Com 2FA3
Tutorial 6
Week of Feb. 25, 2002
Question 1:
The following rates on pure discount investments are being offered: 6% on
a 3-year term, 6.5% on a 4-year term, and 6.76% for a 5-year term. Find the
implied forward rates based on these yields. What are market participants
expecting in years 3 and 4 if UET holds? What if LPT is the correct model?
To find the implied forward rates set the future value of the different
investment strategies to be equal and solve for the forward rate.
FVIF  1  0.06   1  f 3   1  0.065
3
4
f 3  8.01%
FVIF  1  0.065  1  f 4   1  0.0676 
4
5
f 4  7.81%
The implied forward rates are 8% three years from now and 7.8% four
years from now.
If UET is correct, on average, market participants are forecasting
that the one year interest rates are going to be 8% three years from
now, falling to 7.8% a year later.
If the LPT holds then the forecast interest rates are actually lower
than the rates that are implied by the term structure. In other words,
market participants expect a rate lower than 8% three years from now
and the rate four years from now will be lower than 7.8%.
Com 2FA3
Tutorial 6
Week of Feb. 25, 2002
Question 2:
You have been considering purchasing shares in PDG Inc. The company's
dividends have been growing at a rate of 4.5% annually for the last 15 years
and you expect this growth rate to continue indefinitely. If your require a
9.5% rate of return on this sort of investment, and you are willing to pay
$40 for shares of PDG, what dividend are you expecting PDG to pay in one
year?
The assumptions in this question make the Gordon Growth Model the
appropriate valuation model. In this case, you have P0, g, and r, you are
missing the value for D1.
P0 
D1
rg
D1  P0  r  g 
 $40  9.5%  4.5% 
 $2
With the given values, the expected dividend is $2.00.
If you had been asked the most recent dividend, that would have been
D0, which is D1 present valued at the growth rate.
Com 2FA3
Tutorial 6
Week of Feb. 25, 2002
Question 3:
DFP has been very successful recently.
Their dividends have been
increasing at 25% per year. You expect this growth rate to continue for
four years after which time you expect a stable growth rate of 2.5%
indefinitely. How much are DFP shares worth if the most recent dividend
was $4 and your required rate of return is 12% on this investment?
This is a supernormal growth model problem. The initial growth rate is
25% for 4 years falling to 2.5% indefinitely.
t
t
D0  1  g H    1  g H   D0  1  g H   1  g 
P0 
 
1  
r  gH
r  g   1  r t
  1  r  
4
$4  1.25   1.25  
$4  1.254  1.025

 
1  
0.12  0.25   1.12   0.12  0.025  1.12 4
 $21.21  66.96
 $88.17
It is also possible to find the present value of each of the 4 early
dividends and add the PV of the price in 4 years. P4 is forecast as
$115.13 based on the expected dividend in 5 years, the required rate
of return and the indefinite growth rate.
Com 2FA3
Tutorial 6
Week of Feb. 25, 2002
Question 4:
Way2Go shares are currently trading at $57 per share. The latest reported
earnings per share was $3. What percentage of the price of Way2Go shares
is due to the growth potential of the company if the required rate of return
is 12.5%?
The P/E ratio for Way2Go is simply 57/3 = 19.
There are two
components of the P/E ratio, the inverse of the required rate of
return and the portion that is based on growth.
If Way2Go had no growth potential, the P/E ratio would be 1/r or
1/0.125 = 8. The price of Way2Go shares would be 8 x 3 = $24 if
there was no potential for growth.
The part of the P/E ratio that is due to the growth potential of the
company is 19 - 8 = 11.
The fraction of the price of Way2Go that is related to the growth
potential is 11/19 = 58%.