Question

Rana Company has $300,000 to invest and wishes to evaluate the following three projects.

Years	X ($)	Y ($)	Z ($)
0	(150,000)	(150,000)	(100,000)
1	55,000	80,000	70,000
2	55,000	40,000	30,000
3	55,000	40,000	20,000
4	55,000	70,000
cost of capital	10%	10%	10%

Required:

Which project(s) would you recommend using:

1. Payback Period (PP) in nominal and discounted values.
2. Net Present Value (NPV)
3. Profitability Index (PI)
4. The internal rate of return (IRR) (hint: use 30%)

Answer 1

A)

PAYBACK PERIODS:

X = Initial Investment = 150000

Annual Revenue = 55000

Payback period = 150000/55000 = 2.72 years

Y = Intial Investment = 150000

Cummulative Revenue after 1st year = 80000

Cummulative Revenue after 2nd year = 80000 + 40000 = 120000

Cummulative Revenue after 3rd year = 80000 + 40000 + 40000 = 160000

payback Period = 2 years + (10000*12/40000) months = 2years 3 months

Z = Initial Investment = 100000

Cummulative Revenue after 1st year = 70000

Cummulative Revenue after 2nd year = 70000 + 30000 = 100000

Payback Period = 2 years

DISCOUNTED PAYBACK PERIOD:

X:

	Cost of capital	10%
Years	X ($)	PRESENT VALUE
0	-1,50,000	-1,50,000
1	55,000	49,500	-1,00,500
2	55,000	44,550	-55,950
3	55,000	40,095	-15,855
4	55,000	36,086	20,231
	payback period (in months)	41.27247787

Y:

	Cost of capital	10%
Years	X ($)	PRESENT VALUE
0	-1,50,000	-1,50,000
1	80,000	72,000	-78,000
2	40,000	32,400	-45,600
3	40,000	29,160	-16,440
4	70,000	45,927	29,487
	payback period (in months)	40.29551244

Z:

Cost of capital	10%
Years	Z ($)	PRESENT VALUE
0	-1,00,000	-1,00,000
1	70,000	69930	-30,070
2	30,000	29970	-100
3	20,000	19980	19,880
4	0	0
	Payback period	24.06006006

B)

Cost of capital	10%
Years	X ($)	Y ($)	Z ($)
0	-1,50,000	-1,50,000	-1,00,000
1	55,000	80,000	70,000
2	55,000	40,000	30,000
3	55,000	40,000	20,000
4	55,000	70,000	0
NPV	₹ 22,129.64	₹ 30,589.69	₹ 3,141.86

C)

Cost of capital	10%
Years	X ($)	Y ($)	Z ($)
0	-1,50,000	-1,50,000	-1,00,000
1	55,000	80,000	70,000
2	55,000	40,000	30,000
3	55,000	40,000	20,000
4	55,000	70,000	0
NPV	₹ 22,129.64	₹ 30,589.69	₹ 3,141.86
PI	0.148	0.204	0.0314

D)

Cost of capital	10%
Years	X ($)	Y ($)	Z ($)
0	-1,50,000	-1,50,000	-1,00,000
1	55,000	80,000	70,000
2	55,000	40,000	30,000
3	55,000	40,000	20,000
4	55,000	70,000	0
IRR	17.30%	20.50%	12.48%

Generally, NPV is considered to be the best method for deciding upon investments because it considers most of the deciding factors i.e.:

a) Time value of money

b) Considers cash flows after the payback period

c) Consider economies of scale

Based on the above explanation, I would suggest to invest according to NPV of investments.