Question

An engineer in charge of the design of a plant must choose either a batch or a continuous system. The batch system offers a lower initial outlay but, owing to high labor requirements, exhibits a higher operating cost. The cash flows relevant to this problem have been estimated as follows:

	year 0	year 1-10 (after tax)	discounted cash flow rate of return	net present worth at 12%
batch system	-$20,000	$5,600/year	23%	$14,000
continuous system	-$30,000	$7,650/year	20%	$17,600

Check the values given for the discounted cash flow rate of return and net present worth in the table. If the company requires a minimum rate of return of 15 % which system should be used and why? EXPLAIN BRIEFLY.

Answer 1

ANS =

# Check the value for dividend discount rate .

- Present value of cashflow = Cashflow / (1+rate) ^n , N= number of years.

- PV of batch cashflow @23% = 5,600 / (1+0.23)^1 + 5,600 / (1.23)^2 + 5,600 / (1.23)^3 + ...till..+5,600 / (1.23)^10 = 21,2755.91 .

- PV of continous system cashflow @20%= 7,650 / (1+0.20)^1 + 7650 / (1.20)^2 + 7650 / (1.20)^3+...till...+ 7650 /(1.20)^10 = 32,072.414.

# Checking the value for NPV @ 12% , here Rate will be 12%

- NPV= PV of all cash inflow - initial investment.

- PV of batch system = 5,600 / (1.12)^1 + 5600 / (1.12)^2 + 5600 / (1.12)^3 +...till ..+ 5600 /(1.12)^10 = 31,641.249

- NPV of Batch system @ 12% = 31,641.249 - 20,000 = 11,641.249

- PV of continous system = 7650 / (1.12)^1 + 7650 / (1.12)^2+ 7650 / (1.12)^3+....till ..+ 7650 /(1.12)^10= 43,224.2

- NPV of continous system @12%= 43,224.2 - 30,000 = 13,224.206.

# Net present worth with 15%.

- PV of batch system @15% = 5,600 /(1.15)^1 + 5600 /(1.15)^2 + 5600 /(1.15)^3+..till..+5600 /(1.15)^10 =28,105.10

- NPV of batch system @ 15% = 28,105.10 - 20,000 = 8,105.10

- PV of continous system= 7650 / (1.15)^1+ 7650 / (1.15)^2 + 7650 / (1.15)^3+..till..+7650/ (1.15)^10=38,395.58

- NPV of continous system = 38,395.58 - 30,000 = 8,395.58.

# Continous system should be choosen as it have Net present worth 290.48 more than the batch system. Continous system is more profitable as it is more profitable project than batch system. Net present worth determine whether present value of future cash inflow is more or less than the initial investment that investor have done. The project should always chosen on the basis of higher net present value as higher the value of NPV the higher will be return to investor.