Question

Yield to Call and Realized Rates of Return Six years ago, Goodwynn & Wolf Incorporated (G&W) sold a 17-year bond issue with a 12% annual coupon rate and a 7% call premium. Today, G&W called the bonds. The bonds originally were sold at their face value of $1,000. Compute the realized rate of return for investors who purchased the bonds when they were issued and who surrender them today in exchange for the call price. Round your answer to two decimal places.

Answer 1

Answer:

YTC = IRR = 12.844% (exact using excle of financial calculator)

using approximation formula: 12.72%

Explanation:

The call premium means it were called at 107 of the face value

1,000 x 107/100 = 1,070

The investment was for 1,000

The bond yield a six years annuity of 120

and then called at 1,070

We need to know teh YTC:

$YTC = \frac{C + \frac{P-F}{n }}{\frac{P+F}{2}}$

Coupon payment =1,000 x 12% = 120

Call Price: 1070

Face Value: 1000

n: 6 years

$YTC = \frac{120 + \frac{1,070-1,000}{6}}{\frac{1,070+1,000}{2}}$

YTC = 12.7214171%

This method is an aproximation to the YTC

To solve for the YTC we can use excel IRR funtion

we write

-1,000 (investment)

120

120

120

120

120

+1,070+120 = 1,190 (total cashflow at year 6 call price and coupon)

and we calculate IRR selecting this values:

which give us 12.844%

Which is close to our approximation.