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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
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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
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