Final answer:
The proceeds that Longo Corporation will receive from the sale of the notes are the sum of the present value of semiannual interest payments and the present value of the maturity value, discounted at the market yield rate of 8%.
Step-by-step explanation:
To calculate the proceeds that Longo Corporation will receive from the sale of the notes, we must first determine the present value of the future cash flows from the notes using the market yield rate of 8% as the discount rate. The notes have a maturity value of $4 million, a coupon rate of 6%, and mature in 5 years with semiannual interest payments. Given these parameters, the calculation involves finding the present value of the annuity of the semiannual interest payments and the present value of the $4 million principal payment at maturity.
The semiannual interest payment is 6% per year of $4 million, divided by 2, which is $120,000. The present value of these payments can be calculated using the formula for an ordinary annuity:
PV = C * [(1 - (1 + r)^(-n)) / r], where 'C' is the semiannual coupon payment, 'r' is the semiannual market interest rate (8% / 2 = 4%), and 'n' is the total number of semiannual periods (5 years * 2 = 10).
Using this formula, we find the present value of the annuity to be the sum of the present values of all semiannual payments. Additionally, we need to calculate the present value of the $4 million principal to be repaid at maturity, using the formula PV = F / (1 + r)^n, where 'F' is the future value of the principal.
After computing both the present value of the annuity and the present value of the lump sum payment, their sum represents the total proceeds that Longo Corporation will receive. These calculations will give us a value less than the maturity value due to the higher market interest rate of 8%, reflecting the concept that the value of money decreases over time when compared with a risk-free rate.