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

Market value at 8% YTM $ 743.2156

at 10% YTM $ 619.6960

Step-by-step 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 * (1-(1+r)^(-time) )/(rate) = PV\\`

Coupon: $1,000 x 5% = 50

time 15 years

rate 0.08

`50 * (1-(1+0.08)^(-15) )/(0.08) = PV\\`

PV $427.9739

Present Value of the Maturity

`(Maturity)/((1 + rate)^(time) ) = PV`

Maturity 1,000.00

time 15.00

rate 0.08

`(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 * (1-(1+r)^(-time) )/(rate) = PV\\`

C 50.000

time 15

rate 0.1

`50 * (1-(1+0.1)^(-15) )/(0.1) = PV\\`

PV $380.3040

`(Maturity)/((1 + rate)^(time) ) = PV`

Maturity 1,000.00

time 15.00

rate 0.1

`(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