Question

2. Mirha Corp has $40 million of outstanding bonds. The bonds have a $1,000 par value and a 10% coupon rate. They were issued 5 years ago, with 25 years of original maturity, and flotation cost of $200,000. The firm could call these bonds at a 10% call premium. The firm has an opportunity to issue $40 million of bonds with maturity of 20 years and a 7.5% interest rate. The new bonds would require flotation costs of $250,000. To ensure that the funds are available for the refunding, the firm plans to issue the new bonds 3-months before retiring the old bonds. If short-term interest rates are 3%, annually, what is the NPV of the refunding operation? Assume the company is in the 40% tax bracket.

Answer 1

Given data (numbers in $000's except %):
Existing bond issue	40,000	Existing bond issue	40,000
Flotation cost	200	Flotation cost	250
Maturity (years)	25	Maturity (years)	20
Years since issue	5	New cost of debt	7.5%
Call premium (%)	10%	After-tax cost of debt	4.5%
Original coupon rate	10%	Tax rate	40%
		Short-term interest rate	3%

Step 1: Calculate the initial outlay for the refunding decision

Formula		Before-tax	After-tax
After-tax = before-tax*(1-tax rate)	Call premium on the old bond	(4,000)	(2,400)
It cannot be expensed immediately so after-tax = before-tax	Flotation cost of new issue	(250)	(250)
(Number of years remaining/total maturity)*flotation costs; After-tax = before-tax*tax rate	Tax saving on old flotation cost expense	160	64
Before-tax: Debt amount*interest rate*(3/12); After-tax = before-tax*(1-tax rate)	Extra interest paid on old issue	(1,000)	(600)
Interest earned on the new issue for 3 months: Debt amount*short-term interest rate*(3/12); After-tax = before-tax*(1-tax rate)	Interest earned on short-term investment	300	180
	Total after-tax investment		(3,006)

Step 2). Calculate the NPV of the savings from flotation costs

	Annual flotation cost effect:	Before-tax	After-tax
Before-tax :Flotation cost/Maturity; After-tax: before-tax*tax rate	Annual tax savings from new issue flotation costs (a)	12.50	5.00
Before-tax :Flotation cost/Maturity; After-tax: before-tax*tax rate	Annual lost tax savings from old issue flotation costs (b)	(8)	(3)
(a+b)	Net flotation cost savings (annual)		1.80

Calculate NPV of this annual annuity:

(N)	New bond maturity (years)	20
(I)	After-tax cost of new debt	4.5%
(PMT)	Annual flotation cost savings	1.80
(NPV calculated using PV function)	NPV of annual flotation cost savings	23.41

Step 3). Calculate the annual interest savings if refunding happens:

	Annual interest savings due to refunding:	Before-tax	After-tax
Before tax: Debt amount*interest rate; After tax: Before-tax*(1-tax rate)	Interest paid on new bond (a)	(3,000)	(1,800)
Before tax: Debt amount*interest rate; After tax: Before-tax*(1-tax rate)	Interest paid on old bond (b)	4,000	2,400
(a+b)	Net interest savings		600

Calculate NPV of this annual annuity:

(N)	New bond maturity (years)	20
(I)	After-tax cost of new debt	4.5%
(PMT)	Annual net interest savings	600
(NPV calculated using PV function)	NPV of annual interest savings	7,804.76

Step 4:

NPV of the refunding decision = Initial outlay + NPV of annual flotation cost svaings + NPV of annual interest savings

= -3,006 + 23.41 + 7,804.76 = 4,882.18 or $4.88 million (Answer)