Question

The Landers Corporation needs to raise $1.90 million of debt on a 10-year issue. If it places the bonds privately, the interest rate will be 10 percent. Twenty five thousand dollars in out-of-pocket costs will be incurred. For a public issue, the interest rate will be 12 percent, and the underwriting spread will be 4 percent. There will be $110,000 in out-of-pocket costs. Assume interest on the debt is paid semiannually, and the debt will be outstanding for the full 10-year period, at which time it will be repaid. Calculate your final answer using the formula and financial calculator methods.

a. For each plan, compare the net amount of funds initially available—inflow—to the present value of future payments of interest and principal to determine net present value. Assume the stated discount rate is 16 percent annually. Use 8.00 percent semiannually throughout the analysis. (Disregard taxes.) (Assume the $1.90 million needed includes the underwriting costs. Input your present value of future payments answers as negative values. Do not round intermediate calculations and round your answers to 2 decimal places.)

Answer 1

Formula Method

Private Placement

Step 1: Calculate Present Value of Future Payments

The present value of future payments can be calculated as follows:

Present Value of Future Payments = Interest Payment*[(1-(1+Discount Rate)^-Period)/Discount Rate] + Principal Repayment/(1+Discount Rate)^Period

Here, Interest Payment = 1,900,000*10%*1/2 = $95,000, Discount Rate = 8% and Period = 10*2 = 20

Using these values in the above formula, we get,

Present Value of Future Payments = 95,000*[(1-(1+8%)^-20)/8%] + 1,900,000/(1+8%)^20 = -$1,340,365.60 (as required in the question)

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Step 2: Calculate NPV

The NPV of Private Placement is determined as below:

NPV = Net Amount - Present Value of Future Payments = (1,900,000 - 25,000) - 1,340,365.59 = $534,634.40

_____

Public Issue

Step 1: Calculate Present Value of Future Payments

The present value of future payments can be calculated as follows:

Present Value of Future Payments = Interest Payment*[(1-(1+Discount Rate)^-Period)/Discount Rate] + Principal Repayment/(1+Discount Rate)^Period

Here, Interest Payment = 1,900,000*12%*1/2 = $114,000, Discount Rate = 8% and Period = 10*2 = 20

Using these values in the above formula, we get,

Present Value of Future Payments = 114,000*[(1-(1+8%)^-20)/8%] + 1,900,000/(1+8%)^20 = -$1,526,910.40 (as required in the question)

_____

Step 2: Calculate NPV

The NPV of Public Issue is arrived as below:

NPV = Net Amount - Present Value of Future Payments = (1,900,000*(1-4%) - 110,000) - 1,526,910.40 = $187,089.60

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Financial Calculator Method

Private Placement

Step 1: Calculate Present Value of Future Payments

The present value of future payments can be calculated with the use of PV (Present Value) formula/function of Financial Calculator. The function for PV is PV(I/Y,N,PMT,FV) where N = Period, I/Y = Discount Rate, PMT = Payment and FV = Future Value.

Here, I/Y = 8%, N = 10*2 = 20, PMT = 1,900,000*10%*1/2 = $95,000 and FV = $1,900,000

Using these values in the above function for PV, we get,

Present Value of Future Payments = PV(8%,20,95000,1900000) = -$1,340,365.60

_____

Step 2: Calculate NPV

The NPV of Private Placement is determined as below:

NPV = Net Amount - Present Value of Future Payments = (1,900,000 - 25,000) - 1,340,365.59 = $534,634.40

_____

Public Issue

Step 1: Calculate Present Value of Future Payments

The present value of future payments can be calculated with the use of PV (Present Value) formula/function of Financial Calculator. The function for PV is PV(I/Y,N,PMT,FV) where N = Period, I/Y = Discount Rate, PMT = Payment and FV = Future Value.

Here, I/Y = 8%, N = 10*2 = 20, PMT = 1,900,000*12%*1/2 = $114,000 and FV = $1,900,000

Using these values in the above function for PV, we get,

Present Value of Future Payments = PV(8%,20,114000,1900000) = -$1,526,910.40

_____

Step 2: Calculate NPV

The NPV of Public Issue is arrived as below:

NPV = Net Amount - Present Value of Future Payments = (1,900,000*(1-4%) - 110,000) - 1,526,910.40 = $187,089.60

_____

Tabular Representation of Final Answers

	Private Placement	Public Issue
Net Amount to Landers	$1,875,000.00	$1,714,000.00
Present Value of Future Payments	-1,340,365.60	-1,526,910.40
Net Present Value	$ 534,634.40	$187,089.60