Question

a) The ARA Corporation bonds have a coupon of 14%, pay interest semi-annually, and they will
mature in 7 years. Your required rate of return for such an investment is 10% annually.

i) How much should you pay for a $1,000 ARA Corporation bond?
ii) If you are given RM90,000, how many units of bond can you purchase?
iii) What is the yearly interest income for this bond if I purchase it with RM90,000?
iv) You plan to reinvest the coupon interest at 12% rate of return per annum. Calculate the value of the reinvestment, what is the figure will you get at the end of 7th years with your principle.

Answer 1

ARA Corporation bonds features :

Coupon rate - 14% paid semi-annually, hence semi-annual coupon rate = 14%/2 = 7%

Years to maturity - 7. Since coupon is paid semi-annually or twice in a year, the number of payment periods N = 7*2 = 14

Required rate of return : R - 10% annual or 5% semi-annual. This is the appropriate discount rate to price the bond.

1) How much should you pay for the bond :

Face value of the bond is given as $1,000

Coupon amount (semi-annual) = $1,000 x 7% = $70

Price of the bond = Coupon amount x PVIFA (R%, N periods) + Maturity Face Value x PVIF (R%, Nth period)

A simpler way of calculating this is with the PV formula in Excel as follows :

Inputs : Rate = 5%, Nper : N = 14, Pmt = coupon payment each period = $70, Fv = Maturity value = $1,000

(Ignore the negative sign in the formula result. The value is the required price)

How much should you pay for the bond : $1,197.97

2) If you are given RM90,000, how many units of bond can you purchase?

(Note : there seems to be a small mistake in the question since the first part of the question uses the $ currency for the face value, while this part of the question uses the RM currency for the amount of 90,000. I will use the $ currency symbol in all required places to avoid any confusion.)

Price of each bond = $1,197.97

Number of units you can purchase = $90,000 / 1,197.97 = 75.12 or 75 units (rounded down)

3) If you purchase this bond with $90,000, you get 75 units of the bond.

The annual coupon payment from one bond is $70 (semi-annually) x 2 = $140

Yearly interest income on 75 units for this bond = $140 x 75 = $10,500

4) Coupon interest is reinvested at 12% per annum, or 6% semi-annual.

The semi-annual coupon payment is $70.

The figure you will get at the end of 7 years will be the same as the Future value of the periodic coupon payments plus the Face value of $1,000.

Value of the Reinvestment = Future value of the periodic coupon payments = Coupon Amount x [(1 + r)^N - 1 / r]

here r = 0.06 and N = 14 periods

= $70 x [(1 + 0.06)¹⁴ - 1 / 0.06]

= $70 x [1.26 / 0.06]

= $1,470

Figure at the end of 7 years = $1,470 + 1,000 = $2,470