Question

Answer it pls without financial calculator or Excel.

(Bond valuation) National Steel 15-year, $1,000 par value bonds pay 5.5 percent interest annu- ally. The market price of the bonds is $1,085, and your required rate of return is 7 percent.

a. Compute the bond’s expected rate of return.
b. Determine the value of the bond to you, given your required rate of return. c. Should you purchase the bond?

Answer 1

a) expected rate of return = YTM ( yield to maturity) of bond

maturity of the bond, n = 15 years

par value of the bond,M = $1000

Coupon value ,C = coupon rate* M = 0.055*1000 = 55

current price of the bond, P = $1085

YTM = (C + (M - P )/n)/(0.4*M+0.6*P) = (55 + (1000 - 1085 )/15)/(0.4*1000+0.6*1085)

= 0.046939 = 4.6939% or 4.69% or 4.70%

This is an approximate value of YTM,

b)

required rate of return , r = 7% = 0.07

price of bond = present value of coupons + present value of maturity amount

Present value of coupons = C*PVIFA( 7% , 15 years)

PVIFA( 7% , 15 years) = present value interest rate factor of annuity

= [((1+r)ⁿ - 1)/((1+r)ⁿ*r)] = [((1.07)¹⁵ - 1)/((1.07)¹⁵*0.07)] = 9.10791401

Present value(PV) of coupons = C*PVIFA( 7% , 15 years) = 55*9.10791401 = 500.93527028

PV of maturity amount = par value/(1+r)ⁿ = 1000/(1.07)¹⁵ = 362.44601964

Value of bond = 500.93527028 + 362.44601964 = $863.3812899 or $863.38 ( rounding off to 2 decimal places)

c) since the expected return is less than the required return, you should not purchase the bond.