Question

1. Ali invested $300,000 in a small project for an interest rate of 8%. Four years later, he invested another $600,000 in the same project but this time for an interest rate of 10%. What is the total amount of money he is going to receive after 12 years of his investment period?
2. The Petrochemical manufacturing company is planning to increase the production by replacing a new continues stirred tank reactor. The costs of reactor shown in table below. Calculate the present worth of 10 years working at an interest rate of 10% per year.

1. 	Continues stirred tank reactor
   First Cost, $	1000
   Annual cost, $ per year	400
   Annual income, $ per year	1600
   Salvage value, $	2000
   Life, Years	5

2. Chemical manufacturing company expects the costs of expanding the operation section to be a first cost of $40,000, an annual operating cost of $9000, and a service life of 10 years. Calculate the present worth at an interest rate of 10% per year.
3. Compressor that has the following costs are under consideration for using in a new chemical plant. Using interest rate of 10% per year. Calculate Annual worth Aw for the compressor.

	Compressor
First Cost, $	60,000
Annual operating cost, $ per year	20,000
Salvage value, $	5000
Life, Years	5

4.Heat exchanger has the following costs are under consideration for using in a new chemical plant. Using interest rate of 10% per year. Determine Annual worth.

	Heat exchanger
First Cost, $	20,000
Annual operating cost, $ per year	12,000
Salvage value, $	74,300
Life, Years	5

Answer 1

✓ If Ali invest $300,000 in a small project at an interest rate of 8% and another $600,000 in the same project at an interest rate of 10% then after 12 years Ali will receive -

$300,000*(1+ 0.08)^12 + $600,000*(1+0.1)^8

= $300,000*2.51817 + $600,000*1.85093

= $755,451 + $1,110,558

= $1,866,009 (Ans).

✓ Petrochemical manufacturing company is planning to increase production by replacing a new stirred tank reactor.

The PW of the tank reactor can be calculated as follows by PW(Cost ) and PW(Benefit). The Net Present Worth can be calculated as -

-$1000 - $1,000(P/F, 10%, 5) - $400(P/A, 10%, 10) + $1,600(P/A, 10%, 10) + $5,000(P/F, 10%, 5) + $5,000(P/F, 10%, 10)

(Note as the life is 5 years i.e why the tank reactor will be purchased two times because analysis period is 10 years)

= - $1,000 - $1,000/(1+0.1)^5 - $400[{(1+0.1)^10 - 1}/{0.1(1+0.1)^10}] + $1,600[{(1+0.1)^10 - 1}/{0.1(1+0.1)^10}] + $5,000/(1+0.1)^5 + $5,000/(1+0.1)^10

= -$1,000 - $620.92 - $400*6.1446 + $1,600*6.1446 + $3,104.60 + $1,927.72

= - $4,078.76 + $14,863.68

= $10,784.92 = $10,785 (Approx).

The NPW of 10 years working of tank reactor is $10,785 (Ans). We have PW Benefit and PW Cost together.

✓ Chemical Manufacturing expects cost of expanding operation section first cost is $40,000 and an annual operating cost of $9,000 and service life of 10 years.

We can calculate PW Cost at 10% interest is as follows -

$40,000 + $9,000*(P/A, 10%, 10)

= $40,000 + $9,000*6.1446 , [Discounting factor of (P/A, 10%, 10) = 6.1446 we have calculated it in above part]

= $40,000 + $55,301.4

= $95,301.4 = $95,301 (Approx).

There PW cost of expanding operation is $95,301. As it is cost we can represent it - $95,301 as NPW. The minus sign represent negative cash flow.

✓ The Annual Worth of Cost of compressor can be calculated as follows -

[$60,000 + $20,000(P/A, 10%, 5) - $5,000(P/F, 10%,5)]*(A/P, 10%, 5)

= [$60,000 + $20,000*{(1+0.1)^5 - 1}/{0.1(1+0.1)^5} - $5,000*(1+0.1)^-5]*[{0.1(1+0.1)^5}/{(1+0.1)^5 - 1}]

= [$60,000 + $20,000*3.7908 - $5,000*0.6209]*(0.2638)

= ($60,000 + $75,816 - $3104.5)*(0.2638)

= $132,711.5*0.2638

= $35,009.29 = $35,009 (Approx)

Therefore, AW Cost of compressor is $35,009 (Approx).

✓ AW Cost of Heat exchanger at 10% can be calculated as -

[$20,000 + $12,000(P/A, 10%, 5) - $74,300(P/F, 10%, 5)]*(A/P, 10%, 5)

[Note : The discounting factor (P/A, 10%, 5) = 3.7908 , (P/F, 10%, 5) = 0.6209 , (A/P, 10%, 5 = 0.2638 has been calculated above part]

= [$20,000 + $12,000*3.7908 - $74,300*0.6209]*(0.2638)

= ($19,356.73)*(0.2638)

= $5,106.30 = $5,106 (Approx).

Therefore, AW Cost of Heat exchanger is $5,106 (Approx).