Question

In: Finance

A) Draw a timeline for a bullet bond, face value of $1,000, with 3 years remaining...

A) Draw a timeline for a bullet bond, face value of $1,000, with 3 years remaining to maturity that pays a coupon rate of 5.5%/year semi-annually.

B) What is the market price of the bond in A if the current market rate is 3%/year?

Solutions

Expert Solution

Solution
Face value of Bond (FV) 1000 $
Coupon Rate ( r) 5.50%
Therefore, Coupon paid will be = FV * r 55 $
Remember this coupon is paid semi annualy i.e. every six months.
So, semi annual coupon payment will be $55/2 = $27.5
Nature of the bond is Bullet i.e. payment at the end of the tenure.
Remaining tenor of the bond is three years.
A) Time line of the bond is
Months 0 6 12 18 24 30 36
Period 0 1 2 3 4 5 6
Coupon Payment 27.5 27.5 27.5 27.5 27.5 27.5
Maturity Payment 1000
Cash flows from Bond 27.5 27.5 27.5 27.5 27.5 1027.5
B) Market price of the Bond
Market price of the bond can be achieved by discounting the above cash flows with a discount rate.
But what is the applicable discount rate?
Given discount rate is 3% (the market rate). However it is for the year.
Our cash flows are semi annual, so applicable dicount rate is 3/2 = 1.5% per semi annual
Period 0 1 2 3 4 5 6
Cash flows from Bond 27.5 27.5 27.5 27.5 27.5 1027.5
Discount Rate 1.50% 1.50% 1.50% 1.50% 1.50% 1.50%
Discount Factor (1/(1+r)^n) 0.985222 0.970662 0.956317 0.942184 0.92826 0.914542
PV of cash flows (Cash flow * discount factor) 27.0936 26.6932 26.29872 25.91007 25.52716 939.6921
Market price of bond = sum of pv of cash flows
1071.215 $
(Note : As market rate is less that coupon rate, value of bond is higher than face value of bond)
(Note : market price also be calculated using direct formulas = 27.5 * Annuity Factor(1.5%,6) + 1000$/(1.015)^6)

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