Question

Consider the two investments shown below, only one of which can be chosen. They are one-shot investments. Calculate AW_2-1 assuming 10.8354 interest rate.

EOY	Alternative 1	Alternative 2
0	- 20,369	- 56,679
1	3,844	1,000
2	3,844	1,800
3	3,844	2,600
4	3,844	3,400
5	3,844	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

I =rate of interest= 10.8354%

n= life of project

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

The calculations have been given in table below

Year	Alternative 1	Present value	Alternative 2	Present value
0	-20369	-20369	-56679	-56679
1	3844	3547.6309	1000	902.2388
2	3844	3274.1116	1800	1465.2628
3	3844	3021.6804	2600	1909.5801
4	3844	2788.7115	3400	2253.0195
5	3844	2573.7042	4200	2511.0585
6	NPV	-5163.1613	5000	2697.1124
7			5800	2822.7898
8			6600	2898.1175
			NPV	-39219.8207

Now annual worth Alternative 1= -5163.1613*[(.108354*(1.108354^5))/1.108354^5-1)

= -1391.2184

Now Annual worth Alternative 2= -39219.8207*[(.108354*(1.108354^8))/1.108354^8-1)

= -7576.5564

Therefore Alternative 1 is better, has higher annual worth