Question

Hargrave Limited is selling a new bond to raise capital for their factory in Indonesia.
The bond has a face value of $100,000 and pays a coupon rate of 8.25% p.a. Coupon
payments will be made on June 30 and December 31 of each year. The bond’s issue
date is January 1, 2019 and matures on December 31, 2024. By the time the bond is
offered to investors on January 1, 2019, the market interest rate has increased to
11.5% p.a.
a. How much would investors be willing to pay for this bond?
(3 Marks)
b. How much would investors pay for the above-mentioned bond, if the market
interest rate on January 1, 2019 is 6% p.a.?
(3 Marks)
c. Compare your answers from part a. and part b. above with the face value of
$100,000 and explain why the bond value is more (or less) than the face
value. Your answer should not exceed 200 words.

Answer 1

Coupon payment is made every six months and coupon amount = 8.25% of 100,000*1/2 = $4,125

(a): Investors will pay an amount = present value of all future cash flows i.e. present value of all coupon payments+maturity amount.

N = 6 years (i.e. from 1^st January 2019 to 31^st December 2024). No. of coupon payments = 6*2 = 12

In the table below we have computed the present value of the bond with n = 12, 1+r = 1+(11.5%/2) = 1.0575

n (time period)	Cash flow	1+r	PVIF	PV
1	4,125.00	1.05750	0.94563	3,900.71
2	4,125.00		0.89421	3,688.61
3	4,125.00		0.84559	3,488.05
4	4,125.00		0.79961	3,298.39
5	4,125.00		0.75613	3,119.05
6	4,125.00		0.71502	2,949.45
7	4,125.00		0.67614	2,789.08
8	4,125.00		0.63938	2,637.43
9	4,125.00		0.60461	2,494.02
10	4,125.00		0.57174	2,358.41
11	4,125.00		0.54065	2,230.18
12	4,125.00		0.51125	2,108.92
12	100,000.00		0.51125	51,125.26
			Total	86,187.57

Thus the investor will be willing to pay $86,187.57 in this case.

(b) Here 1+r = 1+(6%/2) = 1.03

n (time period)	Cash flow	1+r	PVIF	PV
1	4,125.00	1.03000	0.97087	4,004.85
2	4,125.00		0.94260	3,888.21
3	4,125.00		0.91514	3,774.96
4	4,125.00		0.88849	3,665.01
5	4,125.00		0.86261	3,558.26
6	4,125.00		0.83748	3,454.62
7	4,125.00		0.81309	3,354.00
8	4,125.00		0.78941	3,256.31
9	4,125.00		0.76642	3,161.47
10	4,125.00		0.74409	3,069.39
11	4,125.00		0.72242	2,979.99
12	4,125.00		0.70138	2,893.19
12	100,000.00		0.70138	70,137.99
			Total	111,198.25

Thus the investor will be willing to pay $111,198.25 in this case

(c): We can see that in part “a” the amount that the investor is willing to pay is $86,187.57. This is lower than the face value of the bond (of $100,000). This is because in this case the market interest rate of 11.5% is much higher than the coupon payment of the bond which is being paid at 8.25%. As the coupon rate of bonds is lower than the market interest rate the bonds will trade at a discount as new buyers will not be willing to buy the bond at its face value.

In the second instance the market interest rate is 6% per annum and this is lower than the bond’s coupon rate of 8.25%. Thus the bond is offering a better return and this will increase the demand for the bonds causing it to command a premium over its face value. Hence the investors will be willing to pay $111,198.25 in this case. So we can conclude that price of the bond is inversely related to the interest rates.

(172 words)