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.

b) Find the duration of the bond with the given information.
Face value=RM1000
Maturity=6 years
Coupon=5%
Bond value=RM1020

Answer 1

a.

i. Given,

FV of the bond (FV) = $1,000

Coupon rate = 14% paid semi-annually

Coupon per period (pmt) = (14%*1000)/2 = $70

Maturity (nper) = 7*2 = 14 semi-annual periods

Required rate of return per period (rate) = 10%/2 = 5%

The price of bond can be calculated using PV function in excel.

Thus, price = PV(5%, 14, 70, 1000)

                                = $1,197.97 (ignore the negative sign as it is a cash outflow)

ii. Total investment amount = $90,000

Units of bond that can be purchased with this amount = $90,000/price per bond

                                                                                       = $90,000/$1,197.97 = 75

iii. Yearly interest income per bond = 14%*1000 = $140

Thus, total yearly interest income from 75 bonds = 75*$140 = $10,500

iv. Rate of reinvestment = 12%

Rate of reinvestment per period = 12%/2 = 6%

To calculate the amount at the end of 7 years after reinvestment of coupons, we need to calculate the FV of coupons.

$70 is being reinvested every period at a rate of 6% for 14 periods.

We will use FV function in excel to calculate the same.

Rate = 6%

Nper = 14

PMT = 70

PV = 0

FV = FV(6%,14,70,0) = $1,471.05

The total amount including principle = $1,471.05+$1,000 = $2471.05

b.

Given,

FV = 1000

Maturity = 6 years

Coupon = 5%

Coupon amount (pmt) = 5%*1000 = 50

Bond value (PV) = 1020

Yield of the bond can be calculated using the above details using the Rate function in excel.

Yield = Rate(6,50,-1020,1000) = 4.61%

Now we will calculate the duration of the bond with the following method in excel:

Year(t)	Cash flow	Present Value	PV*t
1	=5%*1000	=O14/(1+4.61%)^N14	=P14*N14
2	=5%*1000	=O15/(1+4.61%)^N15	=P15*N15
3	=5%*1000	=O16/(1+4.61%)^N16	=P16*N16
4	=5%*1000	=O17/(1+4.61%)^N17	=P17*N17
5	=5%*1000	=O18/(1+4.61%)^N18	=P18*N18
6	=(5%*1000)+1000	=O19/(1+4.61%)^N19	=P19*N19
Sum		=SUM(P14:P19)	=SUM(Q14:Q19)

The results are:

Year(t)	Cash flow	Present Value	PV*t
1	50	47.80	47.797
2	50	45.69	91.381
3	50	43.68	131.03
4	50	41.75	167.01
5	50	39.91	199.56
6	1050	801.22	4807.3
Sum		1020.04	5444.1

Duration = Sum of (PV*t)/Bond value = 5444.1/1020= 5.34