Question

You are considering investing some of the money you inherited in bonds. You have identified one corporate bond (CB01) and two government bonds (GBo2 and GB03). All three bonds have a par value of R1000. The corporate bond CB01 offers a coupon rate of 13% per annum, while the two government bonds GB02 and GB03 offer coupon rates of 11% and 12% respectively. All three bonds pay coupons semi-annually and have a face value of R1000. Your intentions are to sell these bonds after one year. Your required rate of return is 12% per annum. 1.1 You have decided to buy the corporate bond (CB01). One CB01 bond is currently selling for R1100. Should you buy the bond? Show your equation, inputs and final decision. 1.2 You were given the choice to receive the coupons paid by the CB01 bond either semi-annually or annually. Which would you prefer? Motivate your answer. 1.3 Calculate the clean price and the all-in price (dirty price) of one CB01 bond if you bought it on 25 January 2016 and intend to sell it on 25 April 2017. The coupons are paid each year on 25 March and 25 September. 1.4 What is the market value of one GB02 bond at maturity?You are considering investing some of the money you inherited in bonds. You have identified one corporate bond (CB01) and two government bonds (GBo2 and GB03). All three bonds have a par value of R1000. The corporate bond CB01 offers a coupon rate of 13% per annum, while the two government bonds GB02 and GB03 offer coupon rates of 11% and 12% respectively. All three bonds pay coupons semi-annually and have a face value of R1000. Your intentions are to sell these bonds after one year. Your required rate of return is 12% per annum. 1.1 You have decided to buy the corporate bond (CB01). One CB01 bond is currently selling for R1100. Should you buy the bond? Show your equation, inputs and final decision. 1.2 You were given the choice to receive the coupons paid by the CB01 bond either semi-annually or annually. Which would you prefer? Motivate your answer. 1.3 Calculate the clean price and the all-in price (dirty price) of one CB01 bond if you bought it on 25 January 2016 and intend to sell it on 25 April 2017. The coupons are paid each year on 25 March and 25 September. 1.4 What is the market value of one GB02 bond at maturity?

Answer 1

1.1

Par Value of all bonds = R1000

CB01 coupon rate = 13%

GB02 coupon rate = 11%

GB03 coupon rate = 12%

Interest is paid annualy.

Market Price of CB01 = R1100

Price of the Bond = C/ PVFA(6%,2) + Face Value / (1+r)^t

    = (130/2) / PVFA(6%,2) + 1000 / (1.06)^2

= R1009.167

As the theoretical price is less than the market value, the bond is overvalued and hence should not be bought.

1.2

Theoretical Price when interest is paid semi-annually = R1009.167

Theoretical Price when interest is paid annually,

Price of the Bond = C/ PVFA(12%,1) + Face Value / (1.12)

= 130/ PVFA(12%,1) + 1000 / (1.12)

= R1008.929

As theoretical price is more when the interest is paid annually, it is more closer to the market value and less loss making. Option for annual interest should be chosen.

1.3

Clean Price = Dirty Price − Accrued Interest

Dirty Price = c × F ×(1 − (1 + r)-n) / r + F / (1 + r)n

c = periodic coupon rate

F = face value

r = yield to maturity

n = total number of coupon payments

Dirty Price = 65 x 1000 x (1-(1.06)-2) / 0.06 + 1000/(1.06)2

= R1009.167 x (1.06)^31/180

= R1019.345

Accrued Interest = (C/M) x (D/T)

M = coupon payments per year

D = days since last payment date

T = total number of days between coupon payments

Accrued Interest = (65/2) x (31/180)

= R5.597

Clean Price = R1019.345 - R5.597

= R1013.74

1.4

Price of the GB02 at maturity = [C/ PVFA(6%,2) + Face Value / (1.06)] x (1+ r)^t

= [(55/2) / PVFA(6%,2) + 1000 / (1.06)^2] x (1.06)^2

= R1113.3