Choice In Increasing Cost Of Funds: Sample Questions

Let’s go ahead and work an example of an increasing cost of funds problem. I’ve created for you, one, two, three, four, four assets. I guess that one’s actually not there. And I have ordered them in terms of their internal rates of return.

So, asset A has a 20% internal rate of return, asset B has a 13% internal rate of return, C has 11% and D has 8%. And what I’ve done is I have allocated for you \$4 worth of retained earnings and I’ve set it up so that assets have a certain amount of initial investment available to them. So, asset A uses \$2 up in order to buy it, asset B uses \$5 and so on down the line. I’ve also established two minimum acceptable rates of return. First a low rate of 10% for the retained earnings, and a higher rate of 15% once you’ve exhausted your retained earnings.

So, let’s go ahead and work through our decision process, knowing that we’re going to start with our retained earnings, and then also knowing that we’ll start with our assets that have the highest internal rate of return.

Asset A only cost \$2, so we know that we can fully fund it out of retained earnings because we still have \$4 worth. So, what we’re doing is we’re comparing the internal rate of return on this asset, which is 20%, with the retained earning rate, which is 10%. We see that it is larger, the internal rate of return is larger, so this asset, we are supposed to buy it, and when we buy it we use up \$2 of our retained earnings, so we’ve got \$2 left over.

Now, what we do with that \$2, is we try to apply it to asset B here, really depends on asset B being divisible, or indivisible. If asset B is divisible, what we can do is say, “Well, look, we have \$2 of retained earnings. That has an incremental cost of 10%,” and what we notice is that the internal rate of return on asset B is 13%. Well, we can clearly go ahead and see the internal rate of return is greater than minimum acceptable for those first \$2, and we can just buy \$2 worth of asset B and then we gotta figure out what we’re going to do with that remaining \$3 of asset B that is available to us.

Well, for that remaining \$3, what we can do is say, “well that’s gotta come out of the loan.” The internal rate of return on the asset remains 13%, but the loan rate is 15%. Now, that means that the incremental cost 15% is greater than the incremental benefits of 13%, so we actually shouldn’t go ahead and buy asset B with the loan. And we know that we have additional loan possibilities for assets C and D, but in neither one of these two cases, because the internal rates of return are only 11% and 8% respectively, would we want to take out a loan in order to purchase them.

Now, that’s dealing with asset B as a divisible asset. If it’s indivisible, we have to see if it makes sense to actually buy this with this combination of loans and retained earnings. So, remember, the internal rate of return on the asset is 13%, but what we have to do is figure out what the lended cost of funds is. So, what we’re actually doing here, is taking \$2, out of the \$5 it costs to buy asset B, and saying, “well, let’s go ahead and take our remaining” - again, this is retained earnings - “at the retained earnings rate of 10%.”

Then let’s go ahead and fund the remaining \$3 out of the \$5, at the loan rate, which is 15%. So, this is just a weighted average of those two interest rates that is just proportional to where our funding is actually coming from. And we see that the blended cost of funds that we get here is, and we’ll go ahead and wait for this thing to come up, desperately waiting for this thing to come up, there we go, ends up being, oh damn! It’s exactly 13%. Let’s go ahead and check a couple of decimal places real fast. Well, it turns out to be exactly 13%. So, our incremental costs of funds are 13% and our incremental benefits are also 13%, and the rule that we have in class is if the incremental benefits are equal to incremental costs, you’re supposed to do it. In which case we’re saying that our internal rate of return is 13% is exactly equal to our blended minimum acceptable rate of return, 13%. So we’ll actually buy asset B.

We attempt to move on asset C and try to buy with a loan, it also doesn’t make any sense. So, following this procedure actually gets you to the maximum possible net.

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