Question

Please, show the formulas and step by step on how to find the answer!!

Two mutually exclusive alternatives of A and B have both useful lives of 5 years. For Alternative A, there is an initial cost of $2,500 and annual benefits of $746. For Alternative B, there is an initial cost of $6,000 and annual benefits of $1,664. By following each of the following methods, define which alternative should be chosen? (30 pts) i. Annual Cash Flow Analysis (the interest rate is 8%) ii. Rate of Return Analysis (Minimum Attractive Rate of Return is 8%)

Answer 1

ANSWER:

1) Annual cash flow analysis:

i = 8% and n = 5 years

aw of alternative a = initial cost(a/p,i,n) + annual benefit = -2,500(a/p,8%,5) + 746 = -2,500 * 0.2505 + 746 = -626.25 + 746 = 119.75

aw of alternative b = initial cost(a/p,i,n) + annual benefit = -6,000(a/p,8%,5) + 1,664 = -6,000 * .2505 + 1,664 = -1,503 + 1,664 = 161

so we will select alternative b as it has a higher annual worth.

2) Ror:

In order to find the ror we will equate the pw to zero.

pw of alternative a = initial cost + annual benefit(p/a,i,n)

0 = -2,500 + 746(p/a,i,5)

2,500 = 746(p/a,i,5)

2,500 / 746 = (p/a,i,5)

3.3512 = (p/a,i,5)

solving via trial and error we get that i is between 15% and 16% as at 15% it is above zero slightly and at 16% it is below zero and solving further we get that i is 15.01%

pw of alternative b = initial cost + annual benefit(p/a,i,n)

0 = -6,000 + 1,664(p/a,i,5)

6,000 = 1,664(p/a,i,5)

6,000 / 1,664 = (p/a,i,5)

3.6057 = (p/a,i,5)

solving via trial and error we get that i is between 11% and 12% as at 11% it is above zero and at 12% it is slightly below zero and solving further we get that i is 11.99%

based on ror , we will choose alternative a as it has a higher ror while alternative b will not be chosen if the projects are mutually exclusive while if both the projects are independent then both will be selected as their ror is higher then marr.