Question

Your broker calls and tell you about a great investment opportunity! You can purchase, right now, XYZ annual coupon bonds that have a par value of $1,000 and which mature in exactly 14 years. The bonds are currently selling for $1,494.93. These bonds have a coupon interest rate of 10%/yr. You tell Susan thanks for the call - you will do a little research and get back to her. After comparing the XYZ bonds with the outstanding debt of other corporations of similiar size, similiar TIEs & DRs, similiar profit margins and overall risk, you return Susan's call: "Well Susan, I would be willing to buy a few hundred thousand dollars worth of these bonds, but my rrr (required rate of return) for this particular investment is 8%. I have lost my TI BA II Plus (should not have had that second Martini!), so tell me, if I buy the bonds at the current market price, what would my expected rate of return be? Assuming all future payments are paid in full and paid on time, and I keep them for 14 years." Susan runs the numbers, and informs you that the expected annual return over the life of the loan is ___________. Choose the closest answer.

Answer 1

Susan runs the numbers, and informs you that the expected annual return over the life of the loan is 5%

Explanation

Calculation of YTM

Value of the bond at an estimated 5.5% rate of return

= Coupon * [ 1 - (1.055)^-14 ] / 0.055 + Face value * (1.055)^-14

= 100 * 9.5896479 + 1000 *  0.472569 = 1431.53

Value of the bond at an estimated 5.5% rate of return

= Coupon * [ 1 - (1.045)^-14 ] / 0.045 + Face value * (1.045)^-14

= 100 * 10.222825 + 1000 *  0.5399729 = 1562.26

Now apply Interpolation method ..........

4.5 % ............1562.26

X % ............ 1494.93

5.5 % ............ 1431.53

( X - 4.5 ) / ( 5.5 - 4.5 ) = ( 1494.93 - 1562.26 ) / ( 1431.53 - 1562.26)

( X - 4.5 ) = -67.33 / -130.73

X - 4.5 = 0.51

X = 5.01 or 5 %