This business/management problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.
ScanSolve AI Answer
To solve this problem, we need to make assumptions for the initial investment and the discount rate, as these are not provided in the question. Assumptions: Initial Investment for both Project A and Project B: 100 Thousand Leones. Discount Rate for Net Present Value (NPV) calculation: 10% (or 0.10). Step 1: Calculate the Payback Period for Project A. The payback period is the time it takes for the cumulative cash inflows to equal the initial investment. Initial Investment (C_0) = 100 Thousand Leones. Cumulative cash flows for Project A: Year 1: 20 Year 2: 20 + 25 = 45 Year 3: 45 + 30 = 75 Year 4: 75 + 35 = 110 The initial investment of 100 Thousand Leones is recovered between Year 3 and Year 4. Amount remaining to be recovered after Year 3 = 100 - 75 = 25 Thousand Leones. Cash flow in Year 4 = 35 Thousand Leones. Fraction of Year 4 needed = (25)/(35) ≈ 0.714 years. Payback Period for Project A = 3 + 0.714 = 3.714 years. Step 2: Calculate the Payback Period for Project B. Initial Investment (C_0) = 100 Thousand Leones. Cumulative cash flows for Project B: Year 1: 30 Year 2: 30 + 35 = 65 Year 3: 65 + 35 = 100 The initial investment of 100 Thousand Leones is recovered exactly at the end of Year 3. Payback Period for Project B = 3.000 years. Step 3: Calculate the Net Present Value (NPV) for Project A. The formula for NPV is NPV = _t=1^n (CF_t)/((1+r)^t) - C_0. Given C_0 = 100 Thousand Leones and r = 0.10. NPV_A = (20)/((1.10)^1) + (25)/((1.10)^2) + (30)/((1.10)^3) + (35)/((1.10)^4) + (40)/((1.10)^5) + (25)/((1.10)^6) + (10)/((1.10)^7) - 100 NPV_A = 18.18 + 20.66 + 22.54 + 23.91 + 24.84 + 14.11 + 5.13 - 100 NPV_A = 129.37 - 100 = 29.37 Thousand Leones Step 4: Calculate the Net Present Value (NPV) for Project B. Given C_0 = 100 Thousand Leones and r = 0.10. NPV_B = (30)/((1.10)^1) + (35)/((1.10)^2) + (35)/((1.10)^3) + (40)/((1.10)^4) + (40)/((1.10)^5) + (40)/((1.10)^6) + (15)/((1.10)^7) - 100 NPV_B = 27.27 + 28.93 + 26.30 + 27.32 + 24.84 + 22.58 + 7.71 - 100 NPV_B = 164.95 - 100 = 64.95 Thousand Leones Step 5: Recommend a project. To recommend a project, we compare the payback periods and NPVs. Project A: Payback Period = 3.714 years, NPV = 29.37 Thousand Leones. Project B: Payback Period = 3.000 years, NPV = 64.95 Thousand Leones. Project B has a shorter payback period (3.000 years vs. 3.714 years), indicating quicker recovery of the initial investment. Project B also has a higher Net Present Value (64.95 Thousand Leones vs. 29.37 Thousand Leones), indicating it is expected to generate more wealth. Based on both criteria, Project B is the more favorable investment. Send me the next one 📸