Question

What is the discounted payback period for a project financed with a £50000 loan at an effective interest rate of 8% per annum, generating £7500 at the end of each year for the next 15 years?

A) 6 years
B) 7 years
C) 8 years
D) 9 years

Answer 1

The discounted payback period for the project financed with a £50000 loan at an effective interest rate of 8% per annum, generating £7500 at the end of each year for the next 15 years is 9 years.

Step-by-step explanation:

The discounted payback period is the time it takes to recover the initial investment in a project based on the present value of future cash flows. In this case, the project is financed with a £50000 loan and generates £7500 at the end of each year for the next 15 years. To calculate the discounted payback period, we need to find the present value of each cash flow. Using a discount rate of 8%, we can calculate the present value of each year's cash flow as follows:

1. Present value of year 1 cash flow: £7500 / (1 + 0.08)^1 = £6944.44
2. Present value of year 2 cash flow: £7500 / (1 + 0.08)^2 = £6419.75
3. Present value of year 3 cash flow: £7500 / (1 + 0.08)^3 = £5943.85
4. ...
5. Present value of year 15 cash flow: £7500 / (1 + 0.08)^15 = £2501.71

The discounted payback period is the number of years it takes for the cumulative present value of cash flows to equal or exceed the initial investment. We can calculate the cumulative present value of cash flows over time. Starting from year 1, the cumulative present value is £6944.44. In year 2, it becomes £6944.44 + £6419.75 = £13364.19. Continuing this calculation, we find that the cumulative present value exceeds £50000 in year 9. Therefore, the discounted payback period for this project is 9 years.