Question

Corporate Financial Management:Valuation of Bonds

9. a. The XYZ Company has €1,000 par value, 9% coupon bonds outstanding. The bonds will mature in 20 years. What is the current price of the bonds if the present yield to maturity is 6%? Suppose the yield to maturity increases to 11%. What do you think will happen to the price of the bond? Explain why.

2. Explain the difference between the real rate of return and the nominal rate of return. An investment offers a 15 per cent total return over the coming year. You think the total real return on this investment will be only 9 per cent. If this turns out to be true, what will the rate of inflation over the next near be?

Answer 1

9 a) Given

Par value = 1000

coupon rate = 9%

coupon = 9% * 1000 = 90

time N = 20

ytm = 6%

Bond price is the present value of all the coupons paid and the maturity value

Bond price = C* [ 1 - ( 1+ ytm ) ^-n / ytm + fv / (1 + ytm)ⁿ

Bond price = 90 * [ 1 - ( 1+ 0.06)^-20 ] / 0.06 + 1000 / ( 1+ 0.06)²⁰

Bond price = 90 * [ 1 - 0.311805 ] / 0.06 + 1000/ 0.311806

Bond Price = 1032.293 + 311.8047

Bond Price = $1344.098

Current price of the bond is $1344.098

Suppose the ytm increases to 11%, then the bond price will fall and will sell at a discount. This is because, the investors are not willing to pay a high amount for a bond which is paying a coupon or interest of only 9% against the market rate of 11%. Thus, the bond will be sold until the price equalizes the yield. Therefore, higher the yield on the bond lower is the price of the bond.

b) Real rate of return is the average rate of return which has factored the effect of inflation on the investments whereas, nominal rate of return is the amount generated from investment without taking in to account the market inflation.

Real rate of return is less than the nominal rate of return since it is inflation adjusted.

Nominal rate of return is a better tool to compare investment returns as it is both tax and inflation adjusted. Therefore, a better comparison tool for bonds, stock or any form of investment.

Given:

Nominal return = 15%

real return = 9%

inflation rate = ?

Using Fischer effect formula

1 + nominal rate = ( 1+ real rate ) * ( 1+ inflation)

1 + inflation = (1 + nominal) / (1 + real rate)

1 + inflation = (1 + 0.15) / ( 1+ 0.09)

1 + inflation = 1.15 / 1.09

1 + inflation = 1.055046

inflation rate = 0.055046

inflation rate = 5.50%

Inflation rate would be 5.50% over the next year.