Question

A 10-year maturity bond with par value of $1,000 makes annual coupon payments at a coupon rate of 12%. Find the bond equivalent and effective annual yield to maturity of the bond for the following bond prices. (Round your answers to 2 decimal places.)a. Find the bond equivalent and effective annual yield to maturity of the bond if the bond price is $940. Bond equivalent yield to maturity %

Effective annual yield to maturity % b. Find the bond equivalent and effective annual yield to maturity of the bond if the bond price is $1,000. Bond equivalent yield to maturity %
Effective annual yield to maturity % c. Find the bond equivalent and effective annual yield to maturity of the bond if the bond price is $1,040. Bond equivalent yield to maturity %
Effective annual yield to maturity %

Answer 1

a) 13.11%

b) as the price matches the bond rate it will be 12%

c) 11.31%

Step-by-step explanation:

We should calcuate usig excel for the rate which makes the present value of the coupon payment and discounted maturity:

A) PV of the coupon payment (PV of an annuity)

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

C $1,000 x 12% = 120.000

time 10

rate 0.1311 (finded with excel)

`120 * (1-(1+0.1311)^(-10) )/(0.1311) = PV\\`

PV $648.2804

PV of the maturity (PV of a lump sum)

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

Maturity 1,000.00

time 10.00

rate 0.1311(finded with excel)

`(1000)/((1 + 0.1311)^(10) ) = PV`

PV 291.72

PV c $648.2804

PV m $291.7198

Total $940.0002

For C we do the same with a present value of 1,040 dollars

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

C 120.000

time 10

rate 0.113118875

`120 * (1-(1+0.113118874891792)^(-10) )/(0.113118874891792) = PV\\`

PV $697.5599

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

Maturity 1,000.00

time 10.00

rate 0.113118875

`(1000)/((1 + 0.113118874891792)^(10) ) = PV`

PV 342.44

PV c $697.5599

PV m $342.4400

Total $1,040.0000