Question

After Dan’s analysis for East Coast Yachts (see the Case study for Module 2), Larissa has decided to expand the company’s operations. She has asked Dan to enlist an underwriter to help sell $50 million in new 20-year bonds to finance new construction. Dan has entered into discussions with Kim McKenzie, an underwriter from the firm of Crowe & Mallard, about which bond features East Coast Yachts should consider and also what coupon rate the issue will likely have. After examining all features of each type of bonds, Dan is considering to issue coupon bearing bonds or zero coupon bonds. The YTM on either bond issue will be 7.5 percent. The coupon bond would have a 7.5 percent coupon rate. The company’s tax rate is 35 percent.

How many of the coupon bonds must East Coast Yachts issue to raise the $50 million? How many of the zeroes must it issue?

In 20 years, what will be the principal repayment due if East Coast Yachts issues the coupon bonds? What if it issues the zeroes?

Answer 1

1..

Before-tax YTM expected = 7.5% p.a.

After-tax YTM expected =7.5%*(1-35%)

4.88%

Assuming a $ 1000 bond with annual coupons,

PV or selling price of 1 bond =PV of its future coupons for 20 years +PV of FV $1000 to be received at maturity (both discounted at the after-tax annual YTM reqd.

so,using the PV of annuity formula,

PV or S.P.of a bond=((1000*7.5%)*(1-1.0488^-20)/0.0488)+(1000/1.0488)

1897.7201

So, for the proceeds of the sale to be $ 50000000,

No.of bonds to be issued=

50000000/1897.72=

26347

Bonds

For SEMI-ANNUAL coupon bonds

Coupon rate=7.5%/2=3.75%

YTM=4.88%/2=2.44%

No.of semi-annual periods=20*2=40

PV of a bond=((1000*3.75%)*(1-1.0244^-40)/0.0244)+(1000/1.0244)

1927.12

So, for the proceeds of the sale to be $ 50000000,

No.of bonds to be issued=

50000000/1927.12=

25945

Bonds

PV or S.P. of a zero coupon bond=

Maturity Value/(1+YTM)^n

As the YTM for Zeros are generally based on semi-annual calculations,

so, the PV=1000/(1.0244)^40=

381.26

So, for the proceeds of the sale to be $ 50000000,

No.of bonds to be issued=

50000000/381.26=

131144

Bonds

2…

The principal (or Face Value) repayment for both the issues will be the same $ 50000000

Coupon bond-- $ 50 mln.

Zero coupon bond= $ 50 mln.