Question

Lance Whittingham IV specializes in buying deep discount bonds. These represent bonds that are trading at well below par value. He has his eye on a bond issued by the Leisure Time Corporation. The $1,000 par value bond pays 6 percent annual interest and has 15 years remaining to maturity. The current yield to maturity on similar bonds is 10 percent. a. What is the current price of the bonds? Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your final answer to 2 decimal places. Assume interest payments are annual.) b. By what percent will the price of the bonds increase between now and maturity? (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)

Answer 1

a) time to maturity = n = 15 years

coupon rate , c = 6% = 0.06

par value of bond , m = $1000

coupon value, C = c*m = 0.06*1000 = 60

yield to maturity , y = 10% = 0.10

price of bond today , p = (present value(PV) of coupon amounts) + (PV of maturity amount )

present value(PV) of coupon amounts = C*PVIFA(10%,15 )

where PVIFA = present value interest rate factor of annuity

PVIFA(10%,15 ) =[ (1+y)ⁿ -1]/((1yr)ⁿ *y)

= [ (1.1)¹⁵ -1]/((1.1)¹⁵ *0.10) = 7.606079506

present value(PV) of coupon amounts = 60*7.606079506 = 456.3647704

PV of maturity amount = par value/((1+y)ⁿ ) = 1000/((1.10)¹⁵ ) = 239.3920494

price of bond today , p = (present value(PV) of coupon amounts) + (PV of maturity amount )

p = 456.3647704 + 239.3920494 = 695.75682 or $695.76 ( rounding off to 2 decimal places)

using financial calculator , enter the following

N = 15                      ( this is the time to maturity of bond)

I/Y = 10                    (this is the yield to maturity of bond)

PMT = 60                 (this is the annual coupon value)

FV = 1000                ( this is the par value of bond)

then press CPT PV

b)

since maturity value of bond , m = 1000

let the % increase between now and maturity = x

(1+x)*price of bond = 1000

x = (1000/price of bond)-1 = (1000/695.75682)-1 = 0.437284 or 43.7284% or 43.73% ( rounding off to 2 decimal places)