Npv Calculation
1. **State the problem:** Calculate the Net Present Value (NPV) for purchasing tourist vans costing 150000 with annual cash inflows of 50000 for 5 years, given a cost of capital of 10%. Then advise on the investment.
2. **Formula for NPV:**
$$\text{NPV} = \sum_{t=1}^{n} \frac{C_t}{(1+r)^t} - C_0$$
Where:
- $C_t$ = cash inflow at year $t$ = 50000
- $r$ = discount rate = 0.10
- $n$ = number of years = 5
- $C_0$ = initial investment = 150000
3. **Calculate the present value factor for each year:** Using
$$\text{PV factor} = \frac{1}{(1+r)^t}$$
Calculate to 3 decimals:
- Year 1: $\frac{1}{1.10^1} = 0.909$
- Year 2: $\frac{1}{1.10^2} = 0.826$
- Year 3: $\frac{1}{1.10^3} = 0.751$
- Year 4: $\frac{1}{1.10^4} = 0.683$
- Year 5: $\frac{1}{1.10^5} = 0.621$
4. **Calculate present value of cash inflows:** Multiply each annual cash flow (50000) by the respective PV factor:
- Year 1: $50000 \times 0.909 = 45450$
- Year 2: $50000 \times 0.826 = 41300$
- Year 3: $50000 \times 0.751 = 37550$
- Year 4: $50000 \times 0.683 = 34150$
- Year 5: $50000 \times 0.621 = 31050$
5. **Sum present values of inflows:**
$$45450 + 41300 + 37550 + 34150 + 31050 = 189500$$
6. **Calculate NPV:**
$$\text{NPV} = \text{Total PV inflows} - \text{Initial investment} = 189500 - 150000 = 39500$$
7. **Investment advice:** Since NPV is positive ($39500 > 0$), the project is expected to add value to the company. Therefore, Chobe Safari Tours should proceed with the investment.