Question

1. The local police department is considering two types of sidearms for its officers. The Glock 40 costs $400 apiece and has a life of 4 years. The other option is a Sauer 45 that costs $800 and has a 12-year life. The Sauer pistol has a residual value of $200 at the end of its 12-year service life. Determine the better choice using the PW method and a study period of 8 years. The department uses a MARR of 5%.
2. Three different methods can be used for recovering by-product heavy metals from a manufacturing site’s liquid waste. The investment costs and incomes associated with each method are shown below. Assuming all methods have a 10-year life and the company’s MARR is 10% per year, determine which method should be selected using Annual Worth Analysis.

3. 	Method 1	Method 2	Method 3
   First Cost, $	20,000	18,000	25,000
   Salvage Value, $	1,000	3,000	1,500
   Annual Income, $	5,000	5,000	7,000

Answer 1

Answer 1. We will compare both the alternatives using the PW method

Purchase of Glock 40 (PW)₄₀ = -$400-$400(PV,5%,4)

=-$400-$313.6

=-$713.60

Purchase of Saucer 45 (PW)₄₅ = -$800+ $200 (to be discounted at 5%)

=-$800+$200*0.557

=-$688.60

The better choice would be to purchase Saucer 45 as it has lower negative value.

Answer 2. First we will calculate the PV

Method 1 -

-$20,000+$1,000*0.386+5,000(to be discounted for 10years at 10%)

=-$20,000+$3860+6.144*5000

=-20,000+34,580

=$14,580

Now, we will calculate the AW which will be as follows-

AW= P{i(1+i)ⁿ}/(1+i)ⁿ -1

=$14,580*.10(1+.10)¹⁰ /(1+.10)¹⁰ -1

=$14,580*.10*2.594/1.594

=$2,372.68

First we will calculate the PV

Method 2-

-$18,000+$3,000*0.386+5,000(to be discounted for 10years at 10%)

=-$18,000+$1158+6.144*5000

  =$13,878

Now, we will calculate the AW which will be as follows-

AW= P{i(1+i)ⁿ}/(1+i)ⁿ -1

=$13,878*.10(1+.10)¹⁰ /(1+.10)¹⁰ -1

=$13,878*.10*2.594/1.594

=$2,257.95

Method 3-

-$25,000+$1,500*0.386+7,000(to be discounted for 10years at 10%)

=-$25,000+$579+6.144*7000

  =$18,587

Now, we will calculate the AW which will be as follows-

AW= P{i(1+i)ⁿ}/(1+i)ⁿ -1

=$18587*.10(1+.10)¹⁰ /(1+.10)¹⁰ -1

=$18,587*.10*2.594/1.594

=$3,024.10

As the AW of method 3 is more than 1 &2 therefore Method 3 should be selected.