Question

Brief Exercise G-14 Sunland Company is about to issue $251,800 of 8-year bonds paying an 9% interest rate, with interest payable semiannually. The discount rate for such securities is 10% Click here to view the factor table. (For calculation purposes, use 5 decimal places as displayed in the factor table provided.) How much can Sun and expect to receive for the sale of these bonds? (Round answer to o decimal places, e.g. 2,575.) Sunland can expect to receive Click If you would like to Show Work for this question: Open Show Work

Answer 1

Facts of the Question:

Face Value	$ 251,800
Tenure	8 years
Coupon Rate	9%
Interest Frequency	Semi-annually
Discount Rate	10%

Answer)

Calculation of Issue Price of Bond

Issue price of bond is the aggregate of present value of amount receivable on maturity (i.e. face value of Bond since the bond is redeemable at face value) and present value of coupon payments discounted at given rate of interest (I.e. 10% in the given case).

In the given question, since coupon payment (i.e. interest on Bonds) is made on semi-annual basis, the effective discount rate of interest will be half the annual rate and the number of periods (i.e. number of coupon payments will be twice the total tenure of bonds in years.

Coupon Payments:

Semi-annual interest payment = $ 251,800 X 9% X ½

                                                       = $ 11,331

Therefore the amount of each semi-annual interest payable will be $ 11,331.     

Effective discount rate:

Effective discount rate = 10%/2

                                         = 5%  

Therefore the effective discount rate is 5%

Effective period:

Number of Semi-annual periods = 8 years X 2

                                                          = 16 semi-annual periods

Therefore the effective period is 16.

Issue price of Bonds:

Issue price of bonds = (Semi-Annual Interest Payments X Present Value Annuity Factor at 5% rate for 16 periods) + (Redemption value X Present value factor at 5% rate at the end of 16 periods)

                                        = ($ 11,331 X 10.83777) + ($ 251,800 X 0.45811)

                                        = $ 122,802.77 + $ 115,352.48

                                        = $ 238,155.25 or $ 238,155 (rounded off)   

Therefore, the issue price of the bond is $ 238,155

Working Notes:

Alternatively Present value of interest payments and redeemable value may be calculated as follows:

Present Value of interest Payments:

Period	Coupon Payments	Discounting Factor @ 5%	Present Value
1	$ 11,331	0.95238	$ 10,791.43
2	$ 11,331	0.90703	$ 10,277.55
3	$ 11,331	0.86384	$ 9,788.14
4	$ 11,331	0.82270	$ 9,322.04
5	$ 11,331	0.78353	$ 8,878.13
6	$ 11,331	0.74622	$ 8,455.37
7	$ 11,331	0.71068	$ 8,052.73
8	$ 11,331	0.67684	$ 7,669.27
9	$ 11,331	0.64461	$ 7,304.06
10	$ 11,331	0.61391	$ 6,956.25
11	$ 11,331	0.58468	$ 6,625.00
12	$ 11,331	0.55684	$ 6,309.52
13	$ 11,331	0.53032	$ 6,009.07
14	$ 11,331	0.50507	$ 5,722.92
15	$ 11,331	0.48102	$ 5,450.40
16	$ 11,331	0.45811	$ 5,190.86
Total		10.83777	$ 122,802.77

Present Value of redemption of face value:

Period	Face Value	Discounting Factor @ 5%	Present Value
16	$ 251,800	0.45811	$ 115,352.48
Total			$ 115,352.48