Question

King Leopold Prawn Farming Ltd plans to raise $3 million to build a new prawn farm near Broome in Western Australia. It will issue bonds with a term to maturity of 15 years. The face value per bond will be $1,000 and the coupon rate will be 8% per annum, paid semi-annually. Similar corporate bonds are trading at a yield to maturity of 10% per annum, compounded semi-annually. It is expected that these new bonds will trade at this rate. How many bonds will the company need to issue?

Select one:

a. 3,598

b. 3,545

c. 3,597

d. 3,544

Answer 1

Price of a bond is the present value of all future cash flows receivable from the bond discounted at required rate of return

Future cash flows are periodic coupons and terminal value

Periodic ( semi-annual ) coupons

= Face Value x Coupon rate x 6 / 12

= $1,000 x 8% x 6 / 12

= $40

Terminal value = $1,000

When interest is paid semi-annually, interest rate of compounding is divided by 2 and time period is multiplied by 2

So, Interest rate of compounding

= 10 / 2

= 5% or 0.05

Time period = 15 x 2 = 30 semi-annual periods

Present value factor

= 1 / ( 1 + Rate of compounding ) ^ Number of periods

So, pv factor for period 2 will be

= 1 / ( 1.05 ^ 2)

= 1 / 1.1025

= 0.907029

The following table shows the calculations

Calculations	A	B	C = A x B
Period	Cash Flow	PV Factor	Present Value
1	40	0.952381	38.10
2	40	0.907029	36.28
3	40	0.863838	34.55
4	40	0.822702	32.91
5	40	0.783526	31.34
6	40	0.746215	29.85
7	40	0.710681	28.43
8	40	0.676839	27.07
9	40	0.644609	25.78
10	40	0.613913	24.56
11	40	0.584679	23.39
12	40	0.556837	22.27
13	40	0.530321	21.21
14	40	0.505068	20.20
15	40	0.481017	19.24
16	40	0.458112	18.32
17	40	0.436297	17.45
18	40	0.415521	16.62
19	40	0.395734	15.83
20	40	0.376889	15.08
21	40	0.358942	14.36
22	40	0.34185	13.67
23	40	0.325571	13.02
24	40	0.310068	12.40
25	40	0.295303	11.81
26	40	0.281241	11.25
27	40	0.267848	10.71
28	40	0.255094	10.20
29	40	0.242946	9.72
30	40	0.231377	9.26
30	1000	0.231377	231.38
		Price	846.28

So, the number of bond required to be issued

= Funds required / Price per bond

= $3,000,000 / $ 846.28

= 3,544.94 or 3,545 ( as bonds cannot be issued in fraction )

So, as per above calculations, option b is the correct option