Choice In Increasing Cost Of Funds

Choice In Increasing Cost Of Funds

Video Transcript Available here

Intuition

The algorithm creates a net benefit function that has a single local max that will be the global max for the divisible asset case but can fail in the indivisible asset case.

Let's do a small problem by brute force, searching through all the combinations of funding, and then change the problem to illustrate how the algorithm can break down. The potential breakdown happens if you find that you should not buy an asset with a mix of retained earnings and loans and you have enough retained earnings to purchase the next asset. Your net benefit function has more than one local max and you may have not found the best combination.

Rearranging Loans to Buy More Assets.

Start with the following three assets:

A B C
1 -1 -2 -3
2 2 3 4
IRR 100 50 33

Given $2 of retained earnings at 10% and access to a loan at 70%, the algorithm says you should buy asset A with retained earnings and asset B with a mix of retained earnings and a loan. Note that the total benefits that you get from the assets in year 2 is $5, $2 from A and $3 from B, and you have pay back the MARR account $2.2 and the loan $1.7, the amount you borrowed plus interest. You have a net benefit of $1.1 in year 2.

Now suppose you wanted to buy all three assets. If you did this you would have benefits of $9, and any way you funded them you would be using $2 of retained earnings and borrowing $4. Paying back the funds in year 2 would cost, $2.2 for the retained earnings (You can leave this out and it does not change the result) and $6.8 for the loan. That leaves you with zero net benefits. It does not make sense through any rearrangement funding to buy asset C.

Breaking the Algorithm

Let's change the assets slightly:
A B C
1 -1 -2 -1
2 2 3 1.3
IRR 100 50 30

The idea is to make it possible to fund both A and C from retained earnings. We also need to change the loan rate to 100%. That makes it so that, if you follow the algorithm, asset B will have a blended cost of funds of, 55%, which is more than the IRR and should not be purchased, leaving you with A alone.

In this case you would have $2 benefit in year 2 from asset A and with the extra $1 in the retained earnings account $1.2 for total benefits of $3.2.

If you instead used the extra $1 to buy asset C, then you would have the $2 benefit from asset A and $1.3 from asset C, yielding $1.3, which is more than A alone.

That is what happens when your cost of funds function is not monotonically increasing.

Sample Questions

video transcript of Sample Problem

Examples:

Situation of increasing cost of fund:

For an investment: if IRR > MARR, the asset is acceptable to buy.
What if Retained Earnings are not enough to cover the cost of investment?
A loan is taken in order to make the investment. Loan rate is usually greater than Retained Earnings rate. This shifts MARR to a higher value, which causes the increasing cost of fund.

Questions:

The following represent good sample questions that would help you prepare for an exam:

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