Question

1. An investment has a cost of $3500. The investment will have a payout of X at the end of the first year. This initial payout X will grow at the rate of 12% per year for the next 4 years, then by 7% per year for the next 4 years, and then at the rate of 3% per year for the following 3 years. You believe the riskiness of this investment is 9%.
   1. Calculate the smallest X that would entice you to invest.

Answer 1

To get the Minimum value of X that would entice you to invest, the PV of all Futures inflow with the 9% (riskiness of the investment ), should be minimum to the cost of project. The calculation for the same will be as below :

Year	Value of inflow in the multiple of X	X Multiple Calculation Criteria	Interest Rate	Discounting Factor (1+Rate) ^ Year)	Discounted Values in the Multiple of X (Value of Inflow in the multiple of X / Discounting Factor)
1	1.00	1st year, inflow will be X	9.00%	1.09	0.92
2	1.12	12% increase in previous year	9.00%	1.19	0.94
3	1.25	12% increase in previous year	9.00%	1.30	0.97
4	1.40	12% increase in previous year	9.00%	1.41	1.00
5	1.57	12% increase in previous year	9.00%	1.54	1.02
6	1.68	7% increase in previous year	9.00%	1.68	1.00
7	1.80	7% increase in previous year	9.00%	1.83	0.99
8	1.93	7% increase in previous year	9.00%	1.99	0.97
9	2.06	7% increase in previous year	9.00%	2.17	0.95
10	2.12	3% increase in previous year	9.00%	2.37	0.90
11	2.19	3% increase in previous year	9.00%	2.58	0.85
11	2.25	3% increase in previous year	9.00%	2.58	0.87
Sum of Discounted Value (PV) in the Multiple of X					11.37

Sum of Discounted Value (PV) in the Multiple of X = 11.37

So the PV of inflow = 11.37X

As discussed earlier, To get the Minimum value of X that would entice you to invest, the PV of all Futures inflow with the 9% (riskiness of the investment ), should be minimum to the cost of project, so

11.37X = $35000

X = $35000 / 11.37

X= $3078.28

So the minimum value of X should be X= $3078.28