Question

Regarding Bond valuation

(a) Mills Company, a large defense contractor, on January 1, 2007, issued a 12% coupon interest rate, 5-year bond with a $1,000 par value that pays interest annually. Do a simple comparison between the Yield to maturity and the coupon interest rate if the Bond is sold at the following prices i. $ 1,000 ii. $ 887.00 iii. $ 1,134.20 (b) The real rate of interest is currently 3%; the inflation expectation and risk premiums for a number of securities follow. Security Inflation expectation Premium Risk Premium 3% 6% 2% 9% 8% 5% 11% 4% 1% Please do the following: i) Find the risk-free rate of interest, RF, that is applicable to each security, and ii) Find the nominal rate of interest for each security.

Answer 1

a. Yield To Maturity (YTM) is a discount rate at which Intrinsic Value of Bond equals its Market Price.

Approximately, YTM is calculated as follows :-

$\small \textrm{YTM = }\frac{\textrm{Annual Interest +} \frac{\textrm{Par Value - Market Price}}{\textrm{Number of years to Maturity}}}{\frac{\textrm{Par Value + Market Price}}{2}}$

i. Bond Price = $ 1,000.

$\small \textrm{YTM = }\frac{\textrm{120 +} \frac{\textrm{1000 - 1000}}{\textrm{5}}}{\frac{\textrm{1000 + 1000}}{2}}$

            = 12%

If bond trades at Par Value then, Coupon Rate is equal to YTM.

ii. Bond Price = $ 887.

$\small \textrm{YTM = }\frac{\textrm{120 +} \frac{\textrm{1000 - 887}}{\textrm{5}}}{\frac{\textrm{1000 + 887}}{2}}$

             = 15.11%

If bond trades at $ 887, Coupon Rate(12%) is lower than YTM (15.11%)

iii. Bond Price = $ 1134.20

$\small \textrm{YTM = }\frac{\textrm{120 +} \frac{\textrm{1000 - 1134.20}}{\textrm{5}}}{\frac{\textrm{1000 + 1134.20}}{2}}$

             = 8.73 %

If bond trades at $ 1134.20, Coupon Rate(12%) is higher than YTM (8.73%)

b. i. Risk Free Rate of Return is calculated as follows :-

Risk Free Rate of Return = Inflation Rate + Real Rate of Return

Real Rate of Return is given in the question as 3%.

Security	Inflation	Risk Free Rate
A	6%	9%
B	9%	12%
C	8%	11%
D	5%	8%
E	11%	14%

ii. Nominal Rate of Return is calculated as follows :-

Nominal Rate of Return = Risk Free Rate of Return + Risk Premium

Security	Inflation	Risk Free Rate	Risk Premium	Nominal Rate
A	6%	9%	3%	12%
B	9%	12%	2%	14%
C	8%	11%	2%	13%
D	5%	8%	4%	12%
E	11%	14%	1%	15%