Question

Problem 1:

Consider a

$

1000

bond with a coupon rate of 10% and annual coupons. The

par value is $1,000, and the bond has 5 years to maturity. The yield to maturity is

9

%.

For

each question,

s

how your

wo

rk/

calculations

.

A.

What is the

present value of coupons

?

B.

What is the

present value

of face value (i.e. par value)

?

C.

What is the value of the bond

?

D.

Is it a prem

i

um

or

discount

bond?

Problem

2

:

Consider a

$

1000

bond with a coupon rate of

7.5

% and annual coupons. The

par value is $1,000, and the bond has

10

years to maturity. The yield to maturity is

10

%.

For

each question,

s

how your

wo

rk/

calculations

.

A.

What is the

present value of coupons

?

B.

What is the

present value

of face value (i.e. par value)

?

C.

What is the value of the bond

?

D.

Is it a prem

i

um

or

discount

bond?

Grading Criteria:

Your submission

will be evaluated based on the following criteria (1%):

•

Content: adequate coverage of topic, logic of arguments,

relevance and indication

of all used resources.

•

Presentation/Clarity: use of appropriate headings, appropriate organization, and

ease of understanding.

•

Accuracy: free of spelling, grammar, and content errors.

Answer 1

Problem 1:

Consider a $1000 bond with a coupon rate of 10% and annual coupons. The par value is $1,000, and the bond has 5 years to maturity. The yield to maturity is 9%.

For each question, show your work/calculations

A. Present value of coupons is calculated below:

We are given the following information

PMT	$100.00 = 10% x 1000
r	9.00%
n	5

We need to solve the following equation to arrive at the required PV

PV = PMT x 1-(1+r)-n 1-(1+0.09) -5 PV = 100 x 0.09 PV = 388.97

So the PV is $388.97

B. Present value of face value is calculated below:

We are given the following information:

r	9.00%
n	5
FV	$              1,000.00

We need to solve the following equation to arrive at the required FV

FV = PV X (1+r) 1000 = PV X (1+0.09) PV = 649.93

So the PV is 649.93

C. Value of the bond = sum of the PV of the coupons + sum of the PV of par value

Value of the bond = 388.97 + 649.93

Value of the bond = 1038.9

We can even create a schedule for the PV as follows:

Year	CF	Discount Factor	Discounted CF
1	$    100.00	1/(1+0.09)^1=	0.917431193	0.91743119266055*100=	$       91.74
2	$    100.00	1/(1+0.09)^2=	0.841679993	0.84167999326656*100=	$       84.17
3	$    100.00	1/(1+0.09)^3=	0.77218348	0.772183480061064*100=	$       77.22
4	$    100.00	1/(1+0.09)^4=	0.708425211	0.708425211065196*100=	$       70.84
5	$1,100.00	1/(1+0.09)^5=	0.649931386	0.649931386298345*1100=	$     714.92
				PV = Sum of all Discounted CF	$ 1,038.90

D.Is it a premium or discount bond?

As the PV of the bond is greater than the par value, so this is a premium bond. This can even be arreived at by the fact that the discount rate < coupon rate, when this is the case, then the bond is a premium bond

Problem 2

Consider a $1000 bond with a coupon rate of 7.5% and annual coupons. The par value is $1,000, and the bond has

10 years to maturity. The yield to maturity is 10%. For each question, show your work/ calculations

A. Present value of coupons

We are given the following information

PMT	$75.00 = 0.075 x 1000
r	10.00%
n	10

We need to solve the following equation to arrive at the required PV

PV = PMTX 1-(1+r)-n PV = 75 x 1-(1 + 0.1) -10 0.1 PV = 460.84

So the PV is $460.84

B. Present value of face value:

We are given the following information:

r	10.00%
n	10
FV	$              1,000.00

We need to solve the following equation to arrive at the required PV

FV = PV X (1+r) 1000 = PV x (1 +0.1)10 PV = 385.54

So the PV is 385.54

C. The value of the bond = 385.54 + 460.84 =  $846.39

Year	CF	Discount Factor	Discounted CF
1	$      75.00	1/(1+0.1)^1=	0.909090909	0.909090909090909*75=	$       68.18
2	$      75.00	1/(1+0.1)^2=	0.826446281	0.826446280991735*75=	$       61.98
3	$      75.00	1/(1+0.1)^3=	0.751314801	0.751314800901578*75=	$       56.35
4	$      75.00	1/(1+0.1)^4=	0.683013455	0.683013455365071*75=	$       51.23
5	$      75.00	1/(1+0.1)^5=	0.620921323	0.620921323059155*75=	$       46.57
6	$      75.00	1/(1+0.1)^6=	0.56447393	0.564473930053777*75=	$       42.34
7	$      75.00	1/(1+0.1)^7=	0.513158118	0.513158118230706*75=	$       38.49
8	$      75.00	1/(1+0.1)^8=	0.46650738	0.466507380209733*75=	$       34.99
9	$      75.00	1/(1+0.1)^9=	0.424097618	0.424097618372485*75=	$       31.81
10	$1,075.00	1/(1+0.1)^10=	0.385543289	0.385543289429531*1075=	$     414.46
				NPV = Sum of all Discounted CF	$     846.39

D. As the PV of the bond is lower than the par value, so this is a discount bond. This can even be arreived at by the fact that the discount rate > coupon rate, when this is the case, then the bond is a discount bond