Let's solve each scenario step by step as requested. --- ## **1. Thomas Company IRR Calculation** **Given:** - Investment = $120,000 - Uniform cash inflows over 4 years - IRR = 14% We need to find the annual cash inflow per year. **Formula:** \[ P = I = df \times CF \] Where: - \( I \) = Investment ($120,000) - \( df \) = Discount factor at 14% for 4 years (from annuity tables) - \( CF \) = Cash flow per year **Step 1: Find Discount Factor (df) for 14% and 4 years.** From the Present Value Annuity Table: - 14% for 4 years ≈ **2.914** **Step 2: Calculate Annual Cash Flow** \[ CF = \frac{I}{df} \] \[ CF = \frac{120,000}{2.914} \approx 41,170 \] --- ### **Blank 1 Answer:** **$41,170 per year** --- ## **2. Video Repair Investment and Savings** **Given:** - NPV = $1,750 - Discount rate = 8% - IRR = 12% - Equipment has a 3-year life - Uniform annual cash savings **Step 1: Find Discount Factors** From tables: - 12% for 3 years ≈ **2.402** - 8% for 3 years ≈ **2.577** ### **a. Find Investment** \[ NPV = (df_{IRR} \times CF) - (df_{discount} \times CF) \] But we have: \[ NPV = (df_{discount} \times CF) - I \] \[ I = (df_{discount} \times CF) - NPV \] ### **b. Find Cash Savings (CF)** \[ NPV = (df_{discount} \times CF) - I \] \[ NPV = (2.577 \times CF) - I \] Also, \[ I = df_{IRR} \times CF = 2.402 \times CF \] Set equal: \[ I = 2.402 \times CF \] \[ NPV = (2.577 \times CF) - (2.402 \times CF) \] \[ NPV = (2.577 - 2.402) \times CF \] \[ NPV = 0.175 \times CF \] \[ CF = \frac{NPV}{0.175} = \frac{1750}{0.175} = 10,000 \] **Investment:** \[ I = 2.402 \times 10,000 = 24,020 \] --- ### **Blank 2 (Savings per year):** **$10,000** ### **Blank 3 (Investment):** **$24,020** --- ## **3. Lathe Life for IRR of 18%** **Given:** - Cost = $60,096 - Annual savings = $12,000 - Need number of years (n) for IRR = 18% \[ I = df \times CF \] \[ 60,096 = df \times 12,000 \] \[ df = \frac{60,096}{12,000} = 5.008 \] From the Present Value Annuity Table at 18%, find n such that the factor is closest to 5.008: - 4 years: 2.690 - 6 years: 3.811 - 8 years: 4.494 - 10 years: 4.947 - **11 years: 5.079** So, **about 11 years**. --- ### **Blank 4 (Years):** **11** --- ## **4. NPV scenario for Project S** **Given:** - NPV = $3,927 - Discount rate = 10% - Project life = 4 years - Cash flows: Y1: $10,000, Y2: $12,000, Y3: $15,000, Y4: ? Cost is **twice the cash flow in Year 4**. **Step 1: Write NPV Equation** \[ NPV = \frac{10,000}{1.1} + \frac{12,000}{1.1^2} + \frac{15,000}{1.1^3} + \frac{CF_4}{1.1^4} - Cost \] But \( Cost = 2 \times CF_4 \). So, \[ 3,927 = \frac{10,000}{1.1} + \frac{12,000}{1.1^2} + \frac{15,000}{1.1^3} + \frac{CF_4}{1.1^4} - 2CF_4 \] **Calculate Present Values:** - \( \frac{10,000}{1.1} = 9,091 \) - \( \frac{12,000}{1.1^2} = 9,917 \) - \( \frac{15,000}{1.1^3} = 11,278 \) - \( \frac{CF_4}{1.1^4} = \frac{CF_4}{1.4641} \) So, \[ 3,927 = 9,091 + 9,917 + 11,278 + \frac{CF_4}{1.4641} - 2CF_4 \] \[ 3,927 = 30,286 + \frac{CF_4}{1.4641} - 2CF_4 \] \[ 3,927 - 30,286 = \frac{CF_4}{1.4641} - 2CF_4 \] \[ -26,359 = \frac{CF_4}{1.4641} - 2CF_4 \] Let \( CF_4 = x \): \[ -26,359 = \frac{x}{1.4641} - 2x \] \[ -26,359 = \frac{x - 2x \times 1.4641}{1.4641} \] \[ -26,359 = \frac{x - 2.9282x}{1.4641} \] \[ -26,359 = \frac{-1.9282x}{1.4641} \] \[ -26,359 \times 1.4641 = -1.9282x \] \[ -38,595 = -1.9282x \] \[ x = \frac{38,595}{1.9282} \approx 20,012 \] **Cost = 2 × $20,012 = $40,024** --- ### **Blank 5 (Cost of Project):** **$40,024** ### **Blank 6 (Year 4 Cash Flow):** **$20,012** --- ## **Summary Table (Final Answers):** | **Blank** | **Answer** | |-------------|----------------| | Blank 1 | $41,170 | | Blank 2 | $10,000 | | Blank 3 | $24,020 | | Blank 4 | 11 | | Blank 5 | $40,024 | | Blank 6 | $20,012 | --- Let me know if you need the answers rewritten in a specific format!