Question

Gamma, inc. must replace its grinding machine. Relevant info about the three best alternatives are below. Each alternative has a 10 year life. Gamm's MARR is 8%. Using ROR analysis, solve for PW_i, then find i by interpolating between the nearest interest rates to pick the best alternative. Please, Do not use Excel, and show all steps.

	A	B	C
First cost	$30,000	$35,000	$28,000
Annual cost	$2,900	$2,200	$3,200

Answer 1

Arranging alternatives in increasing order of initial cost

C < A < B

Incremental analysis (A - C)

Incremental initial cost (A - C) = 30000 - 28000 = 2000

Incremental annual cost (A - C) = 2900 - 3200 = -300 (Annual savings)

Let incremental IRR be i%, then

300*(P/A,i%,10) = 2000

(P/A,i%,10) = 2000 / 300 = 6.666667

using trail and error method

When i = 8%, value of (P/A,i%,10) = 6.710081

When i = 9%, value of (P/A,i%,10) = 6.417658

using interpolation

i = 8% + (6.710081-6.666667)/(6.710081-6.417658)*(9%-8%)

i = 8% + 0.148% = 8.15% (Approx)

As Incremental IRR > MARR, Alt A is selected and C is rejected

Incremental analysis (B - A)

Incremental initial cost (B - A) = 35000 - 30000 = 5000

Incremental annual cost (B - A) = 2200 - 2900 = -700 (Annual savings)

Let incremental IRR be i%, then

700*(P/A,i%,10) = 5000

(P/A,i%,10) = 5000 / 700 = 7.142857

using trail and error method

When i = 6%, value of (P/A,i%,10) = 7.360087

When i = 7%, value of (P/A,i%,10) = 7.023582

using interpolation

i = 6% + (7.360087-7.142857)/(7.360087-7.023582)*(7%-6%)

i = 6% + 0.6455% = 6.65% (Approx)

As Incremental IRR < MARR, Alt A is selected and B is rejected

Finally Alt A should be selected as per IRR Analysis