Question

A five-year-old defender has a current market value of $4,000 and expected O&M costs of $3,400 this year, increasing by $1,200 per year. Future market values are expected to decline by $1,100 per year. The machine can be used for another three years. The challenger costs $6,500 and has O&M costs of $2,200 per year, increasing by $600 per year. The machine will be needed for only three years, and the salvage value at the end of that time is expected to be $1,600. The MARR is 18% Click the icon to view the interest factors for discrete compounding when MARR = 18% per year. (a) Determine the annual cash flows for retaining the old machine for three years. Fill in the table below. (Round to the nearest dollar) Period Cash Flows (Defender) $ 0 1 $ 2 S 3 (b) Determine whether now is the time to replace the old machine. First show the annual cash flows for the challenger. Fill in the table below. (Round to the nearest dollar.) Period Cash Flows (Challenger) 0 2 3 Click to select your answer(s).

Answer 1

Annual worth: All the cash flows (Present, annual and future) are converted to annuity.

Given Data:

Particulars	Defender (In $)	Challenger (In $)
Present Market value	4000	6500
O & M costs	3400 with increase by 1200 per year	2200 with increase by 600 per year
Salvage value	700 (4000 – 1100*3)	1600
MARR	18%
Tenure	3 years

Period	Cash flow (Defender)	Cash flow (challenger)
0	4000	6500
1	3400	2200
2	3400 + 1200 = 4600	2200 + 600 =2800
3	3400 + 2400-700 = 5100	2200 + 1200-1600 = 1800

Solution:

(a) Annual cash flows(ACF) for defender.

ACF = 4000(A/P,18,3) + [ 3400 + 1200(A/G,18,3)] - 700(A/F,18,3)

Using DCIF Tables

ACF = 4000(0.4599) + (3400 + 1200(0.890)) - 700(0.2799)

ACF = $6111.67 = $6112

The equivalent annual cost for retaining the machine is

(b) Annual cash flows(ACF) for Challenger.

ACF = 6500(A/P,18,3) + [ 2200 + 600(A/G,18,3)] - 1600(A/F,18,3)

Using DCIF Tables

ACF = 6500 (0.4599) + (2200 + 600 (0.890)) - 1600 (0.2799)

ACF = $5275.51 = $5276

Based on the above calculations the challenger can be considered as it has a less annual cost compared to the defender