Question

ABC is considering two investment alternatives. Alternative A requires an initial investment
of $10,000; it will yield incomes of $3000, $3500, $4000, and $4500 over its 4-year life.
Alternative B requires an initial investment of $12,000; it is anticipated that the revenue
received each year will increase at a rate of 10%/year (each year’s revenue is 10% higher than
that of the preceding year).
Based on an interest rate of 14% compounded annually, what must be the revenue at the first
year for B in order for alternatives A and B to be equivalent? (Draw the cash flow profiles)

Answer 1

Alternate A					Alternate B
Year	Cash Flow	PVF @ 14%	Present Value		Year	Cash Flow	PVF @ 14%	Present Value
0	$(10,000.00)	1	$ (10,000.00)		0	$(12,000.00)	1	$           (12,000.00)
1	$    3,000.00	0.877	$     2,631.00		1	x	0.877	0.877x
2	$    3,500.00	0.769	$     2,691.50		2	1.1x	0.769	0.85x
3	$    4,000.00	0.675	$     2,700.00		3	1.21x	0.675	0.82x
4	$    4,500.00	0.592	$     2,664.00		4	1.331x	0.592	0.78x
		NPV	$         686.50				NPV	(12,000)+3.327x

revenue at the first year for B in order for alternatives A and B to be equivalent

= NPV of Alternate A = NPV of Alternate B

= 686.50 = (12,000)+3.327x

= x = 3813.2 or 3813.

Alternative B cashflows are :-

Year	Cash Flow	PVF @ 14%	Present Value
0	$(12,000.00)	1	$           (12,000.00)
1	$    3,813.00	0.877	$               3,344.00
2	$    4,194.30	0.769	$               3,225.42
3	$    4,613.73	0.675	$               3,114.27
4	$    5,075.10	0.592	$               3,004.46
		NPV	$                  688.15