Question

Consider the two investments shown below, only one of which can be chosen. They are one-shot investments. Calculate AW_2-1 assuming 15.9081 interest rate.

EOY	Alternative 1	Alternative 2
0	- 23,285	- 40,075
1	3,963	1,000
2	3,963	1,800
3	3,963	2,600
4	3,963	3,400
5	3,963	4,200
6		5,000
7		5,800
8		6,600

Answer 1

Solution

In the given question first we will find out the NPV of both the projects

Then Annual worth= NPV*[(i(1+i)^n)/(1+i)^n-1

Where NPV= net present value of project

NPV= Sum of present values of all projects- Initial investment

I =rate of interest= 15.9081%

n= life of project

NPV= Sum of Present value of all cash flows- Initial investment

Present value= Cash flow/ (1+i) ^n

The calculations have been given in table below

Year	Alternative 1	Present value	Alternative 2	Present value
0	-23285	-23285	-40075	-40075
1	3963	3419.0881	1000	862.7525
2	3963	2949.8267	1800	1339.8153
3	3963	2544.9703	2600	1669.6752
4	3963	2195.6794	3400	1883.7522
5	3963	1894.3278	4200	2007.6147
6	NPV	-10281.1078	5000	2061.9935
7			5800	2063.6284
8			6600	2025.9729
			NPV	-26159.7955

Now annual worth Alternative 1= -10281.1078*[(0.332803/1.092035)

= -3133.2181

Now Annual worth Alternative 2= -26159.7955*[(0.51824/2.25769)

= -6004.791

Therefore Alternative 1 is better, has higher annual worth