A company has the option to build a warehouse now or three years later. The current cost is Rs. 400000, while the cost three years from now will be Rs. 500000. If the minimum attra... A company has the option to build a warehouse now or three years later. The current cost is Rs. 400000, while the cost three years from now will be Rs. 500000. If the minimum attractive rate of return is 12% per year and the inflation rate is 10% per year, what is the present worth cost (in Rs.) of building in three years when inflation is considered? [Rounded off to nearest integer] Read more

Steps to Solve

1. Identify Future Cost and Rates
   The future cost of the warehouse in three years is Rs. 500,000. The company's required rate of return is 12% per year, and the inflation rate is 10% per year.

2. Calculate the Real Rate of Return
   The real rate of return can be calculated using the formula:
   $$ r_{real} = \frac{1 + r}{1 + i} - 1 $$
   where $r$ is the nominal interest rate (12%) and $i$ is the inflation rate (10%).
   Substituting in the values:
   $$ r_{real} = \frac{1 + 0.12}{1 + 0.10} - 1 $$

3. Calculate the Future Value Adjusted for Inflation
   First, calculate the values:
   $$ r_{real} = \frac{1.12}{1.10} - 1 \approx 0.0182 \text{ or } 1.82% $$

4. Calculate Present Worth
   To find the present worth (PW) of the future cost, we use the formula:
   $$ PW = \frac{FV}{(1 + r_{real})^n} $$
   where $FV$ is the future value (Rs. 500,000) and $n$ is the number of years (3).
   Substituting the values:
   $$ PW = \frac{500000}{(1 + 0.0182)^3} $$

5. Compute the Calculation
   Calculate:
   $$ PW = \frac{500000}{(1.0182)^3} $$
   First, compute $(1.0182)^3 \approx 1.0554$, then:
   $$ PW = \frac{500000}{1.0554} \approx 473,385.56 $$

6. Round the Final Result
   Round the present worth to the nearest integer:
   $$ PW \approx 473386 $$