Question

An annual has 15 years to maturity. It has a coupon rate of 5%, a YTM of 8%. Fill in the cells highlighted in yellow, and aswer the questions in the D2L Quiz. You will have 4 attempts to complete this quiz. To start with, assume that interest rates in the market just increased by 2% (this change is entered in cell B28). Hint: Do not enter any numbers manually in any of the cells; always refer to another cell where the number is entered. For example, instead of typing 5% manually, refer to cell B1.

Answer 1

Answer:

Market value at 8% YTM  $ 743.2156

at 10% YTM                       $ 619.6960

Explanation:

Assuming the face value is 1,000 as common outstanding American company's bonds:

Market value under the current scenario:

Present value of the coupon payment:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

Coupon: $1,000 x 5% =  50

time 15 years

rate 0.08

$50 \times \frac{1-(1+0.08)^{-15} }{0.08} = PV$

PV $427.9739

Present Value of the Maturity

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity   1,000.00

time   15.00

rate  0.08

$\frac{1000}{(1 + 0.08)^{15} } = PV$  

PV   315.24

PV c $427.9739

PV m  $315.2417

Total $743.2156

If the interest rate in the market increaseby 2% then investor will only trade the bonds to get a yield 2% higher that is 10% so we recalculate the new price:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 50.000

time 15

rate 0.1

$50 \times \frac{1-(1+0.1)^{-15} }{0.1} = PV$

PV $380.3040

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity   1,000.00

time   15.00

rate  0.1

$\frac{1000}{(1 + 0.1)^{15} } = PV$  

PV   239.39

PV c $380.3040

PV m  $239.3920

Total $619.6960

Giving a lower price than before