Question

Determine if the following is a profitable investment: An industrial machine is bought for $30,000, and a $1000 profit is generated at the end of the first year increasing 20% each year till year 10 and then decreasing by an arithmetic gradient till year 20 where the profit in year 20 is the same as that in year 3. Suppose an interest rate of 7.4%, compounded bi-monthly (i.e. every two months).

(Using factors and cashflows)

Answer 1

Assuming $30,000 is paid at the start of the year & the cash inflow received are not withdrawn until last year, please find below the cashflow. This definately is a profitable project.

Year	Actual cashflow	Discounted rate 7.4% coumpounded annually	Cash Flow
0	-30,000		-30,000
1	1000	0.24724	4,044.67
2	1,200.00	0.26611	4,509.45
3	1,440.00	0.28642	5,027.63
4	1,728.00	0.30828	5,605.36
5	2,073.60	0.33180	6,249.47
6	2,488.32	0.35713	6,967.60
7	2,985.98	0.38438	7,768.25
8	3,583.18	0.41372	8,660.91
9	4,299.82	0.44529	9,656.14
10	5,159.78	0.47928	10,765.73
11	4,787.80	0.51586	9,281.27
12	4,415.82	0.55523	7,953.19
13	4,043.85	0.59760	6,766.80
14	3,671.87	0.64321	5,708.66
15	3,299.89	0.69230	4,766.57
16	2,927.91	0.74514	3,929.37
17	2,555.93	0.80200	3,186.94
18	2,183.96	0.86321	2,530.03
19	1,811.98	0.92909	1,950.27
20	1,440.00	1.00000	1,440.00
		Net benefit	86,768