Question

Ford Motor Company is considering 3 mutually exclusive options for electronic stability control systems for protection against rollover of its automobiles. The investment period is four years (equal lifetimes) and the MARR is 12% per year. The data is below: A Capital Investment 12000 Annual Revenues Less Expenses | 4500 B 15800 | 6500 C 8000 3500 6. Select the best option using Rate of Return Analysis. You must present the IRR for each individual alternative as well as the incremental computations required along the way for each alternative. Do your best to estimate the IRR for this problem.

Answer 1

ANSWER:

1) A:

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

pw = capital investment + annual revenues less expenses(p/a,i,n)

0 = -12,000 + 4,500(p/a,i,4)

12,000 = 4,500(p/a,i,4)

12,000 / 4,500 = (p/a,i,4)

2.67 = (p/a,i,4)

solving via trial and error we get that i is betwen 16% and 17% and solving further we get that i is 16.37%

2) B:

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

pw = capital investment + annual revenues less expenses(p/a,i,n)

0 = -15,800 + 6,500(p/a,i,4)

15,800 = 6,500(p/a,i,4)

15,800 / 6,500 = (p/a,i,4)

2.43 = (p/a,i,4)

solving via trial and error we get that i is betwen 23% and 24% and solving further we get that i is 23.39%

3) C:

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

pw = capital investment + annual revenues less expenses(p/a,i,n)

0 = -8,000 + 3,500(p/a,i,4)

8,000 = 3,500(p/a,i,4)

8,000 / 3,500 = (p/a,i,4)

2.28 = (p/a,i,4)

solving via trial and error we get that i is betwen 26% and 27% and solving further we get that i is 26.86%

4) NOW WE WILL FIND THE INCREMENTAL IRR.

In order to find the incremental irr we will equate the pw to zero.

pw(b - a) = capital investment(b - a) + annual revenues less expenses(b -a)(p/a,i,n)

0 = -15,800 - (-12,000) + 6,500 - 4,500 (p/a,i,4)

0 = -3,800 + 2,000(p/a,i,4)

3,800 = 2,000(p/a,i,4)

3,800 / 2,000 = (p/a,i,4)

1.9 = (p/a,i,4)

solving via trial and error we get that i is betwen 38% and 39% and solving further we get that i is 38.21%

so we select b and reject a as the irr is greater then the marr.

5) In order to find the incremental irr we will equate the pw to zero.

pw(b - a) = capital investment(b - a) + annual revenues less expenses(b -a)(p/a,i,n)

0 = -15,800 - (-8,000) + 6,500 - 3,500 (p/a,i,4)

0 = -7,800 + 3,500(p/a,i,4)

7,800 = 3,500(p/a,i,4)

7,800 / 3,500 = (p/a,i,4)

2.22 = (p/a,i,4)

solving via trial and error we get that i is betwen 19% and 20% and solving further we get that i is 19.77%

so we select b and reject c as the irr is greater then the marr.

so based on irr we will select c but based on incremental irr b will be selected and when we compare both the results we will conclue that b is selected as its irr is greater then the marr.

so b is selected.