Imagine a 10 year, 0%, noncallable loan

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Topic Author
bgf
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Imagine a 10 year, 0%, noncallable loan

Imagine someone were to offer you a 10 year, 0% apr, noncallable loan for the amount of your one year gross income. Every month you have to pay back the principal until at the end of the 10th year, all the money was paid back.

if a banker offered you these terms today, how much would you pay him for the option to take the loan? How did you arrive at that number? how does varying your gross income, up and down, affect your valuation?
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alex_686
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Re: Imagine a 10 year, 0%, noncallable loan

I am confused. You state that the APR is 0%. Ergo, the cost is 0. By definition a 0% APR loan is 0.

You are giving somebody a loan and expect to earn nothing back. This does not hang together so maybe you are asking a different question? Are you talking about a zero coupon loan? Or are you going to get a chunk of cash up front or at the end in excess?

Topic Author
bgf
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Re: Imagine a 10 year, 0%, noncallable loan

alex_686 wrote:
Tue Jun 12, 2018 12:43 pm
I am confused. You state that the APR is 0%. Ergo, the cost is 0. By definition a 0% APR loan is 0.

You are giving somebody a loan and expect to earn nothing back. This does not hang together so maybe you are asking a different question? Are you talking about a zero coupon loan? Or are you going to get a chunk of cash up front or at the end in excess?
sorry if i used the wrong terms. what i am trying to describe is an amount of money, in this hypothetical your one year gross income, will be loaned to you all at once, with no interest. all that is required is for you to pay back the principal in equal payments over a 10 year period. at no point can the banker say, "i want all my money back early." there are no other restrictions or collateral needed. you can do whatever you want with the loan, you just have to pay back the principal every month.

given those terms offered to you today, how much would you be willing to pay the banker today for the option to take the loan? in other words, if the banker were only going to give one loan today, and other people were bidding on it, how much would you bid for it? How did you arrive at that number? how does varying your gross income, up and down, affect your valuation?
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oldcomputerguy
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Re: Imagine a 10 year, 0%, noncallable loan

I think that the OP is implying that the issuer of the loan will expect a lump sum payment up front rather than periodic interest payments, and the OP is asking how much upfront payment would seem reasonable.
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Topic Author
bgf
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Re: Imagine a 10 year, 0%, noncallable loan

oldcomputerguy wrote:
Tue Jun 12, 2018 12:52 pm
I think that the OP is implying that the issuer of the loan will expect a lump sum payment up front rather than periodic interest payments, and the OP is asking how much upfront payment would seem reasonable.
yes, that's probably a better way to word it.
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celia
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Re: Imagine a 10 year, 0%, noncallable loan

bgf wrote:
Tue Jun 12, 2018 12:35 pm
if a banker offered you these terms today, how much would you pay him for the option to take the loan? How did you arrive at that number? how does varying your gross income, up and down, affect your valuation?
It seems you need to understand how to calculate the effective Annual Percentage Rate, instead of the nominal Annual Percentage Rate.
Annual Percentage Rate
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alex_686
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Re: Imagine a 10 year, 0%, noncallable loan

Still confused. Let me run though 2 different cases. Breamking out my NPV calculator.

Case 1: PV = \$10,000, N = 120 months, I = 10%/12 => Payment = \$132.

Case 2. N = \$10,000 N = 120 months, I = 10%/12 , Payment = 10000/120, PV = \$83.33, => PV = \$6,305.67.

So, as a banker, the \$10,000 worth of monthly payments are only worth \$6,306. If, as a banker, I wanted to enter into such a loan I would demand \$3,694 up front. Which kind of does not make a lot of sense.

A loan with a zero interest rate has a cost of zero. You can't disentangle the 2 concepts.

Topic Author
bgf
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Re: Imagine a 10 year, 0%, noncallable loan

alex_686 wrote:
Tue Jun 12, 2018 1:03 pm
Still confused. Let me run though 2 different cases. Breamking out my NPV calculator.

Case 1: PV = \$10,000, N = 120 months, I = 10%/12 => Payment = \$132.

Case 2. N = \$10,000 N = 120 months, I = 10%/12 , Payment = 10000/120, PV = \$83.33, => PV = \$6,305.67.

So, as a banker, the \$10,000 worth of monthly payments are only worth \$6,306. If, as a banker, I wanted to enter into such a loan I would demand \$3,694 up front. Which kind of does not make a lot of sense.

A loan with a zero interest rate has a cost of zero. You can't disentangle the 2 concepts.
i appreciate you working with me on this. so hopefully i can make sense of what i am asking.

i understand that from the banker's point of view this might seem like a bad loan. that isn't what i am concerned about. just take it as a given that for whatever reason, this banker is willing to give you these terms.

my question that i really want to get at is given that you are offered these favorable terms, what would you then be willing to pay up front, all at once, to get the loan? how did you arrive at that value?

i am trying to figure out how to value, in present dollar terms, precisely how favorable this loan is. does that make sense?

so, are you saying that, assuming I make \$10,000 per year, I should be willing to pay \$3,694 up front, all at once for that loan? i don't know how to answer my own question, but i agree with you, that number doesn't sound right...
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alex_686
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Re: Imagine a 10 year, 0%, noncallable loan

bgf wrote:
Tue Jun 12, 2018 1:12 pm
so, are you saying that, assuming I make \$10,000 per year, I should be willing to pay \$3,694 up front, all at once for that loan? i don't know how to answer my own question, but i agree with you, that number doesn't sound right...
I was saying if you wanted to get \$10,000 today and to pay it off at 0% you would need to pony up \$3,694 up front. So much worse.

It might make more sense if you laid out the scenario. I assume this is some type of sweetheart loan being negotiated between yourself and family member or employer. They give you cash or equity up front and you pay them off over 10 years on generous terms.

This is fine but I will repeat myself. If the interest rate is zero than the cost of the loan is zero. No "Time Value of Money". The simplest way is to structure it with interest. If we can't, why not? I am thinking of some religious angle. In any event, context is important.

Topic Author
bgf
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Re: Imagine a 10 year, 0%, noncallable loan

alex_686 wrote:
Tue Jun 12, 2018 1:35 pm
bgf wrote:
Tue Jun 12, 2018 1:12 pm
so, are you saying that, assuming I make \$10,000 per year, I should be willing to pay \$3,694 up front, all at once for that loan? i don't know how to answer my own question, but i agree with you, that number doesn't sound right...
I was saying if you wanted to get \$10,000 today and to pay it off at 0% you would need to pony up \$3,694 up front. So much worse.

It might make more sense if you laid out the scenario. I assume this is some type of sweetheart loan being negotiated between yourself and family member or employer. They give you cash or equity up front and you pay them off over 10 years on generous terms.

This is fine but I will repeat myself. If the interest rate is zero than the cost of the loan is zero. No "Time Value of Money". The simplest way is to structure it with interest. If we can't, why not? I am thinking of some religious angle. In any event, context is important.
unfortunately, this is not a real loan that i have personally been offered. it is a thought experiment that i am having a difficult time working through. on its face, it seems like it should be automatic. like, wow, someone is willing to offer me a 10 year, interest free loan, for as much as i make in an entire year, and i can do anything i want with the money! that's great! but, if it actually is so great, then there must be some rational way of quantifying it. i want to figure out how to value the loan from my point of view. if it is favorable, then how much should I be willing to pay for it?

so, to give more context, say i make \$100,000 per year. this means, that if i take the loan, i have to pay \$833.33 per month, every month, for the next ten years. in exchange for that liability, i get \$100,000 today to do whatever i want with it. how much should i be willing to pay for those favorable terms?

either this is dumber than i think or its more difficult than i think. i thought someone would be able to pop up pretty quickly and give an explanation. i dont think its dumb; if anything, its an interesting thought experiment that could teach me something.
Last edited by bgf on Tue Jun 12, 2018 1:48 pm, edited 1 time in total.
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livesoft
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Re: Imagine a 10 year, 0%, noncallable loan

I just got a 0% interest, noncallable loan for 4 years with monthly payments. These things do exist. I didn't have to pay anything up front, but I did buy a car with the money.
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david
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Re: Imagine a 10 year, 0%, noncallable loan

bgf wrote:
Tue Jun 12, 2018 12:35 pm
Imagine someone were to offer you a 10 year, 0% apr, noncallable loan for the amount of your one year gross income. Every month you have to pay back the principal until at the end of the 10th year, all the money was paid back.

if a banker offered you these terms today, how much would you pay him for the option to take the loan? How did you arrive at that number? how does varying your gross income, up and down, affect your valuation?
This "option" amount. Or a discount in the initial loan amount (i.e., take 9k but pay it back like it was 10k) can be considered interest. In this case, it would be 1k of interest on a 10k loan. (In this case the interest rate can be calculated to be about 2.15%).

So, in effect, the "option" or discount is the same thing as bidding on an interest rate.

corn18
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Re: Imagine a 10 year, 0%, noncallable loan

I would pay \$10,000 to get 1 year salary of \$275,000 at 0% non-callable with a 10 year payback.

Why \$10,000? I don't know, it's just a thought exercise.
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HongKonger
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Re: Imagine a 10 year, 0%, noncallable loan

Maybe look at Sharia banking to see how they price loans.

alex_686
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Re: Imagine a 10 year, 0%, noncallable loan

bgf wrote:
Tue Jun 12, 2018 1:46 pm
so, to give more context, say i make \$100,000 per year. this means, that if i take the loan, i have to pay \$833.33 per month, every month, for the next ten years. in exchange for that liability, i get \$100,000 today to do whatever i want with it. how much should i be willing to pay for those favorable terms?
Assuming a 10% interest rate, \$36,940
Assuming a 0% interest rate, \$0

Mind you, I am using 10% as the interest rate - or discount rate - which is a pretty high value. On the other hand, it is for a unsecured personal loan, so maybe it is low.
bgf wrote:
Tue Jun 12, 2018 1:46 pm
either this is dumber than i think or its more difficult than i think. i thought someone would be able to pop up pretty quickly and give an explanation. i dont think its dumb; if anything, its an interesting thought experiment that could teach me something.
This is a pretty simple and classic "Time Value of Money" question brought up in introduction to finance courses. Read up on NPV or "Internal Rate of Return" calculations. I have had to walk this calculation forwards, backwards, and sideways. It is a good tool with a wide range of applications.

What you are investigating is pretty much the same as figuring out how much to pay "Discount Points" on a mortgage. Pay a upfront fee today to get a lower interest rate over the life of the loan.

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Re: Imagine a 10 year, 0%, noncallable loan

bgf wrote:
Tue Jun 12, 2018 12:35 pm
Imagine someone were to offer you a 10 year, 0% apr, noncallable loan for the amount of your one year gross income. Every month you have to pay back the principal until at the end of the 10th year, all the money was paid back.

if a banker offered you these terms today, how much would you pay him for the option to take the loan? How did you arrive at that number? how does varying your gross income, up and down, affect your valuation?
No banker who wants to remain employed and keep their banking license would offer such terms. What this sounds like is an employer forgivable loan. Is it?
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David Jay
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Re: Imagine a 10 year, 0%, noncallable loan

I would probably take it at under 3%, definitely take it under 2%.

A combination of being able to earn more than the cost (in, say, commercial paper) and paying it back with inflated dollars.

 That is to say, 2% per year.
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Re: Imagine a 10 year, 0%, noncallable loan

Effectively, you are asking what would be the cost of a 10-year mortgage based on the total payments you would need to make. Say you want the total of the payments to be 100,000. You go backwards to find out how much loan you need at the beginning. Suppose you needed to take out a 49,000 mortgage to have to pay 100,000 total after 10 years. Then you could say that the cost to you at the beginning, by your reasoning, was 51,000. Mortgages are sold by the amount available to you at the beginning, but you can look up the total cost after 10 years to figure this out.

mxs
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Re: Imagine a 10 year, 0%, noncallable loan

There would be some kind of cost to this. In livesoft's response above, it would be assumed that a higher price for the vehicle is agreed upon than would be otherwise given in order to receive the 0% loan. Sometimes you will see this in advertising when they say 0% loan or 3,000 in rebates. So the cost, is the difference between the 0% loan price and the otherwise price, sometimes had through negotiating or rebates. With the car example, they are off loading inventory and making a sale, so the manufacturer has another layer of profit/gains/benefit by making that sale and 0% loan.

In a general sense, I would look at something like money market interest rates, CD's, Treasuries, and the like to see how much that money could make, and get an answer that way. You have to look at the time value of the initial 10k (or whatever) and the price paid to receive the money.

Oicuryy
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Re: Imagine a 10 year, 0%, noncallable loan

Say I was willing to pay up to 4% APR in interest. I would use the excel present value function like this.
=PV(1.04^(1/12)-1,120,-1/120)

1.04^(1/12)-1 is the monthly interest rate corresponding to a 4% APR.
120 is the number of future monthly payments
-1/120 is the fraction of my annual salary paid each month.

The result is
0.8258

This means I would not pay more than 1-0.8258 = 0.1742 times my annual salary to get the loan.

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sketchy9
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Re: Imagine a 10 year, 0%, noncallable loan

Sounds almost like you're buying points, as you would with a mortgage. In this case, the points reduce the interest rate to 0. The thing with points, though, is that they still get factored into the APR, which is not the same as the interest rate. So it seems to me that what you're really asking is what is the highest effective APR you would tolerate for a 10 year loan equivalent to one year of your salary.

simplesimon
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Re: Imagine a 10 year, 0%, noncallable loan

The answer depends on the individual's cost of capital. It doesn't matter that the interest rate is 0%, 1%, or 5%, it would all factor in. Everyone would be willing to pay more up front for a 0% loan vs a 5% loan.

As for calculating how much it is up front, calculate it like you're valuing a \$100 zero-coupon bond.

JoeRetire
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Re: Imagine a 10 year, 0%, noncallable loan

bgf wrote:
Tue Jun 12, 2018 12:35 pm
Imagine someone were to offer you a 10 year, 0% apr, noncallable loan for the amount of your one year gross income. Every month you have to pay back the principal until at the end of the 10th year, all the money was paid back.

if a banker offered you these terms today, how much would you pay him for the option to take the loan? How did you arrive at that number? how does varying your gross income, up and down, affect your valuation?
1) \$5, or less if the banker would accept less.

2) I pulled that number from my a\$\$. I don't need a loan. But I'd take whatever I could get at 0% and invest it.

3) I don't think varying my gross income would affect my valuation. No more than \$5. Any takers?

momvesting
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Re: Imagine a 10 year, 0%, noncallable loan

I would probably approach it as an opportunity cost question and compare it to some other known loan, expense, or savings product that was part of my life at the time the loan was offered. For example, if put it directly into prepaying \$10k of my mortgage, I would figure out exactly how much that would save me in interest vs paying an extra \$83.33 towards my mortgage monthly (the payment of \$10k over 120 months) and offer a percentage of 50-75% of that savings as a prepayment.

oldcomputerguy
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Re: Imagine a 10 year, 0%, noncallable loan

bgf wrote:
Tue Jun 12, 2018 1:46 pm
unfortunately, this is not a real loan that i have personally been offered. it is a thought experiment that i am having a difficult time working through.
Given that, is this thread even actionable?
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TravelforFun
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Re: Imagine a 10 year, 0%, noncallable loan

If someone would loan me \$100,000 and wanted me to pay her back \$833.33 per month for 120 months for a total \$100K, how much money would I give her for that privilege?

Let say I take \$100K, put it in a saving account that pays 2.5%, and withdraw \$833.33 per month to pay her. At the end of the term, I would have paid her back \$100K and still have \$14,893 of interest in my account. Subtract out the income taxes, I would have \$11,900 to split with her.

I don't know how you would deposit \$100K check without triggering a SAR or gift tax filing.

TravelforFun

Nate79
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Re: Imagine a 10 year, 0%, noncallable loan

TravelforFun wrote:
Tue Jun 12, 2018 5:19 pm
If someone would loan me \$100,000 and wanted me to pay her back \$833.33 per month for 120 months for a total \$100K, how much money would I give her for that privilege?

Let say I take \$100K, put it in a saving account that pays 2.5%, and withdraw \$833.33 per month to pay her. At the end of the term, I would have paid her back \$100K and still have \$14,893 of interest in my account. Subtract out the income taxes, I would have \$11,900 to split with her.

I don't know how you would deposit \$100K check without triggering a SAR or gift tax filing.

TravelforFun
2.5% savings account rate is not guaranteed for 10 years. What if 3 years from now rates go back to zero but you are stuck with the agreement terms for 10 years? Or would you decide to make a lump sum payment if yields went below a certain threshold (but it sounds like lump sum payment is not an option).

What type of investment options give you a guaranteed rate for 10 years and can take from the principal to pay off the loan?

Topic Author
bgf
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Re: Imagine a 10 year, 0%, noncallable loan

Nate79 wrote:
Tue Jun 12, 2018 5:34 pm
TravelforFun wrote:
Tue Jun 12, 2018 5:19 pm
If someone would loan me \$100,000 and wanted me to pay her back \$833.33 per month for 120 months for a total \$100K, how much money would I give her for that privilege?

Let say I take \$100K, put it in a saving account that pays 2.5%, and withdraw \$833.33 per month to pay her. At the end of the term, I would have paid her back \$100K and still have \$14,893 of interest in my account. Subtract out the income taxes, I would have \$11,900 to split with her.

I don't know how you would deposit \$100K check without triggering a SAR or gift tax filing.

TravelforFun
2.5% savings account rate is not guaranteed for 10 years. What if 3 years from now rates go back to zero but you are stuck with the agreement terms for 10 years? Or would you decide to make a lump sum payment if yields went below a certain threshold (but it sounds like lump sum payment is not an option).

What type of investment options give you a guaranteed rate for 10 years and can take from the principal to pay off the loan?
this is the kind of thing that im getting at with this question. several have compared it to a mortgage, which makes sense given the term and size of the loan, but it is i think very unlike a mortgage in that the money can be used for anything, reinvestment in personal business, stock market, bonds, savings account, yacht, whatever. that decision is entirely up to you, and i think it also directly effects the amount that you would be willing to pay for the loan.

unfortunately, im not even sure i understand exactly what cost of capital is, but from reading up quickly on it, i think that is the right track. i think i would have to determine, 1) how i intended to invest that money and 2) make a guess as to the return i expected to be able to make with it. 3) i would then have to balance that against alternative uses of that money, and 4) all the while taking into account the additional monthly liability, \$833.33, which is not a small sum for someone earning \$100,000 per year. im still not sure how i would take all those factors into account in arriving at a set dollar sum to pay for the loan...
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Jags4186
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Re: Imagine a 10 year, 0%, noncallable loan

Nate79 wrote:
Tue Jun 12, 2018 5:34 pm
What type of investment options give you a guaranteed rate for 10 years and can take from the principal to pay off the loan?
You’d do a CD ladder and keep 1 years worth of payments in a savings/money market account. Every year when a CD matures you migrate that to the the savings account paying market rates.

dknightd
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Re: Imagine a 10 year, 0%, noncallable loan

alex_686 wrote:
Tue Jun 12, 2018 2:04 pm

What you are investigating is pretty much the same as figuring out how much to pay "Discount Points" on a mortgage. Pay a upfront fee today to get a lower interest rate over the life of the loan.
That is the way I would consider it. How many points are you willing to pay to get the interest rate down to zero. I'd probably do it for 1-3 points. I'd prefer 1, but might do 3. So for lets say 0% interest loan \$100,000 I would pay \$1000, I might pay \$3000. I don't think I'd go much higher than that because I'd like a sure thing. YMMV

I bought my solar panels on a 15 year 0% loan. But, it would not surprise me if the points were hidden in the price I paid for the panels. Still it saves me money on electricity every month, so I don't care

CyclingDuo
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Re: Imagine a 10 year, 0%, noncallable loan

bgf wrote:
Tue Jun 12, 2018 12:35 pm
Imagine someone were to offer you a 10 year, 0% apr, noncallable loan for the amount of your one year gross income. Every month you have to pay back the principal until at the end of the 10th year, all the money was paid back.

if a banker offered you these terms today, how much would you pay him for the option to take the loan? How did you arrive at that number? how does varying your gross income, up and down, affect your valuation?
I got that offer and took it.

1983 was the year. A trust was set up from oil money by a woman who had passed away. It was a very dated offer for males only (set up in the 1950's). Any male from my high school that wanted to go to graduate school could borrow up to \$10K per year at 0% interest. The only stipulation was that it had to be paid back within 10 years of graduation. I took the offer. Who wouldn't?

It sure beat out the double digit student loans at the time.
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Re: Imagine a 10 year, 0%, noncallable loan

bgf - Can you provide some background on your question? Ignore the financial details. Just explain what you are trying to do. Once the intent is clear, we'll help you with the math.

The wiki has some background info: Comparing investments
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Topic Author
bgf
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Re: Imagine a 10 year, 0%, noncallable loan

Tue Jun 12, 2018 6:38 pm
bgf - Can you provide some background on your question? Ignore the financial details. Just explain what you are trying to do. Once the intent is clear, we'll help you with the math.

The wiki has some background info: Comparing investments
im afraid that by trying to make my intent clear i might make things more confusing. really, this was presented as an exercise to help me work through and better understand a couple of things. i thought about it before posting and could not come up with even an approach, so i posted the thread.

i think there are two things that i am trying to understand on a fundamental level, 1) how to appropriately value this loan, i.e., leverage, without complicating things with interest rates/payments, and 2) how to quantify/compare the opportunity presented by the loan against the steady liability of the monthly principal payment.

in some ways it is like analyzing a mortgage, but in other ways it is more complicated. with a mortgage, i have to use the money to buy my home. some find incentive in paying down the mortgage quicker based on the interest rate and mortgage payment; others like the "liquidity" of the mortgage.

with this loan, i could use it to invest, for example, in a standard 3 fund portfolio. if that were my intention, what should i be willing to pay for the loan? further, there would be no incentive to pay the loan off faster, as there is no interest.

i would like to know all the variables that should be considered in this valuation process and then the math behind how to take those variables and arrive at a reasoned valuation for paying whatever it is that i would pay.

i apologize if this is the inappropriate forum, but i thought the investing theory forum was the appropriate place to ask.
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grabiner
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Re: Imagine a 10 year, 0%, noncallable loan

bgf wrote:
Tue Jun 12, 2018 7:12 pm
i think there are two things that i am trying to understand on a fundamental level, 1) how to appropriately value this loan, i.e., leverage, without complicating things with interest rates/payments, and 2) how to quantify/compare the opportunity presented by the loan against the steady liability of the monthly principal payment.
The way to value the loan is as a negative bond portfolio.

Suppose you had a portfolio of bonds which paid you \$833 per month for the next ten years. How much would this portfolio be worth? That is the market value of a 10-year loan with a monthly payment of \$833. The interest rate on the loan affects the principal amount, but not the market value, unless it affects what you do with the loan (for example, if you might make extra payments or refinance the loan.)

This is exactly what happens in the bond market. A mortgage-backed security is valued based on the present value of the future mortgage payments. If rates rise, the principal and payments of the mortgages don't change, but the value of the mortgage-backed security falls because the value of those payments to an investor falls.
David Grabiner

evestor
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Re: Imagine a 10 year, 0%, noncallable loan

I would take the loan for as much as they would give me...\$10,000? \$10,000,000? You got it.
I would then turn around and put it in something incredibly secure (savings / CD if below FDIC limits, treasury bills / notes if not) and take the profit.
You can ladder things to maximize interest while still throwing off cash such that you can repay w/o much outside capital.

How much would I pay for it? By definition the upper bound is interest I'll make less taxes. But clearly less than that. There is work to be done in moving this all around, and working through logistics of payback. And I place non-zero value on my time.

dknightd
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Re: Imagine a 10 year, 0%, noncallable loan

bgf wrote:
Tue Jun 12, 2018 12:35 pm
Imagine someone were to offer you a 10 year, 0% apr, noncallable loan for the amount of your one year gross income. Every month you have to pay back the principal until at the end of the 10th year, all the money was paid back.

if a banker offered you these terms today, how much would you pay him for the option to take the loan? How did you arrive at that number? how does varying your gross income, up and down, affect your valuation?
Since this a hypothetical, let me turn it around, how much would you pay?
How much would you want me to pay before you made the 0% loan?
I'll give you \$1000 if you loan me \$100,000 at no interest for 10 years. Interested?
I have \$1000 cash ready to go

Topic Author
bgf
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Re: Imagine a 10 year, 0%, noncallable loan

dknightd wrote:
Tue Jun 12, 2018 7:51 pm
bgf wrote:
Tue Jun 12, 2018 12:35 pm
Imagine someone were to offer you a 10 year, 0% apr, noncallable loan for the amount of your one year gross income. Every month you have to pay back the principal until at the end of the 10th year, all the money was paid back.

if a banker offered you these terms today, how much would you pay him for the option to take the loan? How did you arrive at that number? how does varying your gross income, up and down, affect your valuation?
Since this a hypothetical, let me turn it around, how much would you pay?
How much would you want me to pay before you made the 0% loan?
I'll give you \$1000 if you loan me \$100,000 at no interest for 10 years. Interested?
I have \$1000 cash ready to go
i've had trouble following some of the posts here, but i like what evestor said about the 'upper bound' being what you expected to make on the money over 10 years. i think that makes sense. whatever that amount is, i would also have to take into account the monthly liability of \$833.33, which I have to pay.

so, let's say i make \$100,000 per year, and I decide I want to bid on this \$100,000 no interest loan. assuming my budget is maxed out, so I have no free cash flow. I will have to make my monthly payment using either the loan itself or the earnings generated from the loan.

the 10 year treasury bill pays 2.96% right now. so that would only get me \$2,960 per year, nowhere near the \$10,000 per year that I need to be able to make the payments. so, i wouldn't be able to invest all the money in that, I would have to keep some set aside to cover the principal payments. this means that i am effectively decreasing the leverage provided by the loan, as its just sitting in cash, or an equivalent.

to determine what i would pay in this scenario, i suppose i would just have to optimize using current interest rates how to set up a ladder, as i believe some other posters have already mentioned. once i find out what i stand to earn over 10 years with the ladder, i could do a present value calculation to determine how much that money spread over 10 years is worth today, risk free. it probably wouldn't be a great deal of money.

OR, i could say im going to invest it in this great stock i found, which i think is undervalued with great growth prospects. i estimate that over the next 10 years it will have a 20% annualized return. i would still have to keep some of the money set aside for the first few monthly payments, but i should be able to pay most of the monthly payments from the price appreciation, which would be \$20,000 in the first year alone. more than enough to cover the monthly payments, plus a lot left over to continue compounding at 20% per year.

of course, id have to find some way to take into account the potential volatility of the return. the stock could well return 20% annualized, but drop 30% the first year i held it... at which point, id have no way to pay back the loan. the only option i have under these circumstances is to, again, withhold a portion of the \$100,000 in cash as a cushion to make the payments. on the other hand, any money i keep in cash costs me huge amounts of money 10 years from now, considering it will not be compounding at a 20% annualized rate...

the more i invest, the more i will make over 10 years, and the more i can bid for the loan. the more i hold in cash, the less i'll make, and the less id be willing to bid.

these are the problems i see. i feel like there is a way to solve this problem, but maybe it really is just too difficult for me to do. when i start trying to take into account the potential volatility of a stock (or any portfolio not composed entirely of fixed income) i get the feeling that i am wandering into Black-Scholes option pricing land, as i am attempting to find a value for the volatility of an underlying asset over a specific period of time...

what seems like a simple question, actually gets really complicated.

others i think have made good points about the negative bond portfolio and mortgages, but, and maybe im just not understanding, i still think the ability to invest in anything, a business, or stock, something with inherent volatility, and not just a bond, makes this complicated.
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evestor
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Re: Imagine a 10 year, 0%, noncallable loan

bgf wrote:
Wed Jun 13, 2018 7:36 am
others i think have made good points about the negative bond portfolio and mortgages, but, and maybe im just not understanding, i still think the ability to invest in anything, a business, or stock, something with inherent volatility, and not just a bond, makes this complicated.
To me this is not complicated.
You ladder the whole thing and align to risk.
For money in the first ~year you drop it in savings (~1.5%) and pay out of that to burn to zero.
For years 2-5, you probably do CDs or short term munis (2%-3% depending upon this and that) and buy stuff that is almost zero risk.
For 5-10 years, you have more options. But again I would lean to CDs or munis to keep it low risk.

Can you invest it in the market? Sure. But timing risk is real. I'd want to know I was not sunk if I happened to do this whole deal in 2002. Paying in 2008/2009 would have been pretty tough.
Hence I'd use functionally zero risk gov't backed product for it.

Find me this deal today for \$10M and I'd take it. Back of the envelope, I'd be making \$100K/yr for owning CDs and gov't backed munis. You have yourself a deal.

Meg77
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Re: Imagine a 10 year, 0%, noncallable loan

I'm a banker, and this thought exercise makes total sense to me. And for the record, the idea of a of 0% loan is not necessarily unreasonable from the lender's perspective. Car dealers extend them all the time - in order to induce you to spend more for a newer car than you perhaps otherwise would. There are generally two components to making money from a loan - the interest rate, and the origination fee. You're asking what origination fee would be reasonable to pay in order to get a 0% 10 year fully amortizing loan.

This is a version of the frequent question we get on this forum of whether or not someone should pay off their mortgage. In other words, how cheap does a loan have to be to justify keeping it rather than paying it off?

Personally I'd pay up to 10% of the loan balance up front for this loan. In simple terms that averages out to 1% a year for the original loan balance; since the balance is declining annually the actual effective APR would be higher than 1%, but it's still fairly low - especially for unsecured debt.

If I had a great investment idea or purchase in mind, or any debt at a higher rate, I might pay more. Currently I don't care to invest more in this market cycle, especially using borrowed funds at any rate. I do have a rental mortgage at 5.125% (3.49% after tax) that I could pay off with this loan since it equals right about 1 year of my salary. But the payment is on a 30 year term now - and after inflation I'm almost borrowing with free money already. To induce me to pay it off in 10 years I'd probably need to get the APR on the new loan down to about 1%.
Last edited by Meg77 on Wed Jun 13, 2018 1:12 pm, edited 1 time in total.
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bottlecap
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Re: Imagine a 10 year, 0%, noncallable loan

The way of calculating the value of this loan - what you would be willing to pay today to be able to get it - is a function of the present interest rate.

Calculate the value of all the interest you would pay on a normal market rate loan, discount it to present value, and that’s what you would pay to get it.

JT

Chan_va
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Re: Imagine a 10 year, 0%, noncallable loan

As other people have pointed out, this is equivalent to bidding on the bond yield, which means your APR is no longer 0%.

So let's assume that the banker puts this up for bidding. He/she already has 1 bidder - the US treasury, which is currently offering 3% on a T year t note. So you are going to have to bid > 3%. How much more than 3%? That depends on the % gain of the alternative investment you are going to make with the loan. Let's assume that your expectation on the 10 year return of the alternative investment is 5% with std. deviation of x%. If x was 0, you would bid upto 4.99999%. You could get fancy with the math as x increases, but as a basic starting point, you could do something like a Black Scholes type model to factor the volatility into the equation.

So, basically you would pay Risk free rate + (Expected return-risk free rate)* volatility discount.

not4me
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Re: Imagine a 10 year, 0%, noncallable loan

Meg77 wrote:
Wed Jun 13, 2018 11:53 am
In simple terms that averages out to 2% a year for the original loan balance; since the balance is declining annually the actual effective APR would be higher than 2%, but it's still fairly low - especially for unsecured debt.
I approached a bit differently, but ended up in the same area for a cap. I got to something a bit over 2% by considering what the IRS would tax someone who offered me this deal. I don't recall offhand how they determine that, but believe for a 10 year loan it might work out to about that. I'd probably also look at the zero coupon / strips market to see what those markets are showing.

Of course, I, like many others, wouldn't consider it right now anyway. I'm sure I'd start with bidding 0. Would be interesting to know how thinking would change if it was re-framed to say, "would you pay 1% of original amount?", etc

Meg77
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Re: Imagine a 10 year, 0%, noncallable loan

not4me wrote:
Wed Jun 13, 2018 12:41 pm
Meg77 wrote:
Wed Jun 13, 2018 11:53 am
In simple terms that averages out to 2% a year for the original loan balance; since the balance is declining annually the actual effective APR would be higher than 2%, but it's still fairly low - especially for unsecured debt.
I approached a bit differently, but ended up in the same area for a cap. I got to something a bit over 2% by considering what the IRS would tax someone who offered me this deal. I don't recall offhand how they determine that, but believe for a 10 year loan it might work out to about that. I'd probably also look at the zero coupon / strips market to see what those markets are showing.

Of course, I, like many others, wouldn't consider it right now anyway. I'm sure I'd start with bidding 0. Would be interesting to know how thinking would change if it was re-framed to say, "would you pay 1% of original amount?", etc
Sorry I edited my above post. 10% divided by 10 years is 1% a year. But yes in general anything that costs less than the equivalent of 3% per year is reasonable and would be jumped on by many investors. With inflation running over 2% you're paying very, very little for the use of those funds. Of course adding leverage is always risky though, even when purchasing relatively safe assets.
"An investment in knowledge pays the best interest." - Benjamin Franklin

JoeRetire
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Re: Imagine a 10 year, 0%, noncallable loan

CyclingDuo wrote:
Tue Jun 12, 2018 6:07 pm
I got that offer and took it.

1983 was the year. A trust was set up from oil money by a woman who had passed away. It was a very dated offer for males only (set up in the 1950's). Any male from my high school that wanted to go to graduate school could borrow up to \$10K per year at 0% interest. The only stipulation was that it had to be paid back within 10 years of graduation. I took the offer. Who wouldn't?

It sure beat out the double digit student loans at the time.
So you paid \$0 for it?

If that's the case then I agree - who wouldn't?

CyclingDuo
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Re: Imagine a 10 year, 0%, noncallable loan

Yup. I paid everything back within the ten year time frame stipulation at 0% interest. At the same time - at least for many years - my Citibank money market account and CD’s were making double digit interest. I turned down the bank’s final CD offer to me in 1989 when the had a 5 year CD at 10%. I laughed and said I could do better than that. My bad...
"Everywhere is within walking distance if you have the time." ~ Steven Wright

vineviz
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Re: Imagine a 10 year, 0%, noncallable loan

Here’s the easiest solution I can think of.
Imagine the loan is \$100,000, requiring 10 equal repayments one year apart, starting in August of 2019.

What is the surest way you have to repay the loan? I say it is to take the \$100k and buy equal quantities of 10 different Treasury zero coupon notes, so that \$10k is maturing each August until the loan is repaid. This exposes you to no risk whatsoever.

Buying those Treasuries would cost you about \$85,341 if my math is right. The \$14,659 you have left over is the maximum you’d be willing to pay for this loan.

If it cost more than that and you’re better off not doing it. Anything less than a cost of \$14,659 is free money.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch

finite_difference
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Re: Imagine a 10 year, 0%, noncallable loan

I would lend \$100,000,000.

I would lump sum it into VTSAX.

At the end of each year, I would sell \$10,000,000 worth of shares and return it (plus enough to cover capital gains if any.)

At the end of 10 years hopefully I have made a decent amount, but otherwise I would declare bankruptcy.
Last edited by finite_difference on Wed Jun 13, 2018 8:41 pm, edited 1 time in total.
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2tall4economy
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Re: Imagine a 10 year, 0%, noncallable loan

I had to give it a little thought because it's unusual but I have an answer which I think is correct and makes sense.

A lender would expect to be paid the risk free rate + a rate adder based on your risk profile. That would be an indifferent loan; if he charged less he's giving you wealth, if he charged more he'd be making money on you.

So you'd just do a PV calc with those two rates, the principal and the time. Bingo.
You can do anything you want in life. The rub is that there are consequences.

alex_686
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Re: Imagine a 10 year, 0%, noncallable loan

bgf wrote:
Tue Jun 12, 2018 7:12 pm
in some ways it is like analyzing a mortgage, but in other ways it is more complicated. with a mortgage, i have to use the money to buy my home. some find incentive in paying down the mortgage quicker based on the interest rate and mortgage payment; others like the "liquidity" of the mortgage.
So I will point you back to NPV, IRR, and other Time Value of Money things we talked about. They are a generalized set of tools that can be used to answer specific questions. Ignore the restrictions on the mortgage, the math behind the discount points and your question is the same. Should I get \$3,000 cash back or a 0% auto loan? Should I get a MBA? More on that latter.
bgf wrote:
Wed Jun 13, 2018 7:36 am
these are the problems i see. i feel like there is a way to solve this problem, but maybe it really is just too difficult for me to do. when i start trying to take into account the potential volatility of a stock (or any portfolio not composed entirely of fixed income) i get the feeling that i am wandering into Black-Scholes option pricing land, as i am attempting to find a value for the volatility of an underlying asset over a specific period of time...

what seems like a simple question, actually gets really complicated.
Break it down into simpler questions.

First, think about the loan. This is the wacky part that I think many of us are struggling with.

Option #1: It is a 0% loan. Borrow \$100,000 and pay back \$833 each month. No other strings. This boils down to free money. Take it, invest in low rate savings accounts and CDs. It is a no brainier. Not sure why anybody would offer this except in some-type of sweetheart deal.

Option #2: It is not a 0% loan. There is a upfront fee. There is a back-end fee. You pay it off in 11 years. Something, anything. NPV and IRR can give you what that interest is.

Option #3: Opportunity cost - It is a 0% loan but.... Going back to the sweetheart deal, there is some type of catch. Going to MBA school is one of these. You pay a explicit cost upfront to pay for school. You also pay a implicit cost - or opportunity cost - time. You loose 2 years of your life, and thus give up 2 years worth of salary and advancements. I am willing to bet that you could blow \$100,000 in Vegas, come back, and pay the \$833 per month. 10% of your gross. It is a high rate of savings but not impossible. What would you have to give up? What is that worth to you?

Second, think about the investment. What is the expected return of your investment, what is the spread between your investment and your loan, and what types of risk are you willing to take. Go back to my Vegas example. How much hazard are you willing to take on? How much risk are you willing to bear?

You don't need to go Black-Scholes land. The CBOE does the calculations for you in the VIX index. And then it only gives you limited information. It just gives you the standard deviation of price changes of the index, which is just a single number when it comes to thinking about risk.

One last note, if you use the 3 fund model your return will be less than your payments about 1 year in 4. I mean, over 10 years with a 0% loan odds are that you will smash it out of the park. There is about 1 in 10 chance you will only break even. But even if you do smash it out of the park there may well be some sticky years.

Hey, did you know that a football coach that has a 60% win any game will have a losing season ever 1 in 4 years?

aqan
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Re: Imagine a 10 year, 0%, noncallable loan

bgf wrote:
Tue Jun 12, 2018 12:47 pm
alex_686 wrote:
Tue Jun 12, 2018 12:43 pm
I am confused. You state that the APR is 0%. Ergo, the cost is 0. By definition a 0% APR loan is 0.

You are giving somebody a loan and expect to earn nothing back. This does not hang together so maybe you are asking a different question? Are you talking about a zero coupon loan? Or are you going to get a chunk of cash up front or at the end in excess?
sorry if i used the wrong terms. what i am trying to describe is an amount of money, in this hypothetical your one year gross income, will be loaned to you all at once, with no interest. all that is required is for you to pay back the principal in equal payments over a 10 year period. at no point can the banker say, "i want all my money back early." there are no other restrictions or collateral needed. you can do whatever you want with the loan, you just have to pay back the principal every month.

given those terms offered to you today, how much would you be willing to pay the banker today for the option to take the loan? in other words, if the banker were only going to give one loan today, and other people were bidding on it, how much would you bid for it? How did you arrive at that number? how does varying your gross income, up and down, affect your valuation?
So it's not a 0% APR loan.. i knew it was too good to be true.