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Chapter 10: Problem 14

Issue Price of a Bond Matt Enterprises issued \(\$ 200,000\) of ten percent, five-year bonds with interest payable semiannually. Determine the issue price if the bonds are priced to yield (a) ten percent, (b) six percent, and (c) 12 percent.

Short Answer

Expert verified
The issue prices depend on each yield: $200,000 for 10%, slightly higher for 6%, and lower for 12% yield.

Step by step solution

01

Understanding the Problem

We need to determine the issue price of a bond based on different yield rates: 10%, 6%, and 12%. The face value of the bond is $200,000 with a coupon rate of 10%, payable semiannually for 5 years.
02

Calculating Present Value Factors

First, calculate the present value of annuity and present value of a lump sum tables/factors for the given yields. For 5 years with semiannual payments (i.e., 10 periods), determine the factors to use based on the yield percentage divided by 2.
03

Using the Yield of 10%

For a yield of 10%, the semiannual yield is 5%. Find the present value factor for an annuity of 5% over 10 periods and the present value factor for a lump sum of 5% over 10 periods. Then calculate the issue price using these factors.
04

Calculating Issue Price for 10% Yield

Use the coupon payment calculated as \(200,000 \times \frac{10}{2}\)% and multiply by the annuity factor. Add this to the face value multiplied by the lump sum factor. This will give the bond's issue price under 10% yield.
05

Using the Yield of 6%

For a yield of 6%, the semiannual yield is 3%. Find the present value factor for an annuity of 3% over 10 periods and the present value factor for a lump sum of 3% over 10 periods. Then calculate the issue price using these factors.
06

Calculating Issue Price for 6% Yield

Calculate with the same method as for the 10% yield, but use the 3% annuity and lump sum factors. Calculate the coupon payment and find the bond issue price.
07

Using the Yield of 12%

For a yield of 12%, the semiannual yield is 6%. Find the present value factor for an annuity of 6% over 10 periods and the present value factor for a lump sum of 6% over 10 periods. Then calculate the issue price using these factors.
08

Calculating Issue Price for 12% Yield

Again, use the previously described method to find the bond's issue price under 12% yield. Use the coupon payment and appropriate present value factors.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Present Value Calculation
Understanding present value calculation is crucial when it comes to bond pricing. Present value is the current worth of a sum of money or a stream of cash flows expected in the future, discounted at a particular interest rate. In bond pricing, this helps determine how much you should pay today for cash flows you will receive in the future.

When a bond is issued, it typically promises to pay periodic interest, also known as coupon payments, and a lump sum at maturity, which is the face value. To calculate the present value:
  • Determine the present value of the annual or semiannual coupon payments. This relies on the present value of an annuity formula.
  • Calculate the present value of the lump sum to be received at the end of the bond's life, using the present value of a single sum formula.
Lastly, sum up these two present values to get the bond's issue price, or the amount of money the investor should pay for the bond today.
Yield Rate
The yield rate in bond terms is essentially the return an investor can expect if they hold the bond until maturity. It's a significant factor in determining the bond's price. Yield rates can fluctuate based on interest rate changes, market conditions, and the creditworthiness of the issuer.

To assess the yield rate efficiently:
  • For 5-year bonds with semiannual payments, remember to divide the annual yield rate by 2 to gain the semiannual yield rate.
  • For example, a 10% annual yield results in a 5% semiannual yield.
  • This divided yield rate is then used to determine the present value factors for both coupon payments and the face value at maturity.
Understanding yield also helps investors decide if a bond is a good investment based on the relationship between market interest rates and bond prices.
Semiannual Interest Payments
Bonds often involve semiannual interest payments, meaning that the bondholder earns interest twice a year. This can impact calculations for bond pricing, as every payment needs to be valued separately for the present value.

Here's how to manage calculations for semiannual interest payments:
  • Calculate the coupon payment based on the bond's coupon rate divided by two. For instance, with a 10% annual rate and a \(\\(200,000\) face value, the semiannual coupon payment is \(\\)10,000\).
  • Each of these coupon payments needs to be discounted back to the present using a semiannual yield rate that matches the market yield rate divided by two.
  • Add to this the discounted present value of the bond's face value, and you've got the bond's full price at issue.
Understanding the concept of semiannual interest is essential as it directly affects the calculation of present value and the yield that investors consider when evaluating bonds.

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Most popular questions from this chapter

Effective Interest Amortization On January 1, 2018, Ranier, Inc., issued \(\$ 300,000\) of ten percent, 15 -year bonds for \(\$ 351,876\), yielding an effective interest rate of eight percent. Semiannual interest is payable on June 30 and December 31 each year. The firm uses the effective interest method to amortize the premium. Required a. Prepare an amortization schedule showing the necessary information for the first two interest periods. Round amounts to the nearest dollar. b. Prepare the journal entry for the bond issuance on January 1, \(2018 .\) c. Prepare the journal entry to record the bond interest payment and premium amortization at June 30 . d. Prepare the journal entry to record the bond interest payment and premium amortization at December 31 .

Excise and Sales Tax Calculations Fullerton Corporation initially records its sales at amounts that exclude any related excise and sales taxes. During June, Fullerton recorded total sales of \(\$ 700,000\). An analysis of June sales indicated the following: 1\. Thirty percent of sales were subject to both a ten percent excise tax and a six percent sales tax. 2\. Fifty percent of sales were subject only to the sales tax. 3\. The balance of sales was for labor charges not subject to either excise or sales tax. Required a. Calculate the related liabilities for excise and sales taxes for June. b. Prepare the necessary journal entry at June 30 to record the monthly payment of excise tax and sales tax to the government.

Installment Term Loan On December 31,2017 , James, Inc., borrowed \(\$ 300,000\) on a six percent. 20 -year mortgage note payable. The note is to be repaid in equal semiannual installments of \(\$ 12,979\) (beginning July 1, 2018). Prepare journal entries to reflect (a) the issuance of the mortgage note payable, (b) the payment of the first installment on July 1, 2018, and (c) the payment of the second installment on December 31,2018. Round amounts to the nearest dollar.

Current Ratio, Quick Ratio, and Times-Interest-Earned Ratio The following data are from the current accounting records of Rome Company: The president of the company is concerned that the company is in violation of a debt covenant that requires the company to maintain a minimum current ratio of \(2.0\). He believes the best way to rectify this is to reverse a bad debt write-off in the amount of \(\$ 10\) that the company just recorded. He argues that the write-off was done too early, and that the collections department should be given more time to collect the outstanding receivables. The CFO argues that this will have no effect on the current ratio, so a better idea is to use \(\$ 10\) of cash to pay accounts payable early. Required a. Which idea, the president's or the CFO's, is better for attaining a minimum \(2.0\) current ratio? b. Will either the quick ratio or the times-interest-earned ratios be affected by either of these ideas?

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