Question

Issue Price

Matthison Harcourt plans to issue $500,000 face value bonds with a stated interest rate of 8%. They will mature in 6 years. Interest will be paid semiannually. At the date of issuance, assume that the market rate is (a) 8%, (b) 6%, and (c) 10%.

Use the appropriate present value table:

PV of $1 and PV of Annuity of $1

Required:

For each market interest rate, answer the following questions. Round calculations and answers to the nearest whole dollar. Due to differences in rounding when using the present value factors, you need to round your answer for the ISSUE PRICE in the first column only to the nearest 100.

	Market Rate
	8%	6%	10%
1. What is the amount due at maturity?	$	$	$
2. How much cash interest will be paid every six months?	$	$	$
3. At what price will the bond be issued?	$	$	$

Answer 1

		Market rate
		8%	6%	10%
1	Amount due at maturity	$500,000	$500,000	$500,000
2	Cash interest ($500,000 × 8% × 6/12)	$20,000	$20,000	$20,000
3	Bond issued price (W.N)	$500,000	$549,770	$455,680

1. The market interest rate does not affect the maturity value. hence the same at different market rates.

2. Interest paid semi-annually on the face value of the bond at a stated interest rate, not on the market rate.

3.

Compute bond issue price when the market interest rate at 6%:

Where i = 3% and n = 12 years

PVAF(3%, 12 years) = 9.9540

PVF(3%, 12 years) = 0.70138

Present value of face value of bond = $500,000 $\times$ 0.70138 = $350,690

Present value of cash interest payments = $20,000 $\times$ 9.9540 = $199,080

Issue price = $350,690+$199,080 = $549,770

_______________________________________________________________________

Compute bond issue price when the market interest rate at 10%:

Where i = 5% and n = 12 years

PVAF(5%, 12 years) = 8.86325

PVF(5%, 12 years) = 0.55683

Present value of face value of bond = $500,000 $\times$ 0.55683 = $278,415

Present value of cash interest payments = $20,000 $\times$ 8.86325 = $177,265

Issue price = $278,415+$177,265 = $455,680