Apiece of equipment has a first cost of $170,000, a maximum useful life of 7 years, and a market (salvage) value described by the relation s = 120,000 – 11,000k, where k is the number of years since it was purchased. the salvage value cannot go below zero. the aoc series is estimated using aoc = 60,000 + 14,000k. the interest rate is 12% per year. determine the economic service life and the respective aw.

The answer is economic service life is 8 Years, The Annual worth is $27,225.7

Explanation:

Given the equation

S = 120,000 - 11,000K,and AOC is 60,000 - 14,000K, where K is the number of years since the machine was purchased

Substitute the value of K into the equation

S= 120,000 - 11,000 (7)

S = 120,000 - 11,000 ×7

S= 120,000 - 77,000

S= 43,000

AOC = 60,000 - 14,000 (7)

AOC = 60,000 - 14,000 × 7

AOC = 60,000 - 98,000

A

To calculate the economic useful life,we use the equivalent annual cost( EAC)

Yr particular. CF DF. PV

0. Purchase cost 170,000. 1. ( 170,000)

1-7. Running cost. (38,000) 0.4523. 17,187.4

1-7. Scrap proceed. 43,000. 0.4523. 19,448.9

PV. 133,363.7

Discount Factor is calculated thus

(1 + r)-∧n , since r = 12% ,n = 7 (1+0.12)∧-7 = 0.4523

8years replacement

Yr. Particular. CF. DF. PV

0. Purchase cost. 170,000 1. (170,000)

1-7. Running cost. (38,000) 0.4523. 17,187.4

1-7. Scrap proceed 43,000. 0.4523. 19,448.9

8 Scrap proceed 43,000. 0.4523. 19,448.9

113,914.8

Finding the 7years replacement at the cost of capital using (1+r)∧-n/r

= (1+0.12)∧-7 -1/0.12

= (1.12)∧-7 -1/0.12

= 0.4523-1/0.12

=0.5477/0.12

= 4.5642

Therefore Equivalent Annual Cost

= 133,363.7/4.5642

= $29,219.51

8years replacementat the cost of capital using

(1+r)∧n -1/r

(1+0.12)∧-8 -1/0.12

=(1.12)∧-8 -1/0.12

= 0.4038 -1/0.12

=0.5962/0.12

=4.9683

EAC = 113,914.8/4.9683

= $22,928.33

Since they are both cost we prefer the cheapest, that is 8 years replacement

Therefore the economic life of the machine is 8years

To calculate the AW, we use the formula

AW = -P ( P-S)(A/P r n ) - Sr

AW= -(170,000 - 43,000) ( A/P 12% 7) - 43,000 (0.12)

To calculate (A/P r n ),we use the formula

A= P i (1+ r)∧n/ (1 + r )∧n - 1

0.12 (1+0.12)∧7/(1+0.12)∧7-1

= 0.12 ( 1.12)∧7/(1.12)∧7 -1

0.12 (2.210681407)/1.21061407

= 0.265281768/1.210681407

= 0.2191

AW = -127,000,000 (0.2191) --38,000 - 43,000 (0.12)

= 27,825.7 - 5,000 (0.12)

= 27,825.7 - 600

= $27,225.7

Therefore the economic life is 8years, Annual worth is $27,225.7

answer blank(1).(2); sharpe;

of the three mortgage options that demarco and tanya have to choose from, the balloon payment mortgage would be their best option, over adjustable payment and fixed payment plans.ultimately, the balloon payment plan would save demarco and tanya overall, in interest, would cost less monthly, and they would only have to make these payments for 8 years, opposing to 30 years for adjustable or fixed payment plans. 

overall, demarco and tanya would save $80,811 if they chose balloon payments over fixed payments, and would save $116,711 if they choose balloon payments over adjustable payments. benefits with choosing fixed payments over adjustable payments is that, in the end, the payments will still be $836.30 a month, while with adjustable payments, the initial monthly payments will be $763.38 to $1082.70 a month, ultimately leading to a more costly purchase. benefits with choosing fixed payments over balloon payments are not present. benefits in choosing adjustable payments over is that it has a lower interest rate, and starts with lower monthly payments initially. benefits in choosing adjustable payments over balloon payments include a lower interest rate, and lower initial monthly payments. benefits in choosing balloon payments over fixed payments include lower interest rates, lower overall price, lower monthly payments, takes less time to pay off, and does not require a downpayment. benefits in choosing balloon payments over adjustable payments include, lower monthly payments (when averaged), takes less time to pay off, and lower overall price.

hence, option c, balloon payments, is the best option for demarco and tanya to make this purchase, for it will save them a minimum of $80811, and a maximum of $116,711.