A small company set up a new investment project on 1 January 2017. The initial investment on that date was £2.5 million with a further £2 million required after nine months, on 1 October 2017.
It is expected that from 1 January 2019 to 1 January 2032 inclusive, the company will receive net income from the project once a year. The net income on 1 January 2019 is expected to be £0.3 million, increasing by £0.1 million per annum on 1 January of each subsequent year.
The company expects to sell the business on 31 December 2032 for £3 million.
Calculate the net present value of the project on 1 January 2017 at a rate of interest of 12% per annum effective.
(Total 6 marks)
To calculate the net present value (NPV) of the project on 1 January 2017, we need to discount all the anticipated cash flows to their present values and then subtract the initial investment.
Let's break down the cash flows:
1. Initial investment: £2.5 million on 1 January 2017.
2. Additional investment: £2 million on 1 October 2017 (9 months after 1 January 2017).
3. Net income: Starting from 1 January 2019 to 1 January 2032, the company will receive net income once a year. The income on 1 January 2019 is expected to be £0.3 million, increasing by £0.1 million per year on 1 January of each subsequent year.
4. Sale proceeds: The business is expected to be sold on 31 December 2032 for £3 million.
Now, let's calculate the present values of these cash flows:
1. Present value of the initial investment:
PV_1 = £2.5 million / (1 + 0.12)^0 (since it is already in 2017)
= £2.5 million
2. Present value of the additional investment:
PV_2 = £2 million / (1 + 0.12)^(9/12)
= £1.841 million
3. Present value of net income:
The net income follows a growing annuity pattern. We can use the formula for the present value of a growing annuity to calculate its present value.
PV_n = C * [(1 - (1 + g)^(-n))/ (r - g)]
where:
PV_n = Present value
C = Cash flow in the first year
g = Growth rate
n = Number of years
r = Discount rate
Using this formula, we can calculate the present value of the net income:
PV_net = £0.3 million * [(1 - (1 + 0.1)^(-14))/ (0.12 - 0.1)]
+ £0.4 million * [(1 - (1 + 0.1)^(-13))/ (0.12 - 0.1)]
+ £0.5 million * [(1 - (1 + 0.1)^(-12))/ (0.12 - 0.1)]
+ ... (continuing the pattern until 2032)
4. Present value of sale proceeds:
Since the sale is expected to happen on 31 December 2032, we need to find the present value at that time.
PV_sale = £3 million / (1 + 0.12)^(15/12)
= £1.759 million
Finally, we can calculate the net present value (NPV) by subtracting the total present value of cash flows from the initial investment.
NPV = PV_1 + PV_2 + PV_net - PV_sale
Summing up all the calculations, you should have the NPV of the project on 1 January 2017.