Question

Two projects A and B with the following cash flows with a fix interest rate of 12%.

A. Use the present worth to select which project is better?

Table 1 Project A

0	1	2	3
-9000	3000	3000	6000

Table 2 Project B

0	1	2	3
-12000	4000	3000	8000

B. Repeat the question in part A using AW analysis
C. Repeat the question in part A using FW analysis

Answer 1

Answer and explanation below

Explanation:

a) Present worth = P / (1 + r)^t

Project A

Year 0 = -9,000 / (1 + 0.12)⁰

=9,000 / 1 = -9,000

Year 1 = 3,000 / 1.12¹ = 2,678.5714

Year 2 = 3,000 / 1.2² = 2,391.5816

Year 3 = 6000 / 1.12³ = 4,270.681

NPV = -9,000 + 2,678.5714 + 2,391.5816 + 4,270.681

= 340.834

Project B

Year 0 = -12,000

Year 1 = 4,000 / 1.12 = 3,571.4285

Year 2 = 3000/ 1,12² = 2,391.5816

Year 3 = 8000/ 1.12³ = 5,694. 2419

NPV = -12,000 + 3571.4285 + 2,391.5816 + 5,694.2419

= -342.748

Project A is better since it has a positive present worth.

b) Annual Worth

AW = Future worth * Rate of interest / [ (1 + Rate of interest)^Time - 1

Project A = 232.268 x 0.12/ [( 1 + 0.12)³ - 1]

= 232.268 x 0.12/ 0.4049

= 232.268 x 0.29634

= $68.832

Project B = -233.573 x 0.29634

= -$69.217

Select project A because it has a positive annual worth

c) Future worth = Present worth * ( 1 - interest rate)^time

Project A = 340.834 * ( 1-0.12)³

= 340.834 x 0.681472

= $232.268

Project B = 342.748 x 0.681472

= -233.573

Project A is better because it has a positive future worth.