Answer :
To determine the minimum amount you should accept if a buyer comes along just after the investment has been made, we would need to calculate the present value (PV) of the projected future cash flows from this investment at a discount rate of 10% per annum.
Identify the Cash Flows:
- Initial investment: TZS 3000M (already spent, so not part of future cash flows)
- Cash flow for Year 1: TZS 15M
- Cash flow for Year 12: TZS 45M
Since the growth in cash flow is steady (assuming linear growth for simplicity), we can determine the cash flows for the remaining years by assuming that the cash flow grows evenly every year.
Calculate the Average Annual Growth in Cash Flow:
- Growth from Year 1 (TZS 15M) to Year 12 (TZS 45M) = TZS 45M - TZS 15M = TZS 30M
- Over 11 years, the annual growth is: [tex]\text{Annual Growth} = \frac{30M}{11} = TZS 2.727M[/tex]
Compute the Cash Flows for Each Year:
Year 1: TZS 15M
Year 2: [tex]15M + 2.727M = TZS 17.727M[/tex]
Year 3: [tex]17.727M + 2.727M = TZS 20.454M[/tex]
Continue this calculation incrementally until Year 12.
Calculate the Present Value of Each Year’s Cash Flow:
The formula for present value is:
[tex]PV = \frac{CF_t}{(1 + r)^t}[/tex]
where [tex]CF_t[/tex] is the cash flow in year [tex]t[/tex], and [tex]r[/tex] is the discount rate (10% or 0.10).You would calculate this for each year's cash flow and sum them to get the total present value.
Summing Up the Present Values:
Adding all these PVs together will give the total present value of the investment. The minimum amount you should accept from the buyer would be equivalent to this total PV value, as it represents the value of expected future cash flows in today's terms.
By following these steps, you'll be able to calculate the present value of the investment. Do make sure to calculate each year specifically for a precise answer.
