Chapter 7, Problem 7.32P

To determine

Concept Introduction:

Present value Present value, also known as discounted value is the current value for a future sum of money with a denied rate of return. The present value is computed by using discount rates on the given rate of return. It indicates whether the money received by an investor today would earn a return in the future. It helps to decide whether a particular stock is worth investing in today.

The expected cash flows are discounted at a discount rate which is actually the expected return. Further, the discount rate is inversely proportional to the future cash flows. It can be calculated using the below- mentioned formula:

  

Requirement a:

To calculate:

Proceeds of Learned Inc.'s bonds on January 1, 2016

Answer to Problem 7.32P

Proceeds from Learned Inc.'s bonds as on January 1, 2016= $61,650,540

Explanation of Solution

For calculation of proceeds (issue price) of the bonds on the issue date, firstly the interest payments made semi- annually would be calculated using the following formula:

  

In the given problem, it is given that the bonds have a face value of $70,000,000, interest rate of 14% and the time period is half year since the interest payments are made semi- annually.

  $Thus,Interestamount=\$70,000,000*14\%*1/2=\$49,00,000$

The bonds have been issued on January 1, 2016 and will mature on December 31, 2035; it means they are 20 year bonds. Interest payments are made semi- annually which means twice a year. Thus, the interest will be paid over 40 years.

The stated market rate of interest at the time of issue of bonds was 16%. Therefore, the semi- annual interest rate can be calculated by multiplying the stated rate by half:

  $Semi-annualinterestrate=16\%/2=8\%$

By using the present value table and taking values for 8% in 40 years, the factor is coming out to be 11.9246. Present value of interest payments can be calculated as follows:

  

Now, present value of maturity value needs to be calculated. For that by taking value of 8% in 40^th period row, the factor is coming out to 0.0460. Thus, present value of maturity value would be:

  

Finally for calculating the proceeds of the bond, the present value of maturity value as well as of interest payments would be added and can be seen as follows:

  

Thus, proceeds from Learned Inc.'s bonds on January 1, 2016 are $61,650,540.

To determine

Concept Introduction:

Horizontal model A horizontal model is an arrangement of set of financial statements that encompasses the balance sheet and income statement. In this model, the effect of each transaction on balance sheet as well as income statement is displayed.

Requirement b:

Horizontal model to show effects of semi- annual interest payment and related premium amortization

Answer to Problem 7.32P

Horizontal model showing effects of semi- annual interest payment and related premium amortization in the books of Learned Inc.

Transaction	Balance sheet	Income statement
Assets= Liabilities+ Stockholder equity	Net income= Revenue- Expenses
	Cash -$49,00,000 Premium on bonds payable -$60,000	Interest expense -$48,40,000

Explanation of Solution

To record the effects of semi- annual interest payment and related premium amortization, firstly premium on bonds payable would be calculated. Premium on bonds payable is given as $24, 00,000 which is to be amortized on straight- line basis. This premium is given for 40 year periods, therefore premium amount for 1 year period would be:

  $Premiumonbondspayable=\$24,00,000/40=\$60,000$

For showing the effects of semi- annual interest payment and related premium amortization using horizontal model, following would be the adjustments required:

Horizontal model showing effects of semi- annual interest payment and related premium amortization in the books of Learned Inc.

Transaction	Balance sheet	Income statement
Assets= Liabilities+ Stockholder equity	Net income= Revenue- Expenses
	Cash -$49,00,000 Premium on bonds payable -$60,000	Interest expense -$48,40,000

To determine

Concept Introduction:

Straight- line amortization results in equal interest payment each year. Compound interest amortization results in higher interest expense during the early years of life of bond and decreases over time.

Requirement c:

Effect on interest expense if premium is amortized using compound interest method

Answer to Problem 7.32P

If the premium calculated in part (b) is amortized using the compound interest method, interest expense for the year ended December 31, 2016 would be more than the interest expense calculated using the straight- line method.

Explanation of Solution

If the premium calculated in part (b) is amortized using the compound interest method, interest expense for the year ended December 31, 2016 would be more than the interest expense calculated using the straight- line method.

Straight- line amortization results in equal interest payment each year. Compound interest amortization results in higher interest expense during the early years of life of bond and decreases over time.

Since the bond was issued on January 1, 2016, it can be assumed that compound interest amortization will be higher than straight- line amortization on December 31, 2016.

To determine

Concept Introduction:

Stated interest rate is the rate printed on the face value of bond whereas market rate can change dramatically through the lifespan of bond.

Requirement d:

Causes of difference between stated and market rate

Answer to Problem 7.32P

The difference exists because there is a short delay between time when bond issuer determines the stated interest rate of bonds and when bonds are actually sold.

Explanation of Solution

Normally, there is a small difference between the stated interest rate of bonds and the market interest rate at the time when bonds are issued.

The difference exists because there is a short delay between time bond issuer determines the stated interest rate of bonds and when bonds are actually sold.