Question

1)Cash inflows expected from a project are $28,000 for year 1, $22,000 for year 2, $20,000 for year 3, $25,000 for year 4 and $20,000 for year 5. Given the discount rate of 10%, what is the total present value of cash flow of this project?

2)Melinda needs to accumulate $50,000. In order to do so, she plans to save at the start of every year starting today for 10 years with an interest rate of 10% per annum. How much will she need to deposit every year to reach that amount?

Answer 1

1)Cash inflows expected from a project are $28,000 for year 1, $22,000 for year 2, $20,000 for year 3, $25,000 for year 4 and $20,000 for year 5. Given the discount rate of 10%, what is the total present value of cash flow of this project?  

We calculate the present value of a cashflow using the formula:

$$PV = \dfrac{CF}{(1 + r)^t}$$

2)Melinda needs to accumulate $50,000. In order to do so, she plans to save at the start of every year starting today for 10 years with an interest rate of 10% per annum. How much will she need to deposit every year to reach that amount?

The future value of an annuity is given as:

$$FV = P(1 + r) \left[\dfrac{(1 + r)^n - 1) }{ r}\right]\\[0.3cm]$$

Therefore:

$$FV = P(1 + r) \left[\dfrac{(1 + r)^n - 1) }{ r}\right]\\[0.3cm] 50,000 =P(1 + 0.1)\left[ \dfrac{(1 + 0.1)^{10} - 1}{0.1}\right]\\[0.3cm] 50,000 = 17.5312P\\[0.3cm] P = \dfrac{50,000}{17.5312}\\[0.3cm] \color{red}{P \approx \$2,852.06}$$