Question

Finance: Debt

*Please do not use Excel. If you could show working that would be amazing and appreciated. Thank you very much

1. A bond with a face value of $10,000 that matures in exactly seven years has a price of $10,494.63. The coupon rate is 4.2% p.a. and coupons are paid every six months. Which of the following figures is the closest to the yield to maturity? ( I know the answer is C but I do not know how to work that out)

(a) 4.2% p.a.

(b) 5.40% p.a

(c) 3.40% p.a.

(d) 1.70% p.a.

2. On the 1st October 2016, K.J Limited issued bonds with a maturity date of 1st October 2028. One K.J bond has a face value of $100,000 and the coupon rate is 4.50% p.a. with interest payable half-yearly. Assuming the market yield is 6% p.a. calculate the value of one bond:

(a) on the 1st October 2020.

(b) five years before maturity.

(c) one year before maturity.

Answer 1

1. A bond with a face value of $10,000 that matures in exactly seven years has a price of $10,494.63. The coupon rate is 4.2% p.a. and coupons are paid every six months. Which of the following figures is the closest to the yield to maturity?

We have following formula for calculation of bond’s yield to maturity (YTM)

Bond price P0 = C* [1- 1/ (1+YTM) ^n] /YTM + M / (1+YTM) ^n

Where,

M = value at maturity, or face value = $10,000

P0 = the current market price of bond = $10,494.63

C = coupon payment = 4.2% of $10,000 = $420 but semiannual coupon, therefore C = $420/2 = $210

n = number of payments (time remaining to maturity) = 7 years; therefore number of payments n = 7 *2 = 14

YTM = interest rate, or yield to maturity =?

Now we have,

$10,494.63 = $210 * [1 – 1 / (1+YTM) ^14] /YTM+ 10,000 / (1+YTM) ^14

By trial and error method we can calculate the value of YTM = 1.70% semiannual

Or annual YMT = 2 * 1.70% = 3.40% per year

Therefore correct answer is option: (c) 3.40% p.a.

2. On the 1st October 2016, K.J Limited issued bonds with a maturity date of 1st October 2028. One K.J bond has a face value of $100,000 and the coupon rate is 4.50% p.a. with interest payable half-yearly. Assuming the market yield is 6% p.a. calculate the value of one bond:

(a) on the 1st October 2020.

The Bond’s price can be calculated the help of following formula

Bond price P = C* [1- 1/ (1+i) ^n] /i + M / (1+i) ^n

Where,

The par value or face value of the Bond = $100,000

Current price of the bond P =?

C = coupon payment or annual interest payment = 4.50% per annum, but it makes coupon payments on a semi-annual basis therefore coupon payment = 4.50%/2 of $100,000 = $2250

n = number of payments = 16 (2*8 for semiannual payments of up to remaining maturity of 8 years from Oct 2020 to Oct 2028)

i = yield to maturity or priced to yield (YTM) = 6.0% per annum or 6.0%/2 = 3.0% semiannual

Therefore,

P = $2250 * [1 – 1 / (1+3.0%) ^16] /3.0% + $100,000 / (1+3.0%) ^16

= $28,262.48 + $62,316.69

= $90,579.17

The value of one bond is $90,579.17

(b) five years before maturity.

The Bond’s price can be calculated the help of following formula

Bond price P = C* [1- 1/ (1+i) ^n] /i + M / (1+i) ^n

Where,

The par value or face value of the Bond = $100,000

Current price of the bond P =?

C = coupon payment or annual interest payment = 4.50% per annum, but it makes coupon payments on a semi-annual basis therefore coupon payment = 4.50%/2 of $100,000 = $2250

n = number of payments = 10 (2*5 for semiannual payments of up to remaining maturity of 5 years)

i = yield to maturity or priced to yield (YTM) = 6.0% per annum or 6.0%/2 = 3.0% semiannual

Therefore,

P = $2250 * [1 – 1 / (1+3.0%) ^10] /3.0% + $100,000 / (1+3.0%) ^10

= $19,192.96 + $74,409.39

= $93,602.35

The value of one bond is $93,602.35

(c) one year before maturity.

The Bond’s price can be calculated the help of following formula

Bond price P = C* [1- 1/ (1+i) ^n] /i + M / (1+i) ^n

Where,

The par value or face value of the Bond = $100,000

Current price of the bond P =?

C = coupon payment or annual interest payment = 4.50% per annum, but it makes coupon payments on a semi-annual basis therefore coupon payment = 4.50%/2 of $100,000 = $2250

n = number of payments = 2 (2*1 for semiannual payments of up to remaining maturity of 1 years)

i = yield to maturity or priced to yield (YTM) = 6.0% per annum or 6.0%/2 = 3.0% semiannual

Therefore,

P = $2250 * [1 – 1 / (1+3.0%) ^2] /3.0% + $100,000 / (1+3.0%) ^2

= $4,305.31 + $94,259.59

= $98,564.90

The value of one bond is $98,564.90