(i) A bond has a face value of $1000, a coupon rate of 8% and matures in 5 years

Question

(i) A bond has a face value of $1000, a coupon rate of 8% and matures in 5 years time. If its current yield to maturity is 10% what is the current price of the bond? If the yield falls to 6% determine the bond price. What do these results indicate about the relationship between the price of a bond and its yield to maturity? (ii) You are asked to put a value on a bond which promises eight annual coupon payments of £70 and will repay its face value of £1000 at the end of eight years. You observe that other similar bonds have yields to maturity of 9 per cent. How much is this bond worth? You are offered the bond for a price of £1030.44. What yield to maturity does this represent?

Explanation / Answer

Solution:

i.

Given that face value, F = 1000, Coupon, C = 0.08*1000 = 80, Number of years, n = 5 and yield to maturity, YTM = 10%

The price of the bond, P is

P = C (PVIFA @ YTM, n) + F (PVIF @ YTM, n)

P = 80 (PVIFA @ 10%, 5) + 1000 (PVIF @ 10%, 5)

P = 80 [(1.10^5-1)/(0.10*1.10^5)] + 1000 (1/1.10^5)

P = 80 (3.7908) + 1000 (0.6209)

P = $924.18

When YTM falls to 6%, the price of bond would be

P = C (PVIFA @ YTM, n) + F (PVIF @ YTM, n)

P = 80 (PVIFA @ 6%, 5) + 1000 (PVIF @ 6%, 5)

P = 80 [(1.06^5-1)/(0.06*1.06^5)] + 1000 (1/1.06^5)

P = 80 (4.2124) + 1000 (0.7473)

P = $1084.25

As the yield to maturity increases, the price of bond decreases.

ii.

Given that Coupon, C = 70, face value, F = 1000, Number of years, n = 8 and yield to maturity, YTM = 9%

The price of bond, P is

P = C (PVIFA @ YTM, n) + F (PVIF @ YTM, n)

P = 70 (PVIFA @ 9%, 8) + 1000 (PVIF @ 9%, 8)

P = 70 [(1.09^8-1)/ (0.09*1.09^8)] + 1000 (1/1.09^8)

P = 70 (5.5348) + 1000 (0.5019)

P = $889.30

When P = 1030.44, C = 70, F = 1000 and n = 8

Using YTM approximation formula, we have

YTM = [C + (F – P)/n]/ (F + P)/2

YTM = [70 + (1000 – 1030.44)/8]/ (1000 + 1030.44)/2

YTM = 66.195/1015.22

YTM = 6.50%

The yield to maturity is lower.

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.