Chapter 15, Problem 5CP

A(i)

Summary Introduction

Adequate information:

Par Value - $1000

Current market price of convertible bond - $980

Conversion ratio - 25

Expected market price of convertible bond - $1125

Coupon rate - 4%

Current market price of equity - $35

Expected market price of equity - $45

Requirement 1:

To calculate current market conversion price for Ytel convertible bond.

Introduction:

Market conversion price of bond is the effective price when the investor exercises conversion option to purchase common stock in the form of convertible security. It is calculated by dividing convertible bond market price by convertible bond conversion ratio

Expected rate of return is the profit made on investment over a time period, expressed as a proportion of investment made in beginning.

Explanation of Solution

Computation of current market conversion price

Current market conversion price = Current market price of convertible bond / Conversion ratio

= $980/25

= $39.20

Conclusion

Thus the current market conversion price is $39.20.

A(ii)

Summary Introduction

Requirement 2:

To calculate expected one-year rate of return for Ytel convertible bond.

Introduction:

Market conversion price of bond is the effective price when the investor exercises conversion option to purchase common stock in the form of convertible security. It is calculated by dividing convertible bond market price by convertible bond conversion ratio

Expected rate of return is the profit made on investment over a time period, expressed as a proportion of investment made in beginning.

Explanation of Solution

Calculation of rate of return for Ytel convertible bond

$\begin{array}{l}\text{Rate of return for convertible bond = Expected market price in one year + Coupon price}\hfill \\ \text{ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ -1}\hfill \\ \text{ Current market price of bond}\hfill \\ \text{ = \$1125 +}\left(\text{0}\text{.04}\times \text{\$1000}\right)\hfill \\ \text{ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ -1}\hfill \\ \text{ \$980}\hfill \\ \text{ =0}\text{.188 or 18}\text{.8\%}\hfill \end{array}$

Conclusion

Thus, the rate of return for Ytel convertible bond is 18%.

A(iii)

Summary Introduction

Requirement 3:

To calculate expected one-year rate of return for Ytel common equity.

Introduction:

Market conversion price of bond is the effective price when the investor exercises conversion option to purchase common stock in the form of convertible security.It is calculated by dividing convertible bond market price by convertible bond conversion ratio

Expected rate of return is the profit made on investment over a period of time,expressed as a proportion of investment made in beginning.

Explanation of Solution

Calculation of expected rate of return for Ytel common equity.

$\begin{array}{l}\text{Rate of return for common equity = Expected market price in one year + Dividend}\hfill \\ \text{ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ -1}\hfill \\ \text{ Current market price of common equity}\hfill \\ \hfill \\ \text{ = \$45 +0}\hfill \\ \text{ \_\_\_\_\_\_\_ -1}\hfill \\ \text{ \$35}\hfill \\ \text{ =0}\text{.285 or 28}\text{.5\%}\hfill \end{array}$

Conclusion

Thus, the rate of return for Ytel common equity is 28.5%.

B(i)

Summary Introduction

Adequate information:

Par Value - $1000

Conversion ratio - 25

Increased Common equity price- $51

Requirement 1:

To determine effect of each component of convertible bond's value on increase in Ytel's common equity price.

Introduction:

The conversion value of bond is equal to the value if the bond is converted into stock immediately. Also, an increase in stock price volatility increases the bond price which means if the stock price are volatile, the conversion option on stock is more valuable.

The two components of convertible bond's value are:

1.Straight bond value- In this, increase in interest rates decreases the straight value component of the convertible bond.

2.Option Value- In this, an increase in interest rates increases value of equity call option.

Explanation of Solution

If the common equity price increases, the straight bond value should remain the same and the Option value of the bond should increase. The option value component increases and it becomes "deep in the money" because the price of the equity price is higher ($51 per share) than the bond's contract price ($1000/25= $40 per share)

Conclusion

Thus the straight bond value should remain unchanged and option value should increase with an increase in common equity price.

B(ii)

Summary Introduction

Requirement 2:

To determine effect of each component of convertible bond's value on increase in Ytel's bond yield.

Introduction:

The conversion value of bond is equal to the value if the bond is converted into stock immediately. Also, an increase in stock price volatility increases the bond price which means if the stock price are volatile, the conversion option on stock is more valuable.

The two components of convertible bond's value are:

1.Straight bond value- In this, increase in interest rates decreases the straight value component of the convertible bond.

2.Option Value- In this, an increase in interest rates increases value of equity call option.

Explanation of Solution

If the Ytel's bond yield increases, the straight bond value should decrease and option value should increase. This is because bond value declines when bond yield increases and call option increases when bond yield increases though this increase may be small as compared to change in option value as a result of increase in equity price.

Conclusion

Thus the straight bond value should decrease and option value should increase with an increase in bond yield.