Final answer:
Sheridan Company must discount the cash flows from a 6-year note with 10% interest using a 12% discount rate. The present value calculation would involve using the interest rate to find the annual payments and then discounting these payments along with the principal back to the present at the 12% rate. As for the water company bond, an increase in market interest rates results in a lower price for the bond due to discounted future cash flows.
Step-by-step explanation:
The student's question relates to the present value of a note receivable using a different discount rate from the interest rate specified on the note. Sheridan Company receives a $77,000, 6-year note with 10% interest paid annually. The current discount rate is 12%, which is higher than the interest rate of the note. To calculate the present value of the future cash flows from the note, we need to discount the interest payments and the principal amount back to the present using the 12% discount rate.
The formula for calculating the present value (PV) of a single future cash flow is:
PV = FV / (1 + r)^n
Where:
For an annuity (like regular interest payments), we use the present value of an annuity formula:
PVAnnuity = Pmt * [(1 - (1 + r)^-n) / r]
Where:
In this case, the annual interest payment (Pmt) is $77,000 * 10% = $7,700 per year. We need to calculate the present value of these annual payments for 6 years plus the present value of the $77,000 principal repayment at the end of the 6 years. Each of these cash flows is discounted back to the present using the 12% discount rate.
To answer the question regarding the water company bond, bond pricing is inversely related to interest rates. If interest rates increase, existing bonds with lower interest rates become less attractive, and their price typically decreases. Therefore, if the water company bond has an interest rate of 6% and market rates are now 9%, one would expect to pay less than the face value of $10,000 for this bond.
Calculating the fair price for this bond would require discounting the remaining interest payment and principal payment using the present market interest rate of 9%. The exact amount one would be willing to pay would depend on the specific cash flows and the present value calculations using the 9% discount rate.