Question

Discovery Cafe issues $1 million in 13.000% bonds maturing May 19, 2040. The bond is callable May 19, 2022 at a call premium of 8.750%. May 19, 2022 the prevailing yield is 6.500%. If Discovery Cafe calls the entire issue and replaces it with 6.500% bonds also maturing May 19, 2040 then

Answers:

• Each semi-annual coupon payment will decrease by :$29,656.25

• The present value of the decrease in coupon payments is :$623,970.18

• The principal repayment at maturity will increase by: $87,500.00

• The present value of the increase in the principal repayment is :$27,667.24

• The present value of this decision to the company - to the nearest dollar - is: $596,303

• The company should (CALL / NOT CALL) :CALL the bond.

How do you get the answers above?? Thanks!

Answer 1

a) Exisiting semi-annual coupon = 1,000,000 x 13% / 2 = 65,000

With call premium, new value of bond issue = 1,000,000 x (1 + 8.75%) = 1,087,500

New semi-annual coupon = 1,087,500 x 6.5% / 2 = 35,343.75

=> Change in coupon = $29,656.25

b) PV of decrease in coupon payments can be calculated using PV function on a calculator

N = 18 x 2 = 36, I/Y = 6.5%/2, PMT = 29,656.25, FV = 0

=> Compute PV = $623,970.18

c) Principal repayment at maturity will increase by call premium = 1,000,000 x 8.75% = 87,500.00

d) PV = 87,500 / (1 + 6.5%/2)^36 = $27,667.24

e) PV = 623,970.18 - 27,667.24 = $596,302.94

f) As PV of the decision is positive, we call the bonds.