Question

You are considering two projects. Project A has projected cash flows of $6,500, $4,500, and $2,500 for the next three years, respectively. Project B has projected cash flows of $2,500, $4,500, and $6,500 for the next three years, respectively. Assuming both projects have the same initial cost, you know that:

Answer 1

Answer:

Project A is more valuable than Project B given a positive discount rate.

Explanation:

Let us assume the Discount Rate be r and cash flow for year n be CFn

Also

Let us assume initial Investment be X

So,  

NPV = ΣCFn ÷ (1+r)^n

NPVA = - X + 6500 ÷ (1 + r) + 4500 ÷ (1+r)^2 + 2500 ÷ (1+r)^3

NPVB = - X + 2500 ÷ (1+r) + 4500 ÷ (1+r)^2 + 6500 ÷ (1+r)^3  

NPVA - NPVB = - X + 6500 ÷ (1+r) + 4500 ÷ (1+r)^2 + 2500 ÷ (1+r)^3 - (- X + 2500 ÷ (1+r) + 4500 ÷ (1+r)^2 + 6500 ÷ (1+r)^3)

= 4000 ÷ (1+r) - 4000 ÷ (1+r)^3 = 4000(1 ÷ (1+r) - 1 ÷ (1+r)^3)

In the case when

Ir > 0, 1 ÷ (1+r) > 1 ÷ (1+r)^3

So,  

NPVA - NPVB > 0 => NPVA > NPVB