58.0k views
5 votes
Jiminy’s Cricket Farm issued a bond with 25 years to maturity and a semiannual coupon rate of 6 percent 5 years ago. The bond currently sells for 108 percent of its face value. The company’s tax rate is 24 percent. The book value of the debt issue is $60 million. In addition, the company has a second debt issue on the market, a zero coupon bond with 8 years left to maturity; the book value of this issue is $35

User Topanga
by
8.6k points

1 Answer

4 votes

The market value of Jiminy's Cricket Farm's debt is $350,010,000 and the unrealized gain on the debt is $253,838,800.

How is that so?

Jiminy's Cricket Farm Debt Analysis

Bond 1 Details:

Face value: $100

Coupon rate: 6% (semiannual)

Maturity: 25 years

Years since issued: 5

Current price: 108% of face value

Book value: $60 million

Tax rate: 24%

Bond 2 Details:

Maturity: 8 years

Book value: $35 million

Calculations:

Coupon payment:

Semiannual coupon payment = Face value * Coupon rate / 2

Semiannual coupon payment = $100 * 0.06 / 2 = $3

Periods remaining:

Number of semiannual periods remaining = (Maturity - Years since issued) * 2

Number of semiannual periods remaining = (25 - 5) * 2 = 40

Present value of remaining coupon payments:

PV of coupon payments = Coupon payment * (1 - (1 + (Coupon rate / 2)) ** (-Periods remaining)) / (Coupon rate / 2)

PV of coupon payments = $3 * (1 - (1 + (0.06 / 2)) ** (-40)) / (0.06 / 2) ≈ $84.74

Present value of face value:

PV of face value = Face value / (1 + (Coupon rate / 2)) ** Periods remaining

PV of face value = $100 / (1 + (0.06 / 2)) ** 40 ≈ $17.33

Market value of bond 1:

Market value = PV of coupon payments + PV of face value

Market value = $84.74 + $17.33 ≈ $102.07

Market value of debt:

Market value of debt = Market value of bond 1 + Book value of bond 2

Market value of debt = $102.07 * $60 million + $35 million ≈ $350,010,000

Tax shield:

Tax shield = Coupon payment * Tax rate * Periods remaining

Tax shield = $3 * 0.24 * 40 = $28.80

Carrying value of debt:

Carrying value = Book value of bond 1 + Book value of bond 2 - Tax shield

Carrying value = $60 million + $35 million - $28.80 million ≈ $96,171,200

Unrealized gain or loss:

Unrealized gain or loss = Market value of debt - Carrying value of debt

Unrealized gain or loss = $350,010,000 - $96,171,200 ≈ $253,838,800

Complete Question:

Jiminy’s Cricket Farm issued a bond with 25 years to maturity and a semiannual coupon rate of 6 percent 5 years ago. The bond currently sells for 108 percent of its face value. The company’s tax rate is 24 percent. The book value of the debt issue is $60 million. In addition, the company has a second debt issue on the market, a zero coupon bond with 8 years left to maturity; the book value of this issue is $35. Find the market value of Jiminy's Cricket Farm's debt and the unrealized gain on the debt.

User Tarique Naseem
by
8.8k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.