Question

Consider the following set of investment projects, all of which have a three-year investment life:


N Project A Project B Project C Project D
0 -800 -1,800 -1,000 -6,000
1 0 600 -1,200 1,900
2 0 900 900 1,900
3 3,000 1,700 3,500 2,800

Compute the net present worth of each project at i = 10%.
Explain in detail how you got your answer.

Answer 1

NPV A = -800 + 0*(P/F,i=10%,N=1) + 0*(P/F,i=10%,N=2) + 3,000*(P/F,i=10%,N=3)
NPV A = -800 + 0*(1 + 10%)¹ + 0*(1 + 10%)² + 3,000*(1 + 10%)³
NPV A = -800 + 0*(0.9091) + 0*(0.8264) + 3,000*(0.7513)
NPV A = 1,453.9

NPV B = -1,800 + 600*(P/F,i=10%,N=1) + 900*(P/F,i=10%,N=2) + 1,700*(P/F,i=10%,N=3)
NPV B = -1,800 + 600*(1 + 10%)¹ + 900*(1 + 10%)² + 1,700*(1 + 10%)³
NPV B = -1,800 + 600*(0.9091) + 900*(0.8264) + 1,700*(0.7513)
NPV B = 766.4

NPV C = -1,000 - 1,200*(P/F,i=10%,N=1) + 900*(P/F,i=10%,N=2) + 3,500*(P/F,i=10%,N=3)
NPV C = -1,000 - 1,200*(1 + 10%)¹ + 900*(1 + 10%)² + 3,500*(1 + 10%)³
NPV C = -1,000 - 1,200*(0.9091) + 900*(0.8264) + 3,500*(0.7513)
NPV C = 1,282.4

NPV D = -6,000 + 1,900*(P/F,i=10%,N=1) + 1,900*(P/F,i=10%,N=2) + 2,800*(P/F,i=10%,N=3)
NPV D = -6,000 + 1,900*(1 + 10%)¹ + 1,900*(1 + 10%)² + 2,800*(1 + 10%)³
NPV D = -6,000 + 1,900*(0.9091) + 1,900*(0.8264) + 2,800*(0.7513)
NPV D = - 598.9

If you need to choose the better project, it is project A, because it has the highest Net Present Worth, and therefore it is the most profitable.

Answer 2

NPV of A
-800 + 0/(1+0.1) + 0/(1+0.1)^2 + 3000/(1+0.1)^3
1453.94

NPV of B
-1800 + 600/(1+0.1) + 900/(1+0.1)^2 + 1700/(1+0.1)^3
766.49

NPV of C
-1000 + (-1200)/(1+0.1) + 900/(1+0.1)^2 + 3500/(1+0.1)^3
1282.49

NPV of D
-6000 + 1900/(1+0.1) + 1900/(1+0.1)^2 + 2800/(1+0.1)^3
-598.80