Question

On January 1, 2017, Arbor Corp issued $800,000 of 20-year, 11% bonds at market yield of 12% p.a. Interest is payable semiannually on June 30 and December 31. Compute the issue price of the bonds. Show the financial statements effects using the template for the following: 1) bond issuance, 2) semiannual interest payment and discount amortization on June 30, 2017, and 3) semiannual interest payment and discount amortization on December 31, 2017

Answer 1

The tenure of the bond is 20 years with semiannual coupon. Hence there will be 40 coupon payments.

Computation of issue price:

We model all the cash flows related to this bond in an Excel sheet.

Let us assume any arbitrary issue price (we will solve this further using Excel function to arrive at exact issue price)
This issue price is the cash proceeds received from bond issuance at time 0.

Next, we model coupon payments.
This being a semi-annual coupon paying bond,
Coupon = Face value x coupon rate / 2
Hence Coupon = 800,000 x 11% / 2
Hence coupon payment is $44,000 in each period. This will start from period 1 through period 40

In the period 40, we will repay the bond at face value, which means, there will be a cash outflow of 800,000 in period 40

Next, we find an IRR of these cash flows. Note this is the IRR for semi-annual cash flows. Hence multiply this IRR by 2 to arrive at IRR of annual cash flows. We need to find that value of bond issuance which makes this IRR equal to the market yield of 12% (Don't worry we are not doing this manually).

Go to Data tab of excel, under What-if analysis, go to Goal Seek
Set the cell of IRR to 12% by changing the value of bond issuance and click OK. Excel solves it for us and gives us the bond issuance value as $742,500

The following table shows the calculations

Year	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40
Cash proceeds	$        742,500
Coupon payments		$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$   (44,000)
Principal repayment																																									$ (800,000)
Net cash flow	$        742,500	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (44,000)	$ (844,000)
IRR	12.0%

We see that the bond is issued at a discount.
The discount = Face value - Issuance value

Hence discount = 800,000 - 742,500 = $57,500
This discount will be amortized over 40 periods ($57,500/40 = $1437.5 in each period)

Effect on financial statements

1. Bond issuance
When the bond is issued the company receives $742,500 hence
Debit cash account by 742,500
Debit Bond discount account by $57,500
Credit Long term liabilities by $800,000

2.June 30, 2017
On this day the company makes its first coupon payment of $44,000
Credit cash account by $44,000
Credit Bond discount account by $1,437.5. On balance sheet Bond discount value changes to $56,062.5
Debit Interest expense account by $44,000
Debit Bond discount amortization account by $1,437.5

2.Dec 31, 2017
On this day the company makes its second coupon payment of $44,000
Credit cash account by $44,000
Credit Bond discount account by $1,437.5. On balance sheet Bond discount value changes to $54,625
Debit Interest expense account by $44,000
Debit Bond discount amortization account by $1,437.5