Chapter 16, Problem 1P

Gladstone Corporation is about to launch a new product. Depending on the success of the new product, Gladstone may have one of four values next year: $150 million, $135 million, $95 million, or $80 million. These outcomes are all equally likely, and this risk is diversifiable. Gladstone will not make any payouts to investors during the year. Suppose the risk-free interest rate is 5% and assume perfect capital markets.

1. a. What is the initial value of Gladstone’s equity without leverage? Now suppose Gladstone has zero-coupon debt with a $100 million face value due next year.
2. b. What is the initial value of Gladstone’s debt?
3. c. What is the yield-to-maturity of the debt? What is its expected return?
4. d. What is the initial value of Gladstone’s equity? What is Gladstone's total value with leverage?

Summary Introduction

To determine: The initial value of Company G’s equity without leverage.

Introduction:

The leverage can also refer to the amount of debt used to finance assets. Leverage uses borrowed funds or various financial instruments to increase the returns on the investment. If a company has high leverage, it means that the instrument has more debt than equity.

Answer to Problem 1P

The initial value of equity without leverage is $109.523 million.

Explanation of Solution

Given information:

Company G is about to introduce a new product. Depending on the achievement of the new product, Company G might have any one of four values coming year. $150 million, $135 million, $95 million, or $80 million. These outcomes are similarly likely, and risk is diversifiable. During the year Company G will not make any pay-outs to investors, in this case the risk-free interest is 5% and assuming that it is a perfect capital market.

In case company G has $100 million face value with zero-coupon debt due next year.

Note: The asset value for the firm will be on the total value of debt that is 25% $(100÷4)$

Formula to compute the initial value of equity without leverage:

${\text{V}}^{\text{U}}=\text{Assets}\times \frac{\text{FCF}}{(1+\text{r})},$

Where

${\text{V}}^{\text{U}}$ refers to without leverage.

$\text{FCF}$ refers to free cash flow.

r refers to rate of interest.

Compute the initial value of equity without leverage:

$\begin{array}{c}{\text{V}}^{\text{U}}=\text{Assets}\times \frac{\text{FCF}}{(1+\text{r})}\\ =25\%\times \frac{\$150+\$135+\$95+\$80}{(1+5\%)}\\ =0.25\times \frac{\$460}{(1+0.05)}\\ =0.25\times \frac{\$460}{(1.05)}\end{array}$

$\begin{array}{l}=0.25\times \$438.0952\\ =\$109.523\text{ million}\end{array}$

Hence, the initial value of equity without leverage is $109.523 million.

Summary Introduction

To determine: The initial value of Company G debt.

Introduction:

The leverage can also refer to the amount of debt used to finance assets. Leverage uses borrowed funds or various financial instruments to increase the returns on the investment. If company has high leverage, it means that the instrument has more debt than equity.

Answer to Problem 1P

The initial value of debt without leverage is $89.28 million.

Explanation of Solution

Given information:

Company G is about to introduce a new product. Depending on the achievement of the new product, Company G might have any one of four values coming year. $150 million, $135 million, $95 million, or $80 million. These outcomes are similarly likely, and risk is diversifiable. During the year Company G will not make any pay-outs to investors, in this case the risk-free interest is 5% and assuming that it is a perfect capital market.

In case company G has $100 million face value with zero-coupon debt due next year.

Note: The asset value for the firm will be on the total value of debt that is 25% $(100÷4)$

Formula to compute the initial value of debt:

${\text{V}}^{\text{U}}=\text{Assets}\times \frac{\text{FCF}}{(1+\text{r})},$

Where

${\text{V}}^{\text{U}}$ refers to without leverage.

$\text{FCF}$ refers to free cash flow.

r refers to rate of interest.

Compute the initial value of debt:

$\begin{array}{c}{\text{V}}^{\text{U}}=\text{Assets}\times \frac{\text{FCF}}{(1+\text{r})}\\ =25\%\times \frac{\$100+\$100+\$95+\$80}{(1+5\%)}\\ =0.25\times \frac{\$100+\$100+\$95+\$80}{(1+0.05)}\\ =0.25\times \frac{\$100+\$100+\$95+\$80}{(1.05)}\end{array}$

$\begin{array}{l}=0.25\times \frac{\$375}{(1.05)}\\ =0.25\times \$357.14\\ =\$89.28\text{ million}\end{array}$

Hence, the initial value of debt without leverage is $89.28 million.

Summary Introduction

To determine: The expected returns and the yield to maturity of the debt.

Introduction:

Yield to maturity (YTM) is the total expected return on bond if the bond is held until it maturity. Yield to maturity is considered to be long-term bond yield.

Answer to Problem 1P

The YTM for debt is 26.79%, and the expected return is 5%.

Explanation of Solution

Given information:

Company G is about to introduce a new product. Depending on the achievement of the new product, Company G might have any one of four values coming year. $150 million, $135 million, $95 million, or $80 million. These outcomes are similarly likely, and risk is diversifiable. During the year Company G will not make any pay-outs to investors, in this case the risk-free interest is 5% and assuming that it is a perfect capital market.

In case company G has $100 million face value with zero-coupon debt due next year.

Formula to compute YTM:

$\text{YTM}=\frac{\text{Cash flow}}{\text{Initial debt }}-1$

Compute the YTM:

$\begin{array}{c}\text{YTM}=\frac{\text{Cash flow}}{\text{Initial debt }}-1\\ =\frac{\$100}{\text{\$89}\text{.29 }}-1\\ =1.1199-1\\ =0.1199\end{array}$

$=12\%$

Hence, the YTM for debt is 12%.

Note: The expected returns will be 5% because risk-free interest rate is 5%, as given in question.

Summary Introduction

To determine: The initial value of G’s equity and total value of leverage.

Introduction:

The leverage can also refer to the amount of debt used to finance assets. Leverage uses borrowed funds or various financial instruments to increase the returns on the investment. If company has high leverage, it means that the instrument has more debt than equity.

Answer to Problem 1P

The initial value of equity is $20.238 million, and the total value of leverage is $78.869 million.

Explanation of Solution

Given information:

Company G is about to introduce a new product. Depending on the achievement of the new product, Company G might have any one of four values coming year. $150 million, $135 million, $95 million, or $80 million. These outcomes are similarly likely, and risk is diversifiable. During the year Company G will not make any pay-outs to investors, in this case the risk-free interest is 5% and assuming that it is a perfect capital market.

In case company G has $100 million face value with zero-coupon debt due next year.

Note: The asset value for the firm will be on the total value of debt that is 25% $(100÷4)$

Formula to compute the equity:

$\text{Equity}=\text{Assets}-\text{Liability}$

Compute the total equity:

$\begin{array}{c}\text{Equity}=\text{Assets}-\text{Liability}\\ =\$150-\$100\\ =\$50\end{array}$

$\begin{array}{c}\text{Equity}=\text{Assets}-\text{Liability}\\ =\$135-\$100\\ =\$35\end{array}$

Note: For other two years, it will be zero because it will come in negative.

Formula to compute the initial value of equity:

${\text{V}}^{\text{U}}=\text{Assets}\times \frac{\text{FCF}}{(1+\text{r})},$

Where

E refers to equity.

$\text{FCF}$ refers to free cash flow.

r refers to rate of interest.

Compute the initial value of equity without leverage:

$\begin{array}{c}{\text{V}}^{\text{U}}=\text{Assets}\times \frac{\text{FCF}}{(1+\text{r})}\\ =25\%\times \frac{\$50+\$35+\$0+\$0}{(1+5\%)}\\ =0.25\times \frac{\$85}{(1+0.05)}\\ =0.25\times \frac{\$85}{(1.05)}\end{array}$

$\begin{array}{l}=0.25\times \$80.95\\ =\$20.\text{ 238million}\end{array}$

Hence, the initial value of equity is $20.238 million.

Formula to compute the total value with leverage:

$\text{Total value}={\text{V}}^{\text{U}}+{\text{V}}^{\text{L}},$

Where

${\text{V}}^{\text{U}}$ refers to firm without leverage.

${\text{V}}^{\text{L}}$ refers to firm with leverage.

Compute the total value of firm with leverage:

$\begin{array}{c}\text{Total value}={\text{V}}^{\text{U}}+{\text{V}}^{\text{L}}\\ =\$89.28+\$20.24\\ =\$109.52\end{array}$

Hence, the total value of leverage is $109.52.