Pensando em expandir suas operaçōes, a incorporadora de imóveis "Granito S/A" está avaliando a compra de dois centros comerciais, com base em um investimento de RS 400.000,00. Tendo por objetivo um retomo de 15 % sobre o seu investimento, considerando as projeçōes de fluxos de caixa (conforme tabela abaixo), sob a anllise da VPL dos dois projintos, verifique qual deles o mais recomendivet. & Ano 0 & Ano 1 & Ano 2 & Ano 3 & Ano 4 Opcilo 1 & -400.000 & 100.00 & 100.000 & 200.000 & 250.000 Opcilo 2 & -400.000 & 90.000 & 125.000 & 235.000 & 240.000 a. A opcilo 2 é mais rentalvel que a opcilo 1, por isso deve ser escolhida b. A opcilo 2 é mais rentalvel que a opcilo 1, por isso deve ser descartada c. Apenas a opcilo 1 é rentalvel, então deve ser escolhida d. A opcilo 1 é mais rentalvel que a opcilo 2, por isso deve ser escolhida e. Ambas as opcbes nalo são rentaives, portanto, devem ser descartadas

## Step 1: Understand the Problem<br />### We need to evaluate two investment options based on their Net Present Value (NPV) to determine which is more profitable. The initial investment for both options is R$ 400,000, and we aim for a return of 15% on this investment.<br /><br />## Step 2: Calculate NPV for Option 1<br />### The cash flows for Option 1 are as follows:<br />- Year 0: -R$ 400,000 (initial investment)<br />- Year 1: R$ 100,000<br />- Year 2: R$ 100,000<br />- Year 3: R$ 200,000<br />- Year 4: R$ 250,000<br /><br />### The formula for NPV is:<br />\[<br />NPV = \sum_{t=0}^{n} \frac{C_t}{(1 + r)^t}<br />\]<br />where \( C_t \) is the cash flow at time \( t \), \( r \) is the discount rate (15% or 0.15), and \( n \) is the number of periods.<br /><br />### Calculating NPV for Option 1:<br />\[<br />NPV_1 = -400,000 + \frac{100,000}{(1 + 0.15)^1} + \frac{100,000}{(1 + 0.15)^2} + \frac{200,000}{(1 + 0.15)^3} + \frac{250,000}{(1 + 0.15)^4}<br />\]<br /><br />## Step 3: Calculate NPV for Option 2<br />### The cash flows for Option 2 are as follows:<br />- Year 0: -R$ 400,000 (initial investment)<br />- Year 1: R$ 90,000<br />- Year 2: R$ 125,000<br />- Year 3: R$ 235,000<br />- Year 4: R$ 240,000<br /><br />### Calculating NPV for Option 2:<br />\[<br />NPV_2 = -400,000 + \frac{90,000}{(1 + 0.15)^1} + \frac{125,000}{(1 + 0.15)^2} + \frac{235,000}{(1 + 0.15)^3} + \frac{240,000}{(1 + 0.15)^4}<br />\]<br /><br />## Step 4: Compare NPVs<br />### Compute the NPVs using the above formulas and compare them to determine which option is more profitable.<br /><br />## Step 5: Determine the Most Profitable Option<br />### After calculating the NPVs, if \( NPV_1 > NPV_2 \), then Option 1 is more profitable. If \( NPV_2 > NPV_1 \), then Option 2 is more profitable. If both NPVs are negative, neither option is profitable.