Question

Consider the two investments shown below, only one of which can be chosen. They are one-shot investments. Calculate AW_2-1 assuming 14.7914 interest rate.

EOY	Alternative 1	Alternative 2
0	- 20,301	- 58,577
1	2,706	1,000
2	2,706	1,800
3	2,706	2,600
4	2,706	3,400
5	2,706	4,200
6		5,000
7		5,800
8		6,600

Answer 1

Solution

First we will find out NPV of both the projects

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

Where NPV= net present value

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

I =rate of interest= 14.7914%

n= Useful life of project

Present value of each Cash flow= Cash flow in the year/ (1+i) ^t

Where t= Year for which Cash flow is given

Present value for Alternative 1 year 1=2706/ (1+14.7914) ^1= 2357.319

Similarly we can calculate present values for other cash flows

The calculations have been given in table below

Year	Alternative 1	Present value	Alternative 2	Present value
0	-20301	-20301.000	-58577	-58577.000
1	2706	2357.319	1000	871.145
2	2706	2053.568	1800	1366.010
3	2706	1788.956	2600	1718.879
4	2706	1558.441	3400	1958.130
5	2706	1357.629	4200	2107.184
6	NPV	-11185.086	5000	2185.314
7			5800	2208.323
8			6600	2189.118
			NPV	-43972.897

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

Now annual worth Alternative 1=-11185.086 *[(.147914*(1.147914^5))/1.147914^5-1)

=-3320.2206

Now Annual worth Alternative 2= -43972.897*[(.147914*(1.147914^8))/1.147914^8-1)

= -9732.2404

Therefore Alternative 1 is better, has higher annual worth