Question

a) What is the present value of a series of payments of $2500 every six years in perpetuity with the first payment made immediately, if the annual rate is 8.5% per annum?
b) Polycorp debentures are selling for $110 (FV = 100) and mature in 8 years. The coupon rate is 6%pa. What is the effective annual yield on the debentures?

c) Polycorp debentures are selling for $96 (FV = 100) and mature in ten years. The coupon rate is 5%pa, with coupons paid quarterly. What is the effective annual yield on the debentures? Your supervisor would like you to confirm your answer using the excel Rate Function (Formula).

d) Polycorp shares are currently selling for $20 each. A month ago, they announced a Bonus share issue of one free share for every share owned (one for one Bonus Issue). The shares go ex-bonus tomorrow. “All else equal”, what should happen to the share price of Polycorp when it goes ex?

Pleae show in excel and formula

Answer 1

a) Value of perpetuity = Cash flow per period/rate per period
rate =0.085
per 6 year period, rate = (1.085^6)-1=0.631468

Value of perpetuity= 2500/0.631468=$3959.03
Add to it the present payment = $3959.03+$2,500=$6,459.03

b) Effective annual yield:
n=8
PV=-110
FV=100
pmt=6
Using excel rate function:
=RATE(8,6,-110,100)
=4.48%

c)n=40
pmt=5/4=1.25
pv=-96
fv=100

=RATE(40,1.25,-96,100)
=5.52%

d) As the number of shares shall double, the price shall become half i.e. $10 when it goes ex