Question

What is the value of the following bond?

              Par value: $5,000

              Coupon rate: 2.5% to be paid quarterly

              Maturity: 10 years

              Required rate (YTM): 2%

1. $1,000
2. $1,044.91
3. $1,949.42
4. $5,025.27
5. $5,226.08

Answer 1

Price of bond formulae

= C × [ 1- (1+rate)^ -N] / rate + Fv / (1+rate)^N

Where, C is coupon payment per period - 2.5%/4 = 0.625%

Rate is yield per period- 2%/4 = 0.5%

N is number of periods - (10 × 4 ) = 40

Fv is face value of bond (5,000)

Note : Number of period = Number of quarters in 10 years which is 10 ×4 = 40

Rate and coupon is calculated quarterly, so it will be divided by number of quarters.

Coupon payment = face value × coupon rate

= 5000 × 0.625%

= $31.25

Value of bond = 31.25 × [ 1 - (1+0.5%)^ -40]/0.005 + 5000/(1+0.5%)^40

= 31.25× [ 1- 1.005^ -40] / 0.005 + 5000/ (1.005)^40

= 31.25 × (1-0.81913)/0.005 + 5000 /1.22079

= 31.25 ×( 0.180186/0.005) + 4095.63

= 31.25 × 36.1722 + 4095.63

= $5226.08 ( aprrox)

Therefore, value of bond is 5226.08 option 4