Let's solve the problem step by step. ### **Cash Flows Table** | Year | Cash Flow | |------|-----------| | 0 | -$2,000 | | 1 | $2,000 | | 2 | $1,500 | | 3 | $1,500 | | 4 | $2,500 | --- ## (a) **Net Present Value (NPV) at 10% Opportunity Cost Rate** The NPV formula for uneven cash flows is: \[ NPV = \sum \frac{CF_t}{(1+r)^t} \] Where: - \( CF_t \) = Cash flow at time \( t \) - \( r \) = Discount rate (10% or 0.10 here) - \( t \) = Year Let's calculate each term: ### Year 0: \[ NPV_0 = \frac{-2000}{(1+0.10)^0} = -2000 \] ### Year 1: \[ NPV_1 = \frac{2000}{(1+0.10)^1} = \frac{2000}{1.10} = 1818.18 \] ### Year 2: \[ NPV_2 = \frac{1500}{(1+0.10)^2} = \frac{1500}{1.21} = 1239.67 \] ### Year 3: \[ NPV_3 = \frac{1500}{(1+0.10)^3} = \frac{1500}{1.331} = 1127.49 \] ### Year 4: \[ NPV_4 = \frac{2500}{(1+0.10)^4} = \frac{2500}{1.4641} = 1707.31 \] ### **Sum Up the NPVs:** \[ NPV = -2000 + 1818.18 + 1239.67 + 1127.49 + 1707.31 = 3892.65 \] --- ## **Final Answer for (a):** \[ \boxed{NPV = \$3892.65} \] --- ## (b) **Future Value (FV) of the Cash Flow Stream at Year 4 (using 10% annual rate)** The **future value** of each cash flow compounded to year 4: \[ FV = \sum CF_t \times (1+r)^{n-t} \] Where \( n = 4 \) (the future year we want to accumulate to). ### Year 0: \[ FV_0 = -2000 \times (1.10)^4 = -2000 \times 1.4641 = -2928.20 \] ### Year 1: \[ FV_1 = 2000 \times (1.10)^3 = 2000 \times 1.331 = 2662.00 \] ### Year 2: \[ FV_2 = 1500 \times (1.10)^2 = 1500 \times 1.21 = 1815.00 \] ### Year 3: \[ FV_3 = 1500 \times (1.10)^1 = 1500 \times 1.10 = 1650.00 \] ### Year 4: \[ FV_4 = 2500 \times (1.10)^0 = 2500 \times 1 = 2500.00 \] ### **Add Up the FVs:** \[ FV = -2928.20 + 2662.00 + 1815.00 + 1650.00 + 2500.00 = 5698.80 \] --- ## **Final Answer for (b):** \[ \boxed{FV = \$5,698.80} \] --- ### **Summary** - **a. NPV at 10% = $3892.65** - **b. FV at 10% = $5,698.80** Let me know if you need any clarification or further breakdown!