Why The Answer Is The Answer

So now we have what the correct answer is. Now, what our correct answer is will depend on what the interest rate is. This primarily is a problem of delay. We’re having slightly higher costs out here because we have these increased maintenance expenses. When you do delay installation, the point is that this stuff is layered. So we’re trying to balance off the benefits of delaying with the costs that are just a little bit higher. As a way of sorting out which choice should have an advantage, let’s play with different interest rates.

We’ll start off with one extreme, which is an interest rate equal to infinity. An infinite interest rate means that everything after time period 0 doesn’t matter at all. What you’re doing here is dividing something by infinity, which drives it immediately to 0. So if you consider with an interest rate at infinity that the only thing you’re looking at is your zero cost, and you can see that the all now option costs you $300,000 and the part now option costs you $150,000. So clearly when the interest rate is relatively high, the part now is the best choice. So let’s go down to the other extreme.

Instead of having an infinite interest rate, you look at what happens when there’s a zero interest rate. A zero interest rate just means that all these costs and all these costs are treated as if they’re in the same time period, so you can just add them up. Well you should notice that these together are exactly the same in both cases and these are always $15,000 per year. These on the other hand are $10,000 per year here, and then they increase to $20,000 per year here. All of the maintenance costs add up to get to lower than what these are up here. So as the interest rate goes to zero, the all now option has an advantage.

So you see when the interest rates are high, you have a preference for delaying your installations. When your interest rates are low, you have a preference for doing it all now and economizing on these additional costs. So what the correct answer really is all depends on what your interest rate is, what your MARR is. If you’re dealing with something that’s credit card rates, this will look like a good idea. If you’re starting to look at things which are bond rates, this starts to look like a good idea. Remember that there’s always going to be this one interest rate in the middle where you’re just going to be indifferent between the two.

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