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 RM1,000 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)

Semiannual coupon PMT = 1,000 x 0.14 / 2 = 70

Number of coupon periods n = 7 x 2 = 14

Required rate r = 10% / 2 = 5% semiannually

Face value F = 1,000

Price of the bond PV = PMT x [1 - (1 + r)-n] / r + F / (1 + r)ⁿ = 70 x (1 - 1.05^-14) / 0.05 + 1,000 / 1.0528 = 1,197.97

ii)

You can purchase 90,000 / 1,197.97 = 75.12 or 75 units of the bond

iii)

Yearly interest income = number of units of the bond x annual interest = 75 x 1,000 x 0.14 = 10,500

iv)

The future value FV = PMT x [(1 + r)ⁿ - 1] / r + F = 70 x (1.06¹⁴ - 1) / 0.06 + 1,000 = 2,471.05 per bond

b)

First we need to find the Yield to maturity for the bond priced at 1,020

PV = PMT x [1 - (1 + r)^-n] / r + F / (1 + r)ⁿ

1,020 = 70 x [1 - (1 + r)^-14] / r + F / (1 + r)¹⁴

By trail and error, substituting different values for r, we get r = 6.77%

Period	Cashflow (PMT)	PV of Cashflow [PMT / (1 + r/2]^n	(PV / Total of PV) x period in years
1	70	67.71	0.02
2	70	65.49	0.05
3	70	63.34	0.07
4	70	61.27	0.09
5	70	59.26	0.11
6	70	57.32	0.12
7	70	55.44	0.14
8	70	53.62	0.15
9	70	51.87	0.17
10	70	50.17	0.18
11	70	48.52	0.19
12	70	46.94	0.20
13	70	45.40	0.21
14	1070	671.20	3.36
	Total	1397.54	5.06

The above table shows the calculation for Macaulays Duration

The period column is the semi annual period number

The cashflow column has the cashflows for the period

In the PV of cashflows column, we find the present value of cashflows by using 6.77% as the discount rate.

For the last column, the period in years is the period number divided by 2. The sum of this column gives the Macaulays duration = 5.06 years.

Modified duration = macaulays duration / (1 + r/2) = 5.06 / (1 + 0.0677/2) = 4.894