FV(Premium)

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MrSmart

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When a firm purchases a call on interest rates, why do we compute its future value from its present value by its cost of capital (borrowing)?
If it bought it today at $5,000, then its cost is that, unless we are talking about the opportunity cost of the option, in which case, the risk free rate should be a better discount?
 
You buy call option N days before the actual lending / borrowing. and all your calculations for the effective rate is for the purposes of the borrowed amount only.
 
If I buy a call option today at $5000.
I take a loan 30 days from today at $100,000
The call option FV in 30 days is $5,100 (Using the loan’s discount rate for some reason)
What I recieve net from the loan is $100,000 - $5,100 = $94,900?
Does this assume that I borrow the call option in this case?
 
you would buy a put option and pay the premium too. and lend loan amount. So Loan amount + FV(Premium) is what you totally lent.
you sell a call option, borrow amount so - FV(Premium) + Borrow amount …
it is a netting of the amounts at time 0 that is being done.
 
My question was more simple than that.
Why is the premium of the option bought/sold today being a cash inflow/outflow at it’s FV for the future date. Unless the option was financed as well at the cost of capital.
 
they are making time 0 as the time that the loan / borrowing occurred. since the call / put was purchased N days before they take that cash flow into the time 0 location.
and for EAR take Time_T / Time_0 cash flow.
 
cpk123 wrote:
they are making time 0 as the time that the loan / borrowing occurred. since the call / put was purchased N days before they take that cash flow into the time 0 location.
and for EAR take Time_T / Time_0 cash flow.
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That doesn’t really answer my question, or maybe I’m missing something.
If you buy X for $10, then 60 days later, isn’t your Time_0 cash flow -$10?
 
cpk123 wrote:
is it, have you forgotten the TVM concepts?
Click to expand...
It’s still a cash-outflow at $10, 60 days later, does not change that fact.
At least answer me this. What difference does it make in the equation if I either bought the option, or borrowed it?
At least in the first option, I’d compound forward using the risk-free rate as the opportunity cost of money, but other than that, it does not really make sense to me.
 
if you sold the Call option - you received the premium, but borrowed the loan amount. so the two cash flows have opposite signs from your perspective. At Time 0 it is Borrowed Amount - FV(Call Premium).
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For the Put option - you bought option, also lent the loan amount. So both are outflows from your perspective.
 
I’m not talking about the signs of cash flows, I’m talking about the value of the cash flow for the option.
The current cost today is an outflow/inflow, then the the additional FV difference, as per the TVM concept, implied that I borrowed the option at my cost of borrowing.
So my question is STILL is, why do we use the FV(Premium) as a cash flow, and not the PV/Cost(Premium).
 
look at the timeline …. in fact draw it out.
your time 0 is when you made the borrowing. but your option was purchased N days before.
and then look at how the EAR is calculated … it is Time T cashflow / Time 0 Cashflow.
So Time 0 cashflow does need to adjust for the premium paid N days before … how do you make the cost adjustment - by doing a FV (PRemium) for the N days.
 
What the problem is trying to do is calculate the rate of return from when we borrowed the money to when we pay it back . To do that property, if we add the expense of an option, then we have to include it’s expense in the initial loan amount.
The question comes where do we get the money for the option from? To calculate the loan cost, we are looking at it from only the two points ( when we borrow the money and when we pay it back), so we can assume the earlier option cost is a loan which we repay with interest when we get the loan money giving us only the difference. We still have to repay the full loan amount, but at that time, we also get any proceeds on the option.
I don’t know if that helps.
 
gad4 wrote:What the problem is trying to do is calculate the rate of return from when we borrowed the money to when we pay it back . To do that property, if we add the expense of an option, then we have to include it’s expense in the initial loan amount. The question comes where do we get the money for the option from? To calculate the loan cost, we are looking at it from only the two points ( when we borrow the money and when we pay it back), so we can assume the earlier option cost is a loan which we repay with interest when we get the loan money giving us only the difference. We still have to repay the full loan amount, but at that time, we also get any proceeds on the option. I don’t know if that helps.
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This is the part which was not explicit, but makes sense in the EAR formula.
This is also what I implicity assumed, hence why I asked in the first place where my proposition lies.
 
It’s not spelled out way because it’s a way to help you visualize what is happening with the tvm because when you lend money at time n, there is no money coming in to deduct it from.
The value of that payment based on the interest or return rate at a time n is the more accurate reason.
 
This still doesn’t make sense to me. So we use a future value of the option premium because its assumed to be part of the loan? Also, we’re still borrowing the full amount of the loan, so why do we subtract the option premium when calculating the EAR? If anything, wouldn’t we be adding the FV of the option premium to the loan to be taken out on some future date because thats the full effective amount of the loan?
 
you take the option out N days before the loan.
So today is when you pay the option premium.
You receive the loan 60 days later.
But this is the time 0 for the entire Loan calculation of EAR.
So at time 0 - Loan Amount - FV(Option Premium for 60 days) –> is the amount borrowed. (You pay the option premium, you receive the loan amount - both have opposite signs) but the net amount is used as what you borrowed.
At time T+N -> you pay back the interest + the entire Loan amount.
Now use these two numbers to calculate the EAR.
 
Thanks, I understand how we’re supposed to calculate it, but it doesn’t make intuitive sense.
If we’re paying the option premium N days before the loan we don’t have to pay that premium back when we receive the loan N days later. In other words, we didn’t borrow the option premium for N days. Additionally, it was not part of the loan taken out so why is it subtracted in the EAR calculation.
 
cook29 wrote:
Thanks, I understand how we’re supposed to calculate it, but it doesn’t make intuitive sense.
If we’re paying the option premium N days before the loan we don’t have to pay that premium back when we receive the loan N days later. In other words, we didn’t borrow the option premium for N days. Additionally, it was not part of the loan taken out so why is it subtracted in the EAR calculation.
Click to expand...
For what it’s worth, the option premium was borrowed at the cost of capital (loan interest rate), so you subtract the FV of that premium when you take another loan, that’s effectively the new additional money you borrowed, and calculate the EAR by taking CFt / CF0, where CF0 is the loan issued - FV of the premium, instead of doing two seperate EARs with the PV loan / PV premium as the one before it.
 
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