Final answer:
The issue price of Kalani Corporation's bonds depends on the market interest rate compared to the bond's coupon rate. For rates below the coupon rate, the bond is issued at a premium; for rates equal to the coupon rate, at par value; and for rates above the coupon rate, it is issued at a discount. The present value of future cash flows, discounted at the market rate, determines the issue price.
Step-by-step explanation:
To calculate the issue price of Kalani Corporation's bonds for each case, we need to determine the present value of the bond's cash flows, which includes semiannual interest payments and the face value repayment at maturity. The bond's annual coupon rate is 6%, which means semiannual payments are 3% of the face value ($500,000).
For Case A, with a market interest rate of 4% annually (2% semiannually), the present value of the interest payments (annuity) and the face value (lump sum) at the discounted rate are calculated using the Present Value of Annuity (PVA) and Present Value (PV) formulas, respectively, involving the semiannual market interest rate and the number of semiannual periods (20).
For Case B, when the market rate equals the coupon rate (6% annually, or 3% semiannually), the bonds will typically be issued at par value because the present value of the bond's payments equals its face value when discounted at the coupon rate.
Finally, for Case C, with a market interest rate of 8.5% annually (4.25% semiannually), the bonds would be issued at a discount, as investors would require a higher yield than the coupon rate. The present value of cash flows would be calculated similarly to Case A but at a higher discount rate, resulting in a lower bond price.
Importantly, these calculations are based on the assumption that all future cash flows are risk-free, meaning the bond is set to pay semiannual interest payments and return the principal amount at maturity without default risk.