Question

Cameo’s sales representative has offered an up front price reduction. The proposals are now as follows:

Alternative Apex Brawn Cameo

Up front cost $150,000 $250,000 $190,000

Cost savings / year $65,000 $105,000 $81,000

Economic life, years 4 4 4

Use incremental rate of return analysis to decide which alternative should be recommended. MARR is 12%.

Answer 1

Arranging alternatives in increasing order of initial cost

Apex < Cameo < Brawn

Incremental analysis (Cameo - Apex)

incremental cost = 200000 - 150000 = 50000

incremental cost savings = 81000 - 65000 = 16000

Let incremental IRR be i%, then

16000*(P/A,i%,4) = 50000

(P/A,i%,4) = 50000 / 16000 = 3.125

using trail and error method

When i = 10%, value of (P/A,i%,4) = 3.169865

When i = 11%, value of (P/A,i%,4) = 3.102446

using interpolation

i = 10% + (3.169865-3.125)/(3.169865-3.102446)*(11%-10%)

i = 10% + 0.6654% = 10.67%

As incremental IRR < MARR, Apex option is selected

Incremental analysis (Brawn - Apex)

incremental cost = 250000 - 150000 = 100000

incremental cost savings = 105000 - 65000 = 40000

Let incremental IRR be i%, then

40000*(P/A,i%,4) = 100000

(P/A,i%,4) = 100000 / 40000 = 2.5

using trail and error method

When i = 21%, value of (P/A,i%,4) = 2.540441

When i = 22%, value of (P/A,i%,4) = 2.493641

using interpolation

i = 21% + (2.540441-2.5)/(2.540441-2.493641)*(22%-21%)

i = 21% + 0.86% = 21.86%

As incremental IRR > MARR, Brawn option is selected

Fianlly Brawn option should be selected