Question

Leona Motel’s debt has a face value of $40 million, a coupon rate of 14% (paid semiannually), and expires in 12 years (at t = 12). The current annual yield-to-maturity (stated) for all bonds of the company is 15%.

a. Leona wishes to conserve cash for the next few years. To do this, Leona decides to issue new equity and use the proceeds to purchase the existing debt at the market price. The current stock price of Leona is $60 and there are 2 million shares outstanding. How many shares should Leona issue to purchase the existing debt? Assume the decision to purchase the bond does not change the stock price.

b. Instead, the company decides to issue a zero-coupon bond that matures at t = 5, and use the proceeds to purchase the existing debt at the market price. What is the face value of the zero-coupon bond that Leona needs to issue?

Answer 1

a

Rate

Semi annual Yield to maturity

7.50%

(15/2)

Nper

Number of semi annual period to maturity

24

(12*2)

Pmt

Semi annual coupon payment=($40 million *14%)/2

$2,800,000

Fv

Payment at maturity

$40,000,000

PV

Market Price =Present Value of future cash flows

$37,803,407

(Using PV function of excel with Rate=7.5%, Nper=24, Pmt=-2.8 million,Fv=-40 million)

A

Market Value of Shares to be Issued

$37,803,407

B

Current Stock Price

$60

C=A/B

Number of shares to be issued

630,057

b

Rate

Annual Yield to maturity

15%

Nper

Number of years to maturity of zero coupon Bond

5

Pv

Present Value of the Bond to be issued

$37,803,407

FV

Face Value of the bond issued =Future Value of Current Purchase Price

$76,036,154

(Using FV function of excel with Rate=15%, Nper=5, Pv=-37803407)