In: Finance
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?
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.