .947 \] \[ r_{real} \approx -.053 \text{ or } -5.3\% \] - **Assessment:** The real rate is negative. If the firm's required real rate is positive, **the investment is not suitable**. --- ## **Summary Table** | Year | Production | Sale Price (TL) | Revenue (TL) | Raw Mat. Price (TL) | Raw Mat. Cost (TL) | Gen. Exp. (TL) | Maint. (TL) | Net Cash Flow | |------|------------|-----------------|--------------|---------------------|--------------------|---------------|-------------|---------------| | 1 | 100,000 | 27.5 | 2,750,000 | 10. | 2,000,000 | 500,000 | | 250,000 | | 2 | 95,000 | 36.575 | 3,474,625 | 13.3 | 2,527,000 | 665,000 | | 282,625 | | ... | ... | ... | ... | ... | ... | ... | ... | ... | *(Continue for all 15 years for IRR calculation)* --- If you need the full cash flow table or a specific calculation (such as IRR in Excel), let me know!