Question

The Robinson Corporation has $27 million of bonds outstanding that were issued at a coupon rate of 10.950 percent seven years ago. Interest rates have fallen to 10.250 percent. Mr. Brooks, the Vice-President of Finance, does not expect rates to fall any further. The bonds have 17 years left to maturity, and Mr. Brooks would like to refund the bonds with a new issue of equal amount also having 17 years to maturity. The Robinson Corporation has a tax rate of 30 percent. The underwriting cost on the old issue was 2.70 percent of the total bond value. The underwriting cost on the new issue will be 1.80 percent of the total bond value. The original bond indenture contained a five-year protection against a call, with a call premium of 6 percent starting in the sixth year and scheduled to decline by one-half percent each year thereafter. (Consider the bond to be seven years old for purposes of computing the premium.) Use Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods. Assume the discount rate is equal to the aftertax cost of new debt rounded up to the nearest whole percent (e.g. 4.06 percent should be rounded up to 5 percent)

a. Compute the discount rate. (Do not round intermediate calculations. Input your answer as a percent rounded up to the nearest whole percent.)

b. Calculate the present value of total outflows. (Do not round intermediate calculations and round your answer to 2 decimal places.)

c. Calculate the present value of total inflows. (Do not round intermediate calculations and round your answer to 2 decimal places.)

d. Calculate the net present value. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places.)

Answer 1

Part a)

The value of discount rate is arrived as below:

Discount Rate = Interest Rate*(1-Tax Rate)

Here, Interest Rate = 10.250% and Tax Rate = 30%

Using these values in the above formula, we get,

Discount Rate = 10.250%*(1-30%) = 7.18% or 7% (after rounding off to nearest whole percent)

Answer for Part a) is 7%.

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Part b)

The present value of total outflows is determined as follows:

Payment on Call Provision = Value of Bonds Outstanding*(Call Premium - Percentage Decline for Each Year)*(1-Tax Rate) = 27,000,000*(6% - .50%)*(1-30%) = $1,039,500

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Underwriting Cost on New Issue is calculated as below:

Actual Expenditure (27,000,000*1.8%) [A]	486,000.00
Tax Savings Per Year (486,000/17*30%)	8,576.47
Present Value of Tax Savings (8,576.47*9.763) [B]	83,733.99
Net Cost of Underwriting Expense on New Issue [A-B]	$402,266.01

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Total Present Value of Cash Outflows = Payment on Call Provision + Net Cost of Underwriting Expense on New Issue = 1,039,500 + 402,266.01 = $1,441,766.01 (Answer for Part b)

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Notes:

1) The present value factor is taken for 7% discount rate for 17 years. We wll have to use the present value interest factor for an ordinary annuity table to arrive at the value of 9.763.

2) The final present value of cash outflows may differ slightly because of discount rate used and rounding off values.

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Part c)

The present value of total inflows is determined as follows is calculated as below:

Interest on Old Bond (27,000,000*10.950%)	2,956,500.00
Interest on New Bond	2,767,500.00
Savings Per Year	189,000.00
After-Tax Savings Per Year [189,000*(1-30%)]	132,300.00
Present Value of Savings (132300*9.763)	$1,291,674.40

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Underwriting Cost on Old Issue
Original Value (27,000,000*2.70%)	729,000.00
Less Amount Written Off Over Last 7 Years [729,000/(17+7)*7]	212,625.00
Unamortized Old Underwriting Cost	516,375.00
Less Present Value of Deferred Future Write Off (729,000/(17+7)*9.763]	296,557.90
After-Tax Gain in Old Underwriting Cost Write-Off [(516,375 - 296,557.90)*30%]	$65,945.13

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Total Present Value of Cash Inflows = Present Value of Savings + After-Tax Gain in Old Underwriting Cost Write-Off = 1,291,674.40 + 65,945.13 = $1,357,619.53 (Answer for Part c)

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Notes:

1) The present value factor is taken for 7% discount rate for 17 years. We wll have to use the present value interest factor for an ordinary annuity table to arrive at the value of 9.763.

2) The final present value of cash inflows may differ slightly because of discount rate used and rounding off values.

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Part d)

The net present value is arrived as below:

Net Present Value = Present Value of Total Cash Inflows - Present Value of Total Cash Outflows = 1,357,619.53 - 1,441,766.01 = -$84,146.48 (Answer for Part d)

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Notes:

1) The net present value may differ slightly because of discount rate used and rounding off values in Part b and Part c.