Question

A mortgage bond issued by Automation Engineering is for sale for $8,900. The bond has a face value of $10,000 with a coupon rate of 5% per year, payable annually. What rate of return will be realized if the purchaser holds the bond to maturity 9 years from now? The rate of return will be % per year.

Answer 1

Bond current price = $8,900

Bond Face value F = $10,000

years to maturity n = 9 years

coupon rate C = 5% per annum payable annually = 5% * 10,000 = $500

Yield till maturity =r = ?

We will use the bond pricing formula to calculate the yield till maturity of the bond.

The formula is as follows:

Bond price = C/(1+r) + C/(1+r)² + C/(1+r)³ + C/(1+r)⁴ + ........ + C/(1+r)⁹ + F/(1+r)⁹

Bond price = 500/(1+r) + 500/(1+r)² + 500/(1+r)³ + 500/(1+r)⁴ + ........ + 500/(1+r)⁹ + 10000/(1+r)⁹

this simplifies to the following using the geometric sum formula

Bond price = C * [(1-(1+r)^-n ) / r] + F/(1+r)ⁿ

Substitute the given values in this formula

8900 = 500* [(1-(1+r)^-9 ) / r] + 10000/(1+r)⁹

This can be solved using goal seek method in Microsoft excel. or it can be solved in a financial calculator by entering the cash flows and using the yield function.

Solving for r gives the value as 6.6643%