Question

1 What is the price of a 15-year zero coupon bond paying $1,000 at maturity if the YTM is 5% percent?

Years to maturity	15 yrs
Face value	$1,000
Yield to maturity	5%

(A) $833.33

(B) $2,097.57

(C) $231.38

(D) $476.74

2. Ailerone, Inc. has issued a bond with the following characteristics:

Par Value	1,000
Settlement date	1/1/2000
Maturity date	1/1/2015
Annual coupon rate	12.00%
Coupons per year	2
Yield to maturity	12%

(A) $40.00

(B) $678.89

(C) $1,000.00

(D) $560.59

3. Wing Air, Inc. has issued a bond with the following characteristics:

Par Value	1,000
Settlement date	1/1/2000
Maturity date	1/1/2015
Annual coupon rate	8.00%
Coupons per year	2
Yield to maturity	9%

What is the price of the bond?

(A) $40.00

(B) $918.56

(C) $607.68

(D) $732.51

Given the following information, what would you expect the Treasury Bill rate to be?

Real rate	2.60%
Inflation rate	3.30%

(A) 6.71%

(B) 5.27%

(C) 5.99%

(D) 105.90%

Answer 1

Q1. Price of a zero coupon bond can be calculated using the following formula:

where FV is face value of bond, n is the number of periods and YTM is also periodic

Assuming semi-annual compounding, FV = 1000, YTM = 5%/2 = 2.5% (semi-annual), n = 2 * 15 = 30 semi-annual periods

So, for this question, Price can be calculated as:

P = 476.74 (Option D)

Q2. Now, in this question, we do not need to solve anything, but need to know how the coupon rate and YTM affect bond price.

When coupon rate > YTM, bond price > par value

When coupon rate < YTM, bond price < par value

When coupon rate = YTM, bond price = par value. This is the case applicable in our question and hence, the bond price would be same as par value, which is $1000 (Option C)

Q3. Now, this is also a semi-annual coupon paying bond and for the coupon paying bond, price of it could be calculated using the mathematical relation:

where P is price of bond with periodic coupon C, periodic YTM i, face value M and n periods to maturity.

M = $1000, C = 8% * 1000/2 = $40 (semi-annually), i = 9%/2 = 4.5% (semi-annually), n = 15 years = 30 semi-annual periods

P = 918.56 Option B

Q4. This required application of Fischer relation, according to which,

(1 + Nominal Rate) = (1 + Real Rate) * (1 + Inflation)

(1 + Nominal Rate) = (1 + 2.60%) * ( 1 + 3.30%)

(1 + Nominal Rate) = 1.059858

Nominal Rate = 0.0599 = 5.99% (Option C)

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