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
Step 1: Calculate Payback Period for Project A The payback period is the time it takes for the cumulative cash inflows to equal the initial investment of Le 100,000. Cumulative cash inflows for Project A: Year 1: 20 Thousand Leones Year 2: 20 + 25 = 45 Thousand Leones Year 3: 45 + 30 = 75 Thousand Leones Year 4: 75 + 35 = 110 Thousand Leones The initial investment of 100 Thousand Leones is recovered during Year 4. Amount remaining to be recovered after Year 3 = 100 - 75 = 25 Thousand Leones. Cash inflow in Year 4 = 35 Thousand Leones. Payback Period A = 3 years + (25)/(35) years Payback Period A = 3 + 0.7143 years Payback Period A = 3.7143 years Step 2: Calculate Payback Period for Project B Cumulative cash inflows for Project B: Year 1: 30 Thousand Leones Year 2: 30 + 35 = 65 Thousand Leones Year 3: 65 + 35 = 100 Thousand Leones The initial investment of 100 Thousand Leones is recovered at the end of Year 3. Payback Period B = 3 years Step 3: Calculate Net Present Value (NPV) for Project A The formula for NPV is: NPV = _t=1^n (C_t)/((1+r)^t) - C_0 Where C_t is the cash inflow in year t, r is the discount rate (10% or 0.10), and C_0 is the initial investment (100 Thousand Leones). Present Value (PV) of cash inflows for Project A: | Year (t) | Cash Inflow (C_t) (Thousand Leones) | Discount Factor (1+0.10)^-t | Present Value (C_t × DF) (Thousand Leones) | | :------- | :------------------------------------ | :------------------------------- | :------------------------------------------------ | | 1 | 20 | 0.9091 | 20 × 0.9091 = 18.182 | | 2 | 25 | 0.8264 | 25 × 0.8264 = 20.660 | | 3 | 30 | 0.7513 | 30 × 0.7513 = 22.539 | | 4 | 35 | 0.6830 | 35 × 0.6830 = 23.905 | | 5 | 40 | 0.6209 | 40 × 0.6209 = 24.836 | | 6 | 25 | 0.5645 | 25 × 0.5645 = 14.1125 | | 7 | 10 | 0.5132 | 10 × 0.5132 = 5.132 | | Sum | | | 129.3665 | NPV A = 129.3665 - 100 NPV A = 29.3665 Thousand Leones Step 4: Calculate Net Present Value (NPV) for Project B Present Value (PV) of cash inflows for Project B: | Year (t) | Cash Inflow (C_t) (Thousand Leones) | Discount Factor (1+0.10)^-t | Present Value (C_t × DF) (Thousand Leones) | | :------- | :------------------------------------ | :------------------------------- | :------------------------------------------------ | | 1 | 30 | 0.9091 | 30 × 0.9091 = 27.273 | | 2 | 35 | 0.8264 | 35 × 0.8264 = 28.924 | | 3 | 35 | 0.7513 | 35 × 0.7513 = 26.2955 | | 4 | 40 | 0.6830 | 40 × 0.6830 = 27.320 | | 5 | 40 | 0.6209 | 40 × 0.6209 = 24.836 | | 6 | 40 | 0.5645 | 40 × 0.5645 = 22.580 | | 7 | 15 | 0.5132 | 15 × 0.5132 = 7.698 | | Sum | | | 164.9265 | NPV B = 164.9265 - 100 NPV B = 64.9265 Thousand Leones Step 5: Recommend a Project i) Payback Period: Project B (3 years) has a shorter payback period than Project A (3.7143 years). ii) Net Present Value: Project B (64.9265 Thousand Leones) has a higher NPV than Project A (29.3665 Thousand Leones). Based on both the payback period and Net Present Value criteria, Project B is the more favorable investment. It recovers its initial cost faster and is expected to generate more wealth. 3 done, 2 left today. You're making progress.