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.