Question

14. Consider the following two new chemical plants, each with an initial fixed capital investment (year 0) of $15 x 106. Their cash flows are as follows Year Process 1 (Smion/y) Process 2 (Smillion/y) 5.0 5.0 7.0 2.0 a. Calculate the NPV ofboth plants for interest rates of 6% and 18%. Which plant do you recommend? Explain your results b. Calculate the DCFROR for each plant. Which plant do you recommend? c. Calculate the nondiscounted payback period (PBP) for each plant. Which plant do you recommend? d. Explain any differences in your answers to Parts (a), (b), and (c).

Answer 1

a)

Process- 1
Yean, n	Cash Flow, Co	PV=C/(1+i)/^n, i=6%	PV=C/(1+i)/^n, i=18%
0	-15	-15.000000	-15.000000
1	3	2.830189	2.542373
2	8	7.119972	5.745475
3	7	5.877335	4.260416
4	5	3.960468	2.578944
5	2	1.494516	0.874218
NPV		6.282480	1.001427

Process- 2
Yean, n	Cash Flow, Co	PV=C/(1+i)/^n, i=6%	PV=C/(1+i)/^n, i=18%
0	-15	-15.000000	-15.000000
1	5	4.716981	4.237288
2	5	4.449982	3.590922
3	5	4.198096	3.043154
4	5	3.960468	2.578944
5	5	3.736291	2.185546
NPV		6.061819	0.635855

NPV of Process 1 @6% interest rate=$6.282480 m

NPV of Process 2 @6% interest rate=$6.061819 m

NPV of Process 1 @18% interest rate=$1.001427 m

NPV of Process 2 @18% interest rate=$0.635855 m

NPV means net addition to the present worth. Higher the NPV, better the alternative

NPV is higher for Process 1 @6% interest rate, Accept it

NPV is higher for Process 1 @18% interest rate, Accept it

b)

Yean, n	Cash Flow, Process 1	Cash Flow, Process 2
0	-15	-15
1	3	5
2	8	5
3	7	5
4	5	5
5	2	5
DCFROR	20.99%	19.86%

I have used IRR function in Excel to estimate DCFROR. However financial calculators may also be used. I am enclosing herewith the screen shot of worksheet so that syntax of function can be understood.

DCFROR is the discount rate at which NPV is zero. Typically DCFROR should be higher than required rate of return. In the present case Both DCFRORs are higher than 6% or 18%. Both projects are acceptable. In case of single choice, we can opt for Process 1.

c) Process 1

Yean, n	Cash Flow, Co	Cumulatice Cash Flow
0	-15	-15
1	3	-12
2	8	-4
3	7	3
4	5	8
5	2	10

Payback Period is the period required to recover the investment of process.

If we refer above table, we find that 4 million is to be recovered in Year 3. Payback period will be between 2nd and 3rd year.

Payback period =(Amount to be recovered)/Cash flow in the period=(2+4/7)=2.57 years

Process 2

Yean, n	Cash Flow, Co	Cumulative Cash Flow
0	-15	-15
1	5	-10
2	5	-5
3	5	0
4	5	5
5	5	10

We find that investment is recovered at the end of Year 3.

Payback period= 3 years

Project with lower payback period should be accepted as per payback criteria.

Payback period is lower for process 1, it should be accepted.

d) NPV, payback period and DCFROR may give different results based upon certain factors. But in this case, selection is same in each case.