The ABC company issued two promissory notes for one of its sub-contractors as follows:
1 note @ 7% APR for 8 years for $1,000,000
1 note @5.5% APR for 5 years for $2,000,000
The company wishes to replace the above two notes with one promissory note of $3,000,000 @ 7.5% APR to mature in 4 years. If the sub-contractor consents to this new plan, what would the savings, if any, be to ABC company? If it were a flat transaction, with no profit or loss involved, then what interest rate should the new $3,000,000 promissory note bear?
Thanks for help.
It is "High Finance", but I will take a stab at it!.
Promissory notes , in general, do not pay regular interest payments, but rather promise to pay the par value of the notes at maturity. The interest rates of the two notes quoted here are for the benefit of the sub-contractor who was owed the PV of these two notes by the ABC company. In other words, instead of paying the sub-contractor the money owned to them, the sub-contractor agreed to receive these two promissory note in lieu of cash payments.
So, to find out how much money was owed to the sub-contractor, will simply find the PV of these two notes at their given interest rates:
PV of $1,000,000 at 7% for 8 years =$582,009.10
PV of $2,000,000 at 5.5% for 5 years =$1,530,268.71
Total PV =$582,009.10 + $1,530,268.71 =$2,112,277.81. This is what is owed to the sub-contractor.
Now, ABC company wishes to replace or exchange these two notes for one note for $3,000,000 par value at 7.5% to mature in 4 years. Ordinarily, the ABC company would simply cancel the two promissory notes in exchange for the new note, with the consent of the sub-contractor. If it is simply a matter of issuing a new promissory note for $3,000,000 for 4 years, it is immaterial whether the note has an attached interest rate of 7.5% or not, from the viewpoint of the sub-contractor, since they will receive $3,000,000 in four years' time. If they wish to calculate the rate of return on their new note, then that works out to 9.17%(since they know the PV and the FV and the term.)
The ABC company theoretically isn't making or losing any money, since they owe the same amount of money, but rather accelerate the amortization of their notes by writing them off a bit sooner. So, with rate of 7.5% over 4 years, the PV of the $3,000,000 note would be booked as $2,246,401.59 for a difference of $2,246,401.59 - $2,112,277.81 =$134,123.78.
Note: All these calculations were done using this online financial calculator: https://arachnoid.com/finance/