Question

Use interest rate of 4.8894854% per year compounded monthly, find an appropriate value for A the makes the following two projects equivalent.

Project A		Project B
Year	Cash Flow	Year	Cash Flow
-4	120	0	35
-3	120	1	0
-2	100	2	A
-1	80	3	(1.07)*(A)
0	60	4	(1.07)^2 *(A)
1	40	5	(1.07)^3 *(A)

Answer 1

For the two projects to be equivalent the The value of both projects at time 0 should be equal

PV of A at year 0 = PV of B at Year 0

where r = 4.8894854%

120*(1+r)⁴ + 120*(1+r)³ + 100*(1+r)² + 80*(1+r)¹ + 60 + 40/(1+r) = 35*(1+r)⁴ + 0*(1+r)³ + A*(1+r)² + 1.07A*(1+r)¹ + 1.07^2 *A + 1.07^3 *A/(1+r)

575.7895 = 42.3638 + 4.535335 A

A = 117.62

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