Question

Consider the two investments shown below, only one of which can be chosen. They are one-shot investments. Calculate AW_2-1 assuming 13.2305 interest rate.

EOY	Alternative 1	Alternative 2
0	- 20,286	- 40,370
1	3,741	1,000
2	3,741	1,800
3	3,741	2,600
4	3,741	3,400
5	3,741	4,200
6		5,000
7		5,800
8		6,600

Answer 1

We need to calculate the incremental annual worth of the two investments.

The table shows the the following:

( 2 - 1) = Cash flows of project 2 - csh flows of project 1

K = (1+interest rate) ^ Eoy = 1.132305^ year

J = 1/k

Last column is the present obtained by multipling J * (2-1) cash flows.

Total present value is calculated by adding the individual present valeu in each column.

EOY	Alternative 1	Alternative 2	(2 - 1)	k = (1+13.2305)^Eoy	j = 1/k	j * (2-1)
0	(20,286.0000)	(40,370.0000)	(20,084.0000)	1.0000	1.0000	(20,084.0000)
1	3,741.0000	1,000.0000	(2,741.0000)	1.1323	0.8832	(2,420.7259)
2	3,741.0000	1,800.0000	(1,941.0000)	1.2821	0.7800	(1,513.9052)
3	3,741.0000	2,600.0000	(1,141.0000)	1.4517	0.6888	(785.9508)
4	3,741.0000	3,400.0000	(341.0000)	1.6438	0.6083	(207.4439)
5	3,741.0000	4,200.0000	459.0000	1.8613	0.5373	246.6014
6		5,000.0000	5,000.0000	2.1076	0.4745	2,372.4084
7		5,800.0000	5,800.0000	2.3864	0.4190	2,430.4350
8		6,600.0000	6,600.0000	2.7021	0.3701	2,442.5110
					Present Value	(17,520.0699)

We calculated present value first because the stream of cash flows is different.

Now, we will find the annual worth using the factor formula:

PV = X * (P/A, i, n)

-17520.0699 = X * (P/A, 13.2305, 8)

-17520.0699 = X * 4.711

X = -3679.81 (anuual worth)

Since the annual worth is neagtive, that signifies that project 2 is costly that project 1.

Hence, we will opt for Project 1 as a better investment choice.