Question

Two mutually exclusive alternatives are bring considered: A and B. Both alternatives cost $1,200 at the present. However, the pattern of revenue from them is different. Alternative A has the potential to bring more revenues later in the project life. The expected revenues of alternative A are: $350, $500, and $850 by the ends of years one to three, respectively. Alternative B promises more immediate cash inflow which is expected to diminish with time: $750, $300, and $100 by the ends of years one to three, respectively. Use MARR=8%.

a) Calculate the Internal Rate of Return of each alternative.

b) Which alternatives are feasible?

c) Calculate the Net Present Worth of each alternative and compare them.

Answer 1

Solution :-

(a) :-

Two mutually exclusive alternatives are bring considered: A and B.

Both alternatives cost = $1,200

The expected revenues of alternative A are = $350, $500, and $850 by the ends of years one to three, respectively.

Alternative B promises more immediate cash inflow which is expected to diminish with time = $750, $300, and $100 by the ends of years one to three, respectively.

MARR = 8%

* Calculating the Internal Rate of Return of each alternative.

IRR is computed using excel IRR function as follows :-

Alternative A			Alternative B
Year	cash flow($)		Year	cash flow ($)
0	-1200		0	-1200
1	350		1	750
2	500		2	300
3	850		3	100
IRR =	16.78%		IRR =	-2.91%

(b) :-

As we calculated the Internal Rate of Return of each alternative A and B.

Alternative A has positive IRR that is higher than MRR.

So, Alternative A is feasible and alternative B is not.

(c) :-

Calculating the Net Present Worth of each alternative and comparing them.

Net present worth of,

Alternative A ($) = -1200 + 350 x P/F( 8%, 1) + 500 x P/F ( 8%, 2) + 850 x P/F ( 8%, 3)

= -1200 + 350 x 0.9259 + 500 x 0.8573 + 850 x 0.7938

= -1200 + 324.07 + 428.65 + 674.73

= -1200 + 1427.45

= 227.45

Net present worth of,

Alternative B ($) = -1200 + 750 x P/F( 8%, 1) + 300 x P/F ( 8%, 2) + 100 x P/F ( 8%, 3)

= -1200 + 750 x 0.9259 + 300 x 0.8573 + 100 x 0.7938

= -1200 + 694.43 + 257.19 + 79.38

= -1200 + 1031

= -169

Alternative A has positive net present worth and alternative B has negative net present worth.

So, Alternative A is acceptable.