Question

Dominique LeBlanc is the owner of a new ten-year $40,000 8% par-value bond with a Bermuda option and annual coupons. Allowable call dates are at the ends of years 6 through 10, and the call premium at the end of year n is $300(10 − n).Dominique purchased the bond for $41,248. (a)Find the lowest yield that Dominique may receive during the period she holds the bond as well as the highest. (Round your answers to two decimal places.) lowest yield rate: highest yield rate (b)Upon receipt, Dominique deposits each coupon and the redemption amount in an account earning 6%. Find the lowest yield that Dominique may receive during the ten-year period and also the highest. (Round your answers to two decimal places.) lowest yield rate: highest yield rate:

Answer 1

(a) The lowest yield Dominique may receive during the period she holds the bond is 5.74%, and the highest yield is 7.24%.

(b) Upon receipt, depositing each coupon and the redemption amount in an account earning 6%, the lowest yield Dominique may receive during the ten-year period is 6%, and the highest yield is 7.23%.

Step-by-step explanation:

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In the case of Dominique LeBlanc's bond, the lowest yield during the holding period is determined by considering the bond's purchase price and potential call options.

The yield-to-call is calculated using the formula, taking into account the minimum call premium at the allowable call dates. Similarly, the highest yield is determined using the maximum call premium.

Upon receiving coupons and redemption amounts and depositing them in an account earning 6%, the lowest yield during the ten-year period is simply the interest earned from the coupons and redemption at the 6% rate.

The highest yield considers the interest earned plus the maximum call premium, providing the upper limit of potential returns.

In summary, the lowest and highest yields are calculated based on the bond's characteristics and the interest earned from deposited amounts, providing insights into potential returns for Dominique LeBlanc.

Answer 2

Dominique's lowest yield with reinvestment is 10.14% and her highest is 14.79%.

How to solve

Dominique's Bond Yields:

Part (a) - Without Reinvestment:

Lowest Yield: This occurs if Dominique holds the bond until maturity (year 10) and receives no call. In this case, she receives the face value ($40,000) and all 10 annual coupons ($8,000 each).

Holding period yield:

Total payments = $40,000 (face value) + 10 * $8,000 (coupons) = $120,000

Compound interest factor (1 + 8%)^10 = 5.1597

Holding period yield = (Total payments / Purchase price) / Compound factor

Holding period yield = ($120,000 / $41,248) / 5.1597 = 8.35%

Highest Yield: This occurs if Dominique is called at the end of year 6. Here, she receives the call price ($40,000 + $300(10 - 6) = $46,200) and 6 annual coupons.

Yield to call:

Total payments = $46,200 (call price) + 6 * $8,000 (coupons) = $62,200

Compound factor (1 + 8%)^6 = 2.176

Yield to call = (Total payments / Purchase price) / Compound factor

Yield to call = ($62,200 / $41,248) / 2.176 = 13.31%

Therefore, Dominique's lowest yield without reinvestment is 8.35% and her highest is 13.31%.

Part (b) - With Reinvestment:

Lowest Yield: This occurs again if Dominique holds the bond until maturity (year 10). Now, she reinvests all coupon and redemption payments at 6%.

Holding period yield:

Total payments = $120,000 (as in part a)

Compound interest factor considering reinvestment = 1.06^10 = 1.8383

Holding period yield (with reinvestment) = (Total payments / Purchase price) / Compound factor

Holding period yield (with reinvestment) = ($120,000 / $41,248) / 1.8383 = 10.14%

Highest Yield: Similar to part (a), this occurs if Dominique is called at the end of year 6. However, now she reinvests the call price and remaining coupons at 6%.

Yield to call (with reinvestment):

Total payments = $62,200 (as in part a)

Compound interest factor considering reinvestment = 1.06^6 = 1.4185

Yield to call (with reinvestment) = (Total payments / Purchase price) / Compound factor

Yield to call (with reinvestment) = ($62,200 / $41,248) / 1.4185 = 14.79%

Therefore, Dominique's lowest yield with reinvestment is 10.14% and her highest is 14.79%.