Question

12. (10pts) Project 1 requires an investment of $10,000 at time 0 and an additional investment of $5000 at time 1. It returns $2000 at time 3 and $6000 at time 4, 5, and 6. Project 2 requires an investment of $6000 at time 0 and returns $3500 at time 1 and $5000 at an unknown time. The net present value of the two projects are equal when calculated using compound interest at 4%. Find the unknown time for the secon

Answer 1

Lets first find NPV of project 1

Statement showing NPV

Year	Amount	PVIF @ 4%	PV
0	-10000	1.0000	-10000.0000
1	-5000	0.9615	-4807.6923
2		0.9246	0.0000
3	2000	0.8890	1777.9927
4	6000	0.8548	5128.8251
5	6000	0.8219	4931.5626
6	6000	0.7903	4741.8872
NPV = Sum of PV			1772.5754

Now, NPV of both project are same, hence

1772.5754 = -6000 + [3500 x PVIF(4%,1)] + [5000 x PVIF(4%,n)]
=1772.5754 = -6000 + [3500 x (1/1.04)] + [ 5000 x (1/(1.04)^n]
= 1772.5754 = -6000 + [ 3500 x 0.9615] + [5000 x 0.9615^n]
= 1772.5754 = -6000 + 3365.3846 + [5000 x 0.9615^n]
= 4407.1908 = 5000 x 0.9615^n
= 0.8814 = 0.9615^n
suppose n = 3
= 0.9615^3 = 0.8889
suppose n = 4
= 0.9615^3 = 0.8547

Using interpolation, one can find n

n	0.9615^n
4	0.8547
3	0.8889
1 down	0.0342
?	0.0267

=0.0267/0.0342

= 0.7807

Thus n = 4-0.7807

=3.2193 years