Ugba 103 - Solutions for Midterm Exams

University of California

Walter A. Haas School of Business

UGBA 103

Introduction to Finance

Prof. Dmitry Livdan        02 October 2014

[pic 1]

Solutions to the MIDTERM

1. (6.5 points) Two years ago you have bought Apple stock for $100. You have used growing perpetuity formula to value it

[pic 2],

where you have assumed a constant annual growth rate of earnings, g. Apple’s P/E ratio two years ago (i.e. [pic 3]) was equal to 10. At that time you expected to earn 20% annual return on your investment. Today Apple is traded at $242. If Apple’s growth has not changed (g is the same today as it was 2 years ago) and using the same growing perpetuity formula what return (expected return has changed) do you expect to earn if you’d buy Apple stock today?

The price of Apple stock today is:

[pic 4].

Therefore in order to find r today we need to know g and E1. We can find g from the valuation done two years ago

[pic 5]

Now we know g and thus can calculate E1:

E1 = E−1∗ (1 + g)2 = E−1∗ 1.12.

We still do not know E1 but we can find it from the 2-year old P/E ratio:

[pic 6].

Therefore E1 = E−1∗ 1.12 = $10 ∗ 1.21 = $12.1. Finally we find

[pic 7].

2. You are considering between two bonds, A and B. Both bonds are 1-year bonds and have a face value of $1,000. Bond A pays a 10% semiannual coupon while bond B pays an annual coupon of 10% (i.e. at maturity bond B pays $1,100). Bond A is priced at par while bond B is priced at 0.5% premium (i.e. at $1,005).

UGBA 103        MIDTERM – Solutions        2

[pic 8]

1. (2.5 points) Which bond will you buy?

Note: Show all your calculations;

Since bond A is priced at par it has a semiannual yield of 10%. We need to calculate the yield of bond B in semiannual terms. The price of bond B using semiannual yield is:

s

        $1,100        $1,100[pic 9]

$1,005 = y 2 ⇒ y = 2( $1,005 − 1) = 0.092. (1 + 2)[pic 10]

Since 9.2% (bond B yield) is less than 10% (bond A yield) we buy bond A.

1. (3 points) You plan to buy bond C which is a 1-year bond with a face value of $500 and a semiannual coupon of 8%. If bonds A and B are fairly priced, i.e. discount factors D0.5 and D1 and bond yields are correct, then what is the price of bond C?

We need to find discount factors D0.5 and D1 form prices of bonds A and B. From bond B we have: