Question

1. Renfrow Laboratories purchased $50,000 of bonds on July 1, 2018, priced to yield 8%. The stated interest rate on the bonds is 7%. Interest is paid quarterly on March 31, June 30, September 30, and December 31. The bonds mature on June 30, 2028. The bonds are classified as available-for-sale securities. The fair value of the bonds on December 31, 2018, is $52,500.

   What is the purchase price of the bonds on July 1, 2018? What is the amortized cost of the bonds on December 31, 2018? What is the amount of the net investment shown on Renfrow’s balance sheet on December 31, 2018?

   		Bond purchase price: $46,645 Amortized cost: $46,759 Net investment shown on balance sheet: $52,500
   		Bond purchase price: $46,581 Amortized cost: $46,695 Net investment shown on balance sheet: $52,500
   		Bond purchase price: $46,581 Amortized cost: $46,814 Net investment shown on balance sheet: $52,500
   		Bond purchase price: $46,581 Amortized cost: $46,695 Net investment shown on balance sheet: $46,695
   		Bond purchase price: $46,645 Amortized cost: $46,759 Net investment shown on balance sheet: $46,759
   		None of the other answer choices is correct.

Answer 1

The correct option is

Bond purchase price: $46,581

Amortized cost: $46,695

Net investment shown on the balance sheet: $52,500

1. PURCHASE PRICE OF THE BOND

The bond pays interest quarterly.

Quarterly interest rate = annual rate / 4

= 7/4 = 1.75%

interest payment at the end of each quarter will be

50,000 x 1.75% = $ 875

This is a 10-year bond. Since the investors purchased the bond to yield 8 % return, the purchase price can be determined by discounting the interest payments and principal repayment to the present value at this rate. It is as follows

Year	Payments	Present Value Factor	Present Value
1 - 40	875	27.35548 [note 1]	23,936
40	50,000	0.45289 [note 2]	22,645
		Purchase Price	46,581

Therefore the purchase price for the bond is $ 46,581

note 1:

In case of interest, since it is paid quarterly the term is 40 periods ( 4 quarters of 10 years ) and the discount rate is 8 % p.a. However since the calculation is made on a quarterly basis, the interest rate will be used as 2 % per quarter (8 % x 1/4). The payment is similar to an annuity. Therefore

'r' is the rate of return. ie 0.02

'n' is the number of terms. ie 40

On solving the above formulae, we get

= 27.35548

note 2:

Present value factor of a single payment can be calculated as

In the case of the principal repayment of $ 50,000. The payment is made at the end of the 40th quarter (at the end of the 10th year) with the discounting rate being 2 % per quarter.

therefore,

= 0.45289

2. AMORTIZED COST

The amortization table for the bond till the quarter ended 31st December 2018 can be drawn as follows:

Quarter Ended	Opening Liability	Interest @ 2%	Less: Payment	Closing Balance
30-09-2018	46,581.00	931.62	875	46,637.62
31-12-2018	46,637.62	932.75	875	46,695.37

Therefore the amortized cost as on 31-12-2018 is $ 46,695 (rounded to the nearest dollar)

3. NET INVESTMENT SHOWN ON BALANCE SHEET

Since the bonds are classified as available for sale, it will be shown at fair value in the balance sheet. Therefore the Net investment shown on the balance sheet will be $ 52,500