Question

An 11-year, $1,000 face value bond has an annual coupon rate of 8% and its yield to maturity is 7.5%. The bond can be called 3 years from now at a price of $1,060. What is the bond’s nominal yield to call?

Answer 1

Current price of bond can be computed as:

Price of bond = C x [1-{1/ (1+r) ⁿ}/r] +M/ (1+r) ⁿ

M = Face Value = $ 1,000

C= Coupon amount = (Face Value x Coupon rate) / No. of coupon payments annually

= ($ 1,000 x 8 %)/1 = $ 1,000 x 0.08 = $ 80

r = Rate of interest = 7.5 % or 0.075 p.a.

n = No of periods = 11

Bond Price = $ 80 x [1-{1/ (1+0.075)¹¹}/0.075 ] + $ 1,000/ (1+0.075)¹¹

                    = $ 80 x [1-{1/ (1.075)¹¹}/0.075 ] + $ 1,000/ (1.075)¹¹

                            = $ 80 x [1-{1/ 2.21560892932706}/0.075] + $ 1,000/ 2.21560892932706

                     = $ 80 x [(1-0.451343189117641)/0.075] + $ 451.343189117641

                     = $ 80 x (0.548656810882359/0.075) + $ 451.343189117641

                     = $ 80 x 7.31542414509812 + $ 451.343189117641

                     = $ 585.233931607849 + $ 451.343189117641

                     = $ 1,036.57712072549 or $ 1,036.58

In order to compute yield to call we have to assume that the bond matures in 3 years rather than 11 years. Call price is the principal at maturity.

Current bond price and YTC are related as:

P = C x [1-(1+YTC) ^‑t/YTC] + CP/ (1+YTC) ^t

P = Current bond price = $ 1,036.58

C = Annual coupon payment = $ 80

CP = Call price = $ 1,060

YTC = Yield to call on the bond

t = Time to call = 3 years

We can Compute IRR of investment using excel sheet which is YTC of the bond.

	A	B
1	Year	Cash Flow
2	0	($1,036.58)
3	1	$80
4	2	$80
5	3	$1,140
6	IRR	8.41%

Considering the above table as excel sheet, use formula “=IRR(B2:B5) in cell B6 to get IRR as 8.41%

Hence yield to call of the bond is 8.41 %