Question

On January 1, 2019, Plywood Homes, Inc., issued 20-year, 4% bonds having a face value of $1 million. The interest on the bonds is payable semiannually on June 30 and December 31. The proceeds to the company were $975,000 (i.e. on the day they were issued the bonds had a market value of $975,000). On June 30, 2019, the company’s fiscal closing date, when the bonds were being traded at 98.5, each of the following amounts was suggested as a possible valuation basis for reporting the bond liability on the balance sheet.

1. $975,625 (proceeds, plus six months’ straight-line amortization)
2. $1 million (face value)
3. $1,780,000 (face value plus interest payments)

Required:

a. Distinguish between nominal and effective interest rates.
b. Explain the nature of the $25,000 difference between the face value and market value of the bonds on January 1, 2019.
c. Between January 1 and June 30, the market value of the company’s bonds increased from $975,000 to $985,000. Explain. Discuss the significance of the increase to the company.
d. Evaluate each of the three suggested alternatives for reporting the bond liability on the balance sheet, giving arguments for and against each alternative. Your answer should take the investor and the reporting company into consideration.

Answer 1

Answer:- A).

The Nominal interest rate is also defined as a stated interest rate. This interest works according to the simple interest and does not take into account the compounding periods. An effective interest rate is the one that caters to the compounding periods during a payment plan.

The nominal interest rate is the periodic interest rate times the number of periods per year. For example, a nominal annual interest rate of 12% based on monthly compounding means a 1% interest rate per month (compounded). A nominal interest rate for compounding periods less than a year is always lower than the equivalent rate with annual compounding (this immediately follows from elementary algebraic manipulations of the formula for compound interest). Note that a nominal rate without the compounding frequency is not fully defined: for any interest rate, the effective interest rate cannot be specified without knowing the compounding frequency and the rate. Although some conventions are used where the compounding frequency is understood, consumers, in particular, may fail to understand the importance of knowing the effective rate. Nominal interest rates are not comparable unless their compounding periods are the same; effective interest rates correct for this by "converting" nominal rates into annual compound interest. In many cases, depending on local regulations, interest rates as quoted by lenders and in advertisements are based on nominal, not effective interest rates, and hence may understate the interest rate compared to the equivalent effective annual

In this case, the nominal rate of interest is 4%/2 = 2% whereas the effective rate of interest is 4.04%

Nom - 4.00%, P/YR - 2, EFF - 4.04%

b) The $25,000 difference is the adjustment of the nominal interest rate specified in the bond indenture to the market rate. In other words, for an investment of$975,000 the Company's bondholders will receive an annual interest payment of $40,000 plus $25,000 more than they invested when the bonds mature. Thoughearned throughout the life of the bond contract the bondholders do not receive this portion of the "effective" interest until maturity. This difference is disclosed on the balance sheet as a contra liability in the Discount on Bonds Payable account.

C) The $10,000 increase in the market value of the bonds from January I to June 30is primarily the result of a decrease in the rate of interest at which the Company bonds will trade in the market. The decrease in the market rate of interest at which the bonds will trade may be due to a general change in the conditions of the bond market, to a change in the Company's credit ratings, or to a combination of the two. A minor portion of the increase is due to the fact that the bonds were issued at a discount and are now six months closer to maturity. This portion of the increase is due only to the passage of time and would have taken place without any change in the market rate of interest. In other words, assuming no change in the market rate of interest, the market value of the bonds will increase gradually from $975,000 to$1,000,000 at maturity because of the increase in the present value of the unpaid but accruing interest (discount) of $25,000.Assuming the discount is accumulated on an interest basis, this position of the increase in the market value of the bonds will be reported in the Company'sfinancial statements. The portion of the increase in the market value of the bonds which is due to the decrease in the market rate of interest, though not reported in the financial statements, is significant because only by comparing the effective rate of interest at which the bonds were issued with the current market rate of interest can the Company judge whether or not the rate they are paying is advantageous to them. If the market rate is lower it may be to the Company advantage to refund the old issue even though the funding itself would result in a loss.d.$975,625. This basis for valuing the bond liability--its effective amount as at the date of the issue, plus an accumulated discount on a straight-line basis for the six months since then--is theoretically superior to the other three. It would; however, be more precise to accumulate the discount on an interest basis. The Company actually borrowed $975,000, and the immediate liability incurred can not be more nor less than this amount. The present value of the bond liability is less than maturity value because the effective rate of interest is greater than the nominal rate which appears on the face of the bonds. The actual difference between the present value of the bond liability at the date of issue ($975,000) and its maturity value ($1,000,000) represents that portion of the effective interest on the amount borrowed ($975,000) that will not be paid until maturity. As this amount is accumulated by charges to interest expense and credits to the bond liability, the effective amount of the liability gradually approaches maturity value.

$1,000,000. This basis for valuing bond liabilities, the amount due at maturity, is widely used in practice. Its use is frequently supported on the grounds that it represents the amount of true legal liability since it is this amount that would be due and payable in the event of default. This support disregards the accounting assumption of the going concern and, instead, emphasizes liquidation values. This valuation basis is also supported on the grounds that the discount represents prepaid interest and should, therefore, be classified as an asset. This argument has no merit because the discount represents unpaid interest, not prepaid interest. Any bookkeeping entry which classifies discount as prepaid interest does so only by failing to properly adjust to amount borrowed to its effective amount. The practice of recording bond liabilities at maturity value and setting up the discount as a deferred charge is defensible only if the amounts involved are not material and it can be shown that this treatment is expedient.$1,780,000. The basis for this alternative--the total amount the Company is obligated to repay over the remaining life of the bonds ($1,000,000 at maturity, plus 39 semiannual interest payments of $20,000 each)--has no justification. It would require the difference between the amount actually borrowed ($975,000)and the total amount the Company became obligated to repay ($1,800,000) to be treated as an asset or a loss when the bonds were issued. To assume that assets were acquired in excess of the amount actually borrowed or that a loss was incurred in an arms-length transaction is indefensible. The original bondholders invested $975,000 for the right to receive $1,800,000 under the conditions stipulated in the contract (an annuity of $20,000 for forty periods and $1,000,000at the end of the fortieth period). Thus, at the date of issuance, the Company incurs a liability equal to the amount of the bondholders' investment. The difference between this amount and $1,800,000 is the total amount of interest that will accrue with the passage of time. It does not exist at the date the bonds are issued. Except for the materiality of the amounts involved, the use of this alternative as a valuation basis suffers from the same theoretical shortcomings as does the use office value when bonds are issued at a discount.