Engineering Economics

Question

A manufacturer can choose between two options:  Investing $10000 in upgrades today and earn $20000 per year for the next three years.  Do nothing and earn $16500 per year for the next three years. Assuming an interest rate of 8%, which option has the higher future value?

Answer 1

This is a relatively straightforward NPV problem. Let me show you how to set it up:

1. Let us consider option A: Investing $10000 in upgrades today and earn $20000 per year for the next three years. To do this, we will first write out the cash flow by year.

CF₀ = –$10,000

CF₁ = $20,000

CF₂ = $20,000

CF₃ = $20,000

We will now discount the ones in the future at the interest rate of 8% to bring them back to present value.

PV(CF_t)=CF/(1+r)^t

PVCF₁ = $20,000/(1+.08)^1 = $18,518.52

PVCF₂ = $20,000/(1+.08)^2 = $17,146.78

PVCF₃ = $20,000/(1+.08)^3 = $15,876.64

Let us sum these up to get the NPV.

NPV = CF₀ + PVCF₁ + PVCF₂ + PVCF₃ = –$10,000 + $18,518.52 + $17,146.78 + $15,876.64 = $41,541.94

1. Let us now consider option B: Do nothing and earn $16500 per year for the next three years. To do this, we will first write out the cash flow by year.

CF₀ = $0

CF₁ = $16,500

CF₂ = $16,500

CF₃ = $16,500

We will now discount the ones in the future at the interest rate of 8% to bring them back to present value.

PV(CF_t)=CF/(1+r)^t

PVCF₁ = $16,500/(1+.08)^1 = $15,277.78

PVCF₂ = $16,500/(1+.08)^2 = $14,146.09

PVCF₃ = $16,500/(1+.08)^3 = $13,098.23

Let us sum these up to get the NPV.

NPV = CF₀ + PVCF₁ + PVCF₂ + PVCF₃ = $0 + $15,277.78 + $14,146.09 + $13,098.23 = $42,522.10

Interestingly, we may see that the NPV of option B is higher than the NPV of option A. Therefore, we may conclude that doing nothing and earn $16,500 per year for the next three years is the best option.