Question

Nichols Corp. issued $100,000 of 5-year bonds with a stated rate of 4%. Interest is paid semiannually, and the market rate of interest is 6%. What are the proceeds of the bond sale?

Answer 1

Price of a bond is the present value of all future cash flows receivable from the bonds discounted at market rate of interest

When interest is paid semiannually, rate of interest is divided by 2 and time period is multiplied by 2

So, Rate of discounting r = 6 / 2 = 3% or 0.03

Time period n = 5 x 2 = 10

Cash flows from the bonds are periodic interest and redemption value

Periodic cash flows

= Principal x Rate x Time

= $100,000 x 4% x 6 / 12 months (semiannual payment)

= $2,000

Discounting factor

= 1 / (1 + r) ^ n

Where,

So, Discounting factor for period 2 will be

= 1 / (1.03 ^ 2)

= 1 / 1.0609

= 0.942595

The following table shows the calculations

Calculations	A	B	C = A x B
Period	Cash flows	PV Factor	Present value
1	2000	0.970874	1941.75
2	2000	0.942596	1885.19
3	2000	0.915142	1830.28
4	2000	0.888487	1776.97
5	2000	0.862609	1725.22
6	2000	0.837484	1674.97
7	2000	0.813092	1626.18
8	2000	0.789409	1578.82
9	2000	0.766417	1532.83
10	2000	0.744094	1488.19
10	100000	0.744094	74409.39
		Proceeds	91469.80